求解一类交界面问题的模态基函数谱元法数值实验

A Numerical Study of The Modal Bases Spectral Element Method for Solving Interface Problems

采用模态基函数形式下的谱元法,对一类一维和二维交界面问题进行了数值计算研究。不仅考虑了具有间断系数的方程,还涉及了右端带有奇性源项的方程。对于二维问题的数值计算,研究了四边形单元谱元法和三角单元谱元法的离散格式。通过一些具有精确解的数值算例,验证了基于模态基函数谱元法求解交界面问题的可行性和有效性。与其他数值方法相比,谱元法对于一维问题可以实现指数阶收敛精度,对于二维问题也得到了较高的计算精度。

The numerical solution of one and two dimensional interface problems using the modal bases spectral element method(SEM)was studied.Equations with the discontinuous coefficient or singular source were concerned.For two dimensional cases,the implementations of the quadrilateral element(QSEM)and the triangular element(TSEM)were both investigated.Several numerical examples with exact solutions were provided to illustrate the feasibility and effectiveness of the modal bases SEM.Compared with other numerical results,exponential accuracy was regained for the one dimensional case,and better accuracy was also obtained for the two dimensional case.