Journal Article

FZJ-2023-03463

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png A spectral Galerkin exponential Euler time-stepping scheme for parabolic SPDEs on two-dimensional domains with a $\mathcal{C}^2$ boundary

Clausnitzer, J. (Corresponding author)FZJ* ; Kleefeld, A.FZJ*

2024
American Institute of Mathematical Sciences Springfield, Mo.

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Please use a persistent id in citations: doi:10.3934/dcdsb.2023148

Abstract: We consider the numerical approximation of second-order semi-linear parabolic stochastic partial differential equations interpreted in the mild sense which we solve on general two-dimensional domains with a boundary with homogeneous Dirichlet boundary conditions. The equations are driven by Gaussian additive noise, and several Lipschitz-like conditions are imposed on the nonlinear function. We discretize in space with a spectral Galerkin method and in time using an explicit Euler-like scheme. For irregular shapes, the necessary Dirichlet eigenvalues and eigenfunctions are obtained from a boundary integral equation method. This yields a nonlinear eigenvalue problem, which is discretized using a boundary element collocation method and is solved with the Beyn contour integral algorithm. We present an error analysis as well as numerical results on an exemplary asymmetric shape, and point out limitations of the approach.

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Contributing Institute(s):

1. Jülich Supercomputing Center (JSC)

Research Program(s):

1. 5112 - Cross-Domain Algorithms, Tools, Methods Labs (ATMLs) and Research Groups (POF4-511) (POF4-511)

Appears in the scientific report 2024

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Database coverage:
; Clarivate Analytics Master Journal List ; Current Contents - Physical, Chemical and Earth Sciences ; Essential Science Indicators ; Essential Science Indicators ; IF < 5 ; JCR ; SCOPUS ; Science Citation Index Expanded ; Science Citation Index Expanded ; Web of Science Core Collection

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