A Nonnested Augmented Subspace Method for Eigenvalue Problems with Curved Interfaces

TL;DR

This paper introduces a nonnested augmented subspace algorithm for eigenvalue problems with curved interfaces, enabling efficient solutions by transforming the problem into linear equations and small eigenproblems, supported by theoretical analysis and numerical tests.

Contribution

It proposes a novel nonnested augmented subspace method and multilevel correction technique for eigenvalue problems with curved interfaces, improving computational efficiency.

Findings

The method reduces eigenproblem solving to linear equations and small eigenproblems.

Theoretical analysis confirms the algorithm's convergence and efficiency.

Numerical experiments demonstrate the method's practical effectiveness.

Abstract

In this paper, we present a nonnested augmented subspace algorithm and its multilevel correction method for solving eigenvalue problems with curved interfaces. The augmented subspace algorithm and the corresponding multilevel correction method are designed based on a coarse finite element space which is not the subset of the finer finite element space. The nonnested augmented subspace method can transform the eigenvalue problem solving on the finest mesh to the solving linear equation on the same mesh and small scale eigenvalue problem on the low dimensional augmented subspace. The corresponding theoretical analysis and numerical experiments are provided to demonstrate the efficiency of the proposed algorithms.