Browsing by Author "Styles, Vanessa"
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- ItemEmerging Developments in Interfaces and Free Boundaries(Zürich : EMS Publ. House, 2017) Giga, Yoshikazu; Hinze, Michael; Styles, VanessaThe field of the mathematical and numerical analysis of systems of nonlinear partial differential equations involving interfaces and free boundaries is a well established and flourishing area of research. This workshop focused on recent developments and emerging new themes. By bringing together experts in these fields we achieved progress in open questions and developed novel research directions in mathematics related to interfaces and free boundaries. This interdisciplinary workshop brought together researchers from distinct mathematical fields such as analysis, computation, optimisation and modelling to discuss emerging challenges.
- ItemInterfaces and Free Boundaries: Analysis, Control and Simulation(Zürich : EMS Publ. House, 2013) Giga, Yoshikazu; Hinze, Michael; Styles, VanessaThe field of mathematical and numerical analysis of systems of nonlinear partial differential equations involving interfaces and free boundaries is a flourishing area of research. Many such systems arise from mathematical models in material science, fluid dynamics and biology, for example phase separation in alloys, epitaxial growth, dynamics of multiphase fluids, evolution of cell membranes and in industrial processes such as crystal growth. The governing equations for the dynamics of the interfaces in many of these applications involve surface tension expressed in terms of the mean curvature and a driving force. Here the forcing terms depend on variables that are solutions of additional partial differential equations which hold either on the interface itself or in the surrounding bulk regions. Often in applications of these mathematical models, suitable performance indices and appropriate control actions have to be specified. Mathematically this leads to optimization problems with partial differential equation constraints including free boundaries. Because of the maturity of the field of computational free boundary problems it is now timely to consider such control problems. In order to carry out design, control and simulation of such problems interaction is required between distinct mathematical fields such as analysis, modeling, computation and optimization. By bringing together leading experts and young researchers from these separate fields we intended to develop novel research directions in applied and computational mathematics. The aim of the workshop here was to focus on emerging new themes and developments in these fields and to establish and extend links between them.
- ItemMini-Workshop: Control of Free Boundaries(Zürich : EMS Publ. House, 2007) Hinze, Michael; Styles, VanessaThe field of the mathematical and numerical analysis of systems of nonlinear pdes involving interfaces and free boundaries is a burgeoning area of research. Many such systems arise from mathematical models in material science and fluid dynamics such as phase separation in alloys, crystal growth, dynamics of multiphase fluids and epitaxial growth. In applications of these mathematical models, suitable performance indices and appropriate
- ItemMulti-material phase field approach to structural topology optimization(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Blank, Luise; Farshbaf-Shaker, M. Hassan; Garcke, Harald; Rupprecht, Christoph; Styles, VanessaMulti-material structural topology and shape optimization problems are formulated within a phase field approach. First-order conditions are stated and the relation of the necessary conditions to classical shape derivatives are discussed. An efficient numerical method based on an H1-gradient projection method is introduced and finally several numerical results demonstrate the applicability of the approach.
- ItemNew Directions in Simulation, Control and Analysis for Interfaces and Free Boundaries(Zürich : EMS Publ. House, 2010) Giga, Yoshikazu; Hinze, Michael; Styles, VanessaThe field of mathematical and numerical analysis of systems of nonlinear partial differential equations involving interfaces and free boundaries is a flourishing area of research. Many such systems arise from mathematical models in material science, fluid dynamics and biology, for example phase separation in alloys, epitaxial growth, dynamics of multiphase fluids, evolution of cell membranes and in industrial processes such as crystal growth. The governing equations for the dynamics of the interfaces in many of these applications involve surface tension expressed in terms of the mean curvature and a driving force. Here the forcing terms depend on variables that are solutions of additional partial differential equations which hold either on the interface itself or in the surrounding bulk regions. Often in applications of these mathematical models, suitable performance indices and appropriate control actions have to be specified. Mathematically this leads to optimization problems with partial differential equation constraints including free boundaries. Because of the maturity of the field of computational free boundary problems it is now timely to consider such control problems.
- ItemRelating phase field and sharp interface approaches to structural topology optimization(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Blank, Luise; Farshbaf-Shaker, M. Hassan; Garcke, Harald; Styles, VanessaA phase field approach for structural topology optimization which allows for topology changes and multiple materials is analyzed. First order optimality conditions are rigorously derived and it is shown via formally matched asymptotic expansions that these conditions converge to classical first order conditions obtained in the context of shape calculus. We also discuss how to deal with triple junctions where e.g. two materials and the void meet. Finally, we present several numerical results for mean compliance problems and a cost involving the least square error to a target displacement.