三维高频声波的矩阵压缩边界节点法模拟

本文采用边界节点法(Boundary Knot Method, BKM)求解三维高频声场．由于高频赫姆霍兹方程的解是振荡的，极大影响了数值求解的精确度，需要在计算区域增加离散点，这会增加计算量．同时对于大规模声学问题，依靠边界节点法形成的插值矩阵为满秩，导致计算量过高和存储量过大．所以本文采用矩阵压缩技术(Matrix Compression, MC)，在有效继承边界节点法高精确度的基础上减少计算内存需求和时间，从而提高计算效率．数值实验表明，MC-BKM 求解精度高、收敛速度快、计算时间少，在高频大规模声波问题中应用前景广泛．

Simulation of Three-Dimensional High Frequency Acoustic Wave by Matrix Compression Boundary Knot Method

In this paper, the boundary knot method is used to solve three-dimensional high frequency sound field. Because the solution of high frequency Helmholtz equation is oscillatory, which greatly affects the accuracy of numerical solution, it is necessary to add discrete points in the computational region, leading to the increase of calculation cost. At the same time, for large-scale acoustic problems, the interpolation matrix formed by the boundary knot method is full rank, resulting in excessive computation and excessive storage. The introduction of matrix compression technology can effectively reduce the memory requirement and time while at the same time effectively inherits the high accuracy of the boundary node method, leading to a significant improvement of the computational efficiency. Numerical experiments show that MC-BKM has high accuracy, fast convergence speed and less computation time, and has a wide application prospect in high frequency large scale acoustic wave problems.