修正Helmholtz方程的改进无单元Galerkin法分析

Analysis of Modified Helmholtz Equation with the Improved Element-Free Galerkin Method

【目的】在改进移动最小二乘近似的基础上,讨论了一种稳定化的改进移动最小二乘近似,具有更好的数值稳定性和计算精度。【方法】将稳定化的改进移动最小二乘近似和修正Helmholtz方程的Galerkin积分弱形式相结合,建立了修正Helmholtz方程混合边值问题的改进无单元Galerkin法,并理论分析了在Sobolev空间中的误差。【结果】通过两个数值算例验证了算法的有效性和理论的正确性。【结论】误差随节点间距的减小而降低。

[Purposes]On the basis of the improved moving least square approximation,a stabilized improved moving least squares approximation is discussed to yield results with better computational stability and precision.[Methods]Combining the improved moving least square approximation with Galerkin weak form,the improved element-free Galerkin method is established for the modified Helmholtz equation with mixed boundary value problem.Error analysis of the Galerkin method is provided theoretically in Sobolev spaces.[Findings]Two numerical examples are provided to demonstrate the effectiveness of the method and the correctness of the theoretical analysis.[Conclusions]The errors of the method decrease monotonously as the nodal spacing decreases.