Computational Multiscale Methods for Linear Heterogeneous Poroelasticity

Finite Element Heterogeneous Multiscale Methods with Near Optimal Computational Complexity

This paper is concerned with a numerical method for multiscale elliptic problems. Using the framework of the Heterogeneous Multiscale Methods (HMM), we propose a micro-macro approache which combines finite element method (FEM) for the macroscopic solver and the pseudospectral method for the micro solver. Unlike the micro-macro methods based on standard FEM proposed so far in HMM we obtain, for ...

Linear Poroelasticity

Mixed Multiscale Methods for Heterogeneous Elliptic Problems

We consider a second order elliptic problem written in mixed form, i.e., as a system of two first order equations. Such problems arise in many contexts, including flow in porous media. The coefficient in the elliptic problem (the permeability of the porous medium) is assumed to be spatially heterogeneous. The emphasis here is on accurate approximation of the solution with respect to the scale o...

Computational poroelasticity – A review

Computational physics has become an essential research and interpretation tool in many fields. Particularly, in reservoir geophysics, ultrasonic and seismic modeling in porous media is used to study the properties of rocks and characterize the seismic response of geological formations. Here, we give a brief overview of the most common numerical methods used to solve the partial differential equ...

Computational multiscale modelling of heterogeneous material layers

A computational homogenization procedure for a material layer that possesses an underlying heterogeneous microstructure is introduced within the framework of finite deformations. The macroscopic material properties of the material layer are obtained from multiscale considerations. At the macro level, the layer is resolved as a cohesive interface situated within a continuum, and its underlying m...