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research-article

An improved assembling algorithm in boundary elements with Galerkin weighting applied to three-dimensional Stokes flows

[+] Author and Article Information
Sofía S. Sarraf

Associate professor (UNCo), Research associate (CONICET), IITCI (UNCo-CONICET), Buenos Aires 1400, (Q8300IBX) Neuquén, Argentina
sofia.sarraf@fain.uncoma.edu.ar

Ezequiel Jose Lopez

Associate professor (UNCo), Research associate (CONICET), IITCI (UNCo-CONICET), Buenos Aires 1400, (Q8300IBX) Neuquén, Argentina
ezequiel.lopez@fain.uncoma.edu.ar

Laura Battaglia

Associate professors (UTN, UNL, and UNL), Senior Researchers (CONICET), CIMEC (UNL-CONICET), Predio CONICET-Santa Fe, Colectora RN 168, El Pozo, Santa Fe (3000), Argentina
lbattaglia@santafe-conicet.gob.ar

Gustavo A. Rios Rodriguez

Associate professors (UTN, UNL, and UNL), Senior Researchers (CONICET), CIMEC (UNL-CONICET), Predio CONICET-Santa Fe, Colectora RN 168, El Pozo, Santa Fe (3000), Argentina
gusadrr@santafe-conicet.gov.ar

Jorge D'Elia

Associate professors (UTN, UNL, and UNL), Senior Researchers (CONICET), CIMEC (UNL-CONICET), Predio CONICET-Santa Fe, Colectora RN 168, El Pozo, Santa Fe (3000), Argentina
jdelia@intec.unl.edu.ar

1Corresponding author.

ASME doi:10.1115/1.4037690 History: Received January 15, 2017; Revised August 07, 2017

Abstract

In the Boundary Element Method (BEM), the Galerkin weighting technique allows to obtain numerical solutions of a Boundary Integral Equation (BIE), giving the Galerkin Boundary Element Method (GBEM). In three-dimensional (3D) spatial domains, the nested double surface integration of GBEM leads to a significantly larger computational time for assembling the linear system than with the standard collocation method. In practice, the computational time is roughly an order of magnitude larger, thus limiting the use of GBEM in 3D engineering problems. The standard approach for reducing the computational time of the linear system assembling is to skip integrations whenever possible. In this work, a modified assembling algorithm for the element matrices in GBEM is proposed for solving integral kernels that depend on the exterior unit normal. This algorithm is based on kernels symmetries at the element level and not on the flow nor in the mesh. It is applied to a BIE that models external creeping flows around 3D closed bodies using second-order kernels, and it is implemented using OpenMP. For these BIEs, the modified algorithm is on average 32% faster than the original one.

Copyright (c) 2017 by ASME
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