Showing papers by "Frank J. Rizzo published in 1993"

Nearly Singular and Hypersingular Integrals in the Boundary Element Method

Abstract: Several techniques in dealing with nearly singular and hypersingular integrals which arise in applications of the boundary element method (BEM) are studied in this paper. The approach of using line integrals is emphasized and explored in some detail due to its high efficiency and accuracy. Numerical examples of stress analysis and scattering from an open crack in a 3-D elastic medium are presented to illustrate the ideas.

Boundary element method solutions for elastic wave scattering in 3D

Abstract: Time-harmonic elastic wave scattering problems such as those encountered in ultrasonic non destructive evaluation are solved by the boundary element method (BEM). Selected results for spherical and spheroidal shaped voids and inclusions are compared with analytical and other numerical solutions. Results for ellipsoids, which require a full three-dimensional formulation, are provided as a benchmark for comparison when other numerical methods would be developed for this problem class in the future. The modelling of cracklike defects with this formulation is discussed. Recent theoretical findings regarding the fictitious eigenfrequency difficulty (FED) are confirmed by a numerical study.

Elastic scatterer interaction via generalized Born series and far-field approximations

Abstract: Methods for solving elastic wave scattering problems in three dimensions (3D) with multiple inhomogeneities are discussed. A problem of homogeneous, isotropic elastic defects in an otherwise homogeneous, isotropic elastic full‐space is formulated as a boundary integral equation. This equation is solved by discretizing the surface of each scatterer in a fashion known as the boundary element method. The resulting matrix equation may be solved in a fully implicit manner, but an implicit‐iterative method is more efficient. With this hybrid method, a portion of the nonsingular integral operator is expanded in a Neumann series. Terms in this series correspond physically to Nth‐order Born approximations of the scatterers’ interaction. The relative advantage of this hybrid scheme depends on the number of iterations required. Except for closely situated strong scatterers, terms beyond the first few orders are not significant and thus the method can be quite advantageous. When the separation is large, another appro...

Eddy Current Analysis for 3-D Problems Using the Boundary Element Method

Abstract: A modified boundary integral equation/boundary element method (BIE/BEM) is being developed for eddy current problems in three dimensions. Maxwell’s equations governing the eddy current problems are formulated in two sets of BIE’s, one for the electric field and the other for the magnetic field. These BIE’s involve both the field and the normal derivative of the field, for both exterior (air) and interior (metal) regions. In addition to the usual set of interface conditions involving only the field, a set of interface conditions involving the normal derivatives of the field is derived by applying Maxwell’s equations near the interface. The present approach represents a departure from the existing BIE formulation for eddy current problems (see, e.g. [1–3]) in which normal derivatives of the field do not explicitly appear.