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Active Nematodynamics on Curved Surfaces–The Influence of Geometric Forces on Motion Patterns of Topological Defects

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Communications in Computational Physics 2022年第3期31卷 947-965页

作者： Michael Nestler Axel Voigt institut fur wissenschaftliches rechnen TU Dresden01062 DresdenGermany Center for Systems Biology Dresden(CSBD) Pfotenhauerstraße 10801307 DresdenGermany Cluster of Excellence Physics of Life(PoL) 01062 DresdenGermany

We derive and numerically solve a surface active nematodynamics *** validate the numerical approach on a sphere and analyse the influence of hydro-dynamics on the oscillatory motion of topological *** ellipsoidal surfaces the influence of geometric forces on these motion patterns is addressed by taking into ac-count the effects of intrinsic as well as extrinsic curvature *** numerical experiments demonstrate the stronger coupling with geometric properties if extrinsic curvature contributions are present and provide a possibility to tuneflow and defect motion by surface properties.

关键词： Topological active matter defect dynamics hydrodynamic coupling surfacefinite elements

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Geometric Evolution Laws for Thin Crystalline Films: Modeling and Numerics

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Communications in Computational Physics 2009年第8期6卷 433-482页

作者： Bo Li John Lowengrub Andreas Ratz Axel Voigt Department of Mathematics and Center for Theoretical Biological Physics University of California at San DiegoLa JollaCA 92093-0112USA Department of Mathematics University of California at IrvineIrvineCA 92697-3875USA institut fur wissenschaftliches rechnen Technische Universitat Dresden01062 DresdenGermany Department of Physics Technical University of Helsinki02015 EspooFinland.

Geometrical evolution laws are widely used in continuum modeling of surface and interface motion in materials *** this article,we first give a brief review of various kinds of geometrical evolution laws and their variational derivations,with an emphasis on strong *** then survey some of the finite element based numerical methods for simulating the motion of interfaces focusing on the field of thin film *** discuss the finite element method applied to front-tracking,phase-field and level-set *** describe various applications of these geometrical evolution laws to materials science problems,and in particular,the growth and morphologies of thin crystalline films.

关键词： Interface problems geometric evolution laws anisotropy kinetics front tracking level-set phase-field chemical vapor deposition molecular beam epitaxy liquid phase epitaxy electrodeposition

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Modeling and Numerical Solution of a Cancer Therapy Optimal Control Problem

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Applied Mathematics 2018年第8期9卷 985-1004页

作者： Melina-Lorén Kienle Garrido Tim Breitenbach Kurt Chudej Alfio Borzì institut für Mathematik Universit&auml t Würzburg Würzburg Germany Lehrstuhl für wissenschaftliches rechnen Fakult&uuml t für Mathematik Physik und Informatik Universit&auml t Bayreuth Bayreuth Germany

A mathematical optimal-control tumor therapy framework consisting of radio- and anti-angiogenesis control strategies that are included in a tumor growth model is investigated. The governing system, resulting from the combination of two well established models, represents the differential constraint of a non-smooth optimal control problem that aims at reducing the volume of the tumor while keeping the radio- and anti-angiogenesis chemical dosage to a minimum. Existence of optimal solutions is proved and necessary conditions are formulated in terms of the Pontryagin maximum principle. Based on this principle, a so-called sequential quadratic Hamiltonian (SQH) method is discussed and benchmarked with an “interior point optimizer—a mathematical programming language” (IPOPT-AMPL) algorithm. Results of numerical experiments are presented that successfully validate the SQH solution scheme. further, it is shown how to choose the optimisation weights in order to obtain treatment functions that successfully reduce the tumor volume to zero.

关键词： Cancer Radiotherapy Anti-Angiogenesis Sparse Controls Optimal Control Pontryagin’s Maximum Principle SQH Method

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Fast Solvers of Fredholm Optimal Control Problems

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Numerical Mathematics(Theory,Methods and Applications) 2010年第4期3卷 431-448页

作者： Mario Annunziato Alfio Borzi Universita degli Studi di Salerno Dipartimento di Matematica e InformaticaVia Ponte Don Melillo84084 Fisciano(SA)Italia Universita degli Studi del Sannio Dipartimento e Facolta di IngegneriaPalazzo Dell'Aquila Bosco LucarelliCorso Garibaldi 10782100 BeneventoItalia institutfr Mathematik und wissenschaftliches rechnen Karl-Franzens-Universitt GrazHeinrichstr.368010 GrazAustria.

The formulation of optimal control problems governed by Fredholm integral equations of second kind and an efficient computational framework for solving these control problems is presented. Existence and uniqueness of optimal solutions is proved.A collective Gauss-Seidel scheme and a multigrid scheme are discussed. Optimal computational performance of these iterative schemes is proved by local Fourier analysis and demonstrated by results of numerical experiments.

关键词： Optimal control theory Fredholm integral equations of second kind iterative methods

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