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001     1005457
005     20240226075509.0
024 7 _ |a 2128/34151
|2 Handle
037 _ _ |a FZJ-2023-01486
041 _ _ |a English
100 1 _ |a Müller, Björn
|0 P:(DE-Juel1)173688
|b 0
|e Corresponding author
245 _ _ |a Investigation of Exponential Time Differencing Schemes for Advection-Diffusion-Reaction Problems in the Presence of Significant Advection
|f - 2023-03-09
260 _ _ |c 2022
300 _ _ |a x, 121 p.
336 7 _ |a Output Types/Supervised Student Publication
|2 DataCite
336 7 _ |a Thesis
|0 2
|2 EndNote
336 7 _ |a MASTERSTHESIS
|2 BibTeX
336 7 _ |a masterThesis
|2 DRIVER
336 7 _ |a Master Thesis
|b master
|m master
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|s 1679036549_14798
|2 PUB:(DE-HGF)
336 7 _ |a SUPERVISED_STUDENT_PUBLICATION
|2 ORCID
500 _ _ |a Defense at FH Aachen Campus Jülich March 9th, 2023
502 _ _ |a Masterarbeit, University of Louisiana at Lafayette, 2022
|c University of Louisiana at Lafayette
|b Masterarbeit
|d 2022
|o 2022-12-16
520 _ _ |a Advection-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.
536 _ _ |a 5112 - Cross-Domain Algorithms, Tools, Methods Labs (ATMLs) and Research Groups (POF4-511)
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856 4 _ |u https://juser.fz-juelich.de/record/1005457/files/Masters_Thesis_Mueller_Bjoern.pdf
|y OpenAccess
909 C O |o oai:juser.fz-juelich.de:1005457
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910 1 _ |a Forschungszentrum Jülich
|0 I:(DE-588b)5008462-8
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|6 P:(DE-Juel1)173688
913 1 _ |a DE-HGF
|b Key Technologies
|l Engineering Digital Futures – Supercomputing, Data Management and Information Security for Knowledge and Action
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914 1 _ |y 2023
915 _ _ |a OpenAccess
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980 _ _ |a master
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980 _ _ |a I:(DE-Juel1)JSC-20090406
980 1 _ |a FullTexts

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