Boundary integral equation methods for the elastic and thermoelastic waves in three dimensions
For researchers in computational wave propagation, this work provides a method to simplify the numerical treatment of hyper-singular integrals, though it is an incremental improvement over existing regularization techniques.
The paper proposes new regularized formulations for hyper-singular boundary integral operators in elastic and thermoelastic wave problems, enabling computation with only weak singularities. Numerical examples using Galerkin BEM demonstrate accuracy.
In this paper, we consider the boundary integral equation (BIE) method for solving the exterior Neumann boundary value problems of elastic and thermoelastic waves in three dimensions based on the Fredholm integral equations of the first kind. The innovative contribution of this work lies in the proposal of the new regularized formulations for the hyper-singular boundary integral operators (BIO) associated with the time-harmonic elastic and thermoelastic wave equations. With the help of the new regularized formulations, we only need to compute the integrals with weak singularities at most in the corresponding variational forms of the boundary integral equations. The accuracy of the regularized formulations is demonstrated through numerical examples using the Galerkin boundary element method (BEM).