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Optimal Control of a Phase‐Field Model Using Proper Orthogonal Decomposition
Author(s) -
Volkwein S.
Publication year - 2001
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/1521-4001(200102)81:2<83::aid-zamm83>3.0.co;2-r
Subject(s) - point of delivery , proper orthogonal decomposition , basis (linear algebra) , mathematics , orthogonal basis , hilbert space , optimal control , minification , finite element method , decomposition , mathematical optimization , field (mathematics) , basis function , phase (matter) , mathematical analysis , geometry , pure mathematics , physics , quantum mechanics , ecology , agronomy , biology , thermodynamics
The proper orthogonal decomposition (POD) is a procedure to determine a reduced basis for a reduced order model. In this article POD is formulated as a minimization problem in a general Hilbert space setting. The POD‐basis functions are given by the solution to the first‐order necessary optimality conditions. In this work POD is utilized to solve optimal control problems for a phase‐field model. The numerical results are compared with finite element solutions.