Premium
A Weakly Singular Collocation Boundary Element Formulation for Linear Poroelasticity
Author(s) -
Messner M.,
Schanz M.
Publication year - 2010
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201010274
Subject(s) - mathematics , boundary element method , mathematical analysis , singular boundary method , poromechanics , discretization , biot number , singular integral , integral equation , quadrature (astronomy) , gravitational singularity , boundary value problem , collocation (remote sensing) , collocation method , method of fundamental solutions , nyström method , finite element method , porous medium , differential equation , physics , computer science , ordinary differential equation , mechanics , geotechnical engineering , optics , machine learning , porosity , engineering , thermodynamics
One major problem when discretizing boundary integral equations are the spatial singularities of the appearing integral kernels. For some classical problems, e.g. elastodynamics, this problem has been solved through partial integration yielding at most weakly singular integrals. The aim is to adopt this procedure to the modelling of porous media with boundary elements. This idea is justified by the fact that in saturated linear poroelasticity, Biot's theory couples a linear elastic solid with an acoustic fluid. Therefore, the reduction of the singularities can be achieved by the same techniques as for those problems. Due to the use of the convolution quadrature method, which permits a time domain discretization of boundary integral equations based on the Laplace domain fundamental solution, this is done in Laplace domain. For domains with closed surfaces, a weakly singular representation of the first boundary integral equation is presented. This equation is used for a collocation boundary element formulation involving only the numerical evaluation of weakly singular integrals. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)