Research area C: Models and Approximations
Unit C1: Evolution and asymptotics
Unit C2: Multi-scale phenomena and macroscopic structures
Unit C3: Interacting particle systems and phase transitions
Unit C4: Geometry-based modelling, approximation, and reduction
• Nonlocal Methods for Arbitrary Data Sources online
$\bullet$ Mathematical image processing.
$\bullet$ Inverse problems.
$\bullet$ Topology and shape optimisation.
$\bullet$ Approximation and optimisation methods in nonlinear spaces.
$\bullet$ Calculus of variations.
Selected Publications of Benedikt Wirth
$\bullet$ B. Heeren, M. Rumpf, and B. Wirth. Variational time discretization of Riemannian splines. IMA J. Numer. Anal. (in press), drx077, 2018. doi.org/10.1093/imanum/drx077
$\bullet$ A. Brancolini, C. Rossmanith, and B. Wirth. Optimal micropatterns in 2D transport networks and their relation to image inpainting. Arch. for Ration. Mech. Anal., 228(1):279–308, 2018.
$\bullet$ R. V. Kohn and B. Wirth. Optimal fine-scale structures in compliance minimization for a shear load. Comm. Pure Appl. Math., 69(8):1572–1610, 2016.
$\bullet$ P.-A. Absil, P.-Y. Gousenbourger, P. Striewski, and B. Wirth. Differentiable piecewise- Bézier surfaces on Riemannian manifolds. SIAM J. Imaging Sci., 9(4):1788–1828, 2016.
$\bullet$ M. Elsey and B. Wirth. Redistancing dynamics for vector-valued multilabel segmentation with costly fidelity: grain identification in polycrystal images. J. Sci. Comput., 63(1):279–306, 2015.
$\bullet$ K. Bredies, T. Pock, and B. Wirth. A convex, lower semicontinuous approximation of Euler's elastica energy. SIAM J. Math. Anal., 47(1):566–613, 2015.
$\bullet$ R. V. Kohn and B. Wirth. Optimal fine-scale structures in compliance minimization for a uniaxial load. Proc. R. Soc. A, 470(2170), 2014.
$\bullet$ W. Ring and B. Wirth. Optimization methods on Riemannian manifolds and their application to shape space. SIAM J. Optim., 22(2):596–627, 2012.
$\bullet$ P. Penzler, M. Rumpf, and B. Wirth. A phase-field model for compliance shape optimization in nonlinear elasticity. ESAIM Control Optim. Calc. Var., 18(1):229–258, 2012.
$\bullet$ B. Wirth, J. Gerhard, and W. Marquardt. Robust optimisation with normal vectors on critical manifolds of disturbance-induced stability loss. J. Nonlinear Sci., 21(1):57–92, 2011.
$\bullet $ A. Effland, B. Heeren, M. Rumpf, and B. Wirth. Consistent Curvature Approximation on Riemannian Shape Spaces. arXiv e-prints, December 2019. arXiv:1912.07336.
$\bullet $ C. Dirks, P. Striewski, B. Wirth, A. Aalto, A. Olguin-Olguin, and E. Raz. A mathematical model for cell polarization in zebrafish primordial germ cells. arXiv e-prints, December 2019. arXiv:1912.08627.
$\bullet $ A. Marchese and B. Wirth. Approximation of rectifiable 1-currents and weak-$\ast $ relaxation of the $h$-mass. Journal of Mathematical Analysis and Applications, 479(2):2268–2283, November 2019. URL: https://doi.org/10.1016/j.jmaa.2019.07.059, doi:10.1016/j.jmaa.2019.07.059.
$\bullet $ B. Wirth. Phase field models for two-dimensional branched transportation problems. Calculus of Variations and Partial Differential Equations, 58(5):164, September 2019. doi:10.1007/s00526-019-1615-z.
$\bullet $ B. Schmitzer and B. Wirth. Dynamic models of Wasserstein-1-type unbalanced transport. ESAIM, 25(23):54, July 2019. doi:10.1051/cocv/2018017.
$\bullet $ C. Clason, D. A. Lorenz, H. Mahler, and B. Wirth. Entropic regularization of continuous optimal transport problems. arXiv e-prints, June 2019. arXiv:1906.01333.
$\bullet $ B. Wirth. Green's function for Poisson's equation and the EEG equation with Neumann boundary condition on $n$-balls. arXiv e-prints, February 2019. arXiv:1902.04130.
$\bullet $ B. Schmitzer, K. P. Schäfers, and B. Wirth. Dynamic cell imaging in PET with optimal transport regularization. arXiv e-prints, February 2019. arXiv:1902.07521.
$\bullet $ B. Schmitzer and B. Wirth. A framework for Wasserstein-1-type metrics. Journal of Convex Analysis, 26(2):353–396, 2019.
$\bullet $ B. Heeren, M. Rumpf, M. Wardetzky, and B. Wirth. Discrete Riemannian calculus on shell space. In A. Bonito and R. Nochetto, editors, Geometric partial differential equations, volume 21 of Handbook of Numerical Analysis. Elsevier, 2019.
$\bullet $ U. Böttcher and B. Wirth. Variational methods for nonlinear geometric data and applications. In P. Grohs, M. Holler, and A. Weinmann, editors, Handbook of Variational Methods for Nonlinear Geometric Data, chapter 7. Springer International Publishing, 2019.
$\bullet $ D. P. Bourne, B. Schmitzer, and B. Wirth. Semi-discrete unbalanced optimal transport and quantization. arXiv e-prints, August 2018. arXiv:1808.01962.
$\bullet $ L. A. Davide Ferrari, C. Rossmanith, and B. Wirth. Phase field approximations of branched transportation problems. arXiv e-prints, May 2018. arXiv:1805.11399.