A fast directional BEM for large-scale acoustic problems based on the BurtonMiller formulation
In this paper, a highly efficient fast boundary element method (BEM) for solving large-scale engineering acoustic problems in a broad frequency range is developed and implemented. The acoustic problems are modeled by the BurtonMiller boundary integral equation (BIE), thus the fictitious frequency issue is completely avoided. The BIE is discretized by using the Nystrm method based on the curved quadratic elements, leading to simple numerical implementation (no edge or corner problems) and high accuracy in the BEM analysis. The linear systems are solved iteratively and accelerated by using a newly developed kernel-independent wideband fast directional algorithm (FDA) for fast summation of oscillatory kernels. In addition, the computational efficiency of the FDA is further promoted by exploiting the low-rank features of the translation matrices, resulting in two- to three-fold reduction in the computational time of the multipole-to-local translations. The high accuracy and nearly linear computational complexity of the present method are clearly demonstrated by typical examples. An acoustic scattering problem with dimensionless wave number kD (where k is the wave number and D is the typical length of the obstacle) up to 1000 and the degrees of freedom up to 4 million is successfully solved within 10h on a computer with one core and the memory usage is 24GB.
burtonmiller formulation boundary element method nystrm method fast directional algorithm