Graph grammar based parallel direct solver for 1D and 2D isogeometric finite element method

MacIej R. Paszyński*, Krzysztof M. Kuźnik, Victor Calo

*Corresponding author for this work

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

Abstract

In this paper we present a multi-frontal direct solver algorithm for one and two dimensional isogeometric finite element method. The solver algorithm is tested on heat transfer model problem. The algorithm is partitioned into basic undividable tasks calling graph grammar productions, responsible for generation of the merging and elimination pattern, as well as processing multiple frontal matrices during the computation process. The productions are scheduled into nodes of the GPU graphic card and executed in concurrent. The paper is concluded with numerical results concerning the execution of the solver algorithm on GeForce GTX 260 device in one dimension, delivering O(logN) execution time for linear, quadratic, cubic and higher order B-splines, as well as on NVidia Tesla C2070 device in two dimension, delivering O(NlogN) computational cost for linear, quadratic and cubic B-splines.

Original languageEnglish (US)
Title of host publicationECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers
Pages849-858
Number of pages10
StatePublished - Dec 1 2012
Event6th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2012 - Vienna, Austria
Duration: Sep 10 2012Sep 14 2012

Publication series

NameECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers

Other

Other6th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2012
CountryAustria
CityVienna
Period09/10/1209/14/12

Keywords

  • Graph grammar
  • Isogeometric finite element method
  • Models of concurrency
  • Parallel direct solvers

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Applied Mathematics

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