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A simple and efficient scheme for phase field crystal simulation

Matt ElseyBenedikt Wirth — 2013

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We propose an unconditionally stable semi-implicit time discretization of the phase field crystal evolution. It is based on splitting the underlying energy into convex and concave parts and then performing H gradient descent steps implicitly for the former and explicitly for the latter. The splitting is effected in such a way that the resulting equations are linear in each time step and allow an extremely simple implementation and efficient solution. We provide the associated stability and error...

A phase-field model for compliance shape optimization in nonlinear elasticity

Patrick PenzlerMartin RumpfBenedikt Wirth — 2012

ESAIM: Control, Optimisation and Calculus of Variations

Shape optimization of mechanical devices is investigated in the context of large, geometrically strongly nonlinear deformations and nonlinear hyperelastic constitutive laws. A weighted sum of the structure compliance, its weight, and its surface area are minimized. The resulting nonlinear elastic optimization problem differs significantly from classical shape optimization in linearized elasticity. Indeed, there exist different definitions for the compliance: the change in potential energy of the...

A phase-field model for compliance shape optimization in nonlinear elasticity

Patrick PenzlerMartin RumpfBenedikt Wirth — 2012

ESAIM: Control, Optimisation and Calculus of Variations

Shape optimization of mechanical devices is investigated in the context of large, geometrically strongly nonlinear deformations and nonlinear hyperelastic constitutive laws. A weighted sum of the structure compliance, its weight, and its surface area are minimized. The resulting nonlinear elastic optimization problem differs significantly from classical shape optimization in linearized elasticity. Indeed, there exist different definitions for the compliance: the change in potential energy of the...

A phase-field model for compliance shape optimization in nonlinear elasticity

Patrick PenzlerMartin RumpfBenedikt Wirth — 2012

ESAIM: Control, Optimisation and Calculus of Variations

Shape optimization of mechanical devices is investigated in the context of large, geometrically strongly nonlinear deformations and nonlinear hyperelastic constitutive laws. A weighted sum of the structure compliance, its weight, and its surface area are minimized. The resulting nonlinear elastic optimization problem differs significantly from classical shape optimization in linearized elasticity. Indeed, there exist different definitions for the compliance: the change in potential energy of the...

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