高阶龙格库塔间断有限元方法求解二维谐振腔问题

提出了使用高阶龙格库塔间断有限元方法在时域求解经典的电磁场谐振腔问题，间断有限元方法在空间离散时采用非结构化网格且在时域显式求解方程，这是有限元方法和有限体积方法的最佳结合。该方法通过采用局部高阶多项式插值基函数获得高阶精度。文中使用该方法研究了横磁波在二维谐振腔中的传播情况，以及高阶的拉格朗日基函数。数值实验采用了高阶的二变量拉格朗日多项式基函数，数值计算结果与理论解析解相吻合。文中还讨论了不同阶数多项式插值基函数对计算精度的影响。结果表明，随插值基函数阶数增加，计算精度迅速提高。最后讨论了不同插值基函数阶数对L^2误差的影响，结果显示L^2误差随插值基函数阶数增加呈指数下降。

HIGH-ORDER RUNGE-KUTTA DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD FOR 2-D RESONATOR PROBLEM

The Runge-Kutta discontinuous Galerkin finite element method (RK-DGFEM) is introduced to solve the classical resonator problem in the time domain.DGFEM uses unstructured grid discretization in the space domain and it is explicit in the time domain.Consequently it is a best mixture of FEM and finite volume method (FVM).RK-DGFEM can obtain local high-order accuracy by using high-order polynomial basis.Numerical experiments of transverse magnetic (TM) wave propagation in a 2-D resonator are performed.A high-order Lagrange polynomial basis is adopted.Numerical results agree well with analytical solution.And different order Lagrange interpolation polynomial basis impacts on simulation result accuracy are discussed.Computational results indicate that the accuracy is evidently improved when the order of interpolation basis is increased.Finally,L2 errors of different order polynomial basis in RK-DGFEM are presented.Computational results show that L2 error declines exponentially as the order of basis increases.