An Incomplete Assembly with Thresholding Algorithm for
Systems of Reaction-Diffusion
Equations in Three Space Dimensions
Solving systems of reaction-difusion equations in three space dimensions
can be prohibitively expensive both in terms of storage and cpu time.
Herein I present a new incomplete assembly procedure that is designed to
reduce storage requirements. Incomplete
assembly is analogous to incomplete factorization in that only a fixed number of nonzero entries are stored per row and a drop
tolerance is used to discard small values. The algorithm is incorporated in a finite element method-of-lines code and tested on
a set of reaction-diffusion systems. The effect of incomplete assembly on cpu time and storage and on the performance of the
temporal integrator DASPK, algebraic solver GMRES and preconditioner ILUT is studied.