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.