Artículo
Numerical Maximization of the p-Laplacian Energy of a Two-Phase Material
Autor/es | Casado Díaz, Juan
Conca Rosende, Carlos Vásques Varas, Donato |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 2021-01-01 |
Fecha de depósito | 2022-12-09 |
Publicado en |
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Resumen | For a diffusion problem modeled by thep-Laplacian operator, we are interested inobtaining numerically the two-phase material which maximizes the internal energy. We assume thatthe amount of the best material is limited. ... For a diffusion problem modeled by thep-Laplacian operator, we are interested inobtaining numerically the two-phase material which maximizes the internal energy. We assume thatthe amount of the best material is limited. In the framework of a relaxed formulation, we presenttwo algorithms, a feasible directions method and an alternating minimization method. We show theconvergence for both of them, and we provide an estimate for the error. Since forp >2 both methodsare only well-defined for a finite-dimensional approximation, we also study the difference betweensolving the finite-dimensional and the infinite-dimensional problems. Although the error bounds forboth methods are similar, numerical experiments show that the alternating minimization methodworks better than the feasible directions one. |
Cita | Casado Díaz, J., Conca, C. y Vásques Varas, D. (2021). Numerical Maximization of the p-Laplacian Energy of a Two-Phase Material. SIAM journal on numerical analysis, 59 (6), 3077-3097. https://doi.org/10.1137/20M1353563. |
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