Article ID Journal Published Year Pages File Type
519065 Journal of Computational Physics 2014 17 Pages PDF
Abstract

In this paper we describe a high order spectral algorithm for solving the time-harmonic Navier equations in the exterior of a bounded obstacle in three space dimensions, with Dirichlet or Neumann boundary conditions. Our approach is based on combined-field boundary integral equation (CFIE) reformulations of the Navier equations. We extend the spectral method developed by Ganesh and Hawkins [20] – for solving second kind boundary integral equations in electromagnetism – to linear elasticity for solving CFIEs that commonly involve integral operators with a strongly singular or hypersingular kernel. The numerical scheme applies to boundaries which are globally parametrised by spherical coordinates. The algorithm has the interesting feature that it leads to solve linear systems with substantially fewer unknowns than with other existing fast methods. The computational performances of the proposed spectral algorithm are demonstrated using numerical examples for a variety of three-dimensional convex and non-convex smooth obstacles.

Related Topics
Physical Sciences and Engineering Computer Science Computer Science Applications
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