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2016 | OriginalPaper | Chapter

Space and Time Parallel Multigrid for Optimization and Uncertainty Quantification in PDE Simulations

Authors : Lars Grasedyck, Christian Löbbert, Gabriel Wittum, Arne Nägel, Volker Schulz, Martin Siebenborn, Rolf Krause, Pietro Benedusi, Uwe Küster, Björn Dick

Published in: Software for Exascale Computing - SPPEXA 2013-2015

Publisher: Springer International Publishing

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Abstract

In this article we present a complete parallelization approach for simulations of PDEs with applications in optimization and uncertainty quantification. The method of choice for linear or nonlinear elliptic or parabolic problems is the geometric multigrid method since it can achieve optimal (linear) complexity in terms of degrees of freedom, and it can be combined with adaptive refinement strategies in order to find the minimal number of degrees of freedom. This optimal solver is parallelized such that weak and strong scaling is possible for extreme scale HPC architectures. For the space parallelization of the multigrid method we use a tree based approach that allows for an adaptive grid refinement and online load balancing. Parallelization in time is achieved by SDC/ISDC or a space-time formulation. As an example we consider the permeation through human skin which serves as a diffusion model problem where aspects of shape optimization, uncertainty quantification as well as sensitivity to geometry and material parameters are studied. All methods are developed and tested in the UG4 library.

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previous chapter Accelerating an FMM-Based Coulomb Solver with GPUs

next chapter Domain Overlap for Iterative Sparse Triangular Solves on GPUs

We use the commonly utilized term “energy consumption” despite the fact that electrical energy is converted to thermal energy.

cpufreq_set_frequency()

HLRS, Stuttgart, Germany, http://www.hlrs.de/systems/platforms/cray-xe6-hermit/

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Title: Space and Time Parallel Multigrid for Optimization and Uncertainty Quantification in PDE Simulations
Authors: Lars Grasedyck
Christian Löbbert
Gabriel Wittum
Arne Nägel
Volker Schulz
Martin Siebenborn
Rolf Krause
Pietro Benedusi
Uwe Küster
Björn Dick
Publisher: Springer International Publishing
Book: Software for Exascale Computing - SPPEXA 2013-2015
Print ISBN: 978-3-319-40526-1

Electronic ISBN: 978-3-319-40528-5

Copyright Year: 2016
DOI: https://doi.org/10.1007/978-3-319-40528-5_23

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