| 1. |
- Engblom, Stefan
(författare)
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PARALLEL IN TIME SIMULATION OF MULTISCALE STOCHASTIC CHEMICAL KINETICS
- 2009
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Ingår i: Multiscale Modeling & simulation. - : Society for Industrial & Applied Mathematics (SIAM). - 1540-3459 .- 1540-3467. ; 8:1, s. 46-68
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Tidskriftsartikel (refereegranskat)abstract
- A version of the time-parallel algorithm parareal is analyzed and applied to stochastic models in chemical kinetics. A fast predictor at the macroscopic scale (evaluated in serial) is available in the form of the usual reaction rate equation. A stochastic simulation algorithm is used to obtain an exact realization of the process at the mesoscopic scale (in parallel). The underlying stochastic description is a jump process driven by the Poisson measure. A convergence result in this arguably difficult setting is established, suggesting that a homogenization of the solution is advantageous. We devise a simple but highly general such technique. Three numerical experiments on models representative to the field of computational systems biology illustrate the method. For nonstiff problems, it is shown that the method is able to quickly converge even when stochastic effects are present. For stiff problems, we are instead able to obtain fast convergence to a homogenized solution. Overall, the method builds an attractive bridge between, on the one hand, macroscopic deterministic scales and, on the other hand, mesoscopic stochastic ones. This construction is clearly possible to apply also to stochastic models within other fields.
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| 2. |
- Engblom, Stefan
(författare)
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On well-separated sets and fast multipole methods
- 2011
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Ingår i: Applied Numerical Mathematics. - : Elsevier BV. - 0168-9274 .- 1873-5460. ; 61:10, s. 1096-1102
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Tidskriftsartikel (refereegranskat)abstract
- The notion of well-separated sets is crucial in fast multipole methods as the main idea is to approximate the interaction between such sets via cluster expansions. We revisit the one-parameter multipole acceptance criterion in a general setting and derive a relative error estimate. This analysis benefits asymmetric versions of the method, where the division of the multipole boxes is more liberal than in conventional codes. Such variants offer a particularly elegant implementation with a balanced multipole tree, a feature which might be very favorable on modern computer architectures.
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| 3. |
- Bauer, Pavol, et al.
(författare)
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Fast event-based epidemiological simulations on national scales
- 2016
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Ingår i: The international journal of high performance computing applications. - : SAGE Publications. - 1094-3420 .- 1741-2846. ; 30, s. 438-453
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Tidskriftsartikel (refereegranskat)abstract
- We present a computational modeling framework for data-driven simulations and analysis of infectious disease spread in large populations. For the purpose of efficient simulations, we devise a parallel solution algorithm targeting multi-socket shared-memory architectures. The model integrates infectious dynamics as continuous-time Markov chains and available data such as animal movements or aging are incorporated as externally defined events. To bring out parallelism and accelerate the computations, we decompose the spatial domain and optimize cross-boundary communication using dependency-aware task scheduling. Using registered livestock data at a high spatiotemporal resolution, we demonstrate that our approach not only is resilient to varying model configurations but also scales on all physical cores at realistic workloads. Finally, we show that these very features enable the solution of inverse problems on national scales.
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| 4. |
- Bauer, Pavol
(författare)
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Parallelism and efficiency in discrete-event simulation
- 2015
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Discrete-event models depict systems where a discrete state is repeatedly altered by instantaneous changes in time, the events of the model. Such models have gained popularity in fields such as Computational Systems Biology or Computational Epidemiology due to the high modeling flexibility and the possibility to easily combine stochastic and deterministic dynamics. However, the system size of modern discrete-event models is growing and/or they need to be simulated at long time periods. Thus, efficient simulation algorithms are required, as well as the possibility to harness the compute potential of modern multicore computers. Due to the sequential design of simulators, parallelization of discrete event simulations is not trivial. This thesis discusses event-based modeling and sensitivity analysis and also examines ways to increase the efficiency of discrete-event simulations and to scale models involving deterministic and stochastic spatial dynamics on a large number of processor cores.
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| 5. |
- Engblom, Stefan
(författare)
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A discrete spectral method for the chemical master equation
- 2008
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- As an equivalent formulation of the Markov-assumption of stochastic processes, the master equation of chemical reactions is an accurate description of general systems in chemistry. For D reacting species this is a differential-difference equation in D dimensions, exactly soluble for very simple systems only.We present and analyze a novel solution strategy based upon a Galerkin spectral method with an inherent natural adaptivity and a very favorable choice of basis functions.The method is demonstrated by the numerical solution of two model problems followed by two more realistic systems taken from molecular biology. It is shown that the method remains effective and accurate, providing a viable alternative to other solution methods when the dimensionality is not too high.
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| 6. |
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| 7. |
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| 8. |
- Engblom, Stefan
(författare)
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Parallel in time simulation of multiscale stochastic chemical kinetics
- 2008
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- A version of the time-parallel algorithm parareal is analyzed and applied to stochastic models in chemical kinetics. A fast predictor at the macroscopic scale (evaluated in serial) is available in the form of the usual reaction rate equations. A stochastic simulation algorithm is used to obtain an exact realization of the process at the mesoscopic scale (in parallel).The underlying stochastic description is a jump process driven by the Poisson measure. A convergence result in this arguably difficult setting is established suggesting that a homogenization of the solution is advantageous. We devise a simple but highly general such technique.Three numerical experiments on models representative to the field of computational systems biology illustrate the method. For non-stiff problems, it is shown that the method is able to quickly converge even when stochastic effects are present. For stiff problems we are instead able to obtain fast convergence to a homogenized solution.Overall, the method builds an attractive bridge between on the one hand, macroscopic deterministic scales and, on the other hand, mesoscopic stochastic ones. This construction is clearly possible to apply also to stochastic models within other fields.
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| 9. |
- Engblom, Stefan, et al.
(författare)
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Simulation of stochastic reaction-diffusion processes on unstructured meshes
- 2008
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Stochastic chemical systems with diffusion are modeled with a reaction-diffusion master equation. On a macroscopic level, the governing equation is a reaction-diffusion equation for the averages of the chemical species. On a mesoscopic level, the master equation for a well stirred chemical system is combined with Brownian motion in space to obtain the reaction-diffusion master equation. The space is covered by an unstructured mesh and the diffusion coefficients on the mesoscale are obtained from a finite element discretization of the Laplace operator on the macroscale. The resulting method is a flexible hybrid algorithm in that the diffusion can be handled either on the meso- or on the macroscale level. The accuracy and the efficiency of the method are illustrated in three numerical examples inspired by molecular biology.
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| 10. |
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