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A fast solver for nonlinear systems of diffusion-reaction equations. (English) Zbl 0957.65082

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
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