英语论文翻译

无网格法[ 6] 可以克服传统数值分析方法对网格的依赖性, 彻底或部分消除网格, 抛开网格的初始划分和网格重构, 具有形式简单、易于实施、计算精度高等优点, 代表性的无网格方法有无单元伽辽金法、光滑粒子动力学方法、杂交边界点方法、径向基函数( RBF) 法等. 径向基函数配点法作为一种纯无网格方法, 在求解椭圆型偏微分方程、流体力学中的稳态解和波动方程的频域解( 亥姆霍兹方程) 等方面[ 729] 都得到了广泛的应用, 也有学者将该方法推广到了抛物型和双曲型偏微分方程以及瞬态问题和时域问题的求解[ 10212] . 本研究尝试将径向基函数配点法和Crank2Nicolson 方法结合, 用于求解二阶时域波动方程, 给出了求解的思路和实施方案, 通过数值算例验证了该方法可以用于波动方程的求解.

Many physical phenomena of electromagnetic waves and sound waves, vibration of strings and membranes, the control equations are available to be with the wave equation [1]. To describe the numerical methods for solving the wave equation used in covering the finite difference method, finite element method, the spectral element methodcommonly used in the calculation [224] . However, the accuracy and efficiency of these methods is often subject to quantity and quality of the grid when solving meshing, especially in the complex solution domain or high dimension problems. Followed by the boundary element method [5] because of the small amount of calculation, high accuracy, strong adaptability to complicated boundary shapeof being widely used, however, the boundary element method is still on the boundary mesh, solve the boundary integral equation, this integral calculation due to odd point is very tedious, and time spent with dense linear algebra equations of computation time is considerable.

Meshless method [6] can overcome the traditional numerical analysis method dependent on the grid, completely or partially eliminate the grid, set aside the initial grid division and remeshing, with the form of simple, easy to implement, calculation accuracymeshless methods advantages, representative with element free Galerkin method, smoothed particle hydrodynamics method, the hybrid boundary node method, radial basis function (RBF) method. radial basis function collocation method as a kind of pure meshless methodfor solving elliptic partial differential equations, the steady-state solution in the fluid mechanics and wave equation frequency domain (Helmholtz equation) [729] have been widely used, but also scholars of theextended to the parabolic and hyperbolic partial differential equations as well as transient and time-domain problem solving [10212] this study attempts to radial basis function collocation method and Crank2Nicolson method for solving the second-order time-domain wave equation,solving thinking and implementation of programs, this method can be used for the solution of the wave equation by a numerical example.