Algebraic Multiscale Method for two--dimensional elliptic problems

TL;DR

This paper presents an algebraic multiscale method for 2D elliptic problems using generalized multiscale finite element spaces, dimension reduction, and moment functions to improve basis function construction.

Contribution

It introduces a novel 2D algebraic multiscale method that extends 1D techniques with dimension reduction and moment functions for better basis functions.

Findings

Numerical results demonstrate the effectiveness of the proposed method.

The method achieves accurate approximations for 2D elliptic problems.

It improves upon existing multiscale methods in computational efficiency.

Abstract

We introduce an algebraic multiscale method for two--dimensional problems. The method uses the generalized multiscale finite element method based on the quadrilateral nonconforming finite element spaces. Differently from the one--dimensional algebraic multiscale method, we apply the dimension reduction techniques to construct multiscale basis functions. Also moment functions are considered to impose continuity between local basis functions. Some representative numerical results are presented.