Numerical analysis of unbounded poisson and helmholtz problem using indefinite element approach

Abstract

AbstractIn many cases in electrostatic or acoustic field analysis, the infinite region must be considered; this is difficult to handle by the usual finite‐element method. As a means to handle such cases, the region containing sources and complex configurations are considered as the finite region, and the rest as the infinite region. Then, the usual finite‐element method is applied to the finite region, and the infinite region is partitioned into infinite elements. Two types of infinite element have been proposed: by Bettes‐Zienkiewicz and a hybrid type by Pian‐Moriya. The former does not depend on the model, being general in nature, but integration over the infinite region and the determination of the attenuation parameter are required. In contrast, the latter type of infinite element utilizes the general solution of the system equation in the element, which provides a more accurate solution. Furthermore, since the element is of the boundary type, the integration is generally easier than in the former case. The bandwidth of the discrete equation is the same as that of the finite region. This paper considers Poisson and Helmholtz equations and formulates the three‐dimensional parametric element. As computational examples, simple models for the two‐dimensional electrostatic problem, and two‐ and three‐dimensional acoustic radiation problems are considered as computational examples, and the two types of infinite elements are compared and discussed.