Pomp, A. A fast solver for nonlinear systems of diffusion-reaction equations. (English) Zbl 0957.65082 ZAMM, Z. Angew. Math. Mech. 80, Suppl. 3, S843-S844 (2000). Summary: The underlying application is the diffusion of dopants in a silicon crystal and in overlayers (an essential step in the fabrication process of semiconductors). The changes of concentrations are similar to shock waves. This physical behavior leads to the following structure of the Jacobi matrices generated by the Newton iteration: the main part of the rows is diagonal dominant while the essential couplings are concentrated to a relatively small subset of the indices. We describe an ILU preconditioning strategy which is well-adapted to matrices of this type and which allows a fast solution of the complete (time dependent) system of diffusion-reaction equations. MSC: 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 65H10 Numerical computation of solutions to systems of equations 65F35 Numerical computation of matrix norms, conditioning, scaling 35K57 Reaction-diffusion equations 82D37 Statistical mechanics of semiconductors Keywords:silicon crystal; fabrication process of semiconductors; shock waves; Jacobi matrices; Newton iteration; ILU preconditioning strategy; diffusion-reaction equations PDFBibTeX XMLCite \textit{A. Pomp}, ZAMM, Z. Angew. Math. Mech. 80, S843--S844 (2000; Zbl 0957.65082)