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  • 51.
    Hoffman, Johan
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Johnson, Claes
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Irreversibility in reversible systems2006In: HERMIS The international journal of computer mathematics and its applications, ISSN 1108-7609, Vol. 6, p. 12-33Article in journal (Refereed)
  • 52.
    Hoffman, Johan
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Johnson, Claes
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Resolution of d'Alembert's Paradox2010In: Journal of Mathematical Fluid Mechanics, ISSN 1422-6928, E-ISSN 1422-6952, Vol. 12, no 3, p. 321-334Article in journal (Refereed)
    Abstract [en]

    We propose a resolution of d'Alembert's Paradox comparing observation of substantial drag/lift in fluids with very small viscosity such as air and water, with the mathematical prediction of zero drag/lift of stationary irrotational solutions of the incompressible inviscid Euler equations, referred to as potential flow. We present analytical and computational evidence that (i) potential flow cannot be observed because it is illposed or unstable to perturbations, (ii) computed viscosity solutions of the Euler equations with slip boundary conditions initiated as potential flow, develop into turbulent solutions which are wellposed with respect to drag/lift and which show substantial drag/lift, in accordance with observations.

  • 53.
    Hoffman, Johan
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Johnson, Claes
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Stability of the dual Navier-Stokes equations and efficient computation of mean output in turbulent flow using adaptive DNS/LES2006In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 195, no 13-16, p. 1709-1721Article in journal (Refereed)
    Abstract [en]

    We discuss aspects of adaptive DNS/LES, where adaptive finite element methods are used to accurately compute chosen output from a turbulent flow with the computational power of a PC. The key to this break-through is: (i) application of the general approach to adaptive error control in Galerkin methods based on duality.. coupled with (ii) crucial properties of turbulent flow allowing accurate computation of mean value quantities such as drag and lift without full resolution of all scales.

  • 54.
    Hoffman, Johan
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Johnson, Claes
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    The mathematical secret of flight2009In: Normat, ISSN 0801-3500, Vol. 57, no 4, p. 145-169Article in journal (Other academic)
  • 55.
    Hoffman, Johan
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Johnson, Claes
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    The mathematical theory of flight2009In: Normat, ISSN 0801-3500, Vol. 57, p. 145-169Article in journal (Refereed)
    Abstract [en]

    We show by computational solution of the incompressible Navier-Stokes equations with friction force boundary conditions, that the classical inviscid circulation theory by Kutta-Zhukovsky for lift of a wing and laminar viscous boundary layer theory by Prandtl for drag, which have dominated 20th century flight mechanics, do not correctly describe the real turbulent airflow around a wing. We show that lift and drag essentially originate from a turbulent wake of counter-rotating rolls of low-pressure streamwise vorticity generated by a certain instability mechanism of potential flow at rear separation. The new theory opens the possibility of computational prediction of flight characteristics of an airplane using millions of meshpoints without resolving thin boundary layers, instead of the imposssible quadrillions required according to state-of-the-art for boundary layer resolution.

  • 56.
    Hoffman, Johan
    et al.
    Mathematics, Chalmers.
    Johnson, Claes
    Bertoluzza, S.
    Subgrid modeling for convection-diffusion-reaction in one space dimension using a Haar Multiresolution analysis2005In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 194, no 1, p. 19-44Article in journal (Refereed)
    Abstract [en]

    In this paper we propose and study a subgrid model for linear convection-diffusion-reaction equations with fractal rough coefficients. The subgrid model is based on scale extrapolation of a modeling residual from coarser scales using a computed solution on a finest scale as reference. We show in experiments that a solution with subgrid model on a scale h in most cases corresponds to a solution without subgrid model on a scale less than h/4. We also present error estimates for the modeling error in terms of modeling residuals.

  • 57.
    Hoffman, Johan
    et al.
    Courant Institute, New York University.
    Johnson, Claes
    Logg, Anders
    Simula Research Laboratory.
    Dreams of Calculus: Perspectives on Mathematics Education2004Book (Other academic)
  • 58.
    Hoffman, Johan
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Logg, Anders
    DOLFIN: Dynamic Object oriented Library for FINite element computation2002Report (Other academic)
    Abstract [en]

    In this report, we present a new software project intended to provide a platform for daptive finite element computation in both research and education. The software DOLFIN is implemented in C++ and provides an object-oriented powerful and flexible environment in which finnite element methods for differential equations can be easily implemented. The current version of DOLFIN already includes a nnumber of modules for special differential equations, including the incompressible Navier-Stokes equations. DOLFIN is free and open source, which we believe is a key point in creating truly useful software. 

  • 59.
    Jansson, Johan
    et al.
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Degirmenci, N. C.
    KTH, School of Computer Science and Communication (CSC).
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Adaptive unified continuum FEM modeling of a 3D FSI benchmark problem2017In: International Journal for Numerical Methods in Biomedical Engineering, ISSN 2040-7939, E-ISSN 2040-7947, Vol. 33, no 9, article id e2851Article in journal (Refereed)
    Abstract [en]

    In this paper, we address a 3D fluid-structure interaction benchmark problem that represents important characteristics of biomedical modeling. We present a goal-oriented adaptive finite element methodology for incompressible fluid-structure interaction based on a streamline diffusion–type stabilization of the balance equations for mass and momentum for the entire continuum in the domain, which is implemented in the Unicorn/FEniCS software framework. A phase marker function and its corresponding transport equation are introduced to select the constitutive law, where the mesh tracks the discontinuous fluid-structure interface. This results in a unified simulation method for fluids and structures. We present detailed results for the benchmark problem compared with experiments, together with a mesh convergence study.

  • 60.
    Jansson, Johan
    et al.
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz). Basque Center for Applied Mathematics (BCAM), Bizkaia Basque-Country, Spain .
    Degirmenci, Niyazi Cem
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Framework for adaptive fluid-structure interaction with industrial applications2013In: International Journal of Materials Engineering Innovation, ISSN 1757-2754, Vol. 4, no 2, p. 166-186Article in journal (Refereed)
    Abstract [en]

    We present developments in the Unicorn-HPC framework for unified continuum mechanics, enabling adaptive finite element computation of fluid-structure interaction, and an overview of the larger FEniCS-HPC framework for automated solution of partial diffential equations of which Unicorn-HPC is a part. We formulate the basic model and finite element discretisation method and adaptive algorithms. We test the framework on a 2D model problem consisting of a flexible beam in channel flow, and to illustrate the capabilities of the computational framework, we show two application examples from industry and medicine. We simulate a flexible mixer plate in turbulent flow in an exhaust system where the target output is aeroacoustic quantities. The second example is a self-oscillating vocal fold configuration, where the ultimate goal is to predict how the voice is affected by physiological changes from aerodynamics. Here we give the displacement signal of a point on the folds.

  • 61.
    Jansson, Johan
    et al.
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Degirmenci, Cem
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Adaptive error control in finite element methods using the error representation as error indicator2013Report (Other academic)
    Abstract [en]

    In this paper we present a new a posteriori adaptive finite elementmethod (FEM) directly using the error representation as a local errorindicator, and representing the primal and dual solutions in the samefinite element space (here piecewise continuous linear functions onthe same mesh). Since this approach gives a global a posteriori errorestimate that is zero (due to the Galerkin orthogonality), the errorrepresentation has historically been thought to contain no informationabout the error. However, we show the opposite, that locally, theorthogonal error representation behaves very similar to thenon-orthogonal error representation using a quadratic approximation ofthe dual. We present evidence of this both in the form of an a prioriestimate for the local error indicator and a detailed computationalinvestigation showing that the two methods exhibit very similarbehavior and performance, and thus confirming the theoreticalprediction. We also present a stabilized version of the method fornon-elliptic partial differential equations (PDE) where the errorrepresentation is no longer orthogonal, and where both the local errorindicator and global error estimate behave similar to the errorrepresentation using a quadratic approximation of the dual.

  • 62.
    Jansson, Johan
    et al.
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Degirmenci, Cem
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Spühler, Jeannette
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Automated adaptive error control in finite element methods using the error representation as error indicator2014Report (Other academic)
    Abstract [en]

    In this paper we present a new adaptive finite element method directly using the a posteriori error representation as a local error  indicator, and representing the primal and dual solutions in the same finite element space (here piecewise continuous linear functions on the same mesh). Since this approach gives a global a posteriori error estimate that is zero (due to Galerkin orthogonality), the error representation has traditionally been thought to contain no information about the error. However, we show the opposite, that locally, the orthogonal error representation behaves very similar to the non-orthogonal error representation using a higher order approximation of the dual,  which is a standard approach to overcome the problem of a zero error estimate. We present evidence of this both in the  form of an a priori estimate for the local error indicator for an elliptic model problem  and a detailed computational investigation showing that the two methods exhibit very similar behavior and performance, and thus confirming the theoretical prediction. We also present computational results using a stabilized version of the method for non-elliptic partial differential equations where the error representation is no longer orthogonal, and where both the local error indicator and global error estimate behave similar to the error representation using a higher order approximation of the dual. The benefits of this adaptive method are generality and simplicity in formulation, sharpness, and efficiency since high order approximation of the dual and computation of additional constructs such as jump terms over interior facets or local problems are avoided.

  • 63.
    Jansson, Johan
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Jansson, Niclas
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Simulation of 3D unsteady incompressible flow past a NACA 0012 wing section2012Report (Other academic)
    Abstract [en]

    We present computational simulations of three-dimensional unsteady high Reynolds number incompressible flow past a NACA 0012 wing profile, for a range of angles of attack, from low lift through stall. A stabilized finite element method is used, referred to as General Galerkin (G2), with adaptive mesh refinement with respect to the error in target output, such as aerodynamic forces. Computational predictions of aerodynamic forces are validated against experimental data.

  • 64.
    Jansson, Johan
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Jansson, Niclas
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Simulation of 3d unsteady incompressible flow past a NACA 0012 wing sectionManuscript (preprint) (Other academic)
  • 65.
    Jansson, Johan
    et al.
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Holmberg, Andreas
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, MWL Flow acoustics.
    Vilela De Abreu, Rodrigo
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Degirmenci, Niyazi Cem
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Karlsson, Mikael
    Åbom, Mats
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, MWL Flow acoustics.
    Adaptive stabilized finite element framework for simulation of vocal fold turbulent fluid-structure interaction2013In: Proceedings of Meetings on Acoustics: Volume 19, 2013, Acoustical Society of America (ASA), 2013, p. 1-9Conference paper (Refereed)
    Abstract [en]

    As a step toward building a more complete model of voice production mechanics, we assess the feasibility of a fluid-structure simulation of the vocal fold mechanics in the Unicorn incompressible Unified Continuum framework. The Unicorn framework consists of conservation equations for mass and momentum, a phase function selecting solid or fluid constitutive laws, a convection equation for the phase function and moving mesh methods for tracking the interface, and discretization through an adaptive stabilized finite element method. The framework has been validated for turbulent flow for both low and high Reynolds numbers and has the following features: implicit turbulence modeling (turbulent dissipation only occurs through numerical stabilization), goal-oriented mesh adaptivity, strong, implicit fluid-structure coupling and good scaling on massively parallel computers. We have applied the framework for turbulent fluid-structure interaction simulation of vocal folds, and present initial results. Acoustic quantities have been extracted from the framework in the setting of an investigation of a configuration approximating an exhaust system with turbulent flow around a flexible triangular steel plate in a circular duct. We present some results of the investigation as well as results of the framework applied to other problems.

  • 66.
    Jansson, Johan
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Ioakeimidou, Foteini
    KTH, School of Computer Science and Communication (CSC).
    Ericson, Finn
    KTH, School of Computer Science and Communication (CSC).
    Spühler, Jeannette
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Olwal, Alex
    MIT, USA.
    Sallnäs Pysander, Eva-Lotta
    KTH, School of Computer Science and Communication (CSC), Human - Computer Interaction, MDI (closed 20111231).
    Forsslund, Jonas
    KTH, School of Computer Science and Communication (CSC), Human - Computer Interaction, MDI (closed 20111231).
    Gestural 3D Interaction with a Beating Heart: Simulation Visualization and Interaction2011In: Proceedings of SIGRAD 2011: Evaluations of Graphics and Visualization— Efficiency, Usefulness, Accessibility, Usability / [ed] Thomas Larsson, Lars Kjelldahl & Kai-Mikael Jää-Aro, Linköping University Electronic Press, 2011Conference paper (Refereed)
    Abstract [en]

    The KTH School of Computer Science and Communication (CSC) established a strategic platform in Simulation-Visualization-Interaction (SimVisInt) in 2009, focused on the high potential in bringing together CSC core com-petences in simulation technology, visualization and interaction. The main part of the platform takes the form aset of new trans-disciplinary projects across established CSC research groups, within the theme of ComputationalHuman Modeling and Visualization: (i) interactive virtual biomedicine (HEART), (ii) simulation of human mo-tion (MOTION), and (iii) virtual prototyping of human hand prostheses (HAND). In this paper, we present recentresults from the HEART project that focused on gestural and haptic interaction with a heart simulation.

  • 67.
    Jansson, Johan
    et al.
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Krishnasamy, Ezhilmathi
    Leoni, Massimiliano
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Jansson, Niclas
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Time-resolved Adaptive Direct FEM Simulation of High-lift Aircraft Configurations: Chapter in "Numerical Simulation of the Aerodynamics of High-Lift Configurations'", Springer2018In: Numerical Simulation of the Aerodynamics of High-Lift Configurations / [ed] Omar Darío López Mejia andJaime A. Escobar Gomez, Springer, 2018, p. 67-92Chapter in book (Refereed)
    Abstract [en]

    We present an adaptive finite element method for time-resolved simulation of aerodynamics without any turbulence-model parameters, which is applied to a benchmark problem from the HiLiftPW-3workshop to compute the flowpast a JAXA Standard Model (JSM) aircraft model at realistic Reynolds numbers. The mesh is automatically constructed by the method as part of an adaptive algorithm based on a posteriori error estimation using adjoint techniques. No explicit turbulence model is used, and the effect of unresolved turbulent boundary layers is modeled by a simple parametrization of the wall shear stress in terms of a skin friction. In the case of very high Reynolds numbers, we approximate the small skin friction by zero skin friction, corresponding to a free-slip boundary condition, which results in a computational model without any model parameter to be tuned, and without the need for costly boundary-layer resolution. We introduce a numerical tripping-noise term to act as a seed for growth of perturbations; the results support that this triggers the correct physical separation at stall and has no significant pre-stall effect. We show that the methodology quantitavely and qualitatively captures the main features of the JSM experiment-aerodynamic forces and the stall mechanism-with a much coarser mesh resolution and lower computational cost than the state-of-the-art methods in the field, with convergence under mesh refinement by the adaptive method. Thus, the simulation methodology appears to be a possible answer to the challenge of reliably predicting turbulent-separated flows for a complete air vehicle.

  • 68.
    Jansson, Johan
    et al.
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz). Basque Center for Applied Mathematics, Spain.
    Nava, V.
    Sanchez, M.
    Aguirre, G.
    De Abreu, Rodrigo Vilela
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz). Basque Center for Applied Mathematics, Spain.
    Villate, J. L.
    Adaptive simulation of unsteady flow past the submerged part of a floating wind turbine platform2015In: MARINE 2015 - Computational Methods in Marine Engineering VI, International Center for Numerical Methods in Engineering (CIMNE), 2015, p. 35-46Conference paper (Refereed)
    Abstract [en]

    Offshore floating platforms for wind turbines represent challenging concepts for designers trying to combine an optimal compromise between cost effectiveness and performance. Modelling of the hydrodynamic behaviour of the structure is still the subject of wide debate in the technical communities. The assessment of the hydrodynamics of the support structure is not an easy task as the floaters consist of an assembly of columns, braces and pontoons, commonly also with heave plates: Each of these components corresponds to a different hydrodynamic model and it further interacts with the other elements. This results in very complex non-linear modeling, which makes it necessary to resort to computational fluid dynamics (CFD) methods for the evaluation of the combined hydrodynamics. In the framework of the collaboration between the Basque Centre for Applied Mathematics (BCAM) and Tecnalia R&I, the interaction of the sea flow with a semisubmersible floating offshore wind platform have been calculated by using the open source solver Unicorn in the FEniCS-HPC framework when subject to a steady inflow. The prototype of the platform consists in a semi-submersible 4-columns column stabilized platform - NAUTILUS Floating Solutions concept-; columns are connected by a rigid ring pontoon provided with heave damping plates at the bottom. The novelty of the approach in FEniCS-HPC hinges upon an implicit formulation for the turbulence, a cheap free slip model of the boundary layer and goal-oriented mesh adaptivity [8, 6, 9, 20, 1]. We find that the results are consistent with experimental results for cylinders at high Reynolds number.

  • 69.
    Jansson, Johan
    et al.
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Spühler, Jeannette
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Degirmenci, Cem
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Automated error control in finite element methods withapplications in fluid flow2014Report (Other academic)
    Abstract [en]

    In this paper we present a new adaptive finite element method for thesolution of linear and non-linear partial differential equationsdirectly using the a posteriori error representation as a local errorindicator, with the primal and dual solutions approximated in the samefinite element space, here piecewise continuous linear functions onthe same mesh. Since this approach gives a global a posteriori errorrepresentation that is zero due to Galerkin orthogonality, the errorrepresentation has traditionally been thought to contain noinformation about the error. However, for elliptic andconvection-diffusion model problems we show the opposite, that locallythe orthogonal error representation behaves very similar to thenon-orthogonal error representation using a higher order approximationof the dual.  We have previously proved an a priori estimate of thelocal error indicator for elliptic problems, and in this paper weextend the proof to convection-reaction problems. We also present aversion of the method for non-elliptic and non-linear problems using astabilized finite element method where the a posteriori errorrepresentation is no longer orthogonal. We apply this method to thestationary incompressible Navier-Stokes equation and perform detailednumerical experiments which show that the a posteriori error estimateis within a factor 2 of the error based on a reference value on a finemesh, except in a few data points on very coarse meshes for anon-smooth test case where it is within a factor 3.

  • 70.
    Jansson, Niclas
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    A Hybrid MPI/PGAS Finite Element Solver2012Report (Other academic)
    Abstract [en]

    We present our work on developing a hybrid parallel programming model for a general finite element solver. The main focus of our work is to demonstrate that legacy codes with high latency, two-sided communication in the form of message passing can be improved using lightweight one-sided communication. We introduce a new hybrid MPI/PGAS implementation of the open source finite element framework FEniCS, replacing the linear algebra backend (PETSc) with a new library written in UPC.  A detailed description of the linear algebra backend implementation and the hybrid interface to FEniCS is given. We also present a detailed analysis of the performance of this hybrid solver on the Cray XE6 Lindgren at PDC/KTH including a comparison with the MPI only implementation, where we find that the hybrid implementation results in improvements of up to 33% in communication intensive parts of the solver.

  • 71.
    Jansson, Niclas
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Computer simulation of incompressible flow past a circular cylinder at a very high Reynolds numbers2011Manuscript (preprint) (Other academic)
  • 72.
    Jansson, Niclas
    et al.
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Improving Parallel Performance of FEniCS Finite Element Computations by Hybrid MPI/PGASManuscript (preprint) (Other academic)
    Abstract [en]

    We present our work on developing a hybrid parallel programming model for a general finite element solver. The main focus of our work is to demonstrate that legacy codes with high latency, two-sided communication in the form of message passing can be improved using lightweight one-sided communication. We introduce a new hybrid MPI/PGAS implementation of the open source general finite element framework FEniCS, replacing the linear algebra backend (PETSc) with a new library written in UPC. A detailed description of the linear algebra backend implementation and the hybrid interface to FEniCS is given. We also present a detailed analysis of the performance of this hybrid solver on the Cray XE6 Lindgren at PDC/KTH including a comparison with the MPI only implementation, where we find that the hybrid implementation results in significant improvements in performance of the solver.

  • 73.
    Jansson, Niclas
    et al.
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Improving Parallel Performance of FEniCS Finite Element Computations by Hybrid MPI/PGAS2013Report (Other academic)
    Abstract [en]

    We present our work on developing a hybrid parallel programming model for a general finite element solver. The main focus of our work is to demonstrate that legacy codes with high latency, two-sided communication in the form of message passing can be improved using lightweight one-sided communication. We introduce a new hybrid MPI/PGAS implementation of the open source general finite element framework FEniCS, replacing the linear algebra backend (PETSc) with a new library written in UPC. A detailed description of the linear algebra backend implementation and the hybrid interface to FEniCS is given. We also present a detailed analysis of the performance of this hybrid solver on the Cray XE6 Lindgren at PDC/KTH including a comparison with the MPI only implementation, where we find that the hybrid implementation results in significant improvements in performance of the solver.

  • 74.
    Jansson, Niclas
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Jansson, Johan
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Framework For Massively Parallel Adaptive Finite Element Computational Fluid Dynamics On Tetrahedral Meshes2012In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 34, no 1, p. C24-C42Article in journal (Refereed)
    Abstract [en]

    In this paper we describe a general adaptive finite element framework for unstructured tetrahedral meshes without hanging nodes suitable for large scale parallel computations. Our framework is designed to scale linearly to several thousands of processors, using fully distributed and efficient algorithms. The key components of our implementation, local mesh refinement and load balancing algorithms, are described in detail. Finally, we present a theoretical and experimental performance study of our framework, used in a large scale computational fluid dynamics computation, and we compare scaling and complexity of different algorithms on different massively parallel architectures.

  • 75.
    Jansson, Niclas
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Nazarov, Murtazo
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Adaptive simulation of turbulent flow past a full car model2011In: State of the Practice Reports, SC'11, 2011Conference paper (Refereed)
    Abstract [en]

    The massive computational cost for resolving all turbulent scales makes a direct numerical simulation of the underlying Navier-Stokes equations impossible in most engineering applications. We present recent advances in parallel adaptive finite element methodology that enable us to efficiently compute time resolved approximations for complex geometries with error control. In this paper we present a LES simulation of turbulent flow past a full car model, where we adaptively refine the unstructured mesh to minimize the error in drag prediction. The simulation was partly carried out on the new Cray XE6 at PDC/KTH where the solver shows near optimal strong and weak scaling for the entire adaptive process.

  • 76.
    Jansson, Niclas
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Jansson, Johan
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Adaptive finite element computational fluid dynamics for large scale massiverly parallel computing2012In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197Article in journal (Refereed)
  • 77. Krishnasamy, E.
    et al.
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST). BCAM - Basque Center for Applied Mathematics, Spain.
    Jansson, Johan
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST). BCAM - Basque Center for Applied Mathematics, Spain.
    Direct FEM large scale computation of turbulent multiphase flow in urban water systems and marine energy2016In: ECCOMAS Congress 2016 - Proceedings of the 7th European Congress on Computational Methods in Applied Sciences and Engineering, National Technical University of Athens , 2016, p. 1339-1351Conference paper (Refereed)
    Abstract [en]

    High-Reynolds number turbulent incompressible multiphase flow represents a large class of engineering problems of key relevance to society. Here we describe our work on modeling two such problems: 1. The Consorcio de Aguas Bilbao Bizkaia is constructing a new storm tank system with an automatic cleaning system, based on periodically pushing tank water out in a tunnel 2. In the framework of the collaboration between BCAM - Basque Center for Applied Mathematics and Tecnalia R & I, the interaction of the sea flow with a semi submersible floating offshore wind platform is computationally investigated. We study the MARIA' benchmark modeling breaking waves over objects in marine environments. Both of these problems are modeled in the the Direct FEM/General Galerkin methodology for turbulent incompressible variable-densitv flow 1,2 in the FEniCS software framework.

  • 78.
    Larsson, David
    et al.
    KTH, School of Technology and Health (STH), Medical Engineering, Medical Imaging.
    Spuhler, Jeannette H.
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Nordenfur, Tim
    KTH, School of Technology and Health (STH), Medical Engineering, Medical Imaging.
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Colarieti-Tosti, Massimiliano
    KTH, School of Technology and Health (STH), Medical Engineering, Medical Imaging.
    Gao, Hang
    Larsson, Matilda
    KTH, School of Technology and Health (STH), Medical Engineering, Medical Imaging.
    Patient-specific flow simulation of the left ventricle from 4D echocardiography - feasibility and robustness evaluation2015In: 2015 IEEE INTERNATIONAL ULTRASONICS SYMPOSIUM (IUS), IEEE , 2015Conference paper (Refereed)
    Abstract [en]

    In recent years, computational fluid dynamics (CFD) simulations on in-silico models of the heart have provided a valuable insight into cardiac hemodynamic behaviour. However, so far most models have been either based on simplified geometries or on imaging acquisitions with relatively low temporal resolution. It has been suggested that models based entirely on subject-specific ultrasonic images should be used to capture transient flow changes. Therefore, the aim of this study is to present a pathway from routine 4D echocardiography to a patient-specific flow simulation of the left ventricle (LV), evaluating the model robustness and clinical feasibility. The created pathway consisted of initial LV segmentation and mitral/aortic valve positioning, being subsequently used as input for the CFD simulations (based on solving the Navier-Stokes equation using an Arbitrary Lagrangian-Eulerian approach). The output consisted of 4D blood flow velocities and relative pressures in the entire LV. On five subjects, the model robustness was evaluated with regards to variations in singular boundary conditions. The clinical feasibility of the output was compared to clinical PW Doppler measurements and, as a proof-of-concept, synthetic contrast enhanced ultrasound images were simulated on the flow field using the COLE-method. Results indicated a relatively robust model, with variations in regional flow of approximately 5.1/6.2% and 9.7/7.0% for healthy and pathological subject respectively (end diastole/end systole). Furthermore, showing similar behaviour to clinical Doppler measurements the technique serves as a promising tool for future clinical investigations. Additionally, the ability of simulating synthetic ultrasound images further underlines the applicability of the pathway, being potentially useful in studies on improved echocardiographic image analysis.

  • 79.
    Larsson, David
    et al.
    KTH, School of Technology and Health (STH), Medical Engineering, Medical Imaging.
    Spuhler, Jeannette H.
    Petersson, Sven
    Nordenfur, Tim
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Colarieti-Tosti, Massimiliano
    Winter, Reidar
    Larsson, Matilda
    KTH, School of Technology and Health (STH), Medical Engineering, Medical Imaging.
    Multimodal validation of patient-specific intraventricular flow simulations from 4D echocardiography2016In: 2016 IEEE INTERNATIONAL ULTRASONICS SYMPOSIUM (IUS), IEEE conference proceedings, 2016Conference paper (Refereed)
    Abstract [en]

    The combination of refined medical imaging techniques and computational fluid dynamics (CFD) models has enabled the study of complex flow behavior on a highly regional level. Recently, we have developed a platform for patient-specific CFD modelling of blood flow in the left ventricle (LV), with input data and required boundary conditions acquired from 4D echocardiography. The platform robustness has been evaluated with respect to input variable variations, but for any clinical implementation model flow validation is essential. Therefore, the aim of this study is to evaluate the accuracy of the patient-specific CFD model against multimodal image-based flow measurements. For the validation, 4D echocardiography was acquired from two healthy subjects, from which LV velocity fields were simulated. In-vivo flows from the same two subjects were then acquired by pulsed wave (PW) Doppler imaging over both LV-valves, and by cine phase-contract magnetic resonance imaging (PC-MRI) at eight defined anatomical planes in the LV. By fusing PC-MRI and the ultrasound acquisitions using a three-chamber alignment algorithm, simulated and measured flows were quantitatively compared. General flow pattern correspondence was observed, with a mean error of 1.4 cm/s and root mean square deviation of 5.7 cm/s for all measured PC-MRI LV-planes. For the PW-Doppler comparison, a mean error of 3.6 cm/s was reported. Overall, the following work represents a validation of the proposed patient-specific CFD platform, and the agreement with clinical data highlight the potential for future clinical use of the models.

  • 80.
    Larsson, David
    et al.
    KTH, School of Technology and Health (STH), Medical Engineering, Medical Imaging. KTH.
    Spühler, Jeannette Hiromi
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Petersson, Sven
    Karolinska Universitetssjukhuset.
    Nordenfur, Tim
    KTH, School of Technology and Health (STH), Medical Engineering, Medical Imaging.
    Colarieti-Tosti, Massimiliano
    KTH, School of Technology and Health (STH), Medical Engineering, Medical Imaging.
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Winter, Reidar
    Karolinska Institutet.
    Larsson, Matilda
    KTH, School of Technology and Health (STH), Medical Engineering, Medical Imaging.
    Patient-Specific Left Ventricular Flow Simulations From Transthoracic Echocardiography: Robustness Evaluation and Validation Against Ultrasound Doppler and Magnetic Resonance Imaging2017In: IEEE Transactions on Medical Imaging, ISSN 0278-0062, E-ISSN 1558-254X, Vol. 36, no 11, p. 2261-2275Article in journal (Refereed)
    Abstract [en]

    The combination of medical imaging with computational fluid dynamics (CFD) has enabled the study of 3D blood flow on a patient-specificlevel. However, with models based on gated high-resolution data, the study of transient flows, and any model implementation into routine cardiac care, is challenging. The present paper presents a novel pathway for patient-specific CFD modelling of the left ventricle (LV), using 4D transthoracic echocardiography (TTE) as input modality. To evaluate the clinical usability, two sub-studies were performed. First, a robustness evaluation was performed where repeated models with alternating input variables were generated for 6 subjects and changes in simulated output quantified. Second, a validation study was carried out where the pathway accuracy was evaluated against pulsed-wave Doppler (100 subjects), and 2D through-plane phase-contrast magnetic resonance imaging measurements over 7 intraventricular planes (6 subjects). The robustness evaluation indicated a model deviation of <12%, with highest regional and temporal deviations at apical segments and at peak systole, respectively. The validation study showed an error of < 11% (velocities < 10 cm/s) for all subjects, with no significant regional or temporal differences observed. With the patient-specific pathway shown to provide robust output with high accuracy, and with the pathway dependent only on 4DTTE, the method has a high potential to be used within future clinical studies on 3D intraventricular flowpatterns. To this, future model developments in the form of e.g. anatomically accurate LV valves may further enhance the clinical value of the simulations.

  • 81. Nazarov, M.
    et al.
    Hoffman, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Residual-based artificial viscosity for simulation of turbulent compressible flow using adaptive finite element methods2013In: International Journal for Numerical Methods in Fluids, ISSN 0271-2091, E-ISSN 1097-0363, Vol. 71, no 3, p. 339-357Article in journal (Refereed)
    Abstract [en]

    In this paper, we present a finite element method with a residual-based artificial viscosity for simulation of turbulent compressible flow, with adaptive mesh refinement based on a posteriori error estimation with sensitivity information from an associated dual problem. The artificial viscosity acts as a numerical stabilization, as shock capturing, and as turbulence capturing for large eddy simulation of turbulent flow. The adaptive method resolves parts of the flow indicated by the a posteriori error estimates but leaves shocks and turbulence under-resolved in a large eddy simulation. The method is tested for examples in 2D and 3D and is validated against experimental data.

  • 82.
    Nazarov, Murtazo
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    An adaptive finite element method for inviscid compressible flow2010In: International Journal for Numerical Methods in Fluids, ISSN 0271-2091, E-ISSN 1097-0363, Vol. 64, no 10-12, p. 1102-1128Article in journal (Refereed)
    Abstract [en]

    We present an adaptive finite element method for the compressible Euler equations, based on a posteriori error estimation of a quantity of interest in terms of a dual problem for the linearized equations. Continuous piecewise linear approximation is used in space and time, with componentwise weighted least-squares stabilization of convection terms and residual-based shock-capturing. The adaptive algorithm is demonstrated numerically for the quantity of interest being the drag force on a body.

  • 83.
    Nazarov, Murtazo
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    An adaptive finite element method for the compressible Euler equations2010In: INT J NUMER METHOD FLUID, 2010, Vol. 64, no 10-12, p. 1102-1128Conference paper (Refereed)
    Abstract [en]

    We present an adaptive finite element method for the compressible Euler equations, based on a posteriori error estimation of a quantity of interest in terms of a dual problem for the linearized equations. Continuous piecewise linear approximation is used in space and time, with componentwise weighted least-squares stabilization of convection terms and residual-based shock-capturing. The adaptive algorithm is demonstrated numerically for the quantity of interest being the drag force on a body.

  • 84.
    Nazarov, Murtazo
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    On the stability of the dual problem for high Reynolds number flow past a circular cylinder in two dimensions2011Report (Other academic)
  • 85.
    Nazarov, Murtazo
    et al.
    Texas A and M University, United States.
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    On the stability of the dual problem for high Reynolds number flow past a circular cylinder in two dimensions2012In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 34, no 4, p. A1905-A1924Article in journal (Refereed)
    Abstract [en]

    In this paper we present a computational study of the stability of time dependent dual problems for compressible flow at high Reynolds numbers in two dimensions. The dual problem measures the sensitivity of an output functional with respect to numerical errors and is a key part of goal oriented a posteriori error estimation. Our investigation shows that the dual problem associated with the computation of the drag force for the compressible Euler/Navier-Stokes equations, which are approximated numerically using different temporal discretization and stabilization techniques, is unstable and exhibits blow-up for several Mach regimes considered in this paper.

  • 86.
    Nazarov, Murtazo
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Residual based artificial viscosity for simulation of turbulent compressible flow using adaptive finite element methods2011Report (Other academic)
  • 87.
    Nguyen, Van Dang
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).
    Jansson, Johan
    KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).
    Frachon, Thomas
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Degirmenci, Cem
    Hoffman, Johan
    KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).
    A fluid-structure interaction model with weak slip velocity boundary conditions on conforming internal interfaces2018Conference paper (Other (popular science, discussion, etc.))
    Abstract [en]

    We develop a PUFEM–Partition of Unity Finite Element Method to impose slip velocity boundary conditions on conforming internal interfaces for a fluid-structure interaction model. The method facilitates a straightforward implementation on the FEniCS/FEniCS-HPC platform. We show two results for 2D model problems with the implementation on FEniCS: (1) optimal convergence rate is shown for a stationary Navier-Stokes flow problem, and (2) the slip velocity conditions give qualitatively the correct result for the Euler flow. 

  • 88.
    Nguyen, Van Dang
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).
    Jansson, Johan
    KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).
    Goude, Anders
    Uppsala University, Uppsala, Sweden.
    Hoffman, Johan
    KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).
    Direct Finite Element Simulation of the Turbulent Flow Past a Vertical Axis Wind Turbine2019In: Renewable energy, ISSN 0960-1481, E-ISSN 1879-0682, Vol. 135, p. 238-247Article in journal (Refereed)
    Abstract [en]

    There is today a significant interest in harvesting renewable energy, specifically wind energy, in offshore and urban environments. Vertical axis wind turbines get increasing attention since they are able to capture the wind from any direction. They are relatively easy to install and to transport, cheaper to build and maintain, and quite safe for humans and birds. Detailed computer simulations of the fluid dynamics of wind turbines provide an enhanced understanding of the technology and may guide design improvements. In this paper, we simulate the turbulent flow past a vertical axis wind turbine for a range of rotation angles in parked and rotating conditions. We propose the method of Direct Finite Element Simulation in a rotating ALE framework, abbreviated as DFS-ALE. The simulation results are validated against experimental data in the form of force measurements. We find that the simulation results are stable with respect to mesh refinement and that we capture well the general shape of the variation of force measurements over the rotation angles.

  • 89.
    Nguyen, Van Dang
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).
    Jansson, Johan
    KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).
    Goude, Anders
    Hoffman, Johan
    KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).
    Technical Report -- Comparison of Direct Finite Element Simulation with Actuator Line Models and Vortex Models for Simulation of Turbulent Flow Past a Vertical Axis wind Turbine2019Report (Other (popular science, discussion, etc.))
    Abstract [en]

    We compare three different methodologies for simulation of turbulent flow past a vertical axis wind turbine: (i) full resolution of the turbine blades in a Direct Finite Element Simulation (DFS), (ii) implicit representation of the turbine blades in a 3D Actuator Line Method (ALM), and (iii) implicit representation of the turbine blades as sources in a Vortex Model (VM). The integrated normal force on one blade is computed for a range of azimuthal angles, and is compared to experimental data for the different tip speed ratios, 2.55, 3.44 and 4.09.

  • 90.
    Nguyen, Van Dang
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).
    Jansson, Johan
    KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).
    Hoffman, Johan
    KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).
    Li, Jing-Rebecca
    INRIA Saclay-Equipe DEFI, CMAP, Ecole Polytechnique Route de Saclay, 91128, Palaiseau Cedex, France.
    A partition of unity finite element method for computational diffusion MRI2018In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 375, p. 271-290Article in journal (Refereed)
    Abstract [en]

    The Bloch–Torrey equation describes the evolution of the spin (usually water proton) magnetization under the influence of applied magnetic field gradients and is commonly used in numerical simulations for diffusion MRI and NMR. Microscopic heterogeneity inside the imaging voxel is modeled by interfaces inside the simulation domain, where a discontinuity in the magnetization across the interfaces is produced via a permeability coefficient on the interfaces. To avoid having to simulate on a computational domain that is the size of an entire imaging voxel, which is often much larger than the scale of the microscopic heterogeneity as well as the mean spin diffusion displacement, smaller representative volumes of the imaging medium can be used as the simulation domain. In this case, the exterior boundaries of a representative volume either must be far away from the initial positions of the spins or suitable boundary conditions must be found to allow the movement of spins across these exterior boundaries.

    Many approaches have been taken to solve the Bloch–Torrey equation but an efficient high-performance computing framework is still missing. In this paper, we present formulations of the interface as well as the exterior boundary conditions that are computationally efficient and suitable for arbitrary order finite elements and parallelization. In particular, the formulations are based on the partition of unity concept which allows for a discontinuous solution across interfaces conforming with the mesh with weak enforcement of real (in the case of interior interfaces) and artificial (in the case of exterior boundaries) permeability conditions as well as an operator splitting for the exterior boundary conditions. The method is straightforward to implement and it is available in FEniCS for moderate-scale simulations and in FEniCS-HPC for large-scale simulations. The order of accuracy of the resulting method is validated in numerical tests and a good scalability is shown for the parallel implementation. We show that the simulated dMRI signals offer good approximations to reference signals in cases where the latter are available and we performed simulations for a realistic model of a neuron to show that the method can be used for complex geometries.

  • 91.
    Nguyen, Van Dang
    et al.
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Jansson, Johan
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Li, Jing-Rebecca
    A partition of unity finite element method for computational diffusion MRIManuscript (preprint) (Other academic)
    Abstract [en]

    The Bloch-Torrey equation describes the evolution of the spin (usually water proton) magnetization under the influence of applied magnetic field gradients and is commonly used in numerical simulations for diffusion MRI and NMR. Microscopic heterogeneity inside the imaging voxel is modeled by interfaces inside the simulation domain, where a discontinuity in the magnetization across the interfaces is produced via a permeability coefficient on the interfaces. To avoid having to simulate on a computational domain that is the size of an entire imaging voxel, which is often much larger than the scale of the microscopic heterogeneity as well as the mean spin diffusion displacement, smaller representative volumes of the imaging medium can be used as the simulation domain. In this case, the exterior boundaries of a representative volume either must be far away from the initial positions of the spins or suitable boundary conditions must be found to allow the movement of spins across these exterior boundaries. Many efforts have been made to solve the equation but there is still missing an efficient high performance computing framework. In this work, we present formulations of the interface as well as the exterior boundary conditions that are computationally efficient and suitable for arbitrary order finite elements and parallelization. In particular, the formulations use extended finite elements with weak enforcement of real (in the case of interior interfaces) and artificial (in the case of exterior boundaries) permeability conditions as well as operator splitting for the exterior boundary conditions. The method appears to be straightforward to implement and it is implemented in the FEniCS for moderate-scale simulations and in the FEniCS-HPC for the large-scale simulations. The accuracy of the resulting method is validated numerically and a good scalability is shown for the parallel implementation. We show that the simulated dMRI signals offer good approximations to reference signals in cases where the latter are available. Finally, we do simulations on a complex neuron to study how the signals decay under the effect of the permeable membrane and to show that the method can be used to simulate for complex geometries that we have not done before.

    Highlights:

    • The discontinuity in the magnetization across the interior interfaces of the medium is weakly imposed, allowing generalization to arbitrary order finite elements.
    • Spin exchange across the external boundaries is implemented by weakly imposing an artificial, high permeability, condition, allowing generalization to non-matching meshes.
    • Thus, optimal convergence with respect to the space discretization is achieved.
    • The second-order Crank-Nicolson method is chosen for the time discretization to reduce oscillations at high gradient strengths and allows for larger time-step sizes.
    • The method is of a high level of simplicity and suitable for parallelization.
    • An efficient open-source code is implemented in the FEniCS and FEniCS-HPC platforms.
  • 92.
    Nguyen, Van Dang
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).
    Leoni, Massimiliano
    KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).
    Dancheva, Tamara
    KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).
    Jansson, Johan
    KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).
    Hoffman, Johan
    KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).
    Wassermann, Demian
    Li, Jing-Rebecca
    Portable simulation framework for diffusion MRI2019In: Journal of magnetic resonance, ISSN 1090-7807, E-ISSN 1096-0856, Vol. 309, article id 106611Article in journal (Refereed)
    Abstract [en]

    The numerical simulation of the diffusion MRI signal arising from complex tissue micro-structures is helpful for understanding and interpreting imaging data as well as for designing and optimizing MRI sequences. The discretization of the Bloch-Torrey equation by finite elements is a more recently developed approach for this purpose, in contrast to random walk simulations, which has a longer history. While finite elements discretization is more difficult to implement than random walk simulations, the approach benefits from a long history of theoretical and numerical developments by the mathematical and engineering communities. In particular, software packages for the automated solutions of partial differential equations using finite elements discretization, such as FEniCS, are undergoing active support and development. However, because diffusion MRI simulation is a relatively new application area, there is still a gap between the simulation needs of the MRI community and the available tools provided by finite elements software packages. In this paper, we address two potential difficulties in using FEniCS for diffusion MRI simulation. First, we simplified software installation by the use of FEniCS containers that are completely portable across multiple platforms. Second, we provide a portable simulation framework based on Python and whose code is open source. This simulation framework can be seamlessly integrated with cloud computing resources such as Google Colaboratory notebooks working on a web browser or with Google Cloud Platform with MPI parallelization. We show examples illustrating the accuracy, the computational times, and parallel computing capabilities. The framework contributes to reproducible science and open-source software in computational diffusion MRI with the hope that it will help to speed up method developments and stimulate research collaborations.

  • 93.
    Spühler, Jeannette H.
    et al.
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Jansson, Johan
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Jansson, Niclas
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    3D Fluid-Structure Interaction Simulation of Aortic Valves Using a Unified Continuum ALE FEM Model2018In: Frontiers in Physiology, ISSN 1664-042X, E-ISSN 1664-042X, Vol. 9, article id 363Article in journal (Refereed)
    Abstract [en]

    Due to advances in medical imaging, computational fluid dynamics algorithms and high performance computing, computer simulation is developing into an important tool for understanding the relationship between cardiovascular diseases and intraventricular blood flow. The field of cardiac flow simulation is challenging and highly interdisciplinary. We apply a computational framework for automated solutions of partial differential equations using Finite Element Methods where any mathematical description directly can be translated to code. This allows us to develop a cardiac model where specific properties of the heart such as fluid-structure interaction of the aortic valve can be added in a modular way without extensive efforts. In previous work, we simulated the blood flow in the left ventricle of the heart. In this paper, we extend this model by placing prototypes of both a native and a mechanical aortic valve in the outflow region of the left ventricle. Numerical simulation of the blood flow in the vicinity of the valve offers the possibility to improve the treatment of aortic valve diseases as aortic stenosis (narrowing of the valve opening) or regurgitation (leaking) and to optimize the design of prosthetic heart valves in a controlled and specific way. The fluid-structure interaction and contact problem are formulated in a unified continuum model using the conservation laws for mass and momentum and a phase function. The discretization is based on an Arbitrary Lagrangian-Eulerian space-time finite element method with streamline diffusion stabilization, and it is implemented in the open source software Unicorn which shows near optimal scaling up to thousands of cores. Computational results are presented to demonstrate the capability of our framework.

  • 94.
    Spühler, Jeannette Hiromi
    et al.
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Degirmenci, Niyazi Cem
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Jansson, Johan
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    A 3D full-friction contact model for fluid-structure interaction problemsManuscript (preprint) (Other academic)
  • 95.
    Spühler, Jeannette Hiromi
    et al.
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Jansson, Johan
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Jansson, Niclas
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    3D Fluid-Structure Interaction Simulation of Aortic Valves Using a Unified Continuum ALE-FEM ModelManuscript (preprint) (Other academic)
  • 96.
    Spühler, Jeannette Hiromi
    et al.
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Jansson, Johan
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST). BCAM - Basque Center for Applied Mathematics, Spain.
    Jansson, Niclas
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST). BCAM - Basque Center for Applied Mathematics, Spain.
    A finite element framework for high performance computer simulation of blood flow in the left ventricle of the human heart2015Report (Other academic)
    Abstract [en]

    Progress in medical imaging, computational fluid dynamics and high performance computing (HPC) enables computer simulations to emerge as a significant tool to enhance our understanding of the relationship between cardiac diseases and hemodynamics. The field of cardiac modelling is diverse, covering different aspects on microscopic and macroscopic level. In our research, we develop a cardiac model which is embedded in a computational environment where specific properties of the heart such as fluid-structure interaction of the aortic valve can be modeled, or numerical and computational algorithms as parallel computing or adaptivity can be added in a modular way without extensive efforts. In this paper, we present a patient-specific Arbitrary Lagrangian-Eulerian (ALE) finite element framework for simulating the blood flow in the left ventricle of a human heart using HPC, which forms the core of our cardiac model. The mathematical model is described together with the discretization method, mesh smoothing algorithms, and the parallel implementation in Unicorn which is part of the open source software framework FEniCS-HPC. The parallel performance is demonstrated, a convergence study is conducted and intraventricular flow patterns are visualized. The results capture essential features observed with other computational models and imaging techniques, and thus indicate that our framework possesses the potential to provide relevant clinical information for diagnosis and medical treatment. Several studies have been conducted to simulate the three dimensional blood flow in the left ventricle of the human heart with prescribed wall movement. Our contribution to the field of cardiac research lies in establishing an open source framework modular both in modelling and numerical algorithms.

  • 97.
    Vilela De Abreu, Rodrigo
    et al.
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz). KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Jansson, Johan
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Towards the development of adaptive finite element methods for internal flow aeroacoustics2013In: 19th AIAA/CEAS Aeroacoustics Conference, 2013Conference paper (Refereed)
    Abstract [en]

    We report the latest results obtained in the development of an adaptive finite element method for computational aeroacoustics (CAA). The new methodology is based on the General Galerkin (G2) method, which has been successfully used for the computation of incompressible, turbulent flow. Here, we simulate the flow past an in-duct mixer plate and compare the results with available experimental data. The comparisons include mean velocity profiles and frequency content of the turbulent signal. No direct simulation of sound or sound wave propagation has been performed; instead, simple analogy arguments have been used to extract acoustic results from incompressible simulations by assuming a direct correlation between the computed pressure drop signal and the sound at the far field. We were able to reproduce the sound signal from experiments with our incompressible simulation and our results compared well with both the level and the broadband frequency peak of the measured sound. We suggest that the methodology presented here is mainly suitable for the prediction of sound in low Mach number pipe flows.

  • 98.
    Vilela de Abreu, Rodrigo
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Jansson, Niclas
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Towards the development of adaptive finite element methods for aeroacousticsManuscript (preprint) (Other academic)
    Abstract [en]

    We report the latest results obtained in the development of an adaptive nite ele- ment method for computational aeroacoustics (CAA). The new methodology is based on the General Galerkin (G2) method, which has been successfully used for the computation of incompressible, turbulent ow. Here, we simulate the ow past an in-duct mixer plate and compare the results with available experimental data. The compar- isons include mean velocity pro les and frequency content of the turbulent signal. No direct simulation of sound or sound wave propagation has been performed; instead, simple analogy arguments have been used to extract acoustic results from incompressible simulations by assuming a direct correlation between the computed pressure drop signal and the sound at the far eld. We were able to reproduce the sound signal from experiments with our incompressible simulation and our results compared well with both the level and the broadband frequency peak of the measured sound. We suggest that the methodology presented here is mainly suitable for the prediction of sound in low Mach number pipe flows.

  • 99.
    Vilela de Abreu, Rodrigo
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Jansson, Niclas
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Adaptive computation of aeroacoustic sources for a 4-wheel rudimentary landing gear benchmark problem2010Conference paper (Refereed)
    Abstract [en]

    We present our simulation results for the benchmark Rudimentary Landing Gear using a General Galerkin (G2) nite element method, also referred to as Adaptive DNS/LES. In G2 no explicit subgrid model is used, instead the computational mesh is adaptively re ned with respect to an a posteriori error estimate of a quantity of interest in the computation, in this case drag force. Turbulent boundary layers are modeled using a simple wall shear stress proportional to the skin friction, which here is assumed to be small and is approximated by zero skin friction, resulting in a slip velocity boundary condition. We compare our results with experimental data and other state of the art computations, where we nd good agreement in sound pressure levels, surface velocities and ow separation. We also compare with detailed surface pressure experimental data where we nd largely good agreement, apart from some local dierences for which we discuss possible explanations.

  • 100.
    Vilela de Abreu, Rodrigo
    et al.
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz). KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Jansson, Niclas
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Adaptive Computation of Aeroacoustic Sources for a Rudimentary Landing Gear2014In: International Journal for Numerical Methods in Fluids, ISSN 0271-2091, E-ISSN 1097-0363, Vol. 74, no 6, p. 406-421Article in journal (Refereed)
    Abstract [en]

    We present our simulation results for the benchmark problem of the flow past a rudimentary landing gear using a General Galerkin FEM, also referred to as adaptive DNS/LES. In General Galerkin, no explicit subgrid model is used; instead, the computational mesh is adaptively refined with respect to an a posteriori error estimate of a quantity of interest in the computation, in this case, the drag force on the rudimentary landing gear. Turbulent boundary layers are modeled using a simple wall-layer model with the shear stress at walls proportional to the skin friction, which here is assumed to be small and, therefore, can be approximated by zero skin friction. We compare our results with experimental data and other state of the art computations, where we find good agreement in sound pressure levels, surface velocities, and flow separation. We also compare with detailed surface pressure experimental data where we find largely good agreement, apart from some local differences for which we discuss possible explanations.

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