A level set reduced basis approach to parameter estimation

Martin A. Grepl; Karen Veroy

doi:10.1016/j.crma.2011.10.020

A level set reduced basis approach to parameter estimation

Martin A. Grepl, Karen Veroy

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

2 Citations (Scopus)

Abstract

We introduce an efficient level set framework to parameter estimation problems governed by parametrized partial differential equations. The main ingredients are: (i) an "admissible region" approach to parameter estimation; (ii) the certified reduced basis method for efficient and reliable solution of parametrized partial differential equations; and (iii) a parameter-space level set method for construction of the admissible region. The method can handle nonconvex and multiply connected regions. Numerical results for two examples in design and inverse problems illustrate the versatility of the approach.

Original language	English
Pages (from-to)	1229-1232
Number of pages	4
Journal	Comptes Rendus Mathematique
Volume	349
Issue number	23-24
DOIs	https://doi.org/10.1016/j.crma.2011.10.020
Publication status	Published - Dec 2011
Externally published	Yes

Bibliographical note

Funding Information:
We acknowledge A.T. Patera, D. Knezevic, and M. Bachmayr for fruitful discussions. This work was supported by the German Research Foundation through Grant GSC 111 and the Excellence Initiative of the German federal and state governments.

Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.

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10.1016/j.crma.2011.10.020

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title = "A level set reduced basis approach to parameter estimation",

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author = "Grepl, {Martin A.} and Karen Veroy",

note = "Funding Information: We acknowledge A.T. Patera, D. Knezevic, and M. Bachmayr for fruitful discussions. This work was supported by the German Research Foundation through Grant GSC 111 and the Excellence Initiative of the German federal and state governments. Copyright: Copyright 2011 Elsevier B.V., All rights reserved.",

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doi = "10.1016/j.crma.2011.10.020",

language = "English",

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AU - Grepl, Martin A.

AU - Veroy, Karen

N1 - Funding Information: We acknowledge A.T. Patera, D. Knezevic, and M. Bachmayr for fruitful discussions. This work was supported by the German Research Foundation through Grant GSC 111 and the Excellence Initiative of the German federal and state governments. Copyright: Copyright 2011 Elsevier B.V., All rights reserved.

PY - 2011/12

Y1 - 2011/12

N2 - We introduce an efficient level set framework to parameter estimation problems governed by parametrized partial differential equations. The main ingredients are: (i) an "admissible region" approach to parameter estimation; (ii) the certified reduced basis method for efficient and reliable solution of parametrized partial differential equations; and (iii) a parameter-space level set method for construction of the admissible region. The method can handle nonconvex and multiply connected regions. Numerical results for two examples in design and inverse problems illustrate the versatility of the approach.

AB - We introduce an efficient level set framework to parameter estimation problems governed by parametrized partial differential equations. The main ingredients are: (i) an "admissible region" approach to parameter estimation; (ii) the certified reduced basis method for efficient and reliable solution of parametrized partial differential equations; and (iii) a parameter-space level set method for construction of the admissible region. The method can handle nonconvex and multiply connected regions. Numerical results for two examples in design and inverse problems illustrate the versatility of the approach.

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DO - 10.1016/j.crma.2011.10.020

M3 - Article

AN - SCOPUS:83155181396

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SP - 1229

EP - 1232

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 23-24

ER -

A level set reduced basis approach to parameter estimation

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