78 citations · 95 across the 7 of their papers we have counts for
10 papers
Preconditioning Markov Chain Monte Carlo Method for Geomechanical Subsidence using multiscale method and machine learning technique
Maria Vasilyeva, Aleksei Tyrylgin, Donald L. Brown +1
In this paper, we consider the numerical solution of the poroelasticity problem with stochastic properties. We present a Two-stage Markov Chain Monte Carlo method for geomechanical…
Upscaling Singular Sources in Weighted Sobolev Spaces by Sub-Grid Corrections
Donald L. Brown, Joscha Gedicke
In this paper, we develop a numerical multiscale method to solve elliptic boundary value problems with heterogeneous diffusion coefficients and with singular source terms. When the…
Numerical Homogenization of Heterogeneous Fractional Laplacians
Donald L. Brown, Joscha Gedicke, Daniel Peterseim
In this paper, we develop a numerical multiscale method to solve the fractional Laplacian with a heterogeneous diffusion coefficient. When the coefficient is heterogeneous, this ad…
Multiscale Sub-grid Correction Method for Time-Harmonic High-Frequency Elastodynamics with Wavenumber Explicit Bounds
Donald L. Brown, Dietmar Gallistl
The simulation of the elastodynamics equations at high-frequency suffers from the well known pollution effect. We present a Petrov--Galerkin multiscale sub-grid correction method t…
Multiscale Petrov-Galerkin Method for High-Frequency Heterogeneous Helmholtz Equations
Donald L. Brown, Dietmar Gallistl, Daniel Peterseim
This paper presents a multiscale Petrov-Galerkin finite element method for time-harmonic acoustic scattering problems with heterogeneous coefficients in the high-frequency regime.…
A Generalized Multiscale Finite Element Method for Poroelasticity Problems II: Nonlinear Coupling
Donald L. Brown, Maria Vasilyeva
In this paper, we consider the numerical solution of some nonlinear poroelasticity problems that are of Biot type and develop a general algorithm for solving nonlinear coupled syst…
A Generalized Multiscale Finite Element Method for Poroelasticity Problems I: Linear Problems
Donald L. Brown, Maria Vasilyeva
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 chall…
A Multiscale Method for Porous Microstructures
Donald L. Brown, Daniel Peterseim
In this paper we develop a multiscale method to solve problems in complicated porous microstructures with Neumann boundary conditions. By using a coarse-grid quasi-interpolation op…
An energy-stable convex splitting for the phase-field crystal equation
Philippe Vignal, Lisandro Dalcin, Donald L. Brown +2
The phase-field crystal equation, a parabolic, sixth-order and nonlinear partial differential equation, has generated considerable interest as a possible solution to problems arisi…
Upscaled Lattice Boltzmann Method for Simulations of Flows in Heterogeneous Porous Media
Jun Li, Donald Brown
A upscaled lattice Boltzmann method (LBM) for flow simulations in heterogeneous porous media, at both pore and Darcy scales, is proposed in this paper. In the micro-scale simulatio…