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

We describe an algorithm for solving systems of parabolic partial differential equations in three space dimensions. Approximate solutions are determined using Galerkinʹs 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.