Numerical Homogenization of Elliptic Multiscale Problems by Subspace Decomposition
نویسندگان
چکیده
Numerical homogenization tries to approximate solutions of elliptic partial differential equations with strongly oscillating coefficients by the solution of localized problems over small subregions. We develop and analyze a rapidly convergent iterative method for numerical homogenization that shares this feature with existing approaches and is modeled after the Schwarz method. The method is highly parallelizable and of lower computational complexity than comparable methods that as ours do not make explicit or implicit use of a scale separation.
منابع مشابه
On Wavelet-Based Numerical Homogenization
Recently, a wavelet-based method was introduced for the systematic derivation of subgrid scale models in the numerical solution of partial differential equations. Starting from a discretization of the multiscale differential operator, the discrete operator is represented in a wavelet space and projected onto a coarser subspace. The coarse (homogenized) operator is then replaced by a sparse appr...
متن کاملMixed 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...
متن کاملAn Analysis of a Class of Variational Multiscale Methods Based on Subspace Decomposition
Numerical homogenization tries to approximate the solutions of elliptic partial differential equations with strongly oscillating coefficients by functions from modified finite element spaces. We present a class of such methods that are closely related to the methods that have recently been proposed by Målqvist and Peterseim [Math. Comp. 83, 2014]. Like these methods, the new methods do not make...
متن کاملA Multiscale HDG Method for Second Order Elliptic Equations. Part I. Polynomial and Homogenization-Based Multiscale Spaces
We introduce a finite element method for numerical upscaling of second order elliptic equations with highly heterogeneous coefficients. The method is based on a mixed formulation of the problem and the concepts of the domain decomposition and the hybrid discontinuous Galerkin methods. The method utilizes three different scales: (1) the scale of the partition of the domain of the problem, (2) th...
متن کاملMultiscale mortar mixed methods for heterogeneous elliptic problems
Consider solving a second order elliptic problem when the elliptic coefficient is highly heterogeneous. Generally, a numerical method either uses a very fine computational mesh to resolve the heterogeneities and therefore becomes computationally inefficient, or it performs efficiently on a coarse mesh but gives inaccurate results. Standard nonoverlapping domain decomposition using mortar spaces...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Multiscale Modeling & Simulation
دوره 14 شماره
صفحات -
تاریخ انتشار 2016