Eigen-analysis on some preconditioning for iterative methods to solve linear partial differential equations

摘要

We consider iterative methods for solving linear partial differential equations with one variable parameter which is a function on the domain. Fast direct solvers for the constant parameter problem are used for the preconditioning. We prove that the distribution of the eigenvalues of the preconditioned linear system is a discrete analogue of the distribution of the value of the parameter on the domain.