一种基于波动方程的新高阶FDTD方法

 提出了一种基于二阶波动方程的（2M,4）高阶时域有限差分(FDTD)方法，通过使用辛积分传播子(SIP)在时域上获得4阶精度，使用离散奇异卷积(DSC)方法在空域上达到2M阶精度。与已有的(2M，4) 阶FDTD方法相比，虽然两者都采用SIP和DSC方法，但是此二者的不同点在于：第一，新方法基于二阶波动方程；第二，在离散计算空间时使用单一网格而不是传统的Yee网格；第三，单独计算某一场分量从而节约内存并减少计算量。数值计算结果表明，与传统高阶算法相比，基于波动方程的高阶FDTD方法耗费的机时只有它的50%,内存消耗下降10%, 而两者的计算结果之间相对误差小于5‰。

A new high order FDTD method based on wave equations

A(2M,4) scheme of the high-order finite-difference time-domain(FDTD) method based on the second order wave equation is proposed.This scheme is of the fourth order accuracy in time domain using the symplectic integrator propagator(SIP),and is of the 2Mth order accuracy in space domain using the discrete singular convolution(DSC) method.This scheme is similar to the traditional(2M,4) scheme where SIP and DSC method is used and the distinction between them are listed as follows. Firstly,this new scheme is based on the wave equation.Secondly,computational region is discretized by uniform mesh rather than Yee mesh.Thirdly,the new scheme can save more memory and computation time because only one field component is used for calculation.Numerical examples show that when compared with traditional high order FDTD method,the new high order scheme based on wave equation involves less computation and memory.