基于Matlab求解时谐复系数弹性波方程的超弱变分方法

AN ULTRA WEAK VARIATIONAL FORMULATION FOR SOLVING TIME-HARMONIC ELASTIC WAVE EQUATIONS WITH COMPLEX WAVE COEFFICIENTS BASED ON MATLAB

众所周知,弹性波方程被用来描述工程应用中的弹性波传输问题。高效数值求解弹性波方程是一个重要的研究课题。提出了基于平面波离散的间断有限元超弱变分法。首先,选取满足剖分单元上齐次偏微分方程和其对偶方程的解析解分别作为检验空间和测试空间,得到等价的间断有限元变分形式;然后分别定义二维空间下的矢量平面波检验离散空间和测试离散空间,进而得到离散变分形式。基于Matlab软件的数值实验验证了新算法具有较高的精度。

As is known,some engineering problems,such as the elastic wave transmission,can be described by the elastic wave equation.The efficient numerical algorithms for solving elastic wave equations are important.An ultra weak variational formulation based on the plane wave discretizations is proposed.First,by choosing the analytic solutions satisfying the homogeneous elastic wave equations and its adjoint equations to form the trial space and the test space,respectively,we obtain the equivalent Trefftz variational formulation;then we define the two-dimensional vector plane wave discretized trial space and test space to discretize the proposed continuous variational formulation.Numerical results based on Matlab have validated the proposed method.