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  • 1.
    Brandi, Maya
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Centra, Parallelldatorcentrum, PDC.
    Brocke, E
    Talukdar, Husain Ahammad
    KTH, Skolan för datavetenskap och kommunikation (CSC).
    Hanke, Michael
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Bhalla, US
    Djurfeldt, Mikael
    KTH, Skolan för datavetenskap och kommunikation (CSC), Centra, Parallelldatorcentrum, PDC.
    Hellgren Kotaleski, Jeanette
    INCF.
    Multiscale modeling through MUSIC multi-simulation: Modeling a dendritic spine using MOOSE and NeuroRD2011Ingår i: Front. Neuroinform. Conference Abstract: 4th INCF Congress of Neuroinformatics, 2011Konferensbidrag (Refereegranskat)
    Abstract [en]

    The nervous system encompasses structure and phenomena at different spatial and temporal scales from molecule to behavior. In addition, different scales are described by different physical and mathematical formalisms. The dynamics of second messenger pathways can be formulated as stochastic reaction-diffusion systems [1] while the electrical dynamics of the neuronal membrane is often described by compartment models and the Hodgkin-Huxley formalism. In neuroscience, there is an increasing need and interest to study multi-scale phenomena where multiple scales and physical formalisms are covered by a single model. While there exists simulators/frameworks, such as GENESIS and MOOSE [3], which span such scales (kinetikit/HH-models), most software applications are specialized for a given domain. Here, we report about initial steps towards a framework for multi-scale modeling which builds on the concept of multi-simulations [2]. We aim to provide a standard API and communication framework allowing parallel simulators targeted at different scales and/or different physics to communicate on-line in a cluster environment. Specifically, we show prototype work on simulating the effect on receptor induced cascades on membrane excitability. Electrical properties of a compartment model is simulated in MOOSE, while receptor induced cascades are simulated in NeuroRD  [4,7] . In a prototype system, the two simulators are connected using PyMOOSE [5] and JPype [6]. The two models with their different physical properties (membrane currents in MOOSE, molecular biophysics in NeuroRD), are joined into a single model system.  We demonstrate the interaction of the numerical solvers of two simulators (MOOSE, NeuroRD) targeted at different spatiotemporal scales and different physics while solving a multi-scale problem. We analyze some of the problems that may arise in multi-scale multi-simulations and present requirements for a generic API for parallel solvers. This work represents initial steps towards a flexible modular framework for simulation of large-scale multi-scale multi-physics problems in neuroscience. References 1. Blackwell KT: An efficient stochastic diffusion algorithm for modeling second messengers in dendrites and spines. J Neurosci Meth 2006, 157: 142-153. 2. Djurfeldt M, Hjorth J, Eppler JM, Dudani N, Helias M, Potjans TC, Bhalla US, Diesmann M, Hellgren Kotaleski J, Ekeberg Ö: Run-Time Interoperability Between Neural Network Simulators Based on the MUSIC Framework. Neurinform 2010, 8: 43-60. 3. Dudani N, Ray S, George S, Bhalla US: Multiscale modeling and interoperability in MOOSE. Neuroscience 2009, 10(Suppl 1): 54. 4. Oliveira RF, Terrin A, Di Benedetto G, Cannon RC, Koh W, Kim M, Zaccolo M, Blacwell KT: The Role of Type 4 Phosphdiesterases in Generating Microdomains of cAMP: Large Scale Stochastic Simulations.

  • 2.
    Brandi, Maya
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Beräkningsbiologi, CB. KTH, Skolan för datavetenskap och kommunikation (CSC), Centra, Parallelldatorcentrum, PDC.
    Brocke, Ekaterina
    KTH, Skolan för datavetenskap och kommunikation (CSC), Beräkningsbiologi, CB.
    Talukdar, Husain A.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Beräkningsbiologi, CB.
    Hanke, Michael
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Bhalla, Upinder S.
    National Centre for Biological Sciences, Bangalore, India.
    Hällgren-Kotaleski, Jeanette
    KTH, Skolan för datavetenskap och kommunikation (CSC), Beräkningsbiologi, CB.
    Djurfeldt, Mikael
    KTH, Skolan för datavetenskap och kommunikation (CSC), Centra, Parallelldatorcentrum, PDC.
    Connecting MOOSE and NeuroRD through MUSIC: towards a communication framework for multi-scale modeling2011Ingår i: Twentieth Annual Computational Neuroscience Meeting: CNS*2011, Springer Science+Business Media B.V., 2011Konferensbidrag (Refereegranskat)
  • 3.
    Brocke, Ekaterina
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Beräkningsvetenskap och beräkningsteknik (CST).
    Bhalla, Upinder S.
    Djurfeldt, Mikael
    Hällgren Kotaleski, Jeanette
    KTH, Skolan för datavetenskap och kommunikation (CSC), Beräkningsvetenskap och beräkningsteknik (CST).
    Hanke, Michael
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Efficient Integration of Coupled Electrical-Chemical Systems in Multiscale Neuronal Simulations2016Ingår i: Frontiers in Computational Neuroscience, ISSN 1662-5188, E-ISSN 1662-5188, Vol. 10, artikel-id 97Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Multiscale modeling and simulations in neuroscience is gaining scientific attention due to its growing importance and unexplored capabilities. For instance, it can help to acquire better understanding of biological phenomena that have important features at multiple scales of time and space. This includes synaptic plasticity, memory formation and modulation, homeostasis. There are several ways to organize multiscale simulations depending on the scientific problem and the system to be modeled. One of the possibilities is to simulate different components of a multiscale system simultaneously and exchange data when required. The latter may become a challenging task for several reasons. First, the components of a multiscale system usually span different spatial and temporal scales, such that rigorous analysis of possible coupling solutions is required. Then, the components can be defined by different mathematical formalisms. For certain classes of problems a number of coupling mechanisms have been proposed and successfully used. However, a strict mathematical theory is missing in many cases. Recent work in the field has not so far investigated artifacts that may arise during coupled integration of different approximation methods. Moreover, in neuroscience, the coupling of widely used numerical fixed step size solvers may lead to unexpected inefficiency. In this paper we address the question of possible numerical artifacts that can arise during the integration of a coupled system. We develop an efficient strategy to couple the components comprising a multiscale test problem in neuroscience. We introduce an efficient coupling method based on the second-order backward differentiation formula (BDF2) numerical approximation. The method uses an adaptive step size integration with an error estimation proposed by Skelboe (2000). The method shows a significant advantage over conventional fixed step size solvers used in neuroscience for similar problems. We explore different coupling strategies that define the organization of computations between system components. We study the importance of an appropriate approximation of exchanged variables during the simulation. The analysis shows a substantial impact of these aspects on the solution accuracy in the application to our multiscale neuroscientific test problem. We believe that the ideas presented in the paper may essentially contribute to the development of a robust and efficient framework for multiscale brain modeling and simulations in neuroscience.

  • 4.
    Brocke, Ekaterina
    et al.
    KTH, Centra, Science for Life Laboratory, SciLifeLab.
    Djurfeldt, M.
    Bhalla, U. S.
    Hellgren Kotaleski, Jeanette
    KTH, Skolan för datavetenskap och kommunikation (CSC), Beräkningsvetenskap och beräkningsteknik (CST).
    Hanke, Michael
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA.
    Multirate method for co-simulation of electrical-chemical systems in multiscale modeling2017Ingår i: Journal of Computational Neuroscience, ISSN 0929-5313, E-ISSN 1573-6873, Vol. 42, nr 3, s. 245-256Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Multiscale modeling by means of co-simulation is a powerful tool to address many vital questions in neuroscience. It can for example be applied in the study of the process of learning and memory formation in the brain. At the same time the co-simulation technique makes it possible to take advantage of interoperability between existing tools and multi-physics models as well as distributed computing. However, the theoretical basis for multiscale modeling is not sufficiently understood. There is, for example, a need of efficient and accurate numerical methods for time integration. When time constants of model components are different by several orders of magnitude, individual dynamics and mathematical definitions of each component all together impose stability, accuracy and efficiency challenges for the time integrator. Following our numerical investigations in Brocke et al. (Frontiers in Computational Neuroscience, 10, 97, 2016), we present a new multirate algorithm that allows us to handle each component of a large system with a step size appropriate to its time scale. We take care of error estimates in a recursive manner allowing individual components to follow their discretization time course while keeping numerical error within acceptable bounds. The method is developed with an ultimate goal of minimizing the communication between the components. Thus it is especially suitable for co-simulations. Our preliminary results support our confidence that the multirate approach can be used in the class of problems we are interested in. We show that the dynamics ofa communication signal as well as an appropriate choice of the discretization order between system components may have a significant impact on the accuracy of the coupled simulation. Although, the ideas presented in the paper have only been tested on a single model, it is likely that they can be applied to other problems without loss of generality. We believe that this work may significantly contribute to the establishment of a firm theoretical basis and to the development of an efficient computational framework for multiscale modeling and simulations.

  • 5. Chaudhry, Q. A.
    et al.
    Hanke, Michael
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA.
    Morgenstern, R.
    Dreij, K.
    Surface reactions on the cytoplasmatic membranes - Mathematical modeling of reaction and diffusion systems in a cell2014Ingår i: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 262, s. 244-260Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A human cell consists schematically of an outer cellular membrane, a cytoplasm containing a large number of organelles (mitochondria, endoplasmatic reticulum etc.), a nuclear membrane and finally the cellular nucleus containing DNA. The organelles create a complex and dense system of membranes or sub-domains throughout the cytoplasm. The mathematical description leads to a system of reaction-diffusion equations in a complex geometrical domain, dominated by thin membranous structures with similar physical and chemical properties. In a previous model, we considered only spatially distributed reaction and diffusion processes. However, from experiments it is known that membrane bound proteins play an important role in the metabolism of certain substances. In the present paper we develop a homogenization strategy which includes both volume and surface reactions. The homogenized system is a reaction-diffusion system in the cytoplasm which is coupled to the surrounding cell components by correspondingly modified transfer conditions. The approach is verified by application to a system modeling the cellular uptake and intracellular dynamics of carcinogenic polycyclic aromatic hydrocarbons.

  • 6. Chaudhry, Qasim A.
    et al.
    Hanke, Michael
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA.
    Study of intracellular reaction and diffusion mechanism of carcinogenic PAHs: Using non-standard compartment modeling approach2013Ingår i: Toxicology Letters, ISSN 0378-4274, E-ISSN 1879-3169, Vol. 221, s. S182-S182Artikel i tidskrift (Övrigt vetenskapligt)
  • 7.
    Chaudhry, Qasim Ali
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Dreij, Kristian
    Hanke, Michael
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Morgenstern, Ralf
    Numerical Approximation of Reaction and Diffusion Systems in Mammalian Cell Using Homogenization and Compartment Modelling2010Konferensbidrag (Refereegranskat)
  • 8.
    Chaudhry, Qasim Ali
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Dreij, Kristian
    Hanke, Michael
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Morgenstern, Ralf
    Spatially Distributed Models Instead of Compartment Models are Necessary for Accurate Capture of the Intracellular Dynamics of Lipophilic Compounds2010Konferensbidrag (Refereegranskat)
  • 9.
    Chaudhry, Qasim Ali
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    Hanke, Michael
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    Dreij, Kristian
    Morgenstern, Ralf
    Mathematical Modeling of Reaction and Diffusion Systems in a Cell Including Surface Reactions on the Cytoplasmic Membranes2012Rapport (Övrigt vetenskapligt)
    Abstract [en]

    Benzo[a]pyrene (BP) is a toxic polycyclic aromatic hydrocarbon (PAH) whichis found in our environment. These BPs are metabolized to benzo[a]pyrene diol(BPD) by enzymes bound to the cytoplasmic membranes e.g. members of thecytochrome P450 protein family and epoxide hydrolyses. BPDs are further metabolizedto two stereochemical variants of Benzo[a]pyrene diol expoxide (BPDE) bythe cytochrome P450 family of proteins. These are the two steps of metabolismcategorized as Phase I. In Phase II, BPDEs are further metabolized by soluble enzymesin the cytoplasm e.g. members of the glutathione transferase protein familyto GSH conjugates. BPDE can also diffuse into the cellular nucleus and reactwith DNA forming mutagenic DNA adducts. The formation of GSH conjugatesand DNA adducts, was earlier studied by us by developing a mathematical modeldescribing the intracellular reaction and diffusion of lipophilic PAHs taking intoaccount the partitioning phenomenon (Dreij K et al. PLoS One 6(8), 2011). In thispaper part of Phase I metabolism i.e formation of BPDE metabolites, will be addedto the model, thus enhancing the previous model. These cytochrome P450 reactionstake place on the intracellular membranes, and are modeled as a membranesurface reaction within the cytoplasm using the standard process of adsorption anddesorption. The effective equations are derived using iterative homogenization forthe numerical treatment of the cytoplasm including surface effects. The numericalresults of some of the species have been qualitatively verified against in vitroresults found in the literature.

  • 10.
    Chaudhry, Qasim Ali
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Hanke, Michael
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Morgenstern, Ralf
    Institute of Environmental Medicine, Karolinska Institutet, Stockholm, Sweden.
    On the numerical approximation of drug diffusion in complex cell geometry2009Ingår i: Proceedings of the 6th International Conference on Frontiers of Information Technology, FIT '09, Abbottabad, 2009Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    The mathematical modeling of a mammalian cell is a very tedious work due to its very complex geometry. Especially, taking into account the spatial distribution and the inclusion of lipophilic toxic compounds greatly increases its complexity. The nonhomogeneity and the different cellular architecture of the cell certainly affect the diffusion of these compounds. The complexity of the whole system can be reduced by a homogenization technique. To see the effect of these compounds on different cell architectures, we have implemented a mathematical model. The work has been done in 2-dimensional space. The simulation results have been qualitatively verified using compartmental modeling approach. This work can be extended with a more complex reaction-diffusion system and to 3-dimensional space as well. Copyright 2009 ACM.

  • 11.
    Chaudhry, Qasim Ali
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Hanke, Michael
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Morgenstern, Ralf
    Institute of Environmental Medicine, Karolinska Institutet, Stockholm, Sweden.
    Simulation of transport of lipophilic compounds in complex cell geometry2009Ingår i: Proceedings of the COMSOL Conference, Milan, 2009, 2009Konferensbidrag (Refereegranskat)
  • 12.
    Chaudhry, Qasim Ali
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    Morgenstern, Ralf
    Hanke, Michael
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    Dreij, Kristian
    Influence of Biological Cell Geometry on Reaction and Diffusion Simulation2012Rapport (Övrigt vetenskapligt)
    Abstract [en]

    Mathematical modeling of reaction-diffusion system in a biological cellis an important and difficult task, especially when the chemical compoundsare lipophilic. The difficulty level increases, when we take into account theheterogeneity of the cell, and the variation of cellular architecture. Mathematicalmodeling of reaction-diffusion systems in spherical cell geometryhas earlier been performed by us. In the present paper, we have workedwith non-spherical cell geometry, because the cellular geometry can play animportant role for drug diffusion in the cell. Homogenization techniques,which were earlier applied in the case of a spherical cell model, have beenused for the numerical treatment of the model. This technique considerablyreduces the complexity of the model. To further reduce the complexity ofthe model, a simplified model was also developed. The key idea of this simplifiedmodel has been advocated in Virtual Cell, where PDEs are used forthe extracellular domain, cytoplasm and nucleus, whereas the plasma andnuclear membranes have been taken away, and replaced by membrane flux,using Fick’s Law of diffusion. The numerical results of the non-sphericalcell model have been compared with the results of the spherical cell model,where the numerical results of spherical cell model have already been validatedagainst in vitro cell experimental results. From the numerical results,we conclude that the plasma and nuclear membranes can be protective reservoirsof significance. The numerical results of the simplified model werecompared against the numerical results of our detailed model, revealing theimportance of detailed modeling of membranes in our model.

  • 13.
    Dreij, Kristian
    et al.
    Karolinska Inst, Stockholm, Sweden .
    Chaudhry, Qasim A.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Zhang, Jie
    Karolinska Inst, Stockholm, Sweden .
    Sundberg, Kathrin
    Karolinska Inst, Stockholm, Sweden .
    Jernström, Bengt
    Karolinska Inst, Stockholm, Sweden .
    Hanke, Michael
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Morgenstern, Ralf
    Karolinska Inst, Stockholm, Sweden .
    In silico modeling of the intracellular dynamics of polycyclic aromatic hydrocarbons2012Ingår i: Toxicology Letters, ISSN 0378-4274, E-ISSN 1879-3169, Vol. 211, s. S60-S61Artikel i tidskrift (Övrigt vetenskapligt)
  • 14. Dreij, Kristian
    et al.
    Chaudhry, Qasim Ali
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Jernstrom, Bengt
    Morgenstern, Ralf
    Hanke, Michael
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    A Method for Efficient Calculation of Diffusion and Reactions of Lipophilic Compounds in Complex Cell Geometry2011Ingår i: PLoS ONE, ISSN 1932-6203, E-ISSN 1932-6203, Vol. 6, nr 8, s. e23128-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A general description of effects of toxic compounds in mammalian cells is facing several problems. Firstly, most toxic compounds are hydrophobic and partition phenomena strongly influence their behaviour. Secondly, cells display considerable heterogeneity regarding the presence, activity and distribution of enzymes participating in the metabolism of foreign compounds i.e. bioactivation/biotransformation. Thirdly, cellular architecture varies greatly. Taken together, complexity at several levels has to be addressed to arrive at efficient in silico modelling based on physicochemical properties, metabolic preferences and cell characteristics. In order to understand the cellular behaviour of toxic foreign compounds we have developed a mathematical model that addresses these issues. In order to make the system numerically treatable, methods motivated by homogenization techniques have been applied. These tools reduce the complexity of mathematical models of cell dynamics considerably thus allowing to solve efficiently the partial differential equations in the model numerically on a personal computer. Compared to a compartment model with well-stirred compartments, our model affords a more realistic representation. Numerical results concerning metabolism and chemical solvolysis of a polycyclic aromatic hydrocarbon carcinogen show good agreement with results from measurements in V79 cell culture. The model can easily be extended and refined to include more reactants, and/or more complex reaction chains, enzyme distribution etc, and is therefore suitable for modelling cellular metabolism involving membrane partitioning also at higher levels of complexity.

  • 15. Dreij, Kristian
    et al.
    Chaudhry, Qasim Ali
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    Jernström, Bengt
    Hanke, Michael
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    Morgenstern, Ralf
    In silico Modeling of Intracellular Diffusion and Reaction of Benzo[a]pyrene Diol Epoxide2012Rapport (Övrigt vetenskapligt)
    Abstract [en]

    Several studies has suggested that glutathione conjugation of polycyclicaromatic hydrocarbons (PAHs) catalyzed by glutathione transferases (GSTs)are important factors in protecting cells against toxicity and DNA damagederived from these compounds. To further characterize the intracellular dynamicsof PAH DEs and the role of GSTs in protection against DNA damage,we recently developed a PDE model using techniques for mathematicalhomogenization (Dreij K et al. PLoS One 6(8), 2011). In this study, wewanted to further develop our model by benchmarking against results fromfour V79 cell lines; control cells and cells overexpressing human GSTs A1-1, M1-1 and P1-1. We used an approach of global optimization of the parametersdescribing the diffusion and reaction of the ultimate carcinogenic PAHmetabolite benzo[a]pyrene diol epoxide to fit measured values from the fourV79 cell lines. Numerical results concerning the formation of glutathioneconjugates and hydrolysis were in good agreement with results from measurementsin V79 cell culture. Cellular results showed significant protectionby GST expression against formation of DNA adducts with more than 10-fold reduced levels compared to control cells. Results from the model usingglobally optimized parameters showed that the model cannot predict theprotective effects of GSTs. Extending the model to also include effects fromprotein interactions and GST localization showed the same discrepancy. Insummary, the results show that we have an incomplete understanding of theintracellular dynamics of the interaction between BPDE and GST that warrantsfurther investigation and development of the model.

  • 16.
    Hanke, Michael
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    A note on the consistent initialization for nonlinear index-2 differential-algebraic equations in Hessenberg form2004Rapport (Övrigt vetenskapligt)
    Abstract [en]

    In a previous paper, we developed a new algorithm for the consistent initialization of general index-2 differential-algebraic equations arising within the method of lines for solving partial differential equations. In the case of Hessenberg systems, the structural information allows for a lot of simplifications thus allowing for much larger systems to be solved. The crucial point consists of providing sparse projections by the use of sparse approximations to the inverse of the mass matrix. We obtain almost linear computational complexity with respect to the number of degrees of freedom.

  • 17.
    Hanke, Michael
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Benchmarking Femlab 3.0a: Laminar Flows in 2D2004Rapport (Övrigt vetenskapligt)
    Abstract [en]

    Recently, version 3.0a of the software package FEMLAB for solving multiphysics partialdifferential equations was released. In the present project we compared its performance with the previous release 2.3 and the package Fluent 6.1 in stationary laminar flow benchmarkproblems in two and three dimensions. It turns out that the new version is an essential improvement over the old version. It is much faster than Fluent in 2D.

  • 18.
    Hanke, Michael
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Benchmarking Femlab 3.1i: Solid Structural Mechanics2005Rapport (Övrigt vetenskapligt)
    Abstract [en]

    The software package FEMLAB is an environment for modelling and solving multiphysics applications which are described in terms of partial differential differential equations.

    In this project we tested the performance of the structural mechanics toolbox version 3.1. This version of the toolbox represents a considerable enhancement over previous releases with respect to modelling capabilities. We compare the performance of version 3.1 to that of the older version 2.3 and a state-of-the-art finite element package for solving structural mechanics problems, namely, ANSYS 9.0.

  • 19.
    Hanke, Michael
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Cabauatan-Villanueva, Marry-Chriz
    Chalmers University of Technology, Math. Dept.
    Analytical And Numerical Approximation of Effective Diffusivities in The Cytoplasm of Biological Cells2007Rapport (Övrigt vetenskapligt)
    Abstract [en]

    The simulation of the metabolism in mammalian cells becomes a severe problem if spatial distributions must be taken into account. Especially the cytoplsma has a very complex geometric structure which cannot be handled by standard discretization techniques. In the present paper we propose a homogenization technique for computing effective diffusion constants. This is accomplished by using a two-step strategy. The first step consists of an analytic homogenization from the smallest to an intermediate scale. The homogenization error is estimated by comparing the analytic diffusion constant with a numerical estimate obtained by using real cell geometries. The second step consists of a random homogenization. Since no analytical solution is known to this homogenization problem, a numerical approximation algorithm is proposed. Although rather expensive this algorithm provides a reasonable estimate of the homogenized diffusion constant.

  • 20.
    Hanke, Michael
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Cabauatan-Villanueva, Marry-Chriz
    Chalmers University of Technology, Math Dept..
    On the simulation of the metabolism in mammalian cells using homogenization methods2007Ingår i: European Comsol Conference 2007 / [ed] Petit, Jean-Marc; Squalli, Oumnia, 2007, s. 40-46Konferensbidrag (Övrigt vetenskapligt)
  • 21.
    Hanke, Michael
    et al.
    KTH, Tidigare Institutioner                               , Numerisk analys och datalogi, NADA.
    Lamour, R.
    Consistent initialization for nonlinear index-2 differential-algebraic equation: large sparse systems in MATLAB2003Ingår i: Numerical Algorithms, ISSN 1017-1398, E-ISSN 1572-9265, Vol. 32, nr 1, s. 67-85Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    An important component of any initial-value solver for higher-index differential-algebraic equations consists in the computation of consistent initial values. In a recent paper [5], an algorithm is proposed which is applicable to a very general class of index-2 systems. Unfortunately, the computational expense is rather high. We present a modification of this approach, which gives rise to a MATLAB implementation capable of handling systems of moderate dimension (several thousands of unknowns). The algorithm is illustrated by examples.

  • 22.
    Hanke, Michael
    et al.
    KTH, Tidigare Institutioner                               , Numerisk analys och datalogi, NADA.
    Li, P.
    Simulated annealing for the optimization of batch distillation processes2000Ingår i: Computers and Chemical Engineering, ISSN 0098-1354, E-ISSN 1873-4375, Vol. 24, nr 1, s. 1-8Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Batch distillation processes are widely used in the chemical industry. In this work, we consider the optimization of such processes by simulated annealing. Although this method is stochastically in nature, it has two well-known advantages: it can be readily connected to highly sophisticated simulation codes and it converges towards a global optimum. According to the characteristics of batch distillation operation we propose to use a two-step computation approach. A feasible strategy (admissible control) will be searched for in the first step and it will be optimized in the second step. The approach has been applied to a model of a pilot batch distillation plant. These results show the potential of the method for developing optimal operation strategies for batch chemical processes;

  • 23.
    Hanke, Michael
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Loubenets, Alexei
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    An immersed finite element method and its convergence for elliptic interface problems with discontinuous coefficients and singular sources2007Rapport (Övrigt vetenskapligt)
    Abstract [en]

    This paper is concerned with the analysis of an immersed ginite element method for two dimensional elliptic interface problems. The main idea of the method is to use specifically designed macro elements in the vicinity of the interface, such that the jump conditions are well approximated. In general, the resulting immersed finite element space is non-conforming. It is shown that the presented method is second order accurate in L² norm. The provided numerical results agree with the theoretical estimates.

  • 24.
    Hanke, Michael
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA.
    März, R.
    Tischendorf, C.
    Weinmüller, E.
    Wurm, S.
    Least-squares collocation for linear higher-index differential–algebraic equations2017Ingår i: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 317, s. 403-431Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Differential–algebraic equations with higher index give rise to essentially ill-posed problems. Therefore, their numerical approximation requires special care. In the present paper, we state the notion of ill-posedness for linear differential–algebraic equations more precisely. Based on this property, we construct a regularization procedure using a least-squares collocation approach by discretizing the pre-image space. Numerical experiments show that the resulting method has excellent convergence properties and is not much more computationally expensive than standard collocation methods used in the numerical solution of ordinary differential equations or index-1 differential–algebraic equations. Convergence is shown for a limited class of linear higher-index differential–algebraic equations.

  • 25.
    Hanke, Michael
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA.
    März, Roswitha
    Tischendorf, Caren
    Weinmüller, E.
    Wurm, S.
    Least-Squares Collocation for Higher-Index Linear Differential-Algebraic Equations: Estimating the Instability Threshold2019Ingår i: Mathematics of Computation, ISSN 0025-5718, E-ISSN 1088-6842, Vol. 88, nr 318, s. 1647-1683Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Differential-algebraic equations with higher-index give rise to essentially ill-posed problems. The overdetermined least-squares collocation for differential-algebraic equations which has been proposed recently is not much more computationally expensive than standard collocation methods for ordinary differential equations. This approach has displayed impressive convergence properties in numerical experiments, however, theoretically, till now convergence could be established merely for regular linear differential-algebraic equations with constant coefficients. We present now an estimate of the instability threshold which serves as the basic key for proving convergence for general regular linear differential-algebraic equations.

  • 26.
    Hanke, Michael
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
    Olsson, K. Henrik A.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
    Strömgren, Magnus
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
    Stability Analysis of a Degenerate Hyperbolic System Modelling a Heat Exchanger2007Ingår i: Mathematics and Computers in Simulation, ISSN 0378-4754, E-ISSN 1872-7166, Vol. 74, nr 1, s. 8-19Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Mathematical modelling of a heat exchanger in a carbon dioxide heat pump, an evaporator, is considered. A reduced model, called the the zero Mach-number limit, is derived from the Euler equations of compressible liquid flow through elimination of time scales associated with sound waves. The well-posedness of the resulting partial differential-algebraic equation (PDAE) is investigated by analysis of a frozen coefficient linearisation as well as by numerical experiments.

    The linear stability analysis is done through transformation to a canonical form with one hyperbolic component and one parabolic block of dimension 2. Using this canonical form it is seen how to prescribe boundary and initial data and an energy estimate is derived.

    Numerical experiments on the nonlinear PDAE using a finite difference spatial discretisation support the linear stability analysis.

  • 27.
    Hanke, Michael
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Olsson, K. Henrik A.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Strömgren, Magnus
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Stability Analysis of a Reduced Heat Exchanger Model2005Ingår i: Proceedings in Applied Mathematics and Mechanics: PAMM, ISSN 1617-7061, E-ISSN 1617-7061, Vol. 5, nr 1, s. 805-806Artikel i tidskrift (Refereegranskat)
  • 28.
    Hanke, Michael
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Reis, Timo
    The Perturbation and ADAE Index of a Degenerated Hyperbolic System2009Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider a linear version of the zero Mach-number limit of the Euler equations of compressible fluid flow. This system turns out to be a coupled hyperbolic/parabolic equation with coupled, time-dependent boundary conditions. Using the theory of abstract differential-algebraic equations it is shown that the frozen coefficient system has ADAE index 1. Moreover, the much stronger result is proven that the system has time-perturbation index one and space-perturbation index two even in the case of time-dependent boundary conditions. The results are stated in terms of the original physical variables. The estimates agree well with numerical experiments.

  • 29. Hast, A.
    et al.
    Hanke, Mikael
    Karlsson, H. O.
    Swedish eScience education: A graduate school in eScience2015Ingår i: Proceedings - 11th IEEE International Conference on eScience, eScience 2015, IEEE , 2015, s. 31-35Konferensbidrag (Refereegranskat)
    Abstract [en]

    Swedish eScience Education (SeSE) is a national graduate school in eScience in Sweden. It comes from the collaboration between two major research initiatives in eScience and the school has turned out to be very successful. It has made it possible for students at different universities to get access to education that is not normally available at their home universities. With SeSE they get access to education by the top experts within their respective field. We argue why such graduate school is important and how it is different from training offered by many HPC centres in Europe. Furthermore, examples of courses and their structure is discussed as well as lessons learned from SeSE and its two predecessors in Sweden.

  • 30.
    Loubenets, Alexei
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
    Ali, Tanweer
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
    Hanke, Michael
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
    Highly accurate finite element method for one-dimensional elliptic interface problems2009Ingår i: Applied Numerical Mathematics, ISSN 0168-9274, E-ISSN 1873-5460, Vol. 59, nr 1, s. 119-134Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A high order finite element method for one-dimensional elliptic interface problems is presented. Due to presence of these interfaces the problem will contain discontinuities in the coefficients and singularities in the right hand side that are represented by delta functional with the support on the interfaces. As a result, the solution to the interface problem and its derivatives may have jump discontinuities. The proposed method is specifically designed to handle this features of the solution using non-body fitted grids, i.e. the grids are not aligned with the interfaces.The finite element method will be based on third order Hermitian interpolation. The main idea is to modify the basis functions in the vicinity of the interface such that the jump conditions are well approximated. A rigorous error analysis shows that the presented finite element method is fourth order accurate in L-2 norm. The numerical results agree well with the theoretical analysis. The basic idea can easily be generalized to other finite element ansatz functions.

  • 31.
    Loubenets, Alexei
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
    Engquist, Björn
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
    Hanke, Michael
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
    A Fixed Grid Finite Element Method for Elliptic Interface Problems2006Ingår i: Proceedings of the International Conference on Numerical Analysis and Applied Mathematics, 2006, s. 1-23Konferensbidrag (Refereegranskat)
    Abstract [en]

    A finite element method for two-dimensional elliptic interface problem is presented. Due to the presence of these interfaces the problem will contain discontinuities in the coefficients and singular source terms that are represented by delta functions along the interface. As a result, the solution to the interface problem and its deratives may have jump discontinuities. The new method is specifically designed to handle this feature of the solution in the context of non-interface fitted grids.

    The main idea is to modify the standard basis function in the vicinity of the interface such that the jump conditions are well approximated. The resulting finite element space is, in general, non-conforming. The interface itself is represented by a set of Lagrangian markers together with a parametric description connecting them. To illustrate the abilities of the method, numerical tests are presented. For all the considered test problems, the new method has been shown to have super-linear or second order of convergence. Our approach is also compared with the standard finite element method. Finally, the method has been successfully applied to the Stokes interface problems.

  • 32.
    Loubenets, Alexei
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
    Engquist, Björn
    University of Texas, Austin.
    Hanke, Michael
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
    A non body-fitted finite element method for elliptic interface problems2006Ingår i: Proceedings International Conference on Numerical Analysis and Applied Mathematics 2006, 2006Konferensbidrag (Refereegranskat)
  • 33.
    Loubenets, Alexei
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Hanke, Michael
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    A non-conforming finite element method for interface Stokes problems and its application to two-phase Rayleigh-Taylor instability with solid obstacles2007Rapport (Övrigt vetenskapligt)
    Abstract [en]

    In this paper we establish an immersed finite element method for the solution of interface Stokes problems. The main idea of the method is to use a fixed, uniform mesh everywhere over the computational domain except the vicinity of the interface, where specifically designed macro elements are employed, such that the jump conditions are well approximated. In general, the resulting immersed finite element space is non-conforming. The interface itself is represented with the help of Lagrangian markers. The capabillity of the method is illustrated in the case of a Rayleigh-Taylor two-phase flow instability problem with solid obstacles governed by the Stokes equations.

  • 34. Strömgren, Magnus
    et al.
    Hanke, Michael
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    On the numerical approximation of a degenerated hyperbolic system2009Ingår i: Mathematics and Computers in Simulation, ISSN 0378-4754, E-ISSN 1872-7166, Vol. 79, nr 5, s. 1585-1602Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The heat exchanger in a heat pump system may be conveniently described by a degenerated hyperbolic system, namely the zero Mach-number limit of the Euler equations. This leads to a mixed hyperbolic/parabolic system with coupled time-dependent boundary conditions. We propose a method-of-lines discretisation by using an upwinding scheme. We derive stability estimates for the linearisation with frozen coefficients. The resulting differential-algebraic equation has a perturbation index of 2 and a weak instability with respect to the space step size. The latter property is validated experimentally even for the nonlinear system. In contrast, the perturbation index did not exceed one in the numerical experiments.

1 - 34 av 34
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