Using Krylov Methods in the Solution of Large-Scale Differential-AlgebraicSystems

摘要

In this paper we describe a new algorithm for the solution of large-scale systemsof differential-algebraic equations. It is based in the integration methods in the solver DASSL, but instead of a direct method for the associated linear systems which arise at each time step, we apply the preconditioned GMRES iteration in combination with an Inexact Newton Method. The algorithm, along with those in DASSL, is implemented in a new solver called DASPK. We outline the algorithms and strategies used, and discuss the use of the solver. We develop and analyze some preconditioners for a certain class of DAE systems, and finally demonstrate the application of DASPK on two example problem.