An adaptive fast multipole boundary element method for the Helmholtz equation
نویسندگان
چکیده
The present paper intends to couple the Fast Multipole Method (FMM) with the Boundary Element Method (BEM) in 2D acoustic problems. The evaluation of the integrals involved in the governing Boundary Integral Equations (BIEs) is fasten by the FMM contribution. The multipole expansion and some suitable moment translations make the procedure much faster if compared to the conventional approach. The generalised minimal residual iterative solver (GMRES) is adopted to improve the overall computational efficiency. A simple numerical example is shown to demonstrate the reliability of the method.
منابع مشابه
Fast Multipole Boundary Element Method for 2-D Helmholtz Equation Problems and Its Error Analysis ?
In this paper, a kind of Fast Multipole Boundary Element Method (FM-BEM) based on series form expansion is presented to solve two-dimensional (2-D) Helmholtz equation problems. A theorem of multipole expansion is derived and proved for the fundamental solution, which demonstrates the error source and can be widely used in 2-D electromagnetics and acoustics problems. The truncation error is anal...
متن کاملAn Implementation of Low-Frequency Fast Multipole BIEM for Helmholtz’ Equation on GPU
Acceleration of the fast multipole method (FMM), which is the fast and approximate algorithm to compute the pairwise interactions among many bodies, with graphics processing units (GPUs) has been investigated for the last couple of years. In view of the type of kernel functions, the non-oscillatory kernels (especially, the Laplace kernel) were studied by many researchers (e.g. Gumerov), and the...
متن کاملFast Multipole Accelerated Boundary Element Methods for the 3D Helmholtz Equation
Abstract The development of a fast multipole method accelerated iterative solution of the boundary element equations for large problems involving hundreds of thousands elements for the Helmholtz equations in 3D is described. The BEM requires several approximate computations (numerical quadrature, approximations of the boundary shapes using elements) and the convergence criterion for iterative c...
متن کاملAn adaptive fast multipole boundary element method for three-dimensional acoustic wave problems based on the Burton–Miller formulation
The high solution costs and non-uniqueness difficulties in the boundary element method (BEM) based on the conventional boundary integral equation (CBIE) formulation are two main weaknesses in the BEM for solving exterior acoustic wave problems. To tackle these two weaknesses, an adaptive fast multipole boundary element method (FMBEM) based on the Burton–Miller formulation for 3-D acoustics is p...
متن کاملFast Multipole Accelerated Indirect Boundary Elements for the Helmholtz Equation
The indirect boundary element method for the Helmholtz equation in three dimensions is of great interest and practical value for many problems in acoustics as it is capable of treating infinitely thin plates and allows coupling of interior and exterior scattering problems. In the present paper we provide a new approach for treatment of boundary integrals, including hypersingular, singular, and ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009