Josue Labaki

Constant Boundary Elements on graphics hardware: a GPU-CPU complementary implementation

Numerical simulation of engineering problems has reached such a large scale that the use of a parallel computing approach is required to obtain solutions within a reasonable time. Recent efforts have been made to implement these large scale computational tasks on general-purpose programmable graphics hardware (GPGPU). The Graphics Processing Unit (GPU) is specially well-suited to address problems that can be formulated in form of data-parallel computations with high arithmetic intensity. This work addresses the implementation of the direct version of the Boundary Element Method (DBEM) on a complementary GPU-CPU system. In this article, constant elements were used for the solution of 2D potential problems. A serial implementation of the BEM was rewritten under the SIMT (Single Instruction Multiple Thread) parallel programming paradigm. The code was developed on an NVidiaTM CUDA programming environment. The efficiency of the implemented strategies is investigated by solving a representative 2D potential problem. The paper reviews in detail the classical BEM formulation in order to be able to address the possible parallelization steps in the numerical implementation. The article reports the performance of the GPU-CPU system compared to the classical CPU-based system for an increasing number of boundary elements.

Stationary Dynamic Displacement Solutions for a Rectangular Load Applied within a 3D Viscoelastic Isotropic Full Space—Part II: Implementation, Validation, and Numerical Results

In part I of the present article the formulation for a dynamic stationary semianalytical solution for a spatially constant load applied over a rectangular surface within a viscoelastic isotropic full-space has been presented. The solution is obtained within the frame of a double Fourier integral transform. These inverse integral transforms must be evaluated numerically. In the present paper, the technique to evaluate numerically the inverse double Fourier integrals is described. The procedure is validated, and a number of original displacement results for the stationary loading case are reported.

Stationary Dynamic Displacement Solutions for a Rectangular Load Applied within a 3D Viscoelastic Isotropic Full Space—Part I: Formulation

A dynamic stationary semianalytical solution for a spatially constant load applied over a rectangular surface within a viscoelastic isotropic full space is presented. The solution is obtained within the frame of a double Fourier integral transform. Closed-form solutions for general loadings within the full space are furnished in the transformed wave number domain. Expressions for three boundary value problems, associated to a normal and two tangential rectangular loadings in the original physical space, are given in terms of a double inverse Fourier integral. These inverse integral transforms must be evaluated numerically. In the second part of the present paper a strategy to evaluate these integrals is described, the procedure validated and a number of original results are reported.