Computational cost reduction for coupled system of multiple scale reaction diffusion problems with mixed type boundary conditions having boundary layers

Abstract

In this article, we consider the computational cost reduction of approximating a coupled system of time variant multiscale parameterized problems with mixed type conditions, in addition to the mathematical convergence analysis of this approximation. A triangular splitting based additive approach on equidistributed partition points are considered to reduce the computational cost. The objective of the discretization includes optimal quadratic approximation at the interior points of the domain and preserves this rate of accuracy for the mixed type boundary conditions. Convergence analysis on an adaptive mesh, generated by a specially chosen monitor function, shows that the present approach provides uniform linear accuracy in time and uniform quadratic accuracy in space for parabolic systems. Numerical experiments based on triangular splitting (diagonal or triangular forms) of the reaction matrix in comparison to its coupled form, strongly validate the optimal accurate approximation with reduced computational cost. © 2023, The Author(s) under exclusive licence to The Royal Academy of Sciences, Madrid.