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

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations


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 languageEnglish (US)
Title of host publicationSoftware for Exascale Computing - SPPEXA 2013-2015
EditorsWolfgang E. Nagel, Hans-Joachim Bungartz, Philipp Neumann
PublisherSpringer Verlag
Number of pages17
ISBN (Print)9783319405261
StatePublished - 2016
EventInternational Conference on Software for Exascale Computing, SPPEXA 2015 - Munich, Germany
Duration: Jan 25 2016Jan 27 2016

Publication series

NameLecture Notes in Computational Science and Engineering
ISSN (Print)1439-7358


OtherInternational Conference on Software for Exascale Computing, SPPEXA 2015

ASJC Scopus subject areas

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


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