A comparison of preconditioners in the solution of parabolic systems in three space dimensions using DASPK and a high order finite element method

We describe an algorithm for solving systems of parabolic partial differential equations in three space dimensions. Approximate solutions are determined using Galerkin's method with a high order, piecewise polynomial hierarchical basis in space and the differential algebraic equations code DASPK in time. On three test problems, a variant of DASPK that computes Jacobian vector products with a stored analytic Jacobian is compared with the default matrix-free approximation of the Jacobian vector product. Several preconditioners are compared including incomplete Cholesky, banded LU and element-by-element factorizations.