Multigrid Method And Adaptive Method For Numerical Solution Of Maxwell Equation

In recent years, ground penetrating radar develops as a high-resolution frequency mine detection method. Compared with other means of detection, it is non-destructive, high-resolution and facilitates construction, so it has broad prospects for application. Maxwell's equations are replaced by a set of finite difference equation. If we solve it in time domain, we can get Finite Difference Time domain (FDTD) method. It is show that if one chooses the field points appropriately, the set of finite difference equation is applicable for a boundary condition involving perfectly conducting surfaces. Usually we use Yee scheme as FDTD, but this method is condition stable.A kind of implicit scheme respectively for solving the Maxwell equation are proposed and proved to be unconditional stable. A multigrid technique is employed to accelerate the convergence speed when implicit schemes are used to resolve the hyperbolic problem and fast solutions are obtained. And improve multigrid method to adaptive-multigrid method to reduce computational efficiency. Numerical results prove their accuracy and dependability.In order to reduce model error, we use non-uniform grid, if the parameter's changing is fast, we use fine grid, else we use coarse grid. In this way we can get the accuracy of full field fine grid and less computational than full field fine grid.