Descriptor: "VARIABLE-METRIC METHODS" - Searchworks@Jio Institute Digital Library Search Results

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14 results on '"VARIABLE-METRIC METHODS"'

1. Numerical infinitesimals in a variable metric method for convex nonsmooth optimization.

Author: Gaudioso, Manlio, Giallombardo, Giovanni, and Mukhametzhanov, Marat
Subjects: *INFINITESIMAL geometry, *MATHEMATICAL variables, *NONSMOOTH optimization, *CONVEX domains, *MATHEMATICAL optimization
Abstract: The objective of the paper is to evaluate the impact of the infinity computing paradigm on practical solution of nonsmooth unconstrained optimization problems, where the objective function is assumed to be convex and not necessarily differentiable. For such family of problems, the occurrence of discontinuities in the derivatives may result in failures of the algorithms suited for smooth problems. We focus on a family of nonsmooth optimization methods based on a variable metric approach, and we use the infinity computing techniques for numerically dealing with some quantities which can assume values arbitrarily small or large, as a consequence of nonsmoothness. In particular we consider the case, treated in the literature, where the metric is defined via a diagonal matrix with positive entries. We provide the computational results of our implementation on a set of benchmark test-problems from scientific literature. [ABSTRACT FROM AUTHOR]
Published: 2018
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2. Partitioned Simulation of Fluid-Structure Interaction

Author: Joris Degroote
Subjects: Mathematical optimization, Technology and Engineering, VARIABLE-METRIC METHODS, Fictitious domain method, NAVIER-STOKES EQUATIONS, FREE-SURFACE FLOWS, Coupling algorithm, Parallel computing, FINITE-ELEMENT-METHOD, Black box, Fluid-structure interaction, Convergence (routing), Fluid–structure interaction, Navier–Stokes equations, Mathematics, Quasi-Newton, Applied Mathematics, UNSTRUCTURED DYNAMIC MESHES, Immersed boundary method, Solver, Finite element method, IMMERSED BOUNDARY METHOD, Computer Science Applications, STRUCTURE INTERACTION COMPUTATIONS, ORIENTED ERROR ESTIMATION, FICTITIOUS DOMAIN METHOD, STRUCTURE INTERACTION ALGORITHM, Partitioned simulation
Abstract: In this review article, the focus is on partitioned simulation techniques for strongly coupled fluid-structure interaction problems, especially on techniques which use at least one of the solvers as a black box. First, a number of analyses are reviewed to explain why Gauss-Seidel coupling iterations converge slowly or not at all for fluid-structure interaction problems with strong coupling. This provides the theoretical basis for the fast convergence of quasi-Newton and multi-level techniques. Second, several partitioned techniques that couple two black-box solvers are compared with respect to implementation and performance. Furthermore, performance comparisons between partitioned and monolithic techniques are examined. Subsequently, two similar techniques to couple a black-box solver with an accessible solver are analyzed. In addition, several other techniques for fluid-structure interaction simulations are studied and various methods to take into account deforming fluid domains are discussed.
Published: 2013
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