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A Note on Solving the Generalized Dirichlet to Neumann Map on Irregular Polygons using Generic Factored Approximate Sparse Inverses

E-N.G. Grylonakis1, C.K. Filelis-Papadopoulos1, G.A. Gravvanis1
Department of Electrical and Computer Engineering, School of Engineering, Democritus University of Thrace, University Campus, Kimmeria, GR 67100 Xanthi, Greece.

Computer Modeling in Engineering & Sciences 2015, 109-110(6), 505-517. https://doi.org/10.3970/cmes.2015.109.505

Abstract

A new transform method for solving boundary value problems in two dimensions was proposed by A.S. Fokas, namely the unified transform. This approach seeks a solution to the unknown boundary values by solving a global relation, using the known boundary data. This relation can be used to characterize the Dirichlet to Neumann map. For the numerical solution of the global relation, a collocation-type method was recently introduced. Hence, the considered method is used for solving the 2D Laplace equation in several irregular convex polygons. The linear system, resulting from the collocation-type method, was solved by the Explicit Preconditioned Generalized Minimum Residual restarted method in conjunction with the Modified Generic Factored Approximate Sparse Inverse matrix. Numerical results indicating the applicability of the proposed preconditioning scheme are provided, along with discussions on the implementation details of the method.

Keywords

Laplace Equation, Dirichlet-Neumann map, Global Relation, Collocation, Generic Factored Approximate Sparse Inverses, Preconditioned Generalized Minimum Residual restarted method.

Cite This Article

Grylonakis, E., Filelis-Papadopoulos, C., Gravvanis, G. (2015). A Note on Solving the Generalized Dirichlet to Neumann Map on Irregular Polygons using Generic Factored Approximate Sparse Inverses. CMES-Computer Modeling in Engineering & Sciences, 109-110(6), 505–517.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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