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Matrix-oriented discretization methods for reaction-diffusion PDEs: Comparisons and applications
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DOI：10.1016/j.camwa.2019.10.020.png)
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摘要
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Systems of reaction-diffusion partial differential equations (RD-PDEs) are widely applied for modeling life science and physico-chemical phenomena. In particular, the coupling between diffusion and nonlinear kinetics can lead to the so-called Turing instability, giving rise to a variety of spatial patterns (like labyrinths, spots, stripes, etc.) attained as steady state solutions for large time intervals. To capture the morphological peculiarities of the pattern itself, a very fi ne space discretization may be required, limiting the use of standard (vector-based) ODE solvers in time because of excessive computational costs. By exploiting the structure of the diffusion matrix, we show that matrix-based versions of time integrators, such as Implicit-Explicit (IMEX) and exponential schemes, allow for much finer problem discretizations. We illustrate our findings by numerically solving the Schnakenberg model, prototype of RD-PDE systems with Turing pattern solutions, and the DIB-morphochemical model describing metal growth during battery charging processes. (C) 2019 Elsevier Ltd. All rights reserved.
Keyword:
Reaction-diffusion PDEs
Turing patterns
IMEX methods
ADI method
Sylvester equations
Schnakenberg model
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论文数:
369
被引数:
1.8W
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