Reduced basis approximation of parametric eigenvalue problems in presence of clusters and intersections

Daniele Boffi; Abdul Halim; Gopal Priyadarshi

doi:10.1007/s40314-024-02917-x

Reduced basis approximation of parametric eigenvalue problems in presence of clusters and intersections

Daniele Boffi^*, Abdul Halim, Gopal Priyadarshi

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In this paper we discuss reduced order models for the approximation of parametric eigenvalue problems. In particular, we are interested in the presence of intersections or clusters of eigenvalues. The singularities originating by these phenomena make it hard a straightforward generalization of well known strategies normally used for standards PDEs.

Original language	English (US)
Article number	443
Journal	Computational and Applied Mathematics
Volume	43
Issue number	8
DOIs	https://doi.org/10.1007/s40314-024-02917-x
State	Published - Dec 2024

Keywords

35P15
65F55
65J15
65N25
Finite element method
Parametric eigenvalue problem
Reduced order method
Singular value decomposition
Snapshot matrix

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1007/s40314-024-02917-x

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title = "Reduced basis approximation of parametric eigenvalue problems in presence of clusters and intersections",

abstract = "In this paper we discuss reduced order models for the approximation of parametric eigenvalue problems. In particular, we are interested in the presence of intersections or clusters of eigenvalues. The singularities originating by these phenomena make it hard a straightforward generalization of well known strategies normally used for standards PDEs.",

keywords = "35P15, 65F55, 65J15, 65N25, Finite element method, Parametric eigenvalue problem, Reduced order method, Singular value decomposition, Snapshot matrix",

author = "Daniele Boffi and Abdul Halim and Gopal Priyadarshi",

note = "Publisher Copyright: {\textcopyright} The Author(s) under exclusive licence to Sociedade Brasileira de Matem{\'a}tica Aplicada e Computacional 2024.",

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doi = "10.1007/s40314-024-02917-x",

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T1 - Reduced basis approximation of parametric eigenvalue problems in presence of clusters and intersections

AU - Boffi, Daniele

AU - Halim, Abdul

AU - Priyadarshi, Gopal

N1 - Publisher Copyright: © The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional 2024.

PY - 2024/12

Y1 - 2024/12

N2 - In this paper we discuss reduced order models for the approximation of parametric eigenvalue problems. In particular, we are interested in the presence of intersections or clusters of eigenvalues. The singularities originating by these phenomena make it hard a straightforward generalization of well known strategies normally used for standards PDEs.

AB - In this paper we discuss reduced order models for the approximation of parametric eigenvalue problems. In particular, we are interested in the presence of intersections or clusters of eigenvalues. The singularities originating by these phenomena make it hard a straightforward generalization of well known strategies normally used for standards PDEs.

KW - 35P15

KW - 65F55

KW - 65J15

KW - 65N25

KW - Finite element method

KW - Parametric eigenvalue problem

KW - Reduced order method

KW - Singular value decomposition

KW - Snapshot matrix

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U2 - 10.1007/s40314-024-02917-x

DO - 10.1007/s40314-024-02917-x

M3 - Article

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JO - Computational and Applied Mathematics

JF - Computational and Applied Mathematics

IS - 8

M1 - 443

ER -

Reduced basis approximation of parametric eigenvalue problems in presence of clusters and intersections

Abstract

Keywords

ASJC Scopus subject areas

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