Mimetic Operator Discretization 1D: Exploration of classical iterative methods and preconditioners

Authors

  • Gustavo E. Espínola
  • Juan C. Cabral
  • Christian E. Schaerer

Abstract

This work performs experiments for the numerical resolution of the one-dimensional Poisson equation with Robin boundary conditions, using the second-order mimetic discretization method, based on the 1D Castillo-Grone mimetic operator [1]. Consider the following equation on a uniform grid, ∇2 u(x) = f (x) on [0, 1] (1) subject to Robin boundary conditions αf (0) − βf ′ (0) = −1; αf (1) + βf ′ (1) = 0, where λ2 eλx λ eλ − 1 f (x) = , α = −e , β = , λ = −1. eλx − 1 λ [...]

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Author Biographies

Gustavo E. Espínola

Polytechnic School, National University of Asuncion, San Lorenzo, Paraguay

Juan C. Cabral

Polytechnic School, National University of Asuncion, San Lorenzo, Paraguay

Christian E. Schaerer

Polytechnic School, National University of Asuncion, San Lorenzo, Paraguay

References

José E Castillo and Guillermo F Miranda. Mimetic discretization methods. CRC Press, 2013.

Juan C Cabral, Christian E Schaerer, and Amit Bhaya. “Improving GMRES (m) using an adaptive switching controller”. In: Numerical Linear Algebra with Applications 27.5 (2020), e2305.

FF Hernández, JE Castillo, and GA Larrazábal. “Large sparse linear systems arising from mimetic discretization”. In: Computers & Mathematics with Applications 53.1 (2007), pp. 1–11.

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Published

2023-12-18