This paper describes the author’s RIM3 Fortran code. RIM3 delivers a computational solution to the acoustic field produced by a vibrating plate placed on an infinite baffle. The mathematical model is based on the Rayleigh integral. The method is implemented in three-dimensions in a manner that is similar to the boundary element method and is applied to test cases and results are given. The soft...

An extension of the contour integral method (CIM) for the computation of stress intensity factors for loaded cracks is presented. Numerical solutions of the two-dimensional linear elasticity equations are computed with the p-version of the generalized finite element method. Polynomial enrichment functions as well as enrichment with near crack tip asymptotic expansion are used. The robustness of...

For an integral polyhedral cone C = pos{a, . . . , a}, a ∈ Z, a subset B(C) ⊂ C ∩ Z is called a minimal Hilbert basis of C iff (i) each element of C∩Z can be written as a non-negative integral combination of elements of B(C) and (ii) B(C) has minimal cardinality with respect to all subsets of C ∩ Z for which (i) holds. We give a tight bound for the so-called height of an element of the basis wh...

Integral equations have been of great theoretical importance for analyzing boundary value problems. There is a large amount of literature devoted to the classical potential theory and its applications on solving the boundary value problems of elliptic partial differential equations (see, for example, [5, 20, 23, 25, 26, 31, 32, 36, 37, 40]). For elliptic problems, integral equations have been c...

We present several coupled finite and boundary element formulations for the vibro-acoustic simulation of completely immersed bodies such as submarines. All formulations are based on the different use of standard boundary integral equations. In addition to the well known symmetric coupling we discuss two different approaches which are based on the weakly singular boundary integral equation only.

In this paper we report on a non-overlapping and an overlapping domain decomposition method as preconditioners for the boundary element approximation of an indefinite hypersingular integral equation on a surface. The equation arises from an integral reformulation of the Neumann screen problem with the Helmholtz equation in the exterior of a screen in R. It is well-known that the linear algebrai...

We review non-conformal domain decomposition methods (DDMs) and their applications in solving electrically large and multi-scale electromagnetic (EM) radiation and scattering problems. In particular, a finite-element DDM, together with a finite-element tearing and interconnecting (FETI)-like algorithm, incorporating Robin transmission conditions and an edge corner penalty term, are discussed in...

The complex variable boundary element method, CVBEM, employs the Cauchy integral with any complex variable (e.g., complex potential, complex flux, or complex velocity) to solve boundary value problems. The CVBEM formulation is consistent with the primal and dual solutions of the boundary integral equation, as well as the analytic element method. The resulting problem is overdetermined because t...