Fast Multipole Boundary Element Method for 3-Dimension Acoustic Radiation Problem
In order to reduce computational complexity and memory requirements using conventional boundary element method (CBEM) for large scale acoustical analysis, a fast solving algorithm called the Fast Multipole BEM (FMBEM) based on the fast multipole algorithm and GMRES iterative solver is developed without composing the dense influence coefficient matrices. The multipole level structure is introduced to accelerate the solution of large-scale acoustical problems, by employing a concept of cells clustering boundary elements and hierarchical cell structure. To further improve the efficiency of the FMBEM with iterative solvers, a block diagonal matrix method is used in the system of equations as the left pre-conditioner. Numerical examples are presented to further demonstrate the efficiency, accuracy and potentials of the fast multipole BEM for solving large-scale acoustical problems.
B. R. Zhang et al., "Fast Multipole Boundary Element Method for 3-Dimension Acoustic Radiation Problem", Applied Mechanics and Materials, Vols. 130-134, pp. 80-85, 2012