Abstract
We present computational solutions to the Lengyel-Rabai-Epstein model in three space dimensions. The results show that three-dimensional patterns exist and that they differ significantly from the two-dimensional patterns. Patterns occur at three locations in the reactor corresponding to peaks in the one-dimensional concentration of the starch tri-iodide concentration. Each pattern possesses its own intrinsic wavelength and is neither striped nor hexagonal, the two types that have been shown to exist in two dimensions. Computations suggest a bifurcation exists as a function of the reactor thickness. Solutions are computed using a high-order adaptive finite element method coupled with a multistep integrator in time. Linear systems generated in the multistep solver are solved using the iterative method GMRES with a Jacobi preconditioner. Matrix storage is reduced by incomplete assembly via thresholding. Preconditioner factorization and matrix-vector multiplication efficiency are enhanced by the use of OPENMP.
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