2,089 research outputs found
Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems
The present article presents a summarizing view at differential-algebraic
equations (DAEs) and analyzes how new application fields and corresponding
mathematical models lead to innovations both in theory and in numerical
analysis for this problem class. Recent numerical methods for nonsmooth
dynamical systems subject to unilateral contact and friction illustrate the
topicality of this development.Comment: Preprint of Book Chapte
An Energy-Minimization Finite-Element Approach for the Frank-Oseen Model of Nematic Liquid Crystals: Continuum and Discrete Analysis
This paper outlines an energy-minimization finite-element approach to the
computational modeling of equilibrium configurations for nematic liquid
crystals under free elastic effects. The method targets minimization of the
system free energy based on the Frank-Oseen free-energy model. Solutions to the
intermediate discretized free elastic linearizations are shown to exist
generally and are unique under certain assumptions. This requires proving
continuity, coercivity, and weak coercivity for the accompanying appropriate
bilinear forms within a mixed finite-element framework. Error analysis
demonstrates that the method constitutes a convergent scheme. Numerical
experiments are performed for problems with a range of physical parameters as
well as simple and patterned boundary conditions. The resulting algorithm
accurately handles heterogeneous constant coefficients and effectively resolves
configurations resulting from complicated boundary conditions relevant in
ongoing research.Comment: 31 pages, 3 figures, 3 table
Phase-field approaches to structural topology optimization
The mean compliance minimization in structural topology optimization is solved with the help of a phase field approach. Two steepest descent approaches based on L2- and H-1 gradient flow dynamics are discussed.
The resulting flows are given by Allen-Cahn and Cahn-Hilliard type dynamics coupled to a linear elasticity system. We finally compare numerical results obtained from the two different approaches
Design of of model-based controllers via parametric programming
Imperial Users onl
- …