Fractional PDE constrained optimization: An optimize-then-discretize approach with L-BFGS and approximate inverse preconditioning
Fractional PDE constrained optimization: An optimize-then-discretize approach with L-BFGS and approximate inverse preconditioning
In this paper, using an optimize-then-discretize approach, we address the numerical solution of two Fraction Partial Differential Equation constrained optimization problems: the Fractional Advection Dispersion Equation (FADE) and the two-dimensional semilinear Riesz Space Fractional Diffusion equation. Both a theoretical and experimental analysis of the problem is carried out. The algorithmic framework is based on the L-BFGS method coupled with a Krylov subspace solver. A suitable preconditioning strategy by approximate inverses is taken into account. Graphics Processing Unit (GPU) accelerator is used in the construction of the preconditioners. The numerical experiments are performed with benchmarked software/libraries enforcing the reproducibility of the results.
Approximate inverse preconditioners, Constrained optimization, Fractional differential equation
43-57
Cipolla, Stefano
373fdd4b-520f-485c-b36d-f75ce33d4e05
Durastante, Fabio
56118788-83b2-4273-b959-c45f486f86c1
6 September 2017
Cipolla, Stefano
373fdd4b-520f-485c-b36d-f75ce33d4e05
Durastante, Fabio
56118788-83b2-4273-b959-c45f486f86c1
Cipolla, Stefano and Durastante, Fabio
(2017)
Fractional PDE constrained optimization: An optimize-then-discretize approach with L-BFGS and approximate inverse preconditioning.
Applied Numerical Mathematics, 123, .
(doi:10.1016/j.apnum.2017.09.001).
Abstract
In this paper, using an optimize-then-discretize approach, we address the numerical solution of two Fraction Partial Differential Equation constrained optimization problems: the Fractional Advection Dispersion Equation (FADE) and the two-dimensional semilinear Riesz Space Fractional Diffusion equation. Both a theoretical and experimental analysis of the problem is carried out. The algorithmic framework is based on the L-BFGS method coupled with a Krylov subspace solver. A suitable preconditioning strategy by approximate inverses is taken into account. Graphics Processing Unit (GPU) accelerator is used in the construction of the preconditioners. The numerical experiments are performed with benchmarked software/libraries enforcing the reproducibility of the results.
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Published date: 6 September 2017
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© 2017 IMACS
Keywords:
Approximate inverse preconditioners, Constrained optimization, Fractional differential equation
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Local EPrints ID: 485624
URI: http://eprints.soton.ac.uk/id/eprint/485624
ISSN: 0168-9274
PURE UUID: c88bfa44-84e6-45e7-a677-4fe093c41df2
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Date deposited: 12 Dec 2023 17:35
Last modified: 18 Mar 2024 04:17
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Author:
Stefano Cipolla
Author:
Fabio Durastante
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