Grammar-Based Multi-Frontal Solver for One Dimensional Isogeometric Analysis with Multiple Right-Hand-Sides

Krzysztof Kuźnik, Maciej Paszyński, Victor M. Calo

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

5 Scopus citations

Abstract

This paper introduces a grammar-based model for developing a multi-thread multi-frontal parallel direct solver for one- dimensional isogeometric finite element method. The model includes the integration of B-splines for construction of the element local matrices and the multi-frontal solver algorithm. The integration and the solver algorithm are partitioned into basic indivisible tasks, namely the grammar productions, that can be executed squentially. The partial order of execution of the basic tasks is analyzed to provide the scheduling for the execution of the concurrent integration and multi-frontal solver algo- rithm. This graph grammar analysis allows for optimal concurrent execution of all tasks. The model has been implemented and tested on NVIDIA CUDA GPU, delivering logarithmic execution time for linear, quadratic, cubic and higher order B-splines. Thus, the CUDA implementation delivers the optimal performance predicted by our graph grammar analysis. We utilize the solver for multiple right hand sides related to the solution of non-stationary or inverse problems.
Original languageEnglish (US)
Title of host publicationProcedia Computer Science
PublisherElsevier BV
Pages1574-1583
Number of pages10
DOIs
StatePublished - Jun 1 2013

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