Fields of Interest
- Numerical methods for nonlinear PDEs
- Nonlinear multigrid methods and nonsmooth optimization
- Free boundary problems, phase field models, geometric and surface PDEs
- Multi-scale modeling and simulation of biomembranes
- Mathematical learning and PDEs
- Adaptive discretization methods
- Design of flexible and efficient numerical software
Projects
Running:
- SFB 1114 project A07 Langevin dynamics of particles in membranes
- MATH+ project EF3-4 Physics regularized learning
- BMBF Verbundprojekt ParaPhase
Completed:
- SFB 1114 project AP1 Particles in lipid bilayers
- ECMath project SE12: Fast solvers for heterogenous saddle point problems
Member of
- Berlin Mathematics Research Center MATH+
- SFB 1114 - Scaling Cascades in Complex Systems
- ECMath - Einstein Center of Mathematics Berlin
- DFG Research Center Matheon
- DUNE developer team
Software
Member of the Dune development team and Co-maintainer of the the following Dune modules:
- Dune-functions: a module defining interfaces for functions and global finite element bases
- Dune-subgrid: a meta grid manager that treats a subset of a grid hierarchy as hierarchic grid itself.
- Dune-fufem: a finite-element discretization module
- Dune-solvers: a framework for iterative solvers using dynamic polymorphism
- Dune-tnnmg: building blocks for TNNMG-type solvers
Reviewed Publications
Reviewed Publications
- T. Kies and C. Gräser. On differentiability of the membrane-mediated mechanical interaction energy of discrete--continuum membrane--particle models. Interfaces Free Bound., 23:459–--484, 2021. (accepted). [ DOI | arXiv ]
- P. Bastian, M. Blatt, A. Dedner, N.-A. Dreier, C. Engwer, R. Fritze, C. Gräser, C. Grüninger, D. Kempf, R. Klöfkorn, M. Ohlberger, and O. Sander. The DUNE framework: Basic concepts and recent developments. Comput. Math. Appl., 2020. [ DOI | arXiv ]
- C. Gräser and O. Sander. Truncated nonsmooth Newton multigrid methods for block-separable minimization problems. IMA J. Numer. Anal., 39:454--481, 2019. [ DOI | arXiv ]
- C. Gräser and T. Kies. Discretization error estimates for penalty formulations of a linearized Canham--Helfrich type energy. IMA J. Numer. Anal., 39:626--649, 2019. [ DOI | arXiv ]
- C. Engwer, C. Gräser, S. Müthing, and O. Sander. The interface for functions in the dune-functions module. Archive of Numerical Software, 5(1):95--109, 2017. [ DOI | arXiv | http ]
- C. Gräser, M. Kahnt, and R. Kornhuber. Numerical approximation of multi-phase Penrose--Fife systems. Comput. Methods Appl. Math., 16(4):523--542, 2016. [ DOI | arXiv ]
- M. Blatt, A. Burchardt, A. Dedner, C. Engwer, J. Fahlke, B. Flemisch, C. Gersbacher, C. Gräser, F. Gruber, C. Grüninger, D. Kempf, R. Klöfkorn, T. Malkmus, S. Müthing, M. Nolte, M. Piatkowski, and O. Sander. The distributed and unified numerics environment, version 2.4. Archive of Numerical Software, 4(100):13--29, 2016. [ DOI | http ]
- C. M. Elliott, C. Gräser, G. Hobbs, R. Kornhuber, and M.-W. Wolf. A variational approach to particles in lipid membranes. Arch. Rational Mech. Anal., 222(2):1011--1075, 2016. [ DOI | arXiv ]
- C. Gräser, R. Kornhuber, and U. Sack. Nonsmooth Schur--Newton methods for multicomponent Cahn--Hilliard systems. IMA J. Numer. Anal., 35(2):652--679, 2015. [ DOI | preprint | http ]
- C. Gräser, R. Kornhuber, and U. Sack. Numerical simulation of coarsening in binary solder alloys. Comp. Mater. Sci., 93:221--233, 2014. [ DOI | preprint ]
- C. Gräser and O. Sander. Polyhedral Gauß--Seidel converges. J. Numer. Math., 22(3):221--254, 2014. [ DOI | preprint ]
- G. Jouvet and C. Gräser. An adaptive Newton multigrid method for a model of marine ice sheets. J. Comp. Phys., 252:419--437, 2013. [ DOI | preprint ]
- C. Gräser, R. Kornhuber, and U. Sack. Time discretizations of anisotropic Allen--Cahn equations. IMA J. Numer. Anal., 33(4):1226--1244, 2013. [ DOI ]
- G. Jouvet, E. Bueler, C. Gräser, and R. Kornhuber. A nonsmooth Newton multigrid method for a hybrid, shallow model of marine ice sheets. In J. Li, H. Yang, and E. Machorro, editors, Recent Advances in Scientific Computing and Applications, volume 586 of Contemporary Mathematics, pages 197--205. American Mathematical Society, 2013. [ DOI | preprint ]
- Q. Zou, A. Veeser, R. Kornhuber, and C. Gräser. Hierarchical error estimates for the energy functional in obstacle problems. Numerische Mathematik, 117(4):653--677, 2011. [ DOI | preprint ]
- C. Gräser, R. Kornhuber, and U. Sack. On hierarchical error estimators for time-discretized phase field models. In G. Kreiss, P. Lötstedt, A. Malqvist, and M. Neytcheva, editors, Numerical Mathematics and Advanced Applications 2009, pages 397--405. Springer, 2010. [ DOI | preprint ]
- C. Gräser and R. Kornhuber. Nonsmooth Newton methods for set-valued saddle point problems. SIAM J. Numer. Anal., 47(2):1251--1273, 2009. [ DOI | preprint ]
- C. Gräser and R. Kornhuber. Multigrid methods for obstacle problems. J. Comp. Math., 27(1):1--44, 2009. [ preprint ]
- C. Gräser and O. Sander. The dune-subgrid module and some applications. Computing, 8(4):269--290, 2009. [ DOI | preprint ]
- C. Gräser, U. Sack, and O. Sander. Truncated nonsmooth Newton multigrid methods for convex minimization problems. In M. Bercovier, M. Gander, R. Kornhuber, and O. Widlund, editors, Domain Decomposition Methods in Science and Engineering XVIII, volume 70 of LNCSE, pages 129--136. Springer, 2009. [ DOI | preprint ]
- C. Gräser. Globalization of nonsmooth Newton methods for optimal control problems. In K. Kunisch, G. Of, and O. Steinbach, editors, Numerical Mathematics and Advanced Applications, Proceedings of ENUMATH 2007, pages 605--612, Berlin, 2008. Springer. [ DOI | preprint ]
- C. Gräser and R. Kornhuber. On preconditioned Uzawa-type iterations for a saddle point problem with inequality constraints. In O. B. Widlund and D. E. Keyes, editors, Domain Decomposition Methods in Science and Engineering XVI, volume 55 of LNCSE, pages 91--102, Heidelberg, 2007. Springer. [ DOI | preprint ]
Preprints
- C. Gräser, R. Kornhber, and J. Podlesny. Numerical simulation of multiscale fault systems with rate- and state-dependent friction. Preprint, 2021. arxiv:2110.14429. [ arXiv ]
- T. Kies, C. Gräser, L. Delle Site, and R. Kornhuber. Free energy computation of particles with membrane-mediated interactions via Langevin dynamics. Preprint, 2020. arxiv:2009.14713. [ arXiv ]
- C. Gräser, D. Kienle, and O. Sander. Truncated nonsmooth newton multigrid for phase-field brittle fracture problems. Preprint, 2020. arxiv:2007.12290. [ arXiv ]
- C. Gräser and P. A. Alathur Srinivasan. Error bounds for PDE-regularized learning. Preprint, 2020. arxiv:2003.06524. [ arXiv ]
- C. Engwer, C. Gräser, S. Müthing, and O. Sander. Function space bases in the dune-functions module. Preprint, 2018. arxiv:1806.09545. [ arXiv ]
- J. H. Peters, C. Gräser, and R. Klein. Membrane deformation by N-BAR proteins: Extraction of membrane geometry and protein diffusion characteristics from MD simulations. Preprint, 2017. arxiv:1712.02666. [ arXiv ]
- C. Gräser. A note on Poincaré- and Friedrichs-type inequalities. Technical report, 2015. arxiv:1512.02842. [ arXiv ]
- C. Gräser and O. Sander. Truncated nonsmooth Newton multigrid methods for simplex-constrained minimization problems. Preprint 384, IGPM Aachen, 2014. [ preprint ]
- C. Gräser. Nonsmooth Schur--Newton methods for nonsmooth saddle point problems. Preprint 1004, Matheon Berlin, 2013.
Other Publications
- D. Kienle, C. Gräser, O. Sander, and M.-A. Keip. Efficient and reliable phase-field simulation of brittle fracture using a nonsmooth multigrid solution scheme. PAMM, 18(1):e201800126, 2018. [ DOI ]
Theses
Talks
-
Multiscale modelling of particles in membranes
(invited plenary) SciCADE, Innsbruck, 2019. -
Conforming and dg multigrid for nonsmooth minimization
WIAS Seminar Materialmodellierung, 2019. -
Multi-scale modeling of particles in membranes
Oberwolfach workshop 1904: Surface, Bulk, and Geometric Partial Differential Equations: Interfacial, stochastic, non-local and discrete structures, 2019. -
Langevin dynamics for particles in membranes
CRC 1114 Workshop: Particles in Membranes, 2018. -
Truncated nonsmooth newton multigrid for nonsmooth minimization problems
ECCM-ECFD, Glasgow, 2018. -
Solving nonsmooth pdes in dune
WIAS Seminar Numerical Mathematics, 2017. -
Modeling and simulation of particles in membranes
Scaling Cascades in Complex Systems, CRC 1114 conference, 2017. -
Moving particles in biological membranes
Applied Mathematics Seminars, University of Warwick, 2017. -
Nonlinearly preconditioned inexact Newton methods for nonsmooth
optimization
DD 24, Longyearbyen, Norway, 2017. -
Moving particles in biological membranes
Oberwolfach workshop 1704: Emerging Developments in Interfaces and Free Boundaries, 2017. -
Nonlinearly preconditioned inexact Newton methods for nonsmooth
optimization
7th European Congress of Mathematics, Berlin, 2016. -
Nonlinearly preconditioned inexact Newton methods for nonsmooth
optimization
Seminar des of Instituts für Numerische Mathematik, TU Dresden, 2016. -
Nonlinearly preconditioned inexact Newton methods for nonsmooth
optimization
Colloque de mathématiques, University of Geneva, 2016. -
A variational approach to particles in lipid membranes
Workshop Biological Membranes: Modelling, Analysis and Numerics, Imperial College London, 2016. -
A variational approach to particles in lipid membranes
Oberwolfach workshop 1549: Geometric Partial Differential Equations, 2015. -
Type-erased interfaces in dune-functions
Dune user meeting 2015, Heidelberg, 2015. -
Nonsmooth schur-newton methods for nonsmooth saddle point problems
DD 23, Jeju, 2015. -
Multigrid for block-structured nonsmooth problems
Workshop Long running trends and upcoming traditions in the numerical treatment of PDEs, Berlin, 2015. -
Truncated nonsmooth newton multigrid methods for vector valued minimization
problems
EMG, Leuven, 2014. -
Efficient solution of nonsmooth multicomponent phase field models
AIMS, Madrid, 2014. -
Numerical solution of binary and multicomponent phase field models
IGPM Oberseminar, RWTH Aachen, 2014. -
Nonsmooth Newton multigrid solvers for nonsmooth minimization problems
DD 22, Lugano, Switzerland, 2013. -
Nonsmooth Newton multigrid solvers for nonsmooth minimization problems
IFIP TC 7, Klagenfurt, 2013. -
Nonsmooth Schur--Newton methods for multicomponent Cahn--Hilliard
equations
EUCCO, Chemnitz, 2013. -
What is a ... variational inequality?
”What is ...?” seminar, BMS, Berlin, 2013. -
Nonsmooth Schur--Newton methods for multicomponent Cahn--Hilliard
equations
(short talk) Oberwolfach workshop 1313: Interfaces and Free Boundaries, 2013. -
Robust multigrid solution of phase field models
Lothar-Collatz-Kolloquium, Uni Hamburg, 2012. -
A 20 minute introduction to multigrid methods (for algebraists)
Oberwolfach seminar 1247a: Subspace Correction Methods, 2012. -
Truncated nonsmooth Newton multigrid methods for nonsmooth minimization
ISMP, Berlin, 2012. -
Efficient implementation of Rothe's method with adaptive finite elements
PDESoft, Münster, 2012. -
Nonsmooth Newton multigrid methods for nonlinear minimization problems
Matheon AAC workshop on Optimization with PDE Constraints, Berlin, 2011. -
Convex minimization and phase field models
Oberwolfach workshop 1148: Geometric Partial Differential Equations, 2011. -
Schur nonsmooth Newton methods
IFIP TC 7, Berlin, 2011. -
Nonsmooth Newton multigrid
ISMP, Chicago, 2009. -
Multigrid methods for phase field models
Matheon ICM Workshop, Berlin, 2008. -
Global convergence of nonsmooth Newton methods for constrained
minimization
DD 18, Jerusalem, Israel, 2008. -
Nonsmooth Newton methods for set-valued saddle point problems
Enumath, Graz, 2007. -
Nonsmooth Newton methods for set-valued saddle point problems
DMV Jahrestagung, Berlin, 2007. -
Nonsmooth Newton methods for set-valued saddle point problems
DD 17, Strobl, Austria, 2006. -
On preconditioned Uzawa-type iterations for the Cahn--Hilliard equation
with obstacle potential
EMG, Scheveningen, 2005.
Teaching
- Wintersemester 2021:
- Vorlesung: Analysis 3
- Sommersemester 2021:
- Vorlesung: Analysis 2
- Wintersemester 2020:
- Vorlesung: Analysis 1
- Proseminar: Numerische lineare Algebra
- Sommersemester 2020:
- Vorlesung: Computerorientierte Mathematik 2
- Vorlesung: Numerics IV (Numerical methods for surface and geometric PDEs)
- Wintersemester 2019:
- Vorlesung: Computerorientierte Mathematik 1
- Vorlesung: Advanced finite element methods
- Sommersemester 2019:
- Vorlesung: Computerorientierte Mathematik 2
- Vorlesung: Stochastic Differential Equations
- Seminar: Mathematics of Learning
- Wintersemester 2018/2019:
- Sommersemester 2017:
- Vorlesung: Numerics III
- Summerschool: Modelling of Mass and Energy Transport
- Wintersemester 2017/2018:
- Vorlesung: Numerics II
- Seminar: Mathematical aspects of neural networks
- Seminar: Large deviations
- Sommersemester 2017:
- Vorlesung: Numerik I
- Vorlesung: Design and implementation of numerical software for PDEs
- Summerschool: Modelling of Mass and Energy Transport
- Wintersemester 2016/2017:
- Vorlesung: Numerics IV
- Seminar: Numerical Methods for Geometric PDEs
- Sommersemester 2016:
- Vorlesung: Numerics III
- Seminar: Variationsmethoden in der numerischen Mathematik
- Summerschool: Modelling of Mass and Energy Transport
- Wintersemester 2015/2016:
- Vorlesung: Numerics II
- Sommersemester 2015:
- Vorlesung: Numerik I
- Wintersemester 2014/2015:
- Vorlesung: Fast solvers for nonsmooth PDEs
- Sommersemester 2014:
- Vorlesung: Analysis II (lehramtsbezogen)
- Wintersemester 2013/2014:
- Sommersemester 2013:
- Vorlesung: Teilraumkorrekturmethoden
- Wintersemester 2012/2013:
- Vorlesung: Lineare Algebra I (lehramtsbezogen)