Related papers: A Multiscale Method for Porous Microstructures
We consider the coupled system of equations that describe flow in fractured porous media. To describe such types of problems, multicontinuum and multiscale approaches are used. Because in multicontinuum models, the permeability of each…
In this work, we present an efficient way to decouple the multicontinuum problems. To construct decoupled schemes, we propose Implicit-Explicit time approximation in general form and study them for the fine-scale and coarse-scale space…
We show that in the variational multiscale framework, the weak enforcement of essential boundary conditions via Nitsche's method corresponds directly to a particular choice of projection operator. The consistency, symmetry and penalty terms…
In many models used in engineering and science, material properties are uncertain or spatially varying. For example, in geophysics, and porous media flow in particular, the uncertain permeability of the material is modelled as a random…
This paper is concerned with the approximation of continuously differentiable functions with high-dimensional input by a composition of two functions: a feature map that extracts few features from the input space, and a profile function…
Given a set of inelastic material models, a microstructure, a macroscopic structural geometry, and a set of boundary conditions, one can in principle always solve the governing equations to determine the system's mechanical response.…
We use a discrete multiscale analysis to study the asymptotic integrability of differential-difference equations. In particular, we show that multiscale perturbation techniques provide an analytic tool to derive necessary integrability…
We consider a strongly heterogeneous medium saturated by an incompressible viscous fluid as it appears in geomechanical modeling. This poroelasticity problem suffers from rapidly oscillating material parameters, which calls for a thorough…
We consider the numerical solution of Poisson's equation on structured grids using geometric multigrid with nonstandard coarse grids and coarse level operators. We are motivated by the problem of developing high-order accurate numerical…
Iterative multiscale methods for electronic structure calculations offer several advantages for large-scale problems. Here we examine a nonlinear full approximation scheme (FAS) multigrid method for solving fixed potential and…
The effective, fast transport of matter through porous media is often characterized by complex dispersion effects. To describe in mathematical terms such situations, instead of a simple macroscopic equation (as in the classical Darcy's…
Traditional two level upscaling techniques suffer from a high offline cost when the coarse grid size is much larger than the fine grid size. Thus, multilevel methods are desirable for problems with complex heterogeneities and high contrast.…
We present a multivariate Gaussian process regression approach for parameter field reconstruction based on the field's measurements collected at two different scales, the coarse and fine scales. The proposed approach treats the parameter…
We present a geometric multilevel optimization approach that smoothly incorporates box constraints. Given a box constrained optimization problem, we consider a hierarchy of models with varying discretization levels. Finer models are…
We consider a non-stationary Stokes-Nernst-Planck-Poisson system posed in perforated domains. Our aim is to justify rigorously the homogenization limit for the upscaled system derived by means of two-scale convergence in \cite{RMK12}. In…
An approximative method for solving the Bloch-Torrey equation in general porous media is presented. The method expand the boundaries defining the porous media using electrostatic charges. As a result the eigenvalue problem of the Laplace…
In this work, we propose a generalized multiscale inversion algorithm for heterogeneous problems that aims at solving an inverse problem on a computational coarse grid. Previous inversion techniques for multiscale problems seek a…
In this paper, we use the Poincare separation theorem for estimating the eigenvalues of the fine grid. We propose a randomized version of the algorithm where several different coarse grids are constructed thus leading to more comprehensive…
In this paper, we consider the numerical solution of poroelasticity problems that are of Biot type and develop a general algorithm for solving coupled systems. We discuss the challenges associated with mechanics and flow problems in…
We develop a mixed finite element domain decomposition method on non-matching grids for the Biot system of poroelasticity. A displacement-pressure vector mortar function is introduced on the interfaces and utilized as a Lagrange multiplier…