Finite Element Simulation And Rapid Solution Of The Finite Element Equation In An Electromagnetic Field Applications

Finite element is a powerful tool to model structures of arbitrary shapes. Here we use the finite element method to model electromagnetic problems, which is unable to be solved by normal methods. Some classical structures of open boundary conditions, such as waveguide, micro-strip, in the modeling of them by finite element methods, we finally get a complex super-large sparse linear equations, which are normally ill-conditioned and unable to solve by Gauss-decomposition methods, even normal iterative method doesn't converge well. In this paper, we consider the incomplete LU preconditioning strategies for the conjugate gradient iterative solution to the large sparse non-Hermitian systems resulting from finite element method (FEM). The standard ILU may fail when applied to highly-indefinite matrix when a zero pivot is encountered or the obtained triangular is unstable. Here a perturbed diagonal matrix is added to the coefficient matrix before the ILU factorization process to make the real part of the matrix more diagonally dominant. The main purpose of this study is to evaluate the efficiency of the perturbed ILUP preconditioners applied to highly indefinite matrix obtained by discretize rielmhotz equations. We also considered and compared some other preconditioning techniques commonly used. The numerical efficiency of the preconditioners is illustrated on a set of model problems arising both from academic and from industrial applications. Experimental results showed that the applying of preconditioning techniques, especially ILU preconditioners can greatly reduce the iteration steps. And our ILU preconditioners are fairly robust compared with normal ILU preconditioner...