Space and time parallel multigrid for optimization and uncertainty quantification in PDE simulations

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

doi:10.1007/978-3-319-40528-5_23

Space and time parallel multigrid for optimization and uncertainty quantification in PDE simulations

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

^*Corresponding author for this work

Applied Mathematics and Computational Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

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 spacetime 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.

Original language	English (US)
Title of host publication	Software for Exascale Computing - SPPEXA 2013-2015
Editors	Wolfgang E. Nagel, Hans-Joachim Bungartz, Philipp Neumann
Publisher	Springer Verlag
Pages	507-523
Number of pages	17
ISBN (Print)	9783319405261
DOIs	https://doi.org/10.1007/978-3-319-40528-5_23
State	Published - 2016
Event	International Conference on Software for Exascale Computing, SPPEXA 2015 - Munich, Germany Duration: Jan 25 2016 → Jan 27 2016

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	113
ISSN (Print)	1439-7358

Other

Other	International Conference on Software for Exascale Computing, SPPEXA 2015
Country/Territory	Germany
City	Munich
Period	01/25/16 → 01/27/16

ASJC Scopus subject areas

Modeling and Simulation
General Engineering
Discrete Mathematics and Combinatorics
Control and Optimization
Computational Mathematics

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10.1007/978-3-319-40528-5_23

Cite this

Grasedyck, L., Löbbert, C., Wittum, G., Nägel, A., Schulz, V., Siebenborn, M., Krause, R., Benedusi, P., Küster, U., & Dick, B. (2016). Space and time parallel multigrid for optimization and uncertainty quantification in PDE simulations. In W. E. Nagel, H.-J. Bungartz, & P. Neumann (Eds.), Software for Exascale Computing - SPPEXA 2013-2015 (pp. 507-523). (Lecture Notes in Computational Science and Engineering; Vol. 113). Springer Verlag. https://doi.org/10.1007/978-3-319-40528-5_23

Grasedyck, Lars ; Löbbert, Christian ; Wittum, Gabriel et al. / Space and time parallel multigrid for optimization and uncertainty quantification in PDE simulations. Software for Exascale Computing - SPPEXA 2013-2015. editor / Wolfgang E. Nagel ; Hans-Joachim Bungartz ; Philipp Neumann. Springer Verlag, 2016. pp. 507-523 (Lecture Notes in Computational Science and Engineering).

@inproceedings{2af1d427d8e74de1bdd6058c914535b4,

title = "Space and time parallel multigrid for optimization and uncertainty quantification in PDE simulations",

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 spacetime 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.",

author = "Lars Grasedyck and Christian L{\"o}bbert and Gabriel Wittum and Arne N{\"a}gel and Volker Schulz and Martin Siebenborn and Rolf Krause and Pietro Benedusi and Uwe K{\"u}ster and Bj{\"o}rn Dick",

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year = "2016",

doi = "10.1007/978-3-319-40528-5_23",

language = "English (US)",

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Grasedyck, L, Löbbert, C, Wittum, G, Nägel, A, Schulz, V, Siebenborn, M, Krause, R, Benedusi, P, Küster, U & Dick, B 2016, Space and time parallel multigrid for optimization and uncertainty quantification in PDE simulations. in WE Nagel, H-J Bungartz & P Neumann (eds), Software for Exascale Computing - SPPEXA 2013-2015. Lecture Notes in Computational Science and Engineering, vol. 113, Springer Verlag, pp. 507-523, International Conference on Software for Exascale Computing, SPPEXA 2015, Munich, Germany, 01/25/16. https://doi.org/10.1007/978-3-319-40528-5_23

Space and time parallel multigrid for optimization and uncertainty quantification in PDE simulations. / Grasedyck, Lars; Löbbert, Christian; Wittum, Gabriel et al.
Software for Exascale Computing - SPPEXA 2013-2015. ed. / Wolfgang E. Nagel; Hans-Joachim Bungartz; Philipp Neumann. Springer Verlag, 2016. p. 507-523 (Lecture Notes in Computational Science and Engineering; Vol. 113).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Space and time parallel multigrid for optimization and uncertainty quantification in PDE simulations

AU - Grasedyck, Lars

AU - Löbbert, Christian

AU - Wittum, Gabriel

AU - Nägel, Arne

AU - Schulz, Volker

AU - Siebenborn, Martin

AU - Krause, Rolf

AU - Benedusi, Pietro

AU - Küster, Uwe

AU - Dick, Björn

PY - 2016

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N2 - 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 spacetime 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.

AB - 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 spacetime 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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T3 - Lecture Notes in Computational Science and Engineering

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BT - Software for Exascale Computing - SPPEXA 2013-2015

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A2 - Bungartz, Hans-Joachim

A2 - Neumann, Philipp

PB - Springer Verlag

T2 - International Conference on Software for Exascale Computing, SPPEXA 2015

Y2 - 25 January 2016 through 27 January 2016

ER -

Grasedyck L, Löbbert C, Wittum G, Nägel A, Schulz V, Siebenborn M et al. Space and time parallel multigrid for optimization and uncertainty quantification in PDE simulations. In Nagel WE, Bungartz HJ, Neumann P, editors, Software for Exascale Computing - SPPEXA 2013-2015. Springer Verlag. 2016. p. 507-523. (Lecture Notes in Computational Science and Engineering). doi: 10.1007/978-3-319-40528-5_23

Space and time parallel multigrid for optimization and uncertainty quantification in PDE simulations

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