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Simulation of stochastic reaction-diffusion processes on unstructured meshes
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
2009 (English)In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 31, 1774-1797 p.Article in journal (Refereed) Published
Place, publisher, year, edition, pages
2009. Vol. 31, 1774-1797 p.
National Category
Computational Mathematics Computer Science
Identifiers
URN: urn:nbn:se:uu:diva-97689DOI: 10.1137/080721388ISI: 000267746200008OAI: oai:DiVA.org:uu-97689DiVA: diva2:172726
Available from: 2008-11-07 Created: 2008-11-07 Last updated: 2017-12-14Bibliographically approved
In thesis
1. Numerical Solution Methods in Stochastic Chemical Kinetics
Open this publication in new window or tab >>Numerical Solution Methods in Stochastic Chemical Kinetics
2008 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This study is concerned with the numerical solution of certain stochastic models of chemical reactions. Such descriptions have been shown to be useful tools when studying biochemical processes inside living cells where classical deterministic rate equations fail to reproduce actual behavior. The main contribution of this thesis lies in its theoretical and practical investigation of different methods for obtaining numerical solutions to such descriptions.

In a preliminary study, a simple but often quite effective approach to the moment closure problem is examined. A more advanced program is then developed for obtaining a consistent representation of the high dimensional probability density of the solution. The proposed method gains efficiency by utilizing a rapidly converging representation of certain functions defined over the semi-infinite integer lattice.

Another contribution of this study, where the focus instead is on the spatially distributed case, is a suggestion for how to obtain a consistent stochastic reaction-diffusion model over an unstructured grid. Here it is also shown how to efficiently collect samples from the resulting model by making use of a hybrid method.

In a final study, a time-parallel stochastic simulation algorithm is suggested and analyzed. Efficiency is here achieved by moving parts of the solution phase into the deterministic regime given that a parallel architecture is available.

Necessary background material is developed in three chapters in this summary. An introductory chapter on an accessible level motivates the purpose of considering stochastic models in applied physics. In a second chapter the actual stochastic models considered are developed in a multi-faceted way. Finally, the current state-of-the-art in numerical solution methods is summarized and commented upon.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2008. 68 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 564
Keyword
stochastic models, chemical master equation, mesoscopic kinetics, Markov property, jump process, moment closure problem, spectral-Galerkin method, high dimensional problem, hybrid methods, time-parallel, homogenization
National Category
Computational Mathematics
Research subject
Scientific Computing with specialization in Numerical Analysis
Identifiers
urn:nbn:se:uu:diva-9342 (URN)978-91-554-7322-8 (ISBN)
Public defence
2008-11-28, Room 2446, Polacksbacken, Lägerhyddsvägen 2D, Uppsala, 13:15 (English)
Opponent
Supervisors
Available from: 2008-11-07 Created: 2008-11-07 Last updated: 2011-10-26Bibliographically approved
2. Multiscale Stochastic Simulation of Reaction-Transport Processes: Applications in Molecular Systems Biology
Open this publication in new window or tab >>Multiscale Stochastic Simulation of Reaction-Transport Processes: Applications in Molecular Systems Biology
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Quantitative descriptions of reaction kinetics formulated at the stochastic mesoscopic level are frequently used to study various aspects of regulation and control in models of cellular control systems. For this type of systems, numerical simulation offers a variety of challenges caused by the high dimensionality of the problem and the multiscale properties often displayed by the biochemical model.

In this thesis I have studied several aspects of stochastic simulation of both well-stirred and spatially heterogenous systems. In the well-stirred case, a hybrid method is proposed that reduces the dimension and stiffness of a model. We also demonstrate how both a high performance implementation and a variance reduction technique based on quasi-Monte Carlo can reduce the computational cost to estimate the probability density of the system.

In the spatially dependent case, the use of unstructured, tetrahedral meshes to sample realizations of the stochastic process is proposed. Using such meshes, we then extend the reaction-diffusion framework to incorporate active transport of cellular cargo in a seamless manner. Finally, two multilevel methods for spatial stochastic simulation are considered. One of them is a space-time adaptive method combining exact stochastic, approximate stochastic and macroscopic modeling levels to reduce the simualation cost. The other method blends together mesoscale and microscale simulation methods to locally increase modeling resolution.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2011. 63 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 832
Keyword
stochastic simulation, chemical master equation, reaction-diffusion master equation, unstructured mesh, active transport, hybrid methods, URDME
National Category
Computational Mathematics
Research subject
Scientific Computing
Identifiers
urn:nbn:se:uu:diva-152098 (URN)978-91-554-8089-9 (ISBN)
Public defence
2011-06-10, Room 2446, Polacksbacken, Lägerhyddsvägen 2D, Uppsala, 10:15 (English)
Opponent
Supervisors
Projects
eSSENCE
Available from: 2011-05-19 Created: 2011-04-23 Last updated: 2012-01-26Bibliographically approved

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Engblom, StefanFerm, LarsHellander, AndreasLötstedt, Per

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