Finite-Difference Analysis for the Linear Thermoporoelasticity Problem and Its Numerical Resolution by Multigrid Methods

Abstract

This paper deals with the numerical solution of a two-dimensional thermoporoelasticity problem using a finite-difference scheme. Two issues are discussed: stability and convergence in discrete energy norms of the finite-difference scheme are proved, and secondly, a distributive smoother is examined in order to find a robust and efficient multigrid solver for the corresponding system of equations. Numerical experiments confirm the convergence properties of the proposed scheme, as well as fast multigrid convergence. © 2012 Copyright Vilnius Gediminas Technical University.