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Parallel resolution of the 3D Helmholtz equation based on multi‐graphics processing unit clusters
Author(s) -
Ortega Gloria,
Lobera Julia,
García Inmaculada,
Pilar Arroyo M.,
Garzón Ester M.
Publication year - 2014
Publication title -
concurrency and computation: practice and experience
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.309
H-Index - 67
eISSN - 1532-0634
pISSN - 1532-0626
DOI - 10.1002/cpe.3212
Subject(s) - helmholtz equation , computer science , cuda , graphics processing unit , computational science , parallel computing , sparse matrix , range (aeronautics) , graphics , matrix (chemical analysis) , dimension (graph theory) , supercomputer , mathematics , computer graphics (images) , mathematical analysis , physics , materials science , quantum mechanics , pure mathematics , composite material , gaussian , boundary value problem
Summary The resolution of the 3D Helmholtz equation is required in the development of models related to a wide range of scientific and technological applications. For solving this equation in complex arithmetic, the biconjugate gradient (BCG) method is one of the most relevant solvers. However, this iterative method has a high computational cost because of the large sparse matrix and the vector operations involved. In this paper, a specific BCG method, adapted for the regularities of the Helmholtz equation is presented. This BCG is based on the implementation of a novel format (named ‘Regular Format’) that allows the storage of the large sparse matrix involved in the sparse matrix vector product in a compact form. The contribution of this work is twofold: (1) decreasing the memory requirements of the 3D Helmholtz equation using the ‘Regular Format’ and (2) speeding up the resolution of the equation using high performance computing resources. A hybrid Message Passing Interface (MPI)‐graphics processing unit CUDA GPU parallelization that is capable of solving complex problems in short time has carried out (Fast‐Helmholtz). Fast‐Helmholtz combines optimizations at Message Passing Interface and GPU levels to reduce communications costs and to improve the exploitation of GPU architecture. This strategy makes it possible to extend the dimension of the Helmholtz problem to be solved, thanks to the relevant reduction of memory requirements and runtime. Copyright © 2014 John Wiley & Sons, Ltd.