001005457 001__ 1005457
001005457 005__ 20240226075509.0
001005457 0247_ $$2Handle$$a2128/34151
001005457 037__ $$aFZJ-2023-01486
001005457 041__ $$aEnglish
001005457 1001_ $$0P:(DE-Juel1)173688$$aMüller, Björn$$b0$$eCorresponding author
001005457 245__ $$aInvestigation of Exponential Time Differencing Schemes for Advection-Diffusion-Reaction Problems in the Presence of Significant Advection$$f - 2023-03-09
001005457 260__ $$c2022
001005457 300__ $$ax, 121 p.
001005457 3367_ $$2DataCite$$aOutput Types/Supervised Student Publication
001005457 3367_ $$02$$2EndNote$$aThesis
001005457 3367_ $$2BibTeX$$aMASTERSTHESIS
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001005457 3367_ $$0PUB:(DE-HGF)19$$2PUB:(DE-HGF)$$aMaster Thesis$$bmaster$$mmaster$$s1679036549_14798
001005457 3367_ $$2ORCID$$aSUPERVISED_STUDENT_PUBLICATION
001005457 500__ $$aDefense at FH Aachen Campus Jülich March 9th, 2023
001005457 502__ $$aMasterarbeit, University of Louisiana at Lafayette, 2022$$bMasterarbeit$$cUniversity of Louisiana at Lafayette$$d2022$$o2022-12-16
001005457 520__ $$aAdvection-diffusion-reaction equations are partial differential equations (PDEs)with various applications across the sciences. Exponential time differencing schemesare efficient methods of numerically solving PDEs of this type. We consider anexponential time differencing scheme called ETD-RDP-IF that approximates thearising matrix exponentials using a rational approximation with real distinct poles andemploys a dimensional splitting technique to improve computational performance.The scheme has originally been derived for systems without advection. We show thatthe derivation still holds in the presence of advection and prove new results on thesecond-order temporal accuracy of the scheme. In numerical experiments, weinvestigate the real-world performance of the scheme depending on the strength ofadvection as quantified by the Péclet and Courant numbers. We confirmsecond-order convergence in space and time for linear problems with smooth initialcondition and observe order reduction for non-smooth initial conditions. We furtherfind that upwind-biased discretizations of advection improve computational efficiency.A comparison with an ETD scheme that uses Krylov-subspace approximations of thematrix exponentials shows that the Krylov-subspace technique has a bettercomputational performance in low-advection regimes. Outside of these regimes,ETD-RDP-IF is more robust and therefore more widely applicable.
001005457 536__ $$0G:(DE-HGF)POF4-5112$$a5112 - Cross-Domain Algorithms, Tools, Methods Labs (ATMLs) and Research Groups (POF4-511)$$cPOF4-511$$fPOF IV$$x0
001005457 8564_ $$uhttps://juser.fz-juelich.de/record/1005457/files/Masters_Thesis_Mueller_Bjoern.pdf$$yOpenAccess
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001005457 9101_ $$0I:(DE-588b)5008462-8$$6P:(DE-Juel1)173688$$aForschungszentrum Jülich$$b0$$kFZJ
001005457 9131_ $$0G:(DE-HGF)POF4-511$$1G:(DE-HGF)POF4-510$$2G:(DE-HGF)POF4-500$$3G:(DE-HGF)POF4$$4G:(DE-HGF)POF$$9G:(DE-HGF)POF4-5112$$aDE-HGF$$bKey Technologies$$lEngineering Digital Futures – Supercomputing, Data Management and Information Security for Knowledge and Action$$vEnabling Computational- & Data-Intensive Science and Engineering$$x0
001005457 9141_ $$y2023
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001005457 9201_ $$0I:(DE-Juel1)JSC-20090406$$kJSC$$lJülich Supercomputing Center$$x0
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