Helmholtz方程的微分容积解法

用一种新型的数值技术－－微分容积法（Differential Cubature Method）求解二维Helmholtz方程的边值问题，几个数值算例表明，该方法稳定收敛，并具有较好的数值精度，本文方法适用于求解具有较小波数的Helmholtz方程。

Solution of Helmholtz equation by differential cubature method

A novel numerical solution technique, the differential cubature method is employed to solve the two|dimensional Helmholtz equations. The basic idea of the differential cubature method is to express a linear differential operation such as a continuous function or any orders of partial derivatives of a multivariable function, or combinations of them as a weighted linear sum of the discrete function values chosen within the overall domain of a problem. The weighting coefficients can be obtained by chosing a set of monomials as the trial functions. By using the differential cubature procedure, the governing differential equations and boundary conditions are transformed into a set of linear algebraic equations of the function values at the each discrete point. The convergency, accuracy and applicability of this method are demonstrated through solving some sample problems of the different wave numbers, which have exact solutions. It was found that this method is more suitable for solving the Helmholtz equations of lower wave numbers.