Algebraic Multiscale Method for one--dimensional elliptic problems

TL;DR

This paper introduces an algebraic multiscale method for one-dimensional elliptic problems that constructs a macro-scale system from a micro-scale matrix, enabling cheaper computations while maintaining accuracy.

Contribution

It presents a novel algebraic multiscale approach based on the generalized multiscale finite element method for efficient one-dimensional elliptic problem solving.

Findings

Macro-scale system reduces computational cost

Method maintains accuracy of micro-scale solutions

Numerical results validate effectiveness

Abstract

In this paper we propose an idea of constructing a macro--scale matrix system given a micro--scale matrix linear system. Then the macro--scale system is solved at cheaper computing costs. The method uses the idea of the generalized multiscale finite element method based. Some numerical results are presented.