周期子波在二维声辐射和声散射中的应用

提出了一种新的求解二维Helmholtz积分方程的方法。它通过将边界量用周期子波展开，将Helmhotz积分方程化为一组代数方程求解。即可求解Dirichlet、Neumann问题，也可求解合边值问题，方程的系数形成可用快速子波变换。用该方法形成的Helmholtz积分方程的系数矩阵是一稀疏矩阵，这样大大提高了计算效率，本算例表明：该方法收敛快，精度高，相同的精度下，本方法求解的未知量大大少于边界元所用未知量。

On Reducing High Computational Cost with Periodic Wavelets inSolving Two-Dimensional Acoustic Radiation and Scattering

Traditional methods for solving acoustic problems in engineering often require the solution of non symmetric full matrix, whose dimension may be even higher than 10 000 and thus computational cost becomes quite high. To overcome this serious shortcoming, we propose a new periodic wavelet approach for the Helmholtz integral equation solution of two dimensional acoustic radiation and scattering over curved computation domain. We expand the boundary quantities in terms of periodic and orthogonal wavelets and we obtain the algebraic equations needed for solving the acoustic problems with Dirichlet, Neumann and mixed conditions. We evaluate the coefficients with fast wavelet transform. The advantage of the new approach is a highly sparse matrix system. We compare the numerical results obtained with our new approach, boundary element method or analytical solutions; the numerical results, as given in Table 1, show that our new approach converges rapidly and is of good accuracy.