适用于迭代数值求解的时谐麦克斯韦方程的无旋正定形式
Curl-free positive definite form of time-harmonic Maxwells equations well-suitable for iterative numerical solving
AI总结：
本研究提出一种适用于迭代数值求解的时谐麦克斯韦方程无旋正定新形式，该形式针对四类物理量构建，具备算子正定、无旋度主导项、对角占优等特性，并通过示例验证了其适用性。
摘要：
本文提出并构建了一种用于数值建模的时谐麦克斯韦方程新形式，该形式针对磁场强度、电位移、矢量势和标量势进行构建。该形式具备若干优良特性：其一，作用于这些物理量的微分算子为正定算子；其二，主导阶微分算子中不存在旋度算子，其中磁场强度、矢量势与标量势的方程以拉普拉斯算子为主导阶算子，电位移方程则以散度的梯度为主导阶算子；其三，主导阶微分算子中不含空间变化系数，可保证离散化后所得方程组的矩阵具有对角占优性。文中还给出了一个简单示例，以验证该时谐麦克斯韦方程新形式的适用性。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
