Publications

2023

C. Wieners: Adaptive parallel space-time discontinuous Galerkin Methods for the linear transport equation. Technical Report

2022

D. Corallo, W. Dörfler, C. Wieners: Space-time discontinuous Galerkin methods for weak solutions
of hyperbolic linear symmetric Friedrichs systems. Technical Report

2021

K. Weinberg, C. Wieners:
Dynamic phase-field fracture with a first-order discontinuous Galerkin method for elastic waves.
arXiv:2106.15193 (2021).

T. Gerach, S. Schuler, J. Fröhlich, L. Lindner, E. Kovacheva, R. Moss, E. M. Wülfers, G. Seemann, C. Wieners, A. Loewe:
Electro-Mechanical Whole-Heart Digital Twins: A Fully Coupled Multi-Physics Approach.
Mathematics, 9(11), 1247 (2021)

T. Bohlen, M.R. Fernandez, J. Ernesti, C. Rheinbay, A. Rieder, C. Wieners:
Visco-acoustic full waveform inversion: From a DG forward solver to a Newton-CG inverse solver.
Computers & Mathematics with Applications, 100, 126-140 (2021)

N. Baumgarten, C. Wieners:
The parallel finite element system M++ with integrated multilevel preconditioning and multilevel Monte Carlo methods
Computers & Mathematics with Applications 81, 391-406 (2021)

W. Dörfler, C. Wieners, D. Ziegler, D. (2021). Parallel space-time solutions for the linear visco-acoustic and visco-elastic wave equation. In High Performance Computing in Science and Engineering'19 (pp. 589-599). Springer, Cham.

2020

G. Alefeld, M. Plum, C. Wieners:
Error bounds and enclosures: The development of numerical analysis and the impact of the contributions by Lothar Collatz.
ZAMM 100.10 (2020)

D. Corallo, J. Ernesti, C. Wieners: Full waveform inversion (FWI) meets deep learning: optimization methods in FWI actually train a certain neural network. Technical Report

2019

K. Schulz, L. Wagner, C. Wieners:
A mesoscale continuum approach of dislocation dynamics and the approximation by a Runge-Kutta discontinuous Galerkin method.
International Journal of Plasticity 120, 248--261 (2019)

J. Ernesti, C. Wieners: Space-time discontinuous Petrov-Galerkin methods for linear wave equations in heterogeneous media.
J. Comput. Methods Appl. Math. 19, 465–481 (2019)

W. Dörfler, S. Findeisen, C. Wieners, D. Ziegler: Parallel adaptive discontinuous Galerkin discretizations in space and time for linear elastic and acoustic waves.
In: Space-Time Methods. Applications to Partial Differential Equations, ed. U. Langer, O. Steinbach, Radon Series on Computational and Applied Mathematics 25, 61-88 (2019)

J. Ernesti, C. Wieners: A space-time discontinuous Petrov-Galerkin method for acoustic waves.
In: Space-Time Methods. Applications to Partial Differential Equations, ed. U. Langer, O. Steinbach, Radon Series on Computational and Applied Mathematics 25, 89-116 (2019)

R. Shirazi Nejad, C. Wieners: Parallel inelastic heterogeneous multiscale simulations.
In: Multi-scale Simulation of Composite Materials. Springer, Berlin, Heidelberg, 57-96 (2019)

2018

H.R. Bayat, J. Krämer, L. Wunderlich, S. Wulfinghoff, S. Reese, B. Wohlmuth, C. Wieners: Numerical evaluation of discontinuous and nonconforming finite element methods in nonlinear solid mechanics.
Computational Mechanics 62, 1413-1427 (2018)

2016

D. Maurer, C. Wieners: A scalable parallel factorization of finite element matrices with distributed Schur complements.
Numerical Linear Algebra with Applications 23, 848--864 (2016)

C. Wieners: The skeleton reduction for finite element substructuring methods. ENUMATH Proceedings 2015.

2015

S. Sandfeld, E. Thawinan, C. Wieners: A link between microstructure evolution and macroscopic response in elasto-plasticity: formulation and numerical approximation of the higher-dimensional Continuum Dislocation Dynamics theory. International Journal of Plasticity 72 (2015) 1-20.

M. Hochbruck, T. Pazur, A. Schulz, E. Thawinan, C. Wieners:
Efficient time integration for discontinuous Galerkin
approximations of linear wave equations. ZAMM 95 (2015) 237-259

2014

C. Wieners, B. Wohlmuth:
Robust operator estimates and the application to substructuring methods for first-order systems.
ESAIM: Math. Mod. Numer. Anal. 48 (2014) 161--175.

D. Maurer, C. Wieners:
A scalable parallel factorization of finite element
matrices with distributed Schur complements. Submitted.

2013

C. Wieners, J. Xin:
Boundary Element Approximation for Maxwell's Eigenvalue Problem.
Mathematical Methods in the Applied Sciences 36 (2013) 2524-2539

T. Fritz, C. Wieners, G. Seemann, H. Steen, O. Dössel: Simulation of the contraction of the ventricles in a human
heart model including atria and pericardium, Biomechanics and Modeling in Mechanobiology, 2013

D. Maurer, C. Wieners:
A highly scalable multigrid method with parallel direct coarse grid
solver for Maxwell's equations
in: High Performance Computing in Science and Engineering ‘13,
Transactions of the High Performance Computing Center, Stuttgart (HLRS) 2013
Nagel, Wolfgang E.; Kröner, Dietmar H.; Resch, Michael M. (Eds.)
Springer-Verlag 2013, p 671-677

2012

D. Reddy, C. Wieners, B. Wohlmuth:
Finite element analysis for single-crystal strain-gradient plasticity,
Int. J. Num. Meth. Eng. 90 (2012) 784-804

2011

H.-U. Rempler, C. Wieners, W. Ehlers:
Efficiency comparison of an augmented finite element formulation with standard return mapping algorithms for elastic-inelastic materials.
Computationals Mechanics 48 (2011) 551-562

D. Maurer, C. Wieners:
Parallel multigrid methods and coarse grid solver for maxwell's eigenvalue problem
In Proc. of the CiHPC 2010: Competence in High Performance Computing.
G. Wittum, ed. Gauss-Allianz, Springer, pp. 205-213

D. Maurer, C. Wieners:
A parallel block decomposition method for distributed finite element matrices. Parallel Computing 37 (2011) 742-758

C. Wieners:
Calculation of the photonic band structure
In: Photonic Crystals. Mathematical Analysis and Numerical Approximation
(ed. W. Dörfler)
Birkhäuser, New York (2011) pp. 40-62

M. Sauter, C. Wieners:
On the superlinear convergence in computational elasto-plasticity,
Comp. Meth. Eng. Mech. 200 (2011) 3646-3658

C. Wieners, B. Wohlmuth:
A primal-dual finite element approximation for a nonlocal model in plasticity
SIAM J. Numer. Anal. Vol.49, (2011) pp. 692-710

Christian Wieners:
A primal-dual formulation for infinitesimal nonlocal plasticity with hardening.
GAMM-Mitt. vol.34 no.1 (2011) 45-50

2010

M.Sauter, C. Wieners:
Robust estimates for the approximation of the dynamic consolidation problem
Int. J. Numer. Meth. vol. 30 (2010) 832-856

C. Wieners, P. Neff, W. Müller:
Parallel simulation of an infinitesimal elasto-plastic Cosserat model
GAMM-Mitt. vol.33 no.1 (2010) 79-94

Christian Wieners:
A geometric data structure for parallel finite elements and the application to multigrid methods with block smoothing.
Computing and Visualization on Science, Vol.13, (2010) 161-175

2009

Christian Wieners:
SQP methods for incremental plasticity with kinematic hardening.
In: D. Reddy (editor), IUTAM Symposium on Theoretical, Modelling and Computational
Aspects of Inelastic Media, 143-154, Springer-Verlag Berlin 2008

P. Neff, A. Sydow, and C. Wieners:
Numerical approximation of incremental infinitesimal gradient plasticity.
Int. J. Numer. Meth. Eng. 77 (2009) 414-436

V. Huang, M. Plum, and C. Wieners:
A computer-assisted proof for photonic band gaps.
Z. angew. Math. Phys. (ZAMP) 60 (2009) 1035-1052

2008

Christian Wieners: SQP methods for incremental plasticity with kinematic hardening.
In: D. Reddy (editor), IUTAM Symposium on Theoretical, Modelling and Computational
Aspects of Inelastic Media, 143-154, Springer-Verlag Berlin 2008

Christian Wieners, Nils Karajan, Wolfgang Ehlers:
Parallel 3-d simulations of a twophasic porous media model in
spinemechanics. In: Proceedings of the 3. GAMM-Seminar in
Biomechanics (2008)
(preprint)

2007

Christian Wieners, Michael Plum: Numerical enclosures for variations inequalities,
Computational Methods in Applied Mathematics,
vol. 7 no. 4 (2007) 376-388

Patrizio Neff, Krzysztof Chelminski, Wolfgang Müller, Christian Wieners: A numerical solution method for an inifinitesimal elasto-plastic Cosserat model,
Mathematical Models and Methods in Applied Sciences (M3AS)
vol.17 no.8 (2007) 1211-1240

Christian Wieners: Nonlinear solution methods for infinitesimal perfect plasticity,
Z. Angew. Math. Mech. (ZAMM) 87, No. 8-9, 643-660 (2007)

2006

Christian Wieners, P. Bastian: Multigrid Methods on Adaptively Refind Grids.
In: Computing Sciences and Engineering, Special Issue on Multigrid Computing and Finite Element Methods, vol.8 no. 6, pp. 44-55 (2006)

Christian Wieners, Wolfgang Ehlers, Martin Amman: Distributed Point Objects: A new concept for parallel finite elements applied to a geomechanical problem. Future Generation Computer Systems 22: 532-545

2005

Christian Wieners, Wolfgang Ehlers, Martin Ammann, Tobias Graf: Parallel Solution Methods for Porous Media Models in Biomechanics PAMM 5, pp.35-38 (2005)

Christian Wieners, Wolfgang Ehlers, Martin Amman, Tobias Graf: Parallel Krylov methods and the application to 3-d simulations of a triphasic porous media model in soil mechanics. Comput. Mech. 36: 409-420 (2005)
(preprint)

2004

Christian Wieners, Nicolas Neuss: Criteria for the approximation property for multigrid methods in nonnested spaces. Math. Comp. 73: 1583-1600

Christian Wieners: Distributed Point Objects. A New Concept for Parallel Finite Elements. In: Domain Decomposition Methods in Science and Engineering, ed. R. Kornhuber, R. Hoppe, J. Périaux, O. Pironneau, O. Widlund, J. Xu, Lecture Notes in Computational Science and Engineering 40: Springer 175-183

2003

Christian Wieners, Michael Plum: Optimal a priori estimates for interface problems. Numerische Mathematik 95: 735-759

Christian Wieners, Patrizo Neff: Comparison of models for finite plasticity. A numerical study. Computing and Visualization in Science 6: 23-35

Christian Wieners, Barbara Wohlmuth: Duality estimates for saddle point problems arising from mortar discretizations. SIAM Sci. Comp. 24: 2163-2184

Christian Wieners: Taylor-Hood elements in 3D. In: Analysis and Simulation of Multigrid Problems, ed. W. L. Wendland et al., Springer, 189-196

Christian Wieners, Stefan Lang, Gabriel Wittum: The application of adaptive parallel multigrid methods to problems in nonlinear solid mechanics. In: Error-Controlled Adaptive Finite Element Methods in Solid Mechanics, ed. E. Stein, Wiley 347-384

2002

Christian Wieners, Wolfgang Ehlers, Stefan Diebels, Martin Amman: Parallel 3-D simulations for porous media models in soil mechanics. Comp. Mech. 29: 75-87

Christian Wieners, Michael Plum: New solutions of the Gelfand problem. J. Math. Anal. Appl. 269: 588-606

Christian Wieners: Dual error estimates for polygonal approximations of curved boundaries. PAMM ( Proc. Appl. Math. Mech. ) 1: 532-533

2001

Christian Wieners, P. Bastian, K. Johannsen, Stefan Lang, V. Reichenberger, Gabriel Wittum: High-accuracy simulation of density driven flow in porous media. In: High Performance Computing in Science and Engineering 01, ed. E. Krause, W. Jäger; Springer, 500-511

Christian Wieners: Local multigrid methods on hierarchical meshes. In: Construction of Grid Generation Algorithms, ed. W. Hackbusch, U. Langer, Leipzig, 159-160

2000

Christian Wieners, Michael Plum, H. Behnke, U. Mertins: Eigenvalue inclusions via domain decompositions. Proc. R. Soc. Lond. A 456: 2717-2730

Christian Wieners: Robust multigrid methods for nearly incompressible elasticity. Computing 64: 289-306

Christian Wieners: Efficient elasto-plastic simulation: Multified problems, ed. W. L. Wendland et al.; Springer, 209-216

Christian Wieners: Multigrid methods for finite elements and the application to solid mechanics. Theorie und Numerik der Prandtl-Reus Plastizität. Habilitationsschrift, Universität Heidelberg

Christian Wieners, P. Bastian, K. Birken, K. Johannsen, Stefan Lang, V. Reichenberger, Gabriel Wittum, C. Wrobel: Parallel solutions of partial differential equations with adaptive multigrid methods on unstructured grids. In: High Performance Computing in Science and Engineering 99, ed. E. Krause, W. Jäger, Springer, 496-508

Christian Wieners: Orthogonal projections onto convex sets and the application to plasticity. Universität Stuttgart, SFB 404, Preprint 00/11

Christian Wieners, P. Bastian, K. Johannsen, Stefan Lang, S. Nägele, V. Reichenberger, Gabriel Wittum, C. Wrobel: Advances in High-Performance Computing: Multigrid Methods for Partial Differential Equations and ist Apllications. In: High Performance Computing in Science and Engineering 00, ed. E. Krause, W. Jäger, Springer, 506-519

1999

Christian Wieners, D. Braess, W. Dahmen: A Multigrid Algorithm for the Mortar Finite Element Method. SIAM Numer. Math. 37: 48-69

Christian Wieners: Multigrid methods for Prandtl-Reus-plasticity. Numer. Lin. Alg. 6: 457-478

1998

Christian Wieners, Barbara Wohlmuth: The coupling of mixed and conforming finite element dicretizations. In: AMS Contemporary Mathematics series, Proceedings of the 10th International Conference on Domain Decomposition, ed. Jan Mandel and Charbel Farhat and Xiao-Chuan Cai: 546-553

Christian Wieners, P. Bastian, K. Birken, K. Johannsen, Stefan Lang, V. Reichenberger,H. Rentz-Reichert, Gabriel Wittum, C. Wrobel: A parallel software-platform for solving problems of partial differential equations using unstructured grids and adaptive multigrid methods. In: High Performance Computing in Science and Engineering 98, ed. E. Krause, W. Jäger, Springer, 326-339

Christian Wieners: Parallel linear algebra and the application to multigrid methods. Proc. des Kieler GAMM-Seminars, ed. W. Hackbusch, Gabriel Wittum

1997

Christian Wieners, P. Bastian, K. Birken, K. Johannsen, Stefan Lang, N. Neuss, H. Rentz-Reichert: UG - a flexible software toolbox for solving partial differential equations. Copmputing and Visualization in Science 1: 27-40

Christian Wieners: Bounds for the N lowest eigenvalue of fourth order boundary value equations. Computing 59: 29-42

Christian Wieners: The implementation of adaptive multigrid methods for finite elements. Universität Stuttgart, SFB 404, Preprint 97/12

1996

Christian Wieners: A numerical existence proof of nodal lines fort he first eigenfunction of the plate. Arch. Math. 66: 420-427

Christian Wieners: A parallel Newton multigrid method for high order finite elements and its application to numerical existence proofs for elliptic boundary value equations. Z. angew. Math. Mech. 76: 171-176

Christian Wieners: Numerical enclosures for solutions of the Navier-Stokes equation for small Reynolds numbers. In: Numerical Methods and Error Bounds, ed. G. Alefeld, J. Herzberger, Akademie Verlag Berlin; 280-286

Christian Wieners: Positive solutions of the Bratu problem in nonconvex domains. Z. angew. Math. Mech: 76, Suppl. 1: 583-584

1994

Christian Wieners: Numerische Existenzbeweise für schwache Lösungen nichtlinearer elliptischer Randwertaufgaben. Dissertation, Universität Köln

1990

Christian Wieners: Meataxe in Charakteristik 0 ein Verfahren zur Bestimmung irreduzibler Darstellungen. Diplomarbeit, Universität Köln

1989

Christian Wieners: Die Berechnung von irreduziblen Darstellungen endlicher Gruppen. Examensarbeit für das 1. Staatsexamen, Universität Köln