带有非线性边界条件涡流方程的A-Φ有限元算法

A-Φ Finite Element Scheme for Eddy Current Equations with Nonlinear Boundary Condition

利用A-Φ方法对带有非线性边界条件的涡流方程提出了耦合和解耦两种有限元算法。非线性项表现为指数形式:H×n=n×|E×n|α-1E×nα∈(0,1]。在每一个计算步骤里,耦合算法在一个方程里面同时求解矢量A和标量Φ,而解耦算法在两个不同的方程里面分别求解矢量A和标量Φ;再通过一些数值实验来对两种算法的可行性、收敛性等进行对比。

We use A -Ф method to suggest a coupled and a decoupled fully discrete numerical scheme to solve eddy current equations with nonlinear boundary condition obedient to a power - law form H×n=n×│E×n│^a-1E×n a∈（0,1]. At every time step, the coupled scheme is to solve A and Ф in one equation at the same time, and the decoupled scheme needs to solve two separate equation for the A and the Ф respectively. And we present some numerical experiments to compare the two schemes.