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

Resumo

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 [...]