P. J. Herbert

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20242026

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math.OC2026

Combining diffuse and sharp interface methods in shape optimisation

Philip J. Herbert, Michael Hinze, Christian Kahle

We develop a concept for the numerical treatment of shape optimization problems based on the combination of phase field and sharp interface methods. On the one hand, phase field me…

math.OC2026

Global convergence of $W^{1, \infty}$ -steepest descent for PDE constrained shape optimisation with semilinear elliptic equations in function space

Klaus Deckelnick, Philip J. Herbert, Michael Hinze

We prove global convergence in function space for the steepest descent method in shape optimisation with semilinear elliptic partial differential equations. Steepest descent is rea…

Combining diffuse and sharp interface methods in shape optimisation

Global convergence of W1,∞-steepest descent for PDE constrained shape optimisation with semilinear elliptic equations in function space

Global convergence of $W^{1, \infty}$ -steepest descent for PDE constrained shape optimisation with semilinear elliptic equations in function space