Nonconforming finite element methods for the three dimensional Helmholtz equation: iterativ e domain decomposition or global solution?

PATRICIA M. GAUZELLINO; FABIO I. ZYSERMAN; JUAN E. SANTOS

JOURNAL OF COMPUTATIONAL ACOUSTICS

WORLD SCIENTIFIC PUBL CO PTE LTD

Año: 2009 vol. 17 p. 159 - 173

0218-396X

Iterative domain decomposition nonconforming finite element methodsfor 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 domain decomposition 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 domain decomposition 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 alsoanalyzed. The numerical results show that iterative domain decomposition methods perform far better than global methods. In addition, iterative domain decomposition methods involving small subdomains work better than those withsubdomains involving a large number of elements.Properties of the iterative domain decomposition algorithms such as scalability, robustness and parallel performance are also analyzed.