Adaptive SQP Method for Shape Optimization

P. Morin (), R. H. Nochetto (), M. S. Pauletti () and M. Verani ()
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P. Morin: Universidad Nacional del Litoral, CONICET, Instituto de Matemática Aplicada del Litoral
R. H. Nochetto: University of Maryland, Department of Mathematics and Institute for Physical Science and Technology
M. S. Pauletti: University of Maryland, Department of Mathematics
M. Verani: Politecnico di Milano, MOX – Dipartimento di Matematica “F. Brioschi”

A chapter in Numerical Mathematics and Advanced Applications 2009, 2010, pp 663-673 from Springer

Abstract: Abstract We examine shape optimization problems in the context of inexact sequential quadratic programming. Inexactness is a consequence of using adaptive finite element methods (AFEM) to approximate the state equation, update the boundary, and compute the geometric functional. We present a novel algorithm that uses a dynamic tolerance and equidistributes the errors due to shape optimization and discretization, thereby leading to coarse resolution in the early stages and fine resolution upon convergence. We discuss the ability of the algorithm to detect whether or not geometric singularities such as corners are genuine to the problem or simply due to lack of resolution – a new paradigm in adaptivity.

Keywords: Shape Optimization; Sequential Quadratic Programming; Geometric Error; Partial Differential Equation; Posteriori Error Estimator (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/978-3-642-11795-4_71

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