An Extended Technique for Computation of Laplace Transformed Dynamic Fundamental Solutions for 3D Anisotropic Elastic Solids

Abstract

This paper presents an extended procedure for computation of integral representations of regular parts of Laplace domain three-dimensional dynamic anisotropic elastic full space displacement fundamental solutions and their spatial derivatives. The problem is that under specific conditions these integrals become highly oscillatory. For the modified integral expressions, we present a technique that utilizes specialized quadrature rule which in turn is a variation of well-known Levin's method for solving highly oscillatory integrals. Results of numerical investigations suggest improved performance (regarding number of integration points) compared to using the Gauss-Legendre quadrature.

Full document