Vector Extrapolation Methods Applied To Geometric Multigrid Solvers For Isogeometric Analysis

TL;DR

This paper introduces a novel approach combining vector extrapolation methods with geometric multigrid schemes to efficiently solve large sparse linear systems in isogeometric analysis, significantly accelerating convergence.

Contribution

It develops and tests polynomial extrapolation techniques integrated with multigrid methods specifically for isogeometric analysis, enhancing solver efficiency.

Findings

Polynomial extrapolation speeds up multigrid convergence

Numerical tests confirm improved solver performance

Method reduces computational time for large systems

Abstract

In the present work, we study how to develop an efficient solver for the fast resolution of large and sparse linear systems that occur while discretizing elliptic partial differential equations using isogeometric analysis. Our new approach combines vector extrapolation methods with geometric multigrid schemes. Using polynomial-type extrapolation methods to speed up the multigrid iterations is our main focus. Several numerical tests are given to demonstrate the efficiency of these polynomial extrapolation methods in improving multigrid solvers in the context of isogeometric analysis.