Publication

An optimization-based multiscale coupling method

2015
Journal Articles

Abstract

An optimization based algorithm is proposed for solving elliptic problems with highly oscillatory coecients that do not exhibit scale separation in a subregion of the physical domain. The given method, written as a constrained minimization problem couples a numerical homogenization method in the subregion of the physical domain with scale separation with a ne scale solver in subregions without scale separation. The unknown boundary conditions of both problems in the overlap region are determined by minimizing the discrepancy of the corresponding solutions in this overlap.

Official source

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

2015
Journal Articles

Abstract

Official source

Related concepts (25)

Dirichlet boundary condition

In the mathematical study of differential equations, the Dirichlet (or first-type) boundary condition is a type of boundary condition, named after Peter Gustav Lejeune Dirichlet (1805–1859). When imposed on an ordinary or a partial differential equation, it specifies the values that a solution needs to take along the boundary of the domain. In finite element method (FEM) analysis, essential or Dirichlet boundary condition is defined by weighted-integral form of a differential equation.

Euler method

In mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who first proposed it in his book Institutionum calculi integralis (published 1768–1870).

Iterative method

In computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones. A specific implementation with termination criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS, is an algorithm of the iterative method.

Related publications (2)

An optimization-based multiscale coupling method

Chat with Graph Search

Daylight illuminant retrieval using redundant image elements

Direct electrothermal atomic absorption spectrometric determination of lead in wine