Multipole Accelerated Boundary Element Method Research Articles

Head-related transfer functions via the fast multipole accelerated boundary element method

Computation of head-related transfer functions (HRTF) via geometrical meshes and numerical methods has been suggested by a number of authors. An issue facing this approach is the large computational time needed for high frequencies, where the discretization must include hundreds of thousands of elements. Conventional computational methods are unable to achieve such computations without excessive time or memory. We use a newly developed fast multipole accelerated boundary element method (FMM/BEM) that scales linearly both in time and memory. The method is applied to the mesh of the widely used KEMAR manikin and its HRTF computed up to 20 kHz. The results are compared with available experimental measurements.

New multipole method for 3-D capacitance extraction

This paper describes an efficient improvement of the multipole accelerated boundary element method for 3-D capacitance extraction. The overall relations between the positions of 2-D boundary elements are considered instead of only the relations between the center-points of the elements, and a new method of cube partitioning is introduced. Numerical results are presented to demonstrate that the method is accurate and has nearly linear computational growth as O(n), where n is the number of panels/boundary elements. The proposed method is more accurate and much faster than Fastcap.

Prescribed error tolerances within fixed computational times for scattering problems of arbitrarily high frequency: the convex case.

We present a new algorithm for the numerical solution of problems of electromagnetic or acoustic scattering by large, convex obstacles. This algorithm combines the use of an ansatz for the unknown density in a boundary-integral formulation of the scattering problem with an extension of the ideas of the method of stationary phase. We include numerical results illustrating the high-order convergence of our algorithm as well as its asymptotically bounded computational cost as the frequency increases.

Stokes flow around cylinders in a bounded two-dimensional domain using multipole-accelerated boundary element methods

The multipole technique has recently received attention in the field of boundary element analysis as a means of reducing the order of data storage and calculation time requirements from O(N2) (iterative solvers) or O(N3) (gaussian elimination) to O(N log N) or O(N), where N is the number of nodes in the discretized system. Such a reduction in the growth of the calculation time and data storage is crucial in applications where N is large, such as when modelling the macroscopic behaviour of suspensions of particles. In such cases, a minimum of 1000 particles is needed to obtain statistically meaningful results, leading to systems with N of the order of 10 000 for the smallest problems. When only boundary velocities are known, the indirect boundary element formulation for Stokes flow results in Fredholm equations of the second kind, which generally produce a well-posed set of equations when discretized, a necessary requirement for iterative solution methods. The direct boundary element formulation, on the other hand, results in Fredholm equations of the first kind, which, upon discretization, produce ill-conditioned systems of equations. The model system here is a two-dimensional wide-gap couette viscometer, where particles are suspended in the fluid between the cylinders. This is a typical system that is efficiently modelled using boundary element method simulations. The multipolar technique is applied to both direct and indirect formulations. It is found that the indirect approach is sufficiently well-conditioned to allow the use of fast multipole methods. The direct approach results in severe ill-conditioning, to a point where application of the multipole method leads to non-convergence of the solution iteration. Copyright © 1999 John Wiley & Sons, Ltd.

FastCap: a multipole accelerated 3-D capacitance extraction program

A fast algorithm for computing the capacitance of a complicated three-dimensional geometry of ideal conductors in a uniform dielectric is described and its performance in the capacitance extractor FastCap is examined. The algorithm is an acceleration of the boundary-element technique for solving the integral equation associated with the multiconductor capacitance extraction problem. The authors present a generalized conjugate residual iterative algorithm with a multipole approximation to compute the iterates. This combination reduces the complexity so that accurate multiconductor capacitance calculations grow nearly as nm, where m is the number of conductors. Performance comparisons on integrated circuit bus crossing problems show that for problems with as few as 12 conductors the multipole accelerated boundary element method can be nearly 500 times faster than Gaussian-elimination-based algorithms, and five to ten times faster than the iterative method alone, depending on required accuracy. >