Abstract
In this paper the implementation of an iterative solver based on the Generalized Minimum Residual Method (GMRES) with complex-valued coefficients is explored, with application to the Boundary Element Method (BEM). The solver is designed to be implemented in a GPU (Graphic Processing Unit) device, exploiting its massively parallel capabilities. The framework is in the context of linear water wave problems in the frequency domain. The main objective of the proposed solver is the direct acceleration of existing standard BEM codes, by transfering to the GPU the solver task. The CUDA programming language is used, exploiting the particular architecture of the GPU device for complex-valued systems. To explore the performances of the solver, two linear water wave problems have been tested: the frequency-dependent added mass and damping matrices of a 3D floating body, and the Helmholtz equation in a 2D domain. The parallelized GMRES solver is implemented in a NVidia GeForce GTX 970 graphic card, and shows drastic reductions in computing times when compared with its CPU implementation.
Highlights
The Boundary Element Method (BEM) is a numerical technique to obtain approximated solutions of partial differential equations
With refference to three-dimensional boundary value problem, the basic idea of the BEM is the use of boundary integral equations for primary variables at internal points, and its extension to boundary points after a limit-to-the-boundary process
This paper explores the acceleration of the BEM based on the acceleration of the Generalized Minimum Residual Method (GMRES) solver, in the GPU, for complexvalued systems with a fully-populated matrix, that arises in linear water wave problems
Summary
The Boundary Element Method (BEM) is a numerical technique to obtain approximated solutions of partial differential equations. For large system of equations this problem is crucial and makes the standard BEM not competitive with respect to other domain techniques, such as the Finite Element Method This is notorious in wave problems in the frequency domain, where the system matrix is complex-valued and fine meshes with large number of degrees of freedom are required. This paper explores the acceleration of the BEM based on the acceleration of the GMRES solver, in the GPU, for complexvalued systems with a fully-populated matrix, that arises in linear water wave problems. The main idea of the acceleration scheme is the use of direct BEM codes, in which the CPU is used to assemble the system matrix, and the GPU is used to solve the linear system of equations At this point, the basic GMRES algorithm is explored, in which a preconditioner has not been implemented.
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