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Applying a Patched Mesh Method to Efficiently Solve a Singularly Perturbed Reaction-Diffusion Problem

In: Modeling, Simulation and Optimization of Complex Processes HPSC 2015

Author

Listed:
  • José Luis Gracia

    (University of Zaragoza)

  • Niall Madden

    (National University of Ireland Galway)

  • Thái Anh Nhan

    (Ohlone College)

Abstract

The solution of linear systems of equations that arise when singularly perturbed partial differential equations are discretized can be difficult: direct solvers scale poorly, but are also known not to be robust with respect to the perturbation parameter, while the design of parameter robust preconditioners is not trivial, primarily due to the specialised layer adapted meshes used for such problems; see MacLachlan and Madden (SIAM J Sci Comput 35:A2225–A2254, 2013). Here we present a multigrid solver strategy that circumvents this problem by using a robust patched mesh method proposed by de Falco and O’Riordan (BAIL 2008—Boundary and Interior Layers vol. 69, pp. 117–127. Springer, Berlin, 2009), as well as permitting parallelization. Numerical results demonstrate the efficiency of the method.

Suggested Citation

  • José Luis Gracia & Niall Madden & Thái Anh Nhan, 2017. "Applying a Patched Mesh Method to Efficiently Solve a Singularly Perturbed Reaction-Diffusion Problem," Springer Books, in: Hans Georg Bock & Hoang Xuan Phu & Rolf Rannacher & Johannes P. Schlöder (ed.), Modeling, Simulation and Optimization of Complex Processes HPSC 2015, pages 41-53, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-67168-0_4
    DOI: 10.1007/978-3-319-67168-0_4
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