计算力学学报2019，Vol.36Issue(1)：96-102,7.DOI:10.7511/jslx20171004001
无网格介点法求解Helmholtz方程
Solve Helmholtz equations by the meshless intervention point (MIP) method
摘要
Abstract
As a collocation-type meshless method, the meshless intervention point (MIP) method is simple, accurate and efficient. Furthermore, the method may be suitable for wide applications.The Helmholtz equation is widely used in science and engineering problems.Therefore, the feasibility of solving the Helmholtz equation by the MIP method is verified.Using the d-adaptability of the MIP method, two algorithms for solving the equations are given.In the numerical tests, the Helmholtz equation on a regular domain, on an irregular domain, and on an axisymmetric domain are studied.The results show that the MIP method is fully suitable for solving the Helmholtz equation, and has a higher accuracy and a better convergence than the common collocation method. Besides, for better performance, L2 C0 scheme is suggested as the standard form for the MIP method to solve this kind of equations.关键词
无网格法/Helmholtz方程/无网格介点法/介点原理Key words
meshless method/Helmholtz equation/MIP method/intervention-point principle分类
数理科学引用本文复制引用
杨子乐,黄旺,班游,杨建军..无网格介点法求解Helmholtz方程[J].计算力学学报,2019,36(1):96-102,7.基金项目
国家自然科学基金 (51478053) （51478053）
道路结构与材料交通行业重点实验室 (长沙) 开放基金 (KFJ120201) 资助项目. （长沙）
