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  • 1.
    af Klinteberg, Ludvig
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Tornberg, Anna-Karin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Adaptive Quadrature by Expansion for Layer Potential Evaluation in Two Dimensions2018In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 40, no 3, p. A1225-A1249Article in journal (Refereed)
    Abstract [en]

    When solving partial differential equations using boundary integral equation methods, accurate evaluation of singular and nearly singular integrals in layer potentials is crucial. A recent scheme for this is quadrature by expansion (QBX), which solves the problem by locally approximating the potential using a local expansion centered at some distance from the source boundary. In this paper we introduce an extension of the QBX scheme in two dimensions (2D) denoted AQBX—adaptive quadrature by expansion—which combines QBX with an algorithm for automated selection of parameters, based on a target error tolerance. A key component in this algorithm is the ability to accurately estimate the numerical errors in the coefficients of the expansion. Combining previous results for flat panels with a procedure for taking the panel shape into account, we derive such error estimates for arbitrarily shaped boundaries in 2D that are discretized using panel-based Gauss–Legendre quadrature. Applying our scheme to numerical solutions of Dirichlet problems for the Laplace and Helmholtz equations, and also for solving these equations, we find that the scheme is able to satisfy a given target tolerance to within an order of magnitude, making it useful for practical applications. This represents a significant simplification over the original QBX algorithm, in which choosing a good set of parameters can be hard.

  • 2. Ariel, G.
    et al.
    Kim, S. J.
    Tsai, Richard
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Parareal multiscale methods for highly oscillatory dynamical systems2016In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 38, no 6, p. A3540-A3564Article in journal (Refereed)
    Abstract [en]

    We introduce a new strategy for coupling the parallel in time (parareal) iterative methodology with multiscale integrators. Following the parareal framework, the algorithm computes a low-cost approximation of all slow variables in the system using an appropriate multiscale integrator, which is refined using parallel fine scale integrations. Convergence is obtained using an alignment algorithm for fast phase-like variables. The method may be used either to enhance the accuracy and range of applicability of the multiscale method in approximating only the slow variables, or to resolve all the state variables. The numerical scheme does not require that the system is split into slow and fast coordinates. Moreover, the dynamics may involve hidden slow variables, for example, due to resonances. We propose an alignment algorithm for almost-periodic solutions, in which case convergence of the parareal iterations is proved. The applicability of the method is demonstrated in numerical examples.

  • 3. Bayer, Christian
    et al.
    Hoel, Håkon
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    von Schwerin, Erik
    Tempone, Raul
    On nonasymptotic optimal stopping criteria in monte carlo simulations2014In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 36, no 2, p. A869-A885Article in journal (Refereed)
    Abstract [en]

    We consider the setting of estimating the mean of a random variable by a sequential stopping rule Monte Carlo (MC) method. The performance of a typical second moment based sequential stopping rule MC method is shown to be unreliable in such settings both by numerical examples and through analysis. By analysis and approximations, we construct a higher moment based stopping rule which is shown in numerical examples to perform more reliably and only slightly less efficiently than the second moment based stopping rule.

  • 4.
    Bozorgnia, Farid
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Numerical algorithm for spatial segregation of competitive systems2009In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 31, no 5, p. 3946-3958Article in journal (Refereed)
    Abstract [en]

    Two novel iterative methods for a class of population models of competitive type are considered. This numerical solution is related to the positive solution as the competitive rate tends to infinity. Furthermore, the idea first is applied to an optimal partition problem.

  • 5.
    Engquist, Björn
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Osher, S
    Zhong, S
    Fast wavelet based algorithms for linear evolution equations1994In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, ISSN 1064-8275, Vol. 15, no 4, p. 755-775Article in journal (Refereed)
    Abstract [en]

    The authors devise a class of fast wavelet based algorithms for linear evolution equations whose coefficients are time independent. The method draws on the work of Beylkin, Coifman, and Rokhlin [Comm. Pure Appl. Math., 44 (1991), pp. 141-1841, which they applied to general Calderon-Zygmund type integral operators. The authors apply a modification of their idea to linear hyperbolic and parabolic equations, with spatially varying coefficients. The complexity for hyperbolic equations in one dimension is reduced from O(N2) to O(N log3 N). There are somewhat better gains for parabolic equations in multidimensions

  • 6. Engquist, Björn
    et al.
    Ying, Lexing
    Fast directional multilevel algorithms for oscillatory kernels2007In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 29, no 4, p. 1710-1737Article in journal (Refereed)
    Abstract [en]

    This paper introduces a new directional multilevel algorithm for solving N-body or N-point problems with highly oscillatory kernels. These systems often result from the boundary integral formulations of scattering problems and are difficult due to the oscillatory nature of the kernel and the non-uniformity of the particle distribution. We address the problem by first proving that the interaction between a ball of radius r and a well-separated region has an approximate low rank representation, as long as the well-separated region belongs to a cone with a spanning angle of O(1/r) and is at a distance which is at least O(r(2)) away from from the ball. We then propose an efficient and accurate procedure which utilizes random sampling to generate such a separated, low rank representation. Based on the resulting representations, our new algorithm organizes the high frequency far field computation by a multidirectional and multiscale strategy to achieve maximum efficiency. The algorithm performs well on a large group of highly oscillatory kernels. Our algorithm is proved to have O(N log N) computational complexity for any given accuracy when the points are sampled from a two dimensional surface. We also provide numerical results to demonstrate these properties.

  • 7.
    Engquist, Björn
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Ying, Lexing
    Fast directional multilevel computation for problems with oscillatory kernels2007In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, p. 1710-1737Article in journal (Refereed)
  • 8. Eriksson, K.
    et al.
    Johnson, Claes
    Logg, A.
    Explicit time-stepping for stiff ODES2003In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 25, no 4, p. 1142-1157Article in journal (Refereed)
    Abstract [en]

    We present a new strategy for solving stiff ODEs with explicit methods. By adaptively taking a small number of stabilizing small explicit time steps when necessary, a stiff ODE system can be stabilized enough to allow for time steps much larger than what is indicated by classical stability analysis. For many stiff problems the cost of the stabilizing small time steps is small, so the improvement is large. We illustrate the technique on a number of well-known stiff test problems.

  • 9.
    Gaaf, Sarah W.
    et al.
    TU Eindhoven.
    Jarlebring, Elias
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    The infinite Bi-Lanczos method for nonlinear eigenvalue problems2017In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 39, p. S898-S919Article in journal (Refereed)
  • 10. Hall, E. J.
    et al.
    Hoel, H.
    Sandberg, Mattias
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Szepessy, Anders
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Tempone, R.
    Computable error estimates for finite element approximations of elliptic partial differential equations with rough stochastic data2016In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 38, no 6, p. A3773-A3807Article in journal (Refereed)
    Abstract [en]

    We derive computable error estimates for finite element approximations of linear elliptic partial differential equations with rough stochastic coefficients. In this setting, the exact solutions contain high frequency content that standard a posteriori error estimates fail to capture. We propose goal-oriented estimates, based on local error indicators, for the pathwise Galerkin and expected quadrature errors committed in standard, continuous, piecewise linear finite element approximations. Derived using easily validated assumptions, these novel estimates can be computed at a relatively low cost and have applications to subsurface flow problems in geophysics where the conductivities are assumed to have lognormal distributions with low regularity. Our theory is supported by numerical experiments on test problems in one and two dimensions.

  • 11. Ho, Ching-Tien
    et al.
    Johnsson, Lennart
    KTH, School of Computer Science and Communication (CSC), Centres, Centre for High Performance Computing, PDC.
    Optimizing Tridiagonal Solvers for the Alternating Direction Method on Boolean Cube Multiprocessors1990In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 11, no 3, p. 563-592Article in journal (Refereed)
    Abstract [en]

    Sets of tridiagonal systems occur in many applications. Fast Poisson solvers and Alternate Direction Methods make use of tridiagonal system solvers. Network-based multiprocessors provide a cost-effective alternative to traditional supercomputer architectures. The complexity of concurrent algorithms for the solution of multiple tridiagonal systems on Boolean-cube-configured multiprocessors with distributed memory are investigated. Variations of odd-even cyclic reduction, parallel cyclic reduction, and algorithms making use of data transposition with or without substructuring and local elimination, or pipelined elimination, are considered. A simple performance model is used for algorithm comparison, and the validity of the model is verified on an Intel iPSC/ 1. For many combinations of machine and system parameters, pipelined elimination, or equation transposition with or without substructuring is optimum. Hybrid algorithms that at any stage choose the best algorithm among the considered ones for the remainder of the problem are presented. It is shown that the optimum partitioning of a set of independent tridiagonal systems among a set of processors yields the embarrassingly parallel case. If the systems originate from a lattice and solutions are computed in alternating directions, then to first order the aspect ratio of a computational lattice shall be the same as that of the lattice forming the base for the equations. The experiments presented here demonstrate the importance of combining in the communication system for architectures with a relatively high communications start-up time.

  • 12.
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Computation of mean drag for bluff body problems using adaptive DNS/LES2005In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 27, no 1, p. 184-207Article in journal (Refereed)
    Abstract [en]

    We compute the time average of the drag in two benchmark bluff body problems: a surface mounted cube at Reynolds number 40000, and a square cylinder at Reynolds number 22000, using adaptive DNS/LES. In adaptive DNS/LES the Galerkin least-squares finite element method is used, with adaptive mesh refinement until a given stopping criterion is satisfied. Both the mesh refinement criterion and the stopping criterion are based on a posteriori error estimates of a given output of interest, in the form of a space-time integral of a computable residual multiplied by a dual weight, where the dual weight is obtained from solving an associated dual problem computationally, with the data of the dual problem coupling to the output of interest. No filtering is used, and in particular no Reynolds stresses are introduced. We thus circumvent the problem of closure, and instead we estimate the error contribution from subgrid modeling a posteriori, which we find to be small. We are able to predict the mean drag with an estimated tolerance of a few percent using about 105 mesh points in space, with the computational power of a PC.

  • 13.
    Hoffman, Johan
    Courant Institute, New York University.
    On Duality-Based A Posteriori Error Estimation in Various Norms and Linear Functionals for Large Eddy Simulation2004In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 26, no 1, p. 178-195Article in journal (Refereed)
    Abstract [en]

    We derive a posteriori error estimates for the filtered velocity field in a large eddy simulation in various norms and linear functionals. The a posteriori error estimates take the form of an integral in space-time of a discretization residual and a modeling residual times a dual weight. The discretization residual is directly computable, and the modeling residual is estimated by a scale similarity model. We approximate the dual weight by solving an associated linearized dual problem numerically. Computational examples from transition to turbulence in Couette flow are presented.

  • 14.
    Hoffman, Johan
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Jansson, Johan
    Nazarov, Murtazo
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    A General Galerkin Finite Element Method for the Compressible Euler Equations2008In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197Article in journal (Refereed)
    Abstract [en]

    In this paper we present a General Galerkin (G2) method for the compressible Euler equations, including turbulent ow. The G2 method presented in this paper is a nite element method with linear approximation in space and time, with componentwise stabilization in the form  of streamline diusion and shock-capturing modi cations. The method conserves mass, momentum  and energy, and we prove an a posteriori version of the 2nd Law of thermodynamics for the method.  We illustrate the method for a laminar shock tube problem for which there exists an exact analytical  solution, and also for a turbulent flow problem

  • 15.
    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.

  • 16.
    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)
  • 17.
    Jarlebring, Elias
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Koskela, Antti
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Mele, Giampaolo
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Disguised and new quasi-Newton methods for nonlinear eigenvalue problemsIn: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197Article in journal (Refereed)
  • 18.
    Jarlebring, Elias
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Kvaal, Simen
    Michiels, Wim
    An Inverse Iteration Method for Eigenvalue Problems with Eigenvector Nonlinearities2014In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 36, no 4, p. A1978-A2001Article in journal (Refereed)
    Abstract [en]

    Consider a symmetric matrix A(v) is an element of R-nxn depending on a vector v is an element of R-n and satisfying the property A(alpha v) = A(v) for any alpha is an element of R\{0}. We will here study the problem of finding (lambda,v) is an element of R x R-n\{0} such that (lambda,v) is an eigenpair of the matrix A(v) and we propose a generalization of inverse iteration for eigenvalue problems with this type of eigenvector nonlinearity. The convergence of the proposed method is studied and several convergence properties are shown to be analogous to inverse iteration for standard eigenvalue problems, including local convergence properties. The algorithm is also shown to be equivalent to a particular discretization of an associated ordinary differential equation, if the shift is chosen in a particular way. The algorithm is adapted to a variant of the Schrodinger equation known as the Gross-Pitaevskii equation. We use numerical simulations to illustrate the convergence properties, as well as the efficiency of the algorithm and the adaption.

  • 19.
    Jarlebring, Elias
    et al.
    Katholieke Univ Leuven, Dept Comp Sci, B-3001 Heverlee, Belgium .
    Meerbergen, Karl
    Katholieke Univ Leuven, Dept Comp Sci, B-3001 Heverlee, Belgium .
    Michiels, Wim
    Katholieke Univ Leuven, Dept Comp Sci, B-3001 Heverlee, Belgium .
    A Krylov method for the delay eigenvalue problem2010In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 32, no 6, p. 3278-3300Article in journal (Refereed)
    Abstract [en]

    The Arnoldi method is currently a very popular algorithm to solve large-scale eigenvalue problems. The main goal of this paper is to generalize the Arnoldi method to the characteristic equation of a delay-differential equation (DDE), here called a delay eigenvalue problem (DEP). The DDE can equivalently be expressed with a linear infinite-dimensional operator whose eigenvalues are the solutions to the DEP. We derive a new method by applying the Arnoldi method to the generalized eigenvalue problem associated with a spectral discretization of the operator and by exploiting the structure. The result is a scheme where we expand a subspace not only in the traditional way done in the Arnoldi method. The subspace vectors are also expanded with one block of rows in each iteration. More important, the structure is such that if the Arnoldi method is started in an appropriate way, it has the (somewhat remarkable) property that it is in a sense independent of the number of discretization points. It is mathematically equivalent to an Arnoldi method with an infinite matrix, corresponding to the limit where we have an infinite number of discretization points. We also show an equivalence with the Arnoldi method in an operator setting. It turns out that with an appropriately defined operator over a space equipped with scalar product with respect to which Chebyshev polynomials are orthonormal, the vectors in the Arnoldi iteration can be interpreted as the coefficients in a Chebyshev expansion of a function. The presented method yields the same Hessenberg matrix as the Arnoldi method applied to the operator.

  • 20. Karlsson, Jesper
    et al.
    Larsson, Stig
    Sandberg, Mattias
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Szepessy, Anders
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Tempone, Raul
    An error estimate for symplectic euler approximation of optimal control problems2015In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 37, no 2, p. A946-A969Article in journal (Refereed)
    Abstract [en]

    This work focuses on numerical solutions of optimal control problems. A time discretization error representation is derived for the approximation of the associated value function. It concerns symplectic Euler solutions of the Hamiltonian system connected with the optimal control problem. The error representation has a leading-order term consisting of an error density that is computable from symplectic Euler solutions. Under an assumption of the pathwise convergence of the approximate dual function as the maximum time step goes to zero, we prove that the remainder is of higher order than the leading-error density part in the error representation. With the error representation, it is possible to perform adaptive time stepping. We apply an adaptive algorithm originally developed for ordinary differential equations. The performance is illustrated by numerical tests.

  • 21.
    Lehto, Erik
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Shankar, Varun
    Wright, Grady B.
    A Radial Basis Function (RBF) Compact Finite Difference (FD) Scheme for Reaction-Diffusion Equations on Surfaces2017In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 39, no 5, p. A2129-A2151Article in journal (Refereed)
    Abstract [en]

    We present a new high-order, local meshfree method for numerically solving reaction diffusion equations on smooth surfaces of codimension 1 embedded in R-d. The novelty of the method is in the approximation of the Laplace-Beltrami operator for a given surface using Hermite radial basis function (RBF) interpolation over local node sets on the surface. This leads to compact (or implicit) RBF generated finite difference (RBF-FD) formulas for the Laplace-Beltrami operator, which gives rise to sparse differentiation matrices. The method only requires a set of (scattered) nodes on the surface and an approximation to the surface normal vectors at these nodes. Additionally, the method is based on Cartesian coordinates and thus does not suffer from any coordinate singularities. We also present an algorithm for selecting the nodes used to construct the compact RBF-FD formulas that can guarantee the resulting differentiation matrices have desirable stability properties. The improved accuracy and computational cost that can be achieved with this method over the standard (explicit) RBF-FD method are demonstrated with a series of numerical examples. We also illustrate the flexibility and general applicability of the method by solving two different reaction-diffusion equations on surfaces that are defined implicitly and only by point clouds.

  • 22. Lichtenstein, Woody
    et al.
    Johnsson, Lennart
    KTH, School of Computer Science and Communication (CSC), Centres, Centre for High Performance Computing, PDC.
    Block Cyclic Dense Linear Algebra1993In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 14, no 6, p. 1257-1286Article in journal (Refereed)
    Abstract [en]

     Block-cyclic order elimination algorithms for LU and QR factorization and solve routines are described for distributed memory architectures with processing nodes configured as two-dimensional arrays of arbitrary shape. The cyclic-order elimination, together with a consecutive data allocation, yields good load balance for both the factorization and solution phases for the solution of dense systems of equations by LU and QR decomposition. Blocking may offer a substantial performance enhancement on architectures for which the level-2 or level-3 BLAS (basic linear algebra subroutines) are ideal for operations local to a node. High-rank updates local to a node may have a performance that is a factor of four or more higher than a rank-1 update. This paper shows that in many parallel implementations, the O(N2) work in the factorization may be of the same significance as the O(N3) work, even for large matrices. The O(N2) work is poorly load balanced in two-dimensional nodal arrays, which are shown to be optimal with respect to communication for consecutive data allocation, block-cyclic order elimination, and a simple, but fairly general, communications model. In this Connection Machine system CM-200 implementation, the peak performance for LU factorization is about 9.4 Gflops/s in 64-bit precision and 16 Gflops/s in 32-bit precision. Blocking offers an overall performance enhancement of an approximate factor of two. The broadcast-and-reduce operations fully utilize the bandwidth available in the Boolean cube network interconnecting the nodes along each axis of the two-dimensional nodal array embedded in the cube network.

  • 23.
    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.

  • 24.
    Nordström, Jan
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering.
    Error bounded schemes for time-dependent hyperbolic problems2007In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 30, no 1, p. 46-59Article in journal (Refereed)
    Abstract [en]

    In this paper we address the error growth in time for hyperbolic problems in first order form in bounded domains. The energy method is used to study when an error growth or a fixed error bound is obtained. It is shown that the choice of boundary procedure is a crucial point. Numerical experiments corroborate the theoretical findings.

  • 25.
    Sudhakar, Yogaraj
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. Technical University of Munich, Germany.
    Sommariva, Alvise
    Vianello, Marco
    Wall, Wolfgang A.
    On the use of compressed polyhedral quadrature formulas in embedded interface methods2017In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 39, no 3, p. B571-B587Article in journal (Refereed)
    Abstract [en]

    The main idea of this paper is to apply a recent quadrature compression technique to algebraic quadrature formulas on complex polyhedra. The quadrature compression substantially reduces the number of integration points but preserves the accuracy of integration. The compression is easy to achieve since it is entirely based on the fundamental methods of numerical linear algebra. The resulting compressed formulas are applied in an embedded interface method to integrate the weak form of the Navier-Stokes equations. Simulations of flow past stationary and moving interface problems demonstrate that the compressed quadratures preserve accuracy and rate of convergence and improve the efficiency of performing the weak form integration, while preserving accuracy and order of convergence.

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