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Employing HPC for Analyzing Nonlinear PDE Systems Beyond Simulation

Thies, Jonas and Baars, Sven and Wubs, Fred W. and Song, Weiyan (2017) Employing HPC for Analyzing Nonlinear PDE Systems Beyond Simulation. PARNUM 2017: International Workshop on Parallel Numerics, April 19-21 2017, Waischenfeld, Germany.

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Official URL: https://www.parnum2017.fau.de/


We review techniques of numerical bifurcation and stability analysis with examples from computational fluid dynamics and biology. The methodology allows insight into the complete dynamics of nonlinear PDE systems, where standard simulation tool chains leave the question of existence, proximity and stability of multiple solutions open. The main bottleneck in the method are large and sparse linear systems of equations and eigenvalue problems arising from the discretized steady-state PDE. The use of HPC is therefore attractive to increase the achievable resolution, but remains challenging because nonsymmetric and indefinite systems need to be solved. The `hybrid multi-level solver' HYMLS is a robust multi-level incomplete factorization technique that was designed for this particular class of problems. HYMLS has an intuitive geometric interpretation and good parallelization properties. We present some performance results of a prototypical implementation based on MPI and the Trilinos software. The eigenvalue problems that arise are solved using the Jacobi-Davidson method as implemented in the SPPEXA ESSEX~\cite{essex} project's phist library (https://www.bitbucket.org/essex/phist).

Item URL in elib:https://elib.dlr.de/116837/
Document Type:Conference or Workshop Item (Lecture)
Title:Employing HPC for Analyzing Nonlinear PDE Systems Beyond Simulation
AuthorsInstitution or Email of AuthorsAuthor's ORCID iD
Thies, JonasJonas.Thies (at) dlr.deUNSPECIFIED
Baars, Svens.baars (at) rug.nlUNSPECIFIED
Wubs, Fred W.f.w.wubs (at) rug.nlUNSPECIFIED
Song, Weiyanweiyan.aibao (at) gmail.comUNSPECIFIED
Date:April 2017
Refereed publication:Yes
Open Access:Yes
Gold Open Access:No
In ISI Web of Science:No
Keywords:nonlinear PDE, continuation methods, multi-level solver, CFD
Event Title:PARNUM 2017: International Workshop on Parallel Numerics
Event Location:Waischenfeld, Germany
Event Type:Workshop
Event Dates:April 19-21 2017
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Space System Technology
DLR - Research area:Raumfahrt
DLR - Program:R SY - Space System Technology
DLR - Research theme (Project):R - Vorhaben SISTEC (old)
Location: Köln-Porz
Institutes and Institutions:Institut of Simulation and Software Technology
Institut of Simulation and Software Technology > High Performance Computing
Deposited By: Thies, Jonas
Deposited On:12 Jan 2018 12:04
Last Modified:11 Dec 2020 08:19

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