J.C.F. Telles

Iterative solution of bem equations by GMRES algorithm

Abstract This paper presents a performance study of the GMRES algorithm for the solution of non-symmetric dense systems of equations arising from the boundary element discretization of two-dimensional elasticity. Comparisons with Gauss elimination and bi-conjugate gradients show the computer effectiveness and accuracy of the preconditioned GMRES algorithm.

A solution technique for cathodic protection with dynamic boundary conditions by the boundary element method

Abstract This article is concerned with the application of the Boundary Element Method to cathodic protection problems of submerged structures using polarization curves depending upon time and formation potential. These curves have been adjusted from potentiostatic data obtained from in-situ experiments, yielding a nonlinear functional representation. The solution technique adopts stepwise linearized polarization curves and is employed for sufficiently small time steps. The influence of varying formation potential is introduced into the analysis under two alternative hypotheses here designated fictitious time and fictitious potential.

Streaming SIMD Extensions applied to boundary element codes

Nowadays processor architectures include Streaming SIMD Extensions (SSE) originally developed for multimedia applications, not so well explored for scientific computing. This fact has called the attention of the present authors and this paper introduces the application of SSE, also known as multimedia instructions, to boundary element codes. Since SSE instructions are not widespread among boundary element programmers, the authors present this technique applied to a well-known Fortran program for the solution of two-dimensional elastostatic problems. The vectorization guidelines provided here may also be extended to other numerical methods. Numerical experiments show the effectiveness of the proposed approach.

Parallel boundary elements using LAPACK and ScaLAPACK

The work introduces the main steps towards the parallelization of existing boundary element method (BEM) codes using available standard and portable libraries for writing parallel programs, such as LAPACK and ScaLAPACK. Here, a well-known BEM Fortran implementation is reviewed and rewritten to run on shared and distributed memory systems. This effort is the initial step to develop a new generation of parallel BEM codes to be used in many important engineering problems. Numerical experiments on a SGI Origin 2000 show the effectiveness of the proposed approach.

Parallel boundary elements: a portable 3-D elastostatic implementation for shared memory systems

This paper presents the parallel implementation of a computer program for the solution of three-dimensional elastostatic problems using the Boundary Element Method (BEM). The Fortran code is written for shared memory systems using standard and portable libraries: OpenMP and LAPACK. The implementation process provides guidelines to develop highly portable parallel BEM programs, applicable to many engineering problems. Numerical experiments performed in the solution of a real-life problem on a SGI Origin 2000, a Cray SV1ex and a NEC SX-6 show the effectiveness of the proposed approach.

An optimized block matrix manipulation for boundary elements with subregions

Abstract This work discusses the subregions technique and presents a boundary element formulation with an optimized vector generation for the system of equations. The procedure only requires storage for a minimum number of non-zero matrix coefficients plus the possibly non-zero ones which appear when a maximum pivot selection is activated during a Gauss elimination routine. The technique produces great savings in computer run time and is implemented in a 3-D modular elasticity code with quadrilateral and triangular elements, continuous and discontinuous, constant, linear and quadratic. The FORTRAN computer listing of the main routines developed is included.

On the Implementation of Boundary Element Engineering Codes on the Cell Broadband Engine

Originally developed by the consortium Sony-Toshiba-IBM for the Playstation 3 game console, the Cell Broadband Engine processor has been increasingly used in a much wider range of applications like HDTV sets and multimedia devices. Conforming the new Cell Broadband Engine Architecture that extends the PowerPC architecture, this processor can deliver high computational power embedding nine cores in a single chip: one general purpose PowerPC core and eight vector cores optimized for compute-intensive tasks. The processors performance is enhanced by single-instruction-multiple-data (SIMD) instructions that allow to execute up to four floating-point operations in one clock cycle. This multi-level parallel environment is highly suited to applications processing data streams: encryption/decryption, multimedia, image and signal processing, among others. This paper discusses the use of Cell BE to solve engineering problems and the practical aspects of the implementation of numerical method codes in this new architecture. To demonstrate the Cell BE programming techniques and the efficient porting of existing scalar algorithms to run on a multi-level parallel processor, the authors present the techniques applied to a well-known program for the solution of two dimensional elastostatic problems with the Boundary Element Method. The programming guidelines provided here may also be extended to other numerical methods. Numerical experiments show the effectiveness of the proposed approach.

A new solution technique for cathodic protection systems with homogeneous region by the boundary element method

Abstract The purpose of this work is to efficiently evaluate the design of cathodic protection (CP) systems of tank bottoms using concentric ring or linear anodes. As customary in current CP systems, the outer surface of the tank bottom is usually in electrical contact with a slender homogeneous layer of conductive concrete (or something similar) which in turn is in direct contact with the homogeneous deep soil region. The boundary element method (BEM) together with a subregion technique has been widely adopted to analyse such CP systems where the domain consists of two (or even more) homogeneous zones. However, the numerical solution of the final matrix system of equations can be quite time-consuming, especially if the slender intermediate layer is to be discretised, requiring a considerable number of elements, due to its somewhat reduced thickness. To overcome this problem, the present work proposes a new methodology in which the slender subregion is indirectly introduced, as a theoretically created polarisation curve, acting as a new boundary condition at the boundary of the soil domain (original common interface). Numerical simulations have been carried out using BEM implementations and results are discussed, including CP studies of practical axisymmetric and three-dimensional engineering problems.