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.

A boundary element method (BEM) for large-scale acoustic analysis is accelerated efficiently and precisely with Graphics Processing Units (GPUs). Based on Burton-Miller boundary integral equation, an implementation scheme that can be handled efficiently in GPU is derived and applied to accelerate conventional BEM. Data caching techniques in GPU are introduced to improve efficiency of the prototype algorithm. A double-single precision algorithm implemented with single-precision floating-point numbers is employed to reduce numerical errors. It shows that the improved algorithm sustained a highest GPU efficiency of 89.8% for large-scale problems, and its accuracy was almost the same as that with double-precision numerals directly while costing only 1/28 in time and half in GPU memory consumption of the latter. The largest problem size up to 3 million unknowns was solved rapidly on a desktop PC (8GB RAM, NVIDIA GeForce 660 Ti) by the method. Its performance was better than the fast BEM algorithms in both time and memory consumption.

A boundary element method (BEM) for Burton-Miller boundary integral equation is accelerated efficiently with Graphics Processing Units (GPUs).Conventional BEM formulations are reformulated so that they can be handled efficiently in GPU.Singularity extraction and local correction techniques are used to evaluate singular integrals,including strong-and hyper-singular ones.Numerical results show that:(1)The proposed method obtains unique and correct solutions at fictitious frequencies;(2)Accuracy of the method is almost the same as that of conventional BEM;(3)Computational time and memory consumptions of the proposed method are much lower than reported results.It shows that GPU-accelerated BEM based on Burton-Miller equation is a fast,efficient and simple method for medium-or large-scale acoustic problems in engineering.

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.