Comparison of mixed and isoparametric boundary elements in time domain poroelasticity

A poroelastodynamic Boundary Element (BE) formulation in time domain based on the Convolution Quadrature Method (CQM) is used to model wave propagation phenomena. In the conventional BEM implementation, the same shape functions are applied to all state variables.Motivated by the improvements due to mixed elements in FEM, i.e. the shape function for the pore pressure is chosen one degree lower than for the displacement, such elements have been added to the BEM implementation in both two dimensional (2-d) and three dimensional (3-d) formulations. A study about the influence of the mixed shape functions to the quality of numerical results and the stability of the time-stepping scheme is presented. The mixed elements increase the numerical cost significantly and the results are inconclusive as to whether they improve the CQM based BEM. Therefore, they are only recommended for special cases, in particular the incompressible model in 2-d, where they tend to a significant reduction of the lower stability limit.