Publikationen

Peer Reviewed Publications

L. Baumgärtner, R. Bergmann, R. Herzog, S. Schmidt and J. Vidal-Núnez. “Total Generalized Variation for Piecewise Constant Functions on Triangular Meshes with Applications in Imaging”. SIAM Journal on Imaging Sciences 16.1 (2023), pp. 313–339. DOI: doi.org/10.1137/22M1505281.
S. Schmidt and V. Schulz. “A Linear View on Shape Optimization”. accepted for publication: SIAM Journal on Control and Optimization (SICON) (2023). eprint arXive:2203.07175. DOI: doi.org/10.48550/arXiv.2203.07175.
B. Zapf, J. Haubner, L. Baumgärtner and S. Schmidt. “Medical Image Registration using optimal control of a linear hyperbolic transport equation with a DG discretization”. eprint arXive: 2305.03020 (in review). 2023. DOI: doi.org/10.48550/arXiv.2305.03020.
T. Dick, S. Schmidt and N. R. Gauger. “Combining Sobolev Smoothing with Parameterized Shape Optimization”. Computers & Fluids 244.15 (2022), p. 105568. DOI: doi.org/10.1016/j.compfluid.2022.105568.
S. Schmidt, M. Gräßer and H.-J. Schmid. “A Shape Newton Scheme for Deforming Shells with Application to Capillary Bridges”. SIAM Journal on Scientific Computing 44.4 (2022), B1175–B1194. DOI: doi.org/10.1137/20M1389054.
R. Bergmann, M. Herrmann, R. Herzog, S. Schmidt and J. Vidal Núñez. “Discrete Total Variation of the Normal Vector Field as Shape Prior with Applications in Geometric Inverse Problems”. Inverse Problems 36.5 (2020), p. 054003. DOI: doi.org/10.1088/1361-6420/ab6d5c.
R. Bergmann, M. Herrmann, R. Herzog, S. Schmidt and J. Vidal Núñez. “Total Variation of the Normal Vector Field as Shape Prior”. Inverse Problems 36.5 (2020), p. 054004. DOI: doi.org/10.1088/1361-6420/ab6d5b.
A. Walther, O. Weiß, A. Griewank and S. Schmidt. “Nonsmooth optimization by successive abs-linearization in function spaces”. Applicable Analysis (2020), pp. 1–16. DOI: doi.org/10.1080/00036811.2020.1738397.
J. S. Dokken, S. W. Funke, A. Johansson and S. Schmidt. “Shape Optimization using MultiMesh FEM with Nitsche coupling”. SIAM Journal on Scientific Computing 41.3 (2019), A1923–A1948. DOI: doi.org/10.1137/18M1189208.
M. Herrmann, R. Herzog, S. Schmidt, J. Vidal-Núñez and G. Wachsmuth. “Discrete Total Variation with Finite Elements and Applications to Imaging”. Journal of Mathematical Imaging and Vision 61.4 (2019), pp. 411–431. DOI: doi.org/10.1007/s10851-018-0852-7.
M. Herrmann, R. Herzog, H. Kröner, S. Schmidt and J. V. Núñez. “Analysis and an Interior Point Approach for TV Image Reconstruction Problems on Smooth Surfaces”. SIAM Journal on Imaging Sciences 11.2 (2018), pp. 889–922. DOI: doi.org/10.1137/17M1128022.
S. Schmidt. “Weak and Strong Form Shape Hessians and Their Automatic Generation”. SIAM Journal on Scientific Computing 40.2 (2018), pp. C210–C233. DOI: doi.org/10.1137/16M1099972.
S. Schmidt, M. Schütte and A. Walther. “Efficient Numerical Solution of Geometric Inverse Problems Involving Maxwell’s Equations Using Shape Derivatives and Automatic Code Generation”. SIAM Journal on Scientific Computing 40.2 (2018), B405–B428. DOI: doi.org/10.1137/16M110602X.
S. Schmidt, E. Wadbro and M. Berggren. “Large-Scale Three-Dimensional Acoustic Horn Optimization”. SIAM Journal on Scientific Computing 38.6 (2016), B917–B940. DOI: doi.org/10.1137/15M1021131.
M. Sonntag, S. Schmidt and N. R. Gauger. “Shape Derivatives for the compressible Navier–Stokes equations in variational form”. Journal of Computational and Applied Mathematics 296 (2016). (published online 11.11.2015), pp. 334–351. DOI: doi.org/10.1016/j.cam.2015.09.010.
S. Schmidt, C. Ilic, V. Schulz and N. R. Gauger. “Three Dimensional Large Scale Aerodynamic Shape Optimization based on Shape Calculus”. AIAA Journal 51.11 (2013), pp. 2615–2627. DOI: doi.org/10.2514/1.J052245.
M. Siebenborn, V. Schulz and S. Schmidt. “A curved-element unstructured discontinuous Galerkin method on GPUs for the Euler equations”. Computing and Visualization in Science 15.2 (2012). (published online 17.08.2013), pp. 61–73. DOI: doi.org/10.1007/s00791-013-0197-0.
C. Schillings, S. Schmidt and V. Schulz. “Efficient Shape Optimization for Certain and Uncertain Aerodynamic Design”. Computers & Fluids 46.1 (2011), pp. 78–87. DOI: doi.org/10.1016/j.compfluid.2010.12.007.
S. Schmidt, C. Ilic, N. R. Gauger and V. Schulz. “Airfoil design for compressible inviscid flow based on shape calculus”. Optimization and Engineering 12.3 (2011), pp. 349–369. DOI: doi.org/10.1007/s11081-011-9145-3.
S. Schmidt and V. Schulz. “A 2589 Line Topology Optimization Code Written for the Graphics Card”. Computing and Visualization in Science 14.6 (2011). (published online 14.08.2012), pp. 249–256. DOI: doi.org/10.1007/s00791-012-0180-1.
S. Schmidt and V. Schulz. “Shape derivatives for general objective functions and the incompressible Navier-Stokes equations”. Control and Cybernetics 39.3 (2010), pp. 677–713.
K. Eppler, S. Schmidt, V. Schulz and C. Ilic. “Preconditioning the Pressure Tracking in Fluid Dynamics by Shape Hessian Information”. Journal of Optimization Theory and Applications 141.3 (2009), pp. 513–531. DOI: doi.org/10.1007/s10957-008-9507-y.
S. Schmidt and V. Schulz. “Impulse Response Approximations of Discrete Shape Hessians with Application in CFD”. SIAM Journal on Control and Optimization 48.4 (2009), pp. 2562–2580. DOI: doi.org/10.1137/080719844.
S. Schmidt and V. Schulz. “Pareto-curve continuation in multi-objective optimization”. Pacific Journal of Optimization 4.2 (2008), pp. 243–257.

Refereed Conference Publications

L. Claes, N. Feldmann, B. Jurgelucks, V. Schulze, S. Schmidt, A. Walther and B. Henning. “Optimized Multi-Electrode Topology for Piezoelectric Material Characterisation”. SMSI 2021 Conference – Sensor and Measurement Science International. 2021. DOI: doi.org/10.5162/SMSI2021/A10.1
R. Bergmann, M. Herrmann, R. Herzog, S. Schmidt and J. Vidal-Núñez. “Geometry Processing Problems Using the Total Variation of the Normal Vector Field”. PAMM 19.1 (2019). DOI: doi.org/10.1002/pamm.201900189
J. Kusch, N. R. Gauger, S. Müller and S. Schmidt. “Frequency based preconditioning and smoothing for shape optimization”. PAMM 16.1 (2016), pp. 701–702. DOI: doi.org/10.1002/pamm.201610339
C. Ilic, S. Schmidt, V. Schulz and N. R. Gauger. “Detailed Aerodynamic Shape Optimization Based on an Adjoint Method with Shape Derivatives”. Fifth SIAM Workshop on Combinatorial Scientific Computing. Ed. by M. Beckers, J. Lotz, V. Mosenkis and U. Naumann. Vol. 2011-09. ISSN 0935–3232. Aachener Informatik-Berichte (AIB), 2011, pp. 8–10.
S. Schmidt, V. Schulz, C. Ilic and N. R. Gauger. “Large Scale Aerodynamic Shape Optimization Based on Shape Calculus”. ECCOMAS-CFD&Optimization. Ed. by I. H. Tuncer. 2011-054. ISBN 978-605-61427-4-1, 2011.
S. Schmidt, V. Schulz, C. Ilic and N. R. Gauger. “Three Dimensional Large Scale Aerodynamic Shape Optimization based on Shape Calculus”. 41st AIAA Fluid Dynamics Conference and Exhibit. AIAA 2011-3718. Honolulu, Hawaii, 2011.

Invited Conference Publications

S. Schmidt. “Structure Exploitation, AD and the Continuous Problem”. Adjoint Methods in Computational Science, Engineering, and Finance. Ed. by N. R. Gauger, M. Giles, M. Gunzburger and U. Naumann. Vol. 4 (9). Report from Dagstuhl Seminar 14371. Schloss Dagstuhl–Leibniz-Zentrum für Informatik, 2015, pp. 23–24. DOI: doi.org/10.4230/DagRep.4.9.1
S. Schmidt, N. Popescu, M. Berggren, V. Schulz, N. R. Gauger and A. Walther. “Large Scale Shape Optimization for Deterministic Problems”. Numerical Methods for PDE Constrained Optimization with Uncertain Data. Ed. by M. Heinkenschloss and V. Schulz. Oberwolfach Reports 4/2013. Mathematisches Forschungszentrum Oberwolfach. 2013, pp. 284–285
S. Schmidt and V. Schulz. “Large Scale Aerodynamic Shape Optimization”. New Directions in Simulation, Control and Analysis for Interfaces and Free Boundaries. Ed. by C. M. Elliott, Y. Giga, M. Hinze and V. Styles. Oberwolfach Reports 7/2010. Mathematisches Forschungszentrum Oberwolfach. 2010, pp. 307–308
S. Schmidt, C. Ilic, V. Schulz and N. R. Gauger. “Fast Non-Parametric Large Scale Aerodynamic Shape Optimization”. Numerical Techniques for Optimization Problems with PDE Constraints. Ed. by M. Heinkenschloss, R. Hoppe and V. Schulz. Oberwolfach Reports 4/2009. Mathematisches Forschungszentrum Oberwolfach. 2009, pp. 69–71.

Books and/or Book Chapters

L. Baumgärtner, R. Herzog, S. Schmidt and M. Weiß. “A Calculus for Non-Smooth Shape Optimization with Applications to Geometric Inverse Problems”. Non-Smooth and Complementarity-Based Distributed Parameter Systems. (submitted), 2023.
O. Ebel, S. Schmidt and A. Walther. “Algorithms based on Abs-Linearization for Nonsmooth Optimization with PDE Constraints”. Non-Smooth and Complementarity-Based Distributed Parameter Systems. Vol. 172. International Series of Numerical Mathematics. Birkhäuser, Cham, 2022, pp. 377–395. DOI: doi.org/10.1007/978-3-030-79393-7
M. Herrmann, R. Herzog, S. Schmidt and J. V. Núñez. “A Calculus for Non-Smooth Shape Optimization with Applications to Geometric Inverse Problems”. Non-Smooth and Complementarity-Based Distributed Parameter Systems. Vol. 172. International Series of Numerical Mathematics. Birkhäuser, Cham, 2022, pp. 101–120. DOI: doi.org/10.1007/978-3-030-79393-7
S. Schmidt, C. Ilic, V. Schulz and N. R. Gauger. “Constrained Optimization and Optimal Control for Partial Differential Equations”. Vol. 160. International Series of Numerical Mathematics. ISBN-13: 978-3034801324. Birkhäuser Basel, 2011. Chap. Non-Parametric Aerodynamic Shape Optimization, pp. 289–300. DOI: doi.org/10.1007/978-3-0348-0133-1_16.

Preprints and Technical Reports

L. Baumgärtner, R. Herzog, S. Schmidt and M. Weiß. “The Proximal Map of the Weighted Mean Absolute Error”. eprint arXive:2209.13545. 2022. DOI: doi.org/10.48550/arXiv.2209.13545.
L. Baumgärtner, R. Bergmann, M. Herrmann, R. Herzog, S. Schmidt and J. Vidal-Núñez. “Mesh Denoising and Inpainting using the Total Variation of the Normal”. eprint arXiv:2012.11748.2020
O. Weiß, S. Schmidt and A. Walther. “A Structure Exploiting Algorithm for Non-Smooth Semi-Linear Elliptic Optimal Control Problems”. Optimization Online 8157 (2020)
J. Kusch, S. Schmidt and N. R. Gauger. “An Approximate Newton Smoothing Method for Shape Optimization”. eprint arXiv:1807.11232. 2018
A. Borzì, J. Merger, J. Müller, A. Rosch, C. Schenk, D. Schmidt, S. Schmidt, V. Schulz, K. Velten, C. von Wallbrunn and M. Zänglein. “Novel model for wine fermentation including the yeast dying phase”. eprint arXiv:1412.6068.2014.
S. Schmidt. “A Two Stage CVT / Eikonal Convection Mesh Deformation Approach for Large Nodal Deformations”. eprint arXiv:1411.7663.2014.

Other Publications

S. Schmidt. “Geometric Inverse Problems, Images and SQP Methods Based on Weak Shape Hessians”. Habilitation. Universität Würzburg, 2018
S. Schmidt. “Efficient Large Scale Aerodynamic Design Based on Shape Calculus”. PhD thesis. Trier University, Germany, 2010.