Based on the Rizzo’s direct boundary integral equation formulation for elasticity problems, elastic bodies with randomly distributed circular inclusions are simulated using the boundary element method. The given numerical examples show that the boundary element method is more accurate and…

This paper discusses a three dimensional implementation of boundary integral equation method (BIEM) for large scale time domain elastodynamic problems and its application to ultrasonic nondestructive evaluation (NDE). We improve the time integration algorithm of the BIEM in order to…

The boundary and domain-type approximations are discussed in boundary integral equation formulations for solution of boundary value problems. A new approach is proposed with using a domain-type approximation of the primary field and collocation of boundary conditions at boundary nodes…

In this paper a new general algorithm is presented for the direct evaluation of all singular double integrals arising in the 2D Galerkin BEM, including those with hypersingular kernels. A distinguishing feature of the proposed method is that double singular…

The present paper discusses the author’s experience and contributions to the implementation and development of the boundary element method (BEM). The main motivation for this descriptive text is to pay homage to Professor Frank Rizzo’s well known career, dedicated to…

Frank Rizzo proposed the first Boundary Integral Equation (BIE) formulation for linear elasticity in a seminal paper in 1967. I have had the very good fortune to call Frank a friend of mine for many years. The present paper describes…

The development of boundary element methods as seen by one researcher in the field is described, from publication of the first results in 1963 to the present day. Details are given of the circumstances in which research was carried out.…

This paper presents a technique to establish the strain incremental formulation in the boundary element method applied to elastoplasticity problem. In this technique, the application of second order singularity problem is avoided, and only first order singularity problem is sufficient.…

The Fast Multipole Method was introduced by Greengard and Rokhlin in a seminal paper appeared in 1987 for studying large systems of particle interactions with reduced algorithmic and memory complexity [60]. Developments of the original idea are successfully applied to…

In this study, we investigate the problem of reconstruction of a stationary temperature field from given temperature and heat flux on a part of the boundary of a semi-infinite region containing an inclusion. This situation can be modelled as a…