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

Authors

José Luis Gracia
Niall Madden
Thái Ahn Nhan, Santa Clara UniversityFollow

Document Type

Conference Proceeding

Publication Date

11-2017

Publisher

Springer

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.

Chapter of

Modeling, Simulation and Optimization of Complex Processes HPSC 2015

Editor

Hans Georg Bock
Hoang Xuan Phu
Rolf Rannacher
Johannes P. Schlöder

Comments

Proceedings of the Sixth International Conference on High Performance Scientific Computing, March 16-20, 2015, Hanoi, Vietnam

Recommended Citation

Gracia, J. L., Madden, N., & Nhan, T. A. (2017). Applying a Patched Mesh Method to Efficiently Solve a Singularly Perturbed Reaction-Diffusion Problem. In H. G. Bock, H. X. Phu, R. Rannacher, & J. P. Schlöder (Eds.), Modeling, Simulation and Optimization of Complex Processes HPSC 2015 (pp. 41–53). Springer International Publishing. https://doi.org/10.1007/978-3-319-67168-0_4