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View all- Casado-díaz J(2022)The Maximization of the First Eigenvalue for a Two-Phase MaterialApplied Mathematics and Optimization10.1007/s00245-022-09825-886:1Online publication date: 7-Jun-2022
Numerical Maximization of the p-Laplacian Energy of a Two-Phase Material
Pages 3077 - 3097
Abstract
For a diffusion problem modeled by the $p$-Laplacian operator, we are interested in obtaining numerically the two-phase material which maximizes the internal energy. We assume that the amount of the best material is limited. In the framework of a relaxed formulation, we present two algorithms, a feasible directions method and an alternating minimization method. We show the convergence for both of them, and we provide an estimate for the error. Since for $p>2$ both methods are only well-defined for a finite-dimensional approximation, we also study the difference between solving the finite-dimensional and the infinite-dimensional problems. Although the error bounds for both methods are similar, numerical experiments show that the alternating minimization method works better than the feasible directions one.
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Published: 01 January 2021
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View all- Casado-díaz J(2022)The Maximization of the First Eigenvalue for a Two-Phase MaterialApplied Mathematics and Optimization10.1007/s00245-022-09825-886:1Online publication date: 7-Jun-2022