Iterative Analysis of Pore-Dynamic Models Discretized by Meshless Local Petrov-Galerkin Formulations

This work proposes an iterative procedure to analyse pore-dynamic models discretized by time-domain Meshless Local Petrov-Galerkin formulations. By considering an iterative procedure based on a successive renew of variables, each phase of the coupled problem in focus can be treated separately, uncoupling the governing equations of the model. Thus, smaller and better conditioned systems of equations are obtained, rendering a more attractive methodology. A relaxation parameter is introduced here in order to improve the efficiency of the iterative procedure and an expression to compute optimal values for the relaxation parameter is discussed. Linear and nonlinear models are focused, highlighting that the analysis of the nonlinear relations can be carried out along the iterative steps of the coupled model solution, adding no further computational costs to the analysis. At the end of the paper, numerical examples illustrate the performance and potentialities of the proposed techniques.