7 citations · 24 across the 12 of their papers we have counts for
12 papers
Total Generalized Variation for Piecewise Constant Functions on Triangular Meshes with Applications in Imaging
Lukas Baumgärtner, Ronny Bergmann, Roland Herzog +2
We propose a novel discrete concept for the total generalized variation (TGV), which has originally been derived to reduce the staircasing effect in classical total variation (TV)…
A Linear View on Shape Optimization
Stephan Schmidt, Volker H. Schulz
Shapes do not define a linear space. This paper explores the linear structure of deformations as a representation of shapes. This transforms shape optimization to a variant of opti…
Combining Sobolev Smoothing with Parameterized Shape Optimization
Thomas Dick, Stephan Schmidt, Nicolas R. Gauger
On the one hand, Sobolev gradient smoothing can considerably improve the performance of aerodynamic shape optimization and prevent issues with regularity. On the other hand, Sobole…
A Shape Newton Scheme for Deforming Shells with Application to Capillary Bridges
Stephan Schmidt, Melanie Gräßer, Hans-Joachim Schmid
We present a second order numerical scheme to compute capillary bridges between arbitrary solids by minimizing the total energy of all interfaces. From a theoretical point of view,…
Discrete Total Variation of the Normal Vector Field as Shape Prior with Applications in Geometric Inverse Problems
Ronny Bergmann, Marc Herrmann, Roland Herzog +2
An analogue of the total variation prior for the normal vector field along the boundary of piecewise flat shapes in 3D is introduced. A major class of examples are triangulated sur…
Total Variation of the Normal Vector Field as Shape Prior
Ronny Bergmann, Marc Herrmann, Roland Herzog +2
An analogue of the total variation prior for the normal vector field along the boundary of smooth shapes in 3D is introduced. The analysis of the total variation of the normal vect…
An Approximate Newton Smoothing Method for Shape Optimization
Jonas Kusch, Stephan Schmidt, Nicolas R. Gauger
A novel methodology to efficiently approximate the Hessian for numerical shape optimization is considered. The method enhances operator symbol approximations by including body fitt…
Shape Optimization using the Finite Element Method on Multiple Meshes
Jorgen S. Dokken, Simon W. Funke, August Johansson +1
An important step in shape optimization with partial differential equation constraints is to adapt the geometry during each optimization iteration. Common strategies are to employ…
Discrete Total Variation with Finite Elements and Applications to Imaging
Marc Herrmann, Roland Herzog, Stephan Schmidt +2
The total variation (TV)-seminorm is considered for piecewise polynomial, globally discontinuous (DG) and continuous (CG) finite element functions on simplicial meshes. A novel, di…
A Two Stage CVT / Eikonal Convection Mesh Deformation Approach for Large Nodal Deformations
Stephan Schmidt
A two step mesh deformation approach for large nodal deformations, typically arising from non-parametric shape optimization, fluid-structure interaction or computer graphics, is co…
Shape Derivatives for the Compressible Navier-Stokes Equations in Variational Form
Matthias Sonntag, Stephan Schmidt, Nicolas R. Gauger
Shape optimization based on surface gradients and the Hadarmard-form is considered for a compressible viscous fluid. Special attention is given to the difference between the 'funct…
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…