Home > Publications database > Numerical solution of SPDEs on a class of two-dimensional domains and of random differential equations using PCE with exponential time differencing > print

001     1043284
005     20250724210254.0
024 7 _ |a urn:nbn:de:kobv:co1-opus4-70206
|2 URN
024 7 _ |a 10.34734/FZJ-2025-02810
|2 datacite_doi
037 _ _ |a FZJ-2025-02810
041 _ _ |a English
100 1 _ |a Clausnitzer, Julian
|0 P:(DE-Juel1)184646
|b 0
|e Corresponding author
245 _ _ |a Numerical solution of SPDEs on a class of two-dimensional domains and of random differential equations using PCE with exponential time differencing
|f 2020-05-01 - 2023-10-31
260 _ _ |c 2025
300 _ _ |a 129 p.
336 7 _ |a Output Types/Dissertation
|2 DataCite
336 7 _ |a DISSERTATION
|2 ORCID
336 7 _ |a PHDTHESIS
|2 BibTeX
336 7 _ |a Thesis
|0 2
|2 EndNote
336 7 _ |a Dissertation / PhD Thesis
|b phd
|m phd
|0 PUB:(DE-HGF)11
|s 1753339409_4439
|2 PUB:(DE-HGF)
336 7 _ |a doctoralThesis
|2 DRIVER
502 _ _ |a Dissertation, Brandenburgische Technische Universität Cottbus-Senftenberg, 2024
|c Brandenburgische Technische Universität Cottbus-Senftenberg
|b Dissertation
|d 2024
|o 2024-12-04
520 _ _ |a The first part of this thesis deals with the numerical solution of semilinear parabolic stochastic partial differential equations on general two-dimensional C²-bounded domains. The existing exponential Euler time stepping scheme is used on two-dimensional domains, using a spectral approximation in space. Since the base functions are not given analytically, they are numerically approximated using a boundary element method combined with a contour integral method to solve nonlinear eigenvalue problems. An error analysis is given, and numerical experiments conclude the investigation of the method.The second part of the thesis compares the performance of non-intrusive and intrusive polynomial chaos expansion methods based on exponential time differencing schemes for a range of random ordinary and partial differential equations. It is shown in comprehensive numerical experiments that the two approaches are competitive for a range of different equations, but intrusive polynomial chaos becomes less efficient for polynomial nonlinearities of degree greater than two and breaks down for a reaction-diffusion equation exhibiting complex pattern formation behavior.
536 _ _ |a 5112 - Cross-Domain Algorithms, Tools, Methods Labs (ATMLs) and Research Groups (POF4-511)
|0 G:(DE-HGF)POF4-5112
|c POF4-511
|f POF IV
|x 0
588 _ _ |a Dataset connected to DataCite
856 4 _ |u https://doi.org/10.26127/BTUOpen-7020
856 4 _ |u https://juser.fz-juelich.de/record/1043284/files/Clausnitzer_Julian.pdf
|y OpenAccess
909 C O |o oai:juser.fz-juelich.de:1043284
|p openaire
|p open_access
|p urn
|p driver
|p VDB
|p dnbdelivery
910 1 _ |a Forschungszentrum Jülich
|0 I:(DE-588b)5008462-8
|k FZJ
|b 0
|6 P:(DE-Juel1)184646
913 1 _ |a DE-HGF
|b Key Technologies
|l Engineering Digital Futures – Supercomputing, Data Management and Information Security for Knowledge and Action
|1 G:(DE-HGF)POF4-510
|0 G:(DE-HGF)POF4-511
|3 G:(DE-HGF)POF4
|2 G:(DE-HGF)POF4-500
|4 G:(DE-HGF)POF
|v Enabling Computational- & Data-Intensive Science and Engineering
|9 G:(DE-HGF)POF4-5112
|x 0
914 1 _ |y 2025
915 _ _ |a OpenAccess
|0 StatID:(DE-HGF)0510
|2 StatID
920 _ _ |l yes
920 1 _ |0 I:(DE-Juel1)JSC-20090406
|k JSC
|l Jülich Supercomputing Center
|x 0
980 _ _ |a phd
980 _ _ |a VDB
980 _ _ |a UNRESTRICTED
980 _ _ |a I:(DE-Juel1)JSC-20090406
980 1 _ |a FullTexts

LibraryCollectionCLSMajorCLSMinorLanguageAuthor
Marc 21