Parallel resolution of the 3D Helmholtz equation based on multi-graphics processing unit clusters

摘要

The resolution of the 3D Helmholtz equation is required in the development of models related to a widernrange of scientific and technological applications. For solving this equation in complex arithmetic, the biconjugaterngradient (BCG) method is one of the most relevant solvers. However, this iterative method has arnhigh computational cost because of the large sparse matrix and the vector operations involved. In this paper,rna specific BCG method, adapted for the regularities of the Helmholtz equation is presented. This BCG isrnbased on the implementation of a novel format (named ‘Regular Format’) that allows the storage of thernlarge sparse matrix involved in the sparse matrix vector product in a compact form. The contribution of thisrnwork is twofold: (1) decreasing the memory requirements of the 3D Helmholtz equation using the ‘RegularrnFormat’ and (2) speeding up the resolution of the equation using high performance computing resources. Arnhybrid Message Passing Interface (MPI)-graphics processing unit CUDA GPU parallelization that is capablernof solving complex problems in short time has carried out (Fast-Helmholtz). Fast-Helmholtz combinesrnoptimizations at Message Passing Interface and GPU levels to reduce communications costs and to improvernthe exploitation of GPU architecture. This strategy makes it possible to extend the dimension of thernHelmholtz problem to be solved, thanks to the relevant reduction of memory requirements and runtime.