论文标题
无卷曲的正定形式的定时谐波麦克斯韦方程非常适合迭代数值求解
Curl-free positive definite form of time-harmonic Maxwells equations well-suitable for iterative numerical solving
论文作者
论文摘要
开发并提出了一种新形式的时间谐波麦克斯韦方程，并提出用于数值建模。它是为磁场强度，电位移，向量电势和标量电势而编写的。该形式有几个吸引人的功能。第一个是对这些数量作用的差分运算符是积极的。第二个是领先阶差分运算符之间没有卷曲操作员。拉普拉斯（Laplacian）代表方程中的领先订单操作员的磁场强度，矢量电势和标量电势，而发散的梯度则代表电位移。第三个特征是在领先顺序差分运算符中没有空间变化的系数，该系数提供了离散方程所得矩阵的对角线支配。给出了一个简单的示例，以说明这种新形式的时谐麦克斯韦方程的适用性。
A new form of time-harmonic Maxwells equations is developed and proposed for numerical modeling. It is written for the magnetic field strength, electric displacement, vector potential and the scalar potential. There are several attractive features of this form. The first one is that the differential operator acting on these quantities is positive. The second is absence of curl operators among the leading order differential operators. The Laplacian stands for the leading order operator in the equations for the magnetic field strength, vector potential and the scalar potential, while the gradient of divergence stands for the electric displacement. The third feature is absence of space varied coefficients in the leading order differential operators that provides diagonal domination of the resulting matrix of the discretized equations. A simple example is given to demonstrate the applicability of this new form of time-harmonic Maxwells equations.
