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math.NA2019★ 2 cited
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…
math.NA2014
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…
math.NA2012★ 7 cited
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…