Preconditioned Conjugate Gradient Techniques for the Solution of Time-DependentDifferential Equations

摘要

The conjugate gradient method for the solution of symmetric systems, and theconjugate gradient squared method for unsymmetric systems, are considered. Application of the method of lines to partial differential equations leads to very large, sparse systems of ordinary differential equations, which are usually stiff. Implicit Runge-Kutta methods for the time integration of these systems, and the use of iterative methods for the solution of the resulting linear systems, are considered. The effect of preconditioners, and their performance on vector and parallel computers is discussed. Some results for iterative methods applied to the incompressible Navier-Stokes equation are presented.