超弱变分方法在一类介质散射问题数值计算中的应用

Application of Ultra Weak Variational Method to Numerical Calculation of a Class of Scattering Problem by Medium

应用超弱变分方法数值求解一类时谐波被介质散射的问题.在区域被人工吸收边界截断的基础上,根据间断有限元(DG)方法导出超弱变分公式,并利用平面波函数的逼近性质去近似场的局部性态,将问题转化到网格边界上求解.结果表明,该算法能有效地数值模拟介质散射问题,适用于大波数情形,收敛速度较快.数值模拟验证了算法的可行性和有效性.

We applied ultra weak variational method tonumerically solve a class of time harmonic scattering problem by medium.On the basis of truncation of the domain by artificial absorbing boundary,we derived ultra weak variational formula according tothe discontinuous Galerkin(DG)method,and used the approximation property of plane wave functions to approximate the local behavior of the field,then transformed the problem to the solution of the network boundary.The results show that the algorithm can effectively simulatethe medium scattering problem,and is suitable for the case of bigwave number with fast convergence rate.Numerical simulations verify the feasibility and validity of the algorithm.