Relaxing the roles of corners in BDDC by perturbed formulation

Santiago Badia, Hieu Nguyen

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearch

2 Citations (Scopus)

Abstract

We present a perturbed formulation of the BDDC method where the invertibility of the global coarse matrix is automatically guaranteed and positive direct solvers can be used without corner constraints or a change of basis. The perturbed method has the same polylogarithmic bounds for the precondition number and is weakly scalable. It is suitable for large scale simulations as small coarse spaces associated with only edge or/and face constraints can be used. In addition, it offers extra robustness when there are disconnected subdomains or in other situations where constraints fails to fix a small number of rigid body modes.

Original languageEnglish
Title of host publicationDomain Decomposition Methods in Science and Engineering XXIII
EditorsHyea Hyun Kim, Axel Klawonn, Eun-Jae Park, Chang-Ock Lee, Olof B. Widlund, Xiao-Chuan Cai, David E. Keyes
Place of PublicationCham Switzerland
PublisherSpringer-Verlag London Ltd.
Pages397-405
Number of pages9
Volume116
ISBN (Electronic)9783319523897
ISBN (Print)9783319523880
DOIs
Publication statusPublished - 1 Jan 2017
Externally publishedYes
EventInternational Conference on Domain Decomposition Methods 2015 - International Convention Center Jeju, Jeju Island, Korea, Republic of (South)
Duration: 6 Jul 201510 Jul 2015
Conference number: 23rd
http://dd23.kaist.ac.kr/

Publication series

NameLecture Notes in Computational Science and Engineering
PublisherSpringer International Publishing
Volume116
ISSN (Print)1439-7358
ISSN (Electronic)2197-7100

Conference

ConferenceInternational Conference on Domain Decomposition Methods 2015
Abbreviated titleDD23
CountryKorea, Republic of (South)
City Jeju Island
Period6/07/1510/07/15
OtherThe main technical content of the DD conference series has always been mathematical, but the principal motivation was and is to make efficient use of distributed memory computers for complex applications arising in science and engineering. As we approach the dawn of exascale computing, where we will command 1018 floating-point operations per second, clearly efficient and mathematically well-founded methods for the solution of large-scale systems become more and more important—as does their sound realization in the framework of modern HPC architectures. In fact, the massive parallelism, which makes exascale computing possible, requires the development of new solution methods, which are capable of efficiently exploiting this large number of cores as the connected hierarchies for memory access. Ongoing developments such as parallelization in time asynchronous iterative methods or nonlinear domain decomposition methods show that this massive parallelism does not only demand for new solution and discretization methods but also allows to foster the development of new approaches.
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