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

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

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.

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Code and data availability

For the sake of reproducibility, all computations are carried out using Matlab. Code can be obtained from the author Sumit Saini, upon request.

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Funding

This research is supported by the Science and Engineering Research Board (SERB) under the Project Grant No. MTR/2021/000797 for the author Pratibhamoy Das.

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Author notes

  1. Pratibhamoy Das and Sunil Kumar contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics, Maulana Azad National Institute of Technology, Bhopal, M.P., 462003, India

    Sumit Saini

  2. Department of Mathematics, Indian Institute of Technology, Patna, Bihar, 801106, India

    Pratibhamoy Das

  3. Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, Uttar Pradesh, 221005, India

    Sunil Kumar

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  1. Sumit Saini
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  3. Sunil Kumar
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Saini, S., Das, P. & Kumar, S. Computational cost reduction for coupled system of multiple scale reaction diffusion problems with mixed type boundary conditions having boundary layers. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 117, 66 (2023). https://doi.org/10.1007/s13398-023-01397-8

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  • DOI: https://doi.org/10.1007/s13398-023-01397-8

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