A fast directional boundary element method for large scale wideband elastodynamic analysis is developed. Directional low rank property of elastodynamic kernels is shown which serves as the theoretical basis of its fast directional algorithm. By only considering S-wave number, interactions of different nodes are divided into low-frequency interactions and high-frequency interactions, and the latter is further divided into interactions with directional wedges on which the directional low rank property is applied. Low-frequency interactions are computed in same manner with that in kernel independent fast multipole BEM for elastodynamics, and translation matrices for different directional wedges are calculated efficiently by coordinate frame rotations. Thus harmonic responses for any frequencies can be computed efficiently. Numerical examples show that the computational complexity for wideband elastodynamic problems are successfully brought down to O(N log^αN). It can also be applied to transient elastodynamic analysis combined with convolution quadrature method.

We describe an improved perturbation approach for electrostatic analysis of three-dimensional structures consisting of dielectrics with high-permittivity ratios. Unlike original perturbation approach, the new approach uses only one system matrix with different right hand sides. A fast wavelet Galerkin boundary element method (WGBEM) is used to solve integral equations. Compared with wavelets defined in parameter spaces in a conventional WGBEM, the wavelets here are directly constructed on usual boundary element triangulation. It enables the proposed WGBEM to solve electrostatic problems in complicated geometries, unstructured meshes and comparatively coarse discretizations. Numerical results show that the improved perturbation approach combined with WGBEM has high accuracy and almost linear computational complexity.