97 citations · 335 across the 19 of their papers we have counts for
20 papers
Shape optimization in with geometric constraints: a study in distributed-memory systems
Philip J. Herbert, Jose A. Pinzon Escobar, Martin Siebenborn
In this paper we present a shape optimization scheme which utilizes the alternating direction method of multipliers (ADMM) to approximate a direction of steepest descent in $W^{1,\…
Towards computing high-order p-harmonic descent directions and their limits in shape optimization
Henrik Wyschka, Martin Siebenborn
We present an extension of an algorithm for the classical scalar -Laplace Dirichlet problem to the vector-valued -Laplacian with mixed boundary conditions in order to solve p…
Application of p-Laplacian relaxed steepest descent to shape optimization in two-phase flows
Peter Marvin Müller, Martin Siebenborn, Thomas Rung
The paper is concerned with the minimal drag problem in shape optimization of merchant ships exposed to turbulent two-phase flows. Attention is directed to the solution of Reynolds…
A Scalable Algorithm for Shape Optimization with Geometric Constraints in Banach Spaces
Peter Marvin Müller, Jose Pinzon, Thomas Rung +1
This work develops an algorithm for PDE-constrained shape optimization based on Lipschitz transformations. Building on previous work in this field, the -Laplace operator is util…
Fluid dynamic shape optimization using self-adapting nonlinear extension operators with multigrid preconditioners
Jose Pinzon, Martin Siebenborn
In this article we propose a scalable shape optimization algorithm which is tailored for large scale problems and geometries represented by hierarchically refined meshes. Weak scal…
A Novel -Harmonic Descent Approach Applied to Fluid Dynamic Shape Optimization
Peter Marvin Müller, Niklas Kühl, Martin Siebenborn +3
We introduce a novel method for the implementation of shape optimziation in fluid dynamics applications, where we propose to use the shape derivative to determine deformation field…
Adjoint Complement to the Volume-of-Fluid Method for Immiscible Flows
Niklas Kühl, Jörn Kröger, Martin Siebenborn +2
The paper is concerned with an adjoint complement to the Volume-of-Fluid (VoF) method for immiscible two-phase flows, e.g. air and water, which is widely used in marine engineering…
Mesh quality preserving shape optimization using nonlinear extension operators
Sofiya Onyshkevych, Martin Siebenborn
In this article, we propose a shape optimization algorithm which is able to handle large deformations while maintaining a high level of mesh quality. Based on the method of mapping…
A continuous perspective on modeling of shape optimal design problems
Johannes Haubner, Martin Siebenborn, Michael Ulbrich
In this article we consider shape optimization problems as optimal control problems via the method of mappings. Instead of optimizing over a set of admissible shapes a reference do…
Parallel 3d shape optimization for cellular composites on large distributed-memory clusters
Jose Pinzon, Martin Siebenborn, Andreas Vogel
Skin modeling is an ongoing research area that highly benefits from modern parallel algorithms. This article aims at applying shape optimization to compute cell size and arrangemen…
A shape optimization algorithm for cellular composites
Martin Siebenborn, Andreas Vogel
We propose and investigate a mesh deformation technique for PDE constrained shape optimization. Introducing a gradient penalization to the inner product for linearized shape spaces…
A Multigrid Preconditioner for Tensor Product Spline Smoothing
Martin Siebenborn, Julian Wagner
Uni- and bivariate data smoothing with spline functions is a well established method in nonparametric regression analysis. The extension to multivariate data is straightforward, bu…
Optimum Experimental Design for Interface Identification Problems
Tommy Etling, Roland Herzog, Martin Siebenborn
The identification of the interface of an inclusion in a diffusion process is considered. This task is viewed as a parameter identification problem in which the parameter space bea…
A shape optimization algorithm for interface identification allowing topological changes
Martin Siebenborn
In this work we investigate a combination of classical PDE constrained optimization methods and a rounding strategy based on shape optimization for the identification of interfaces…
Algorithmic aspects of multigrid methods for optimization in shape spaces
Martin Siebenborn, Kathrin Welker
We examine the interaction of multigrid methods and shape optimization in appropriate shape spaces. Our aim is a scalable algorithm for application on supercomputers, which can onl…
Computational comparison of surface metrics for PDE constrained shape optimization
Volker Schulz, Martin Siebenborn
We compare surface metrics for shape optimization problems with constraints, consisting mainly of partial differential equations (PDE), from a computational point of view. In parti…
Efficient PDE constrained shape optimization based on Steklov-Poincaré type metrics
Volker Schulz, Martin Siebenborn, Kathrin Welker
Recent progress in PDE constrained optimization on shape manifolds is based on the Hadamard form of shape derivatives, i.e., in the form of integrals at the boundary of the shape u…
Structured inverse modeling in parabolic diffusion processess
Volker Schulz, Martin Siebenborn, Kathrin Welker
Often, the unknown diffusivity in diffusive processes is structured by piecewise constant patches. This paper is devoted to efficient methods for the determination of such structur…
Towards a Lagrange-Newton approach for PDE constrained shape optimization
Volker H. Schulz, Martin Siebenborn, Kathrin Welker
The novel Riemannian view on shape optimization developed in [Schulz, FoCM, 2014] is extended to a Lagrange-Newton approach for PDE constrained shape optimization problems. The ext…
A curved-element unstructured discontinuous Galerkin method on GPUs for the Euler equations
M. Siebenborn, V. Schulz, S. Schmidt
In this work we consider Runge-Kutta discontinuous Galerkin methods (RKDG) for the solution of hyperbolic equations enabling high order discretization in space and time. We aim at…