Adaptive Gaussian particle method for the solution of the Fokker-Planck equation
| Autor: | M.D. Scharpenberg, M. Lukáčová-Medviová |
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| Rok vydání: | 2012 |
| Předmět: |
Mathematical optimization
Partial differential equation Applied Mathematics Gaussian Computational Mechanics Basis function Probability density function Multivariate normal distribution Residual symbols.namesake Ordinary differential equation symbols Applied mathematics Fokker–Planck equation Mathematics |
| Zdroj: | ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik. 92:770-781 |
| ISSN: | 0044-2267 |
| DOI: | 10.1002/zamm.201100088 |
| Popis: | The Fokker-Planck equation describes the evolution of the probability density for a stochastic ordinary differential equation (SODE). A solution strategy for this partial differential equation (PDE) up to a relatively large number of dimensions is based on particle methods using Gaussians as basis functions. An initial probability density is decomposed into a sum of multivariate normal distributions and these are propagated according to the SODE. The decomposition as well as the propagation is subject to possibly large numeric errors due to the difficulty to control the spatial residual over the whole domain. In this paper a new particle method is derived, which allows a deterministic error control for the resulting probability density. It is based on global optimization and allows an adaption of an efficient surrogate model for the residual estimation. Copyright line will be provided by the publisher |
| Databáze: | OpenAIRE |
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