A second-order shape optimization algorithm for solving the exterior Bernoulli free boundary problem using a new boundary cost functional

The exterior Bernoulli problem is rephrased into a shape optimization problem using a new type of objective function called the Dirichlet-data-gap cost function which measures the L 2 -distance between the Dirichlet data of two state functions. The first-order shape derivative of the cost function i...

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Vydáno v:Computational optimization and applications Ročník 77; číslo 1; s. 251 - 305
Hlavní autoři: Rabago, Julius Fergy T., Azegami, Hideyuki
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.09.2020
Springer Nature B.V
Témata:
Algorithms
Convex and Discrete Geometry
Cost function
Dirichlet problem
Free boundaries
Management Science
Mathematics
Mathematics and Statistics
Operations Research
Operations Research/Decision Theory
Optimization
Shape optimization
Statistics
Free boundary
Shape derivative
Domain perturbation
Bernoulli problem
Shape optimization
ISSN:0926-6003, 1573-2894
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Shrnutí:The exterior Bernoulli problem is rephrased into a shape optimization problem using a new type of objective function called the Dirichlet-data-gap cost function which measures the L 2 -distance between the Dirichlet data of two state functions. The first-order shape derivative of the cost function is explicitly determined via the chain rule approach. Using the same technique, the second-order shape derivative of the cost function at the solution of the free boundary problem is also computed. The gradient and Hessian informations are then used to formulate an efficient second-order gradient-based descent algorithm to numerically solve the minimization problem. The feasibility of the proposed method is illustrated through various numerical examples.
Bibliografie:ObjectType-Article-1
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ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-020-00199-7