Solution of the generalized eigenvalue problem using overlapping finite elements

doi:10.1016/j.advengsoft.2022.103241

Solution of the generalized eigenvalue problem using overlapping finite elements

2022-11-01

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Klaus‐Jürgen Bathe *

DOI：10.1016/j.advengsoft.2022.103241

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Abstract

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Our objective in this paper is to present the use of the overlapping finite elements and the AMORE scheme for the solution of the generalized eigenvalue problem of solids and structures - to calculate frequencies and mode shapes - and the solution of dynamic response by mode superposition. For the solution of eigenvalues and vectors, we use the enriched subspace iteration scheme. We focus on the differences in use that arise when employing the overlapping finite elements versus traditional finite elements and the convergence of the eigenvalues and vectors as the mesh is refined. Our studies show that the use of the overlapping finite elements for frequency and dynamic solutions can be quite effective.

Keywords:

Overlapping finite elements and AMORE

Generalized eigenvalue problem

Frequencies and mode shapes

Mode superposition

Accuracy and convergence

Computational effort

Solution of the generalized eigenvalue problem using overlapping finite elements

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