Krylov Subspace Methods for the Solution of Large Systems of ODE’s

Abstract

When solving large systems of ODE’S like those appearing in air-pollution problems some kind of implicitness in the solver is necessary. The implicit equations that have to be solved are large and often it is preferred to use parallel computers for the solution. It is necessary to use linear systems solvers that parallellize well. Among such methods are different kinds of Krylov subspace methods. The presentation will show several examples of preconditioned conjugate gradient type methods and examples from air pollution problems will be used to make comparisons on the efficiency of such methods. The platform that has been used for carrying out the tests is a general DAE-solving platform developed for such purposes. GODESS is a Generic ODE Solving System implementing an Object Oriented platform for solving systems of ODE’s and DAE’s. The choice of method is made by the user and several methods have been tried out. A comparison between methods with different linear solvers are presented.