title: Three-dimensional patterns in the Lengyel-Rabai-Epstein model of the chlorine dioxide-iodine-malonic acid reaction.
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.
authors.affiliation: Department of Mathematics, Southern Methodist University, Dallas, Texas 75275, USA.
authors.forename: Peter K
authors.initials: PK
authors.lastname: Moore
authors.forename: Werner
authors.initials: W
authors.lastname: Horsthemke
mesh_terms: D017606:Chlorine Compounds / Q000737:chemistry*; D003198:Computer Simulation; D004058:Diffusion; D007455:Iodine / Q000737:chemistry*; D008314:Malonates / Q000737:chemistry*; D008956:Models, Chemical; D017711:Nonlinear Dynamics; D010087:Oxides / Q000737:chemistry*; D012212:Rheology / Q000379:methods*
chemical_list: D017606:Chlorine Compounds; D008314:Malonates; D010087:Oxides; C025109:chlorine dioxide; D007455:Iodine; C030290:malonic acid