Using Krylov Methods in the Solution of Large-Scale Differential-Algebraic Systems
Peter N. Brown, A.C. Hindmarsh, Linda Ruth Petzold · SIAM Journal on Scientific Computing · 1994
In this paper, a new algorithm for the solution of large-scale systems of differential-algebraic equations is described. It is based on 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 stems, and finally demonstrate the application of DASPK on two example problems.