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NONCONFORMING FINITE ELEMENT METHODS FOR THE THREE-DIMENSIONAL HELMHOLTZ EQUATION: ITERATIVE DOMAIN DECOMPOSITION OR GLOBAL SOLUTION?

PATRICIA M. GAUZELLINO

Facultad de Ciencias Astronómicas y Geofísicas, UNLP, Paseo del Bosque s/n, B1900FWA – La Plata, Argentina

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FABIO I. ZYSERMAN

CONICET, Facultad de Ciencias Astronómicas y Geofísicas, UNLP, Paseo del Bosque s/n, B1900FWA – La Plata, Argentina

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JUAN E. SANTOS

CONICET, Facultad de Ciencias Astronómicas y Geofísicas, UNLP, Paseo del Bosque s/n, B1900FWA – La Plata, Argentina

Department of Mathematics, Purdue University, W. Lafayette, IN 47907, USA

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https://doi.org/10.1142/S0218396X09003902Cited by:8 (Source: Crossref)

Abstract

Iterative domain decomposition (DD) nonconforming finite element methods for the Helmholtz equation attempt to solve two problems. First, there exists no efficient algorithms able to solve the large sparse linear system arising from the discretization of the equation via the standard finite elements method. Secondly, even when DD methods generally yield small matrices, standard conforming elements, such as Q1 elements, force the transmission of a relatively large amount of data among subdomains.

In this paper, we compared performance of global methods and a set of DD techniques to solve the Helmholtz equation in a three-dimensional domain. The efficiency of the algorithms is measured in terms of CPU time usage and memory requirements. The role of domain size and the linear solver type used to solve each local problem within each subdomain was also analyzed. The numerical results show that iterative DD methods perform far better than global methods. In addition, iterative DD methods involving small subdomains work better than those with subdomains involving a large number of elements. Properties of the iterative DD algorithms such as scalability, robustness, and parallel performance are also analyzed.

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