Homepages

Team

• Sofiya Onyshkevych, M.Sc.
• Jose Alfonso Pinzon Escobar, M.Sc.
• Henrik Wyschka, M.Sc.

Projekte

• 04/2022 - 03/2023, HLRN Projekt, An optimal shape matters - Developing Scalable Shape Optimization Algorithms for Fluid Dynamics and Structural Mechanics, Link
• 04/2020 - 10/2023, Landesforschungsförderung LFF-GK11, Simulationsbasierte Entwurfsoptimierung dynamischer Systeme unter Unsicherheiten, Link
• 04/2020 - 10/2024, DFG-GRK 2583, Modellierung, Simulation und Optimierung mit fluiddynamischen Anwendungen, Link
• 04/2016 - 10/2020, DFG-GRK 2126, Algorithmische Optimierung, Link

Forschungsschwerpunkte

• Shape optimization and interface identification
• High performance optimization algorithms
• Algorithmic scalability for PDE constrained optimization

Example: Reference surface mesh and optimized geometry in stationary Navier Stokes flow

Lehre

Sprechstunden

Publikationen

Submitted preprints:

• J. Pinzon, M. Siebenborn, and A. Vogel. Scalable Multigrid Algorithms for Fluid Dynamic Shape Optimization. Accepted for publication: Proceedings of the High Performance Computing in Science & Engineering - 24rd Results and Review Workshop (2021).
• P.M. Müller, J. Pinzon, T. Rung, M. Siebenborn. A Scalable Algorithm for Shape Optimization with Geometric Constraints in Banach Spaces. Submitted to: SIAM Journal on Scientific Computing (2022), arxiv:2205.01912.

Journal articles:

• J. Pinzon and M. Siebenborn. Fluid dynamic shape optimization using self-adapting nonlinear extension operators with multigrid preconditioners. In: Optimization and Engineering (2022), 10.1007/s11081-022-09721-8.
• P. M. Müller, N. Kühl, M. Siebenborn, K. Deckelnick, M. Hinze, and T. Rung. A Novel p-Harmonic Descent Approach Applied to Fluid Dynamic Shape Optimization. Journal on Structural and Multidisciplinary Optimization (2021), 10.1007/s00158-021-03030-x.
• N. Kühl, J. Kröger, M. Siebenborn, M. Hinze, and T. Rung. Adjoint Complement to the Volume-of-Fluid Method for Immiscible Flows. Journal of Computational Physics (2021), 10.1016/j.jcp.2021.110411.
• M. Siebenborn and J. Wagner. A multigrid preconditioner for tensor product spline smoothing. In: Computational Statistics 36.4 (2021), pp. 2379–2411, 10.1007/s00180-021-01104-4.
• S. Onyshkevych and M. Siebenborn. Mesh quality preserving shape optimization using nonlinear extension operators. In: Journal of Optimization Theory and Applications 189.1 (2021), pp. 291–316, 10.1007/s10957-021-01837-8.
• J. Haubner, M. Siebenborn, and M. Ulbrich. A Continuous Perspective on Shape Optimization Via Domain Transformations. In: SIAM Journal on Scientific Computing 43.3 (2021), A1997-A2018, 10.1137/20m1332050.
• M. Siebenborn and A. Vogel. A shape optimization algorithm for cellular composites. In: PINT Computing and Visualization in Science (2021), 10.51375/IJCVSE.2021.1.5.
• J. Pinzon, M. Siebenborn, and A. Vogel. Parallel 3d shape optimization for cellular composites on large distributed-memory clusters. In: Journal of Advanced Simulation in Science and Engineering 7.1 (2020), pp. 117–135, 10.15748/jasse.7.117.
• T. Etling, R. Herzog, and M. Siebenborn. Optimum Experimental Design for Interface Identification Problems. In: SIAM Journal on Scientific Computing 41.6 (2019), 10.1137/18M1208125.
• M. Siebenborn. A shape optimization algorithm for interface identification allowing topological changes. In: Journal of Optimization Theory and Applications 177(2) (2018), 306-328, 10.1007/s10957-018-1279-4.
• M. Siebenborn and K. Welker. Algorithmic Aspects of Multigrid Methods for Optimization in Shape Spaces. In: SIAM Journal on Scientific Computing 39.6 (2017), B1156-B1177, 10.1137/16m1104561.
• V. Schulz, M. Siebenborn, and K. Welker. Efficient PDE constrained shape optimization based on Steklov-Poincare-Type metrics. In: SIAM Journal on Optimization 26.4 (2016), pp. 2800-2819, 10.1137/15M1029369.
• L. Grasedyck, C. Löbbert, G. Wittum, A. Nägel, V. Schulz, M. Siebenborn, R. Krause, P. Benedusi, U. Küster, and B. Dick. Space and Time Parallel Multigrid for Optimization and Uncertainty Quantification in PDE Simulations. In: Software for Exascale Computing - SPPEXA 2013-2015. Ed. by H.-J. Bungartz, P. Neumann, and E. W. Nagel. Springer International Publishing, (2016), pp. 507-523, 10.1007/978-3-319-40528-5_23.
• V. Schulz and M. Siebenborn. Computational comparison of surface metrics for PDE constrained shape optimization. In: Computational Methods in Applied Mathematics 16.3 (2016), pp. 485-496, 10.1515/cmam-2016-0009.
• A. Nägel, V. Schulz, M. Siebenborn, and G. Wittum. Scalable shape optimization methods for structured inverse modeling in 3D diffusive processes. In: Computing and Visualization in Science 17.2 (2015), pp. 79-88, 10.1007/s00791-015-0248-9.
• V. Schulz, M. Siebenborn, and K. Welker. Structured Inverse Modeling in Parabolic Diffusion Problems. In: SIAM Journal on Control and Optimization 53.6 (2015), pp. 3319-3338, 10.1137/140985883.
• M. Siebenborn, V. Schulz, and S. Schmidt. A curved-element unstructured discontinuous Galerkin method on GPUs for the Euler equations. In: Computing and Visualization in Science 15.2 (2012), pp. 61-73, 10.1007/s00791-013-0197-0.

Refereed proceedings:

• J. Pinzon, M. Siebenborn, and A. Vogel. High-Performance Shape Optimization for Linear Elastic Models of Epidermal Cell Structures. In: High Performance Computing in Science and Engineering '20. Ed. by W. E. Nagel, D. H. Kröner, and M. M. Resch. Springer International Publishing, 2021, pp. 579–594. 10.1007/978-3-030-80602-6.
• V. Schulz, M. Siebenborn, and K. Welker. PDE constrained shape optimization as optimization on shape manifolds. In: Geometric Science of Information. Ed. by F. Nielsen and F. Barbaresco. Vol. 9389. Lecture Notes in Computer Science. 2015, 10.1007/978-3-319-25040-3_54.
• V. Schulz, M. Siebenborn, and K. Welker. Towards a Lagrange-Newton approach for PDE constrained shape optimization. In: New trends in shape optimization. International Series of Numerical Mathematics. Springer, 2015, 10.1007/978-3-319-17563-8.
• M. Siebenborn and V. Schulz. GPU Accelerated Discontinuous Galerkin Methods for Euler Equations and Its Adjoint. In: Proceedings of the High Performance Computing Symposium HPC 13. San Diego, California: Society for Computer Simulation International, 2013, 3:1-3:7.

Other publications:

• M. Siebenborn. Discontinuous Galerkin approaches for HPC flow simulations on stream processors. PhD thesis. Trier University, Germany, 2014.

Software:

• MinFEM: A minimal finite element tool for demonstration and teaching. (github.com/msiebenborn/MinFEM.jl)
• MGSS: A multigrid spline smoothing toolbox for high dimensional data analysis. (CRAN.R-project.org/package=mgss)
• MGSS-Grid: Efficient spline smoothing toolbox for high dimensional data on grids. (github.com/SplineSmoothing/MGSS_grid)
• MultigridShapeOpt: Codes for the publication Fluid dynamic shape optimization using self-adapting nonlinear extension operators with multigrid preconditioners. (github.com/MultigridShapeOpt)

CV