Publications
Books
Numerische Mathematik 3. Adaptive Lösung partieller Differentialgleichungen.
de Gruyter.
ed. 2.
2020.
Inside Finite Elements.
de Gruyter.
2016.
Refereed Articles
Multilevel optimization for policy design with agent-based epidemic models.
J. Comput. Sci. 102242,
2024.
Continuity of Microscopic Cardiac Conduction in a Computational Cell-by-Cell Model.
In
Computing in Cardiology 50. 2023.
Unrefereed Articles
Efficient numerical methods for simulating cardiac electrophysiology with cellular resolution.
In
10th Int. Conf. Computational Methods for Coupled Problems in Science and Engineering 2023. 2023.
A Bayesian Framework for Simulation-based Digital Twins of Bridges.
ce/papers 6:
734-740,
2023.
Theses
Function Space Complementarity Methods for Optimal Control Problems.
2001.
Newton-artige Iterationsverfahren zur Minimierung strikt konvexer Funktionale. Freie Universität Berlin 1995. P. Deuflhard
Popular Science Articles
Molekülbillard.
In
- K. Biermann
- M. Grötschel
- B. Lutz-Westphal
Books
Das Lehrbuch behandelt adaptive Algorithmen für die numerische Lösung von elliptischen und parabolischen Gleichungen, wobei der Schwerpunkt auf der algorithmischen Effizienz liegt und die notwendige Theorie so elementar wie möglich gehalten wird. Die zweite Ausgabe wurde korrigiert und ergänzt. Insbesondere der Abschnitt über spektrale Defektkorrekturmethoden wurde wesentlich erweitert.
- Band 3 des Standardwerks zur Numerik partieller Differentialgleichungen
- Fokus auf Effizienz adaptiver Algorithmen sowie Scientific Computing
- Elementare und verständliche Darstellung der Theorie
All relevant implementation aspects of finite element methods are discussed in this book. The focus is on algorithms and data structures as well as on their concrete implementation. Theory is covered only as far as it gives insight into the construction of algorithms. In the exercises, a complete FE-solver for stationary 2D problems is implemented in Matlab/Octave.
- A concise guide to algorithmic and implementation aspects of finite elements.
- A complete FE-solver for 2D problems implemented in Matlab/Octave exercises.
- Both advanced algorithmic concepts and application aspects are covered.
This book deals with the general topic “Numerical solution of partial differential equations (PDEs)” with a focus on adaptivity of discretizations in space and time. By and large, introductory textbooks like “Numerical Analysis in Modern Scientific Computing” by Deuflhard and Hohmann should suffice as a prerequisite. The emphasis lies on elliptic and parabolic systems. Hyperbolic conservation laws are treated only on an elementary level excluding turbulence.
Numerical Analysis is clearly understood as part of Scientific Computing. The focus is on the efficiency of algorithms, i.e. speed, reliability, and robustness, which directly leads to the concept of adaptivity in algorithms. The theoretical derivation and analysis is kept as elementary as possible. Nevertheless required somewhat more sophisticated mathematical theory is summarized in comprehensive form in an appendix. Complex relations are explained by numerous figures and illustrating examples. Non-trivial problems from regenerative energy, nanotechnology, surgery, and physiology are inserted.
The text will appeal to graduate students and researchers on the job in mathematics, science, and technology. Conceptually, it has been written as a textbook including exercises and a software list, but at the same time it should be well-suited for self-study.
- Standard work on numerics of partial differential equations
- Elementary and understandable presentation of the mathematical theory
- Covers efficiency of numerical algorithms and scientific computing
- Includes in-depth mathematical tools in the appendix
Dieses Lehrbuch behandelt das Thema Numerik partieller Differentialgleichungen, im Wesentlichen aufbauend auf dem Band Numerische Mathematik 1. Der Schwerpunkt liegt auf elliptischen und parabolischen Systemen; hyperbolische Erhaltungsgleichungen werden aber ebenfalls elementar behandelt.
Numerische Mathematik wird verstanden als Teilgebiet des Scientific Computing, zu Deutsch auch Wissenschaftliches Rechnen. Im Vordergrund steht hier die Effizienz von Algorithmen, d.h. Schnelligkeit, Verlässlichkeit und Robustheit, dies führt zu adaptiven Algorithmen. Die theoretische Herleitung und Analyse von Algorithmen ist in diesem Buch so elementar wie möglich gehalten; die benötigte etwas anspruchsvollere mathematische Theorie ist im Anhang zusammengefasst. Zahlreiche Abbildungen und Illustrationsbeispiele erläutern die komplexen Sachverhalte. Als nichttriviale Beispiele dienen Probleme aus Nanotechnologie, Chirurgie und Physiologie.
Das Buch richtet sich an Studierende sowie an bereits im Beruf stehende Mathematiker, Naturwissenschaftler und Ingenieure. Es ist als Lehrbuch konzipiert, aber auch gut für ein Selbststudium geeignet.
- Band 3 des Standardwerkszur Numerik partieller Differentialgleichungen
- Deckt Effizienz numerischer Algorithmen sowie Scientific Computing ab
- Elementare und verständliche Darstellung der mathematischen Theorie
- Vertieftes mathematisches Handwerkszeug in den Anhängen
Refereed Articles in Journals and Conference Proceedings
- Multilevel optimization for policy design with agent-based epidemic models. J. Comput. Sci. 102242, 2024.
- Continuity of Microscopic Cardiac Conduction in a Computational Cell-by-Cell Model. In Computing in Cardiology 50. 2023.
- Convergence Analysis of BDDC Preconditioners for Composite DG Discretizations of the Cardiac Cell-By-Cell Model. SIAM J. Sci. Comp. 45 (6): A2836-A2857, 2023.
- Adaptive Gaussian Process Regression for Efficient Building of Surrogate Models in Inverse Problems. Inverse Problems 39: 125003, 2023.
- Convergence Properties of Newton’s Method for Globally Optimal Free Flight Trajectory Optimization.
In
- D. Frigioni
- P. Schiewe
- Newton's Method for Global Free Flight Trajectory Optimization. Operations Research Forum 4: 63, 2023.
- Error Bounds for Discrete-Continuous Free Flight Trajectory Optimization. Journal of Optimization Theory and Applications 198: 830-856, 2023.
- On the accuracy of eikonal approximations in cardiac electrophysiology in the presence of fibrosis.
In
- O. Bernard
- P. Clarysse
- N. Duchateau
- J. Ohayon
- M. Viallon
- Sensitivity of temperature-based time since death estimation on measurement location. Int. J. Legal Med. 137: 1815-1837, 2023.
- The impact of anatomy variation on temperature based time of death estimation. Int. J. Legal Med. 137: 1615-1627, 2023.
- Fast Floating-Point Filters for Robust Predicates. BIT Numerical Mathematics 63: 31, 2023.
- A Discrete-Continuous Algorithm for Globally Optimal Free Flight Trajectory Optimization. In 22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022). 2022.
- Quantitative Analysis of Nonlinear Multifidelity Optimization for Inverse Electrophysiology.
In
- S.C. Brenner
- E.T. Chung
- A. Klawonn
- F. Kwok
- J. Xu
- J. Zou
- The HighPerMeshes Framework for Numerical Algorithms on Unstructured Grids. Concurrency and Computation: Practice and Experience 34 (14): e6616, 2022.
- Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods.
In
- P. Nithiarasu
- C. Vergara
- Navigation of Concentric Tube Continuum Robots using Optimal Control. In Proceedings of the 19th International Conference on Informatics in Control, Automation and Robotics. pp. 146-154, 2022.
- Multilevel augmented Lagrangian solvers for overconstrained contact formulations.
In
- D. Auroux
- J.-B. Caillau
- R. Duvigneau
- A. Habbal
- O. Pantz
- L. Pronzato
- L. Rifford
- Efficient Identification of Scars using Heterogeneous Model Hierarchies. EP Europace 23: i113-i122, 2021.
- HighPerMeshes - A Domain-Specific Language for Numerical Algorithms on Unstructured Grids.
In
- B. Balis et al.
- Impact of mixed precision and storage layout on additive Schwarz smoothers. Numerical Linear Algebra with Applications 28 (4): e2366, 2021.
- A Discrete-Continuous Algorithm for Free Flight Planning. Algorithms 14 (1): 4, 2021.
- Kaskade 7 - a Flexible Finite Element Toolbox. Comp. Math. Appl. 81: 444-458, 2021.
- A primal dual projection algorithm for efficient constraint preconditioning. SIAM J. Sci. Comp. 43 (6): A4095-A4120, 2021.
- Compression Challenges in Large Scale Partial Differential Equation Solvers. algorithms 12 (9): 197, 2019.
- Serial synapse formation through filopodial competition for synaptic seeding factors. Developmental Cell 50 (4): 447-461, 2019.
- Optimal Design of Experiments for Estimating the Time of Death in Forensic Medicine. Inverse Problems 34 (12): 125005, 2018.
- Uncertainty in Temperature-Based Determination of Time of Death. Heat and Mass Transfer 54 (9): 2815-2826, 2018.
- Lossy data compression reduces communication time in hybrid time-parallel integrators. Comput. Vis. Sci. 19 (1): 19-30, 2018.
- Novel relocation methods for automatic external defibrillator improve out-of-hospital cardiac arrest coverage under limited resources. Resuscitation 125: 83-89, 2018.
- Theoretically optimal inexact spectral deferred correction methods. Comm. Appl. Math. Comp. Sci. 13 (1): 53-86, 2018.
- Spectral Deferred Correction methods for adaptive electro-mechanical coupling in cardiac simulation.
In
- G. Russo
- V. Capasso
- G. Nicosia
- V. Romano
- An affine covariant composite step method for optimization with PDEs as equality constraints. Optim. Meth. Softw. 32 (5): 1132-1161, 2017.
- Determining the material parameters for the reconstruction of defects in carbon fiber reinforced polymers from data measured by flash thermography. In AIP Conference Proceedings. pp. 100006, 2017.
- Automatic CT based Finite Element Model Generation for Temperature based Death Time Estimation: Feasibility Study and Sensitivity Analysis. Int. J. Legal Medicine 131 (3): 699-712, 2017.
- Using sparse kernels to design computer experiments with tunable precision.
In
- A. Colubi
- A. Blanco
- C. Gatu
- Faster SDC convergence on non-equidistant grids with DIRK sweeps. BIT Numerical Mathematics 55 (4): 1219-1241, 2015.
- Reducing Memory Requirements in Scientific Computing and Optimal Control.
In
- T. Carraro
- M. Geiger
- S. Körkel
- R. Rannacher
- Lossy Compression for PDE-constrained Optimization: Adaptive Error Control. Comput. Optim. Appl. 62 (1): 131-155, 2015.
- Optimal control for a tuberculosis model with undetected cases in Cameroon. Comm. Nonlin. Sci. Num. Sim. 20 (3): 986-1003, 2015.
- An optimal control problem in polyconvex hyperelasticity. SIAM J. Control Opt. 52 (3): 1403-1422, 2014.
- Lossy Compression in Optimal Control of Cardiac Defibrillation. J. Sci. Comp. 60 (1): 35-59, 2014.
- Flexible shape matching with finite element based LDDMM. International Journal of Computer Vision 105 (2): 128-143, 2013.
- Fast Defect Shape Reconstruction Based on the Travel Time in Pulse Thermography.
In
- O. Büyüköztürk
- M.A. Taşdemir
- O. Güneş
- Y. Akkaya
- On goal-oriented adaptivity for elliptic optimal control problems. Opt. Meth. Softw. 28 (13): 969-992, 2013.
- Mathematical Cancer Therapy Planning in Deep Regional Hyperthermia. Acta Numerica 21: 307-378, 2012.
- Solving Optimal Control Problems with the Kaskade 7 Finite Element Toolbox.
In
- A. Dedner
- B. Flemisch
- R. Klöfkorn
- State Trajectory Compression for Optimal Control with Parabolic PDEs. SIAM J. Sci. Comp. 34 (1): A161-A184, 2012.
- Direct LDDMM of Discrete Currents with Adaptive Finite Elements.
In
- X. Pennec
- S. Joshi
- M. Nielsen
- Barrier methods for a control problem from hyperthermia treatment planning.
In
- M. Diehl
- F. Glineur
- E. Jarlebring
- W. Michiels
- Development and test of a numerical model for pulse thermography in civil engineering. Heat Mass Transf. 46 (11-12): 1419-1428, 2010.
- Regularized Antenna Profile Adaptation in Online Hyperthermia Treatment. Medical Physics 37: 5382-5394, 2010.
- Craniofacial Surgery Planning Based on Virtual Patient Models. Inform. Techn. 52 (5): 258-263, 2010.
- Optimization and Identification in Regional Hyperthermia. Int. J. Appl. Electromagn. and Mech. 30: 265-275, 2009.
- Pointwise Nonlinear Scaling for Reaction-Diffusion Equations. Appl. Num. Math. 59 (8): 1858-1869, 2009.
- Inertia Revealing Preconditioning For Large-Scale Nonconvex Constrained Optimization. SIAM J. Sci. Comp. 31 (2): 939-960, 2008.
- A control reduced primal interior point method for a class of control constrained optimal control problems. Comp. Opt. Appl. 41 (1): 127-145, 2008.
- Modellgestützte Operationsplanung in der Kopfchirurgie.
In
- W. Niederlag
- H. Lemke
- J. Meixensberger
- M. Baumann
- Superlinear convergence of the Control Reduced Interior Point Method for PDE Constrained Optimization. Comp. Opt. Appl. 39 (3): 369-393, 2008.
- The convergence of an interior point method for an elliptic control problem with mixed control-state constraints. Comp. Opt. Appl. 39 (2): 183-218, 2008.
- On the Interplay Between Interior Point Approximation and Parametric Sensitivities in Optimal Control. Journal of Mathematical Analysis and Applications 337: 771-793, 2008.
- Adaptation of antenna profiles for control of MR guided hyperthermia (HT) in a hybrid MR-HT system. Medical Physics 34 (12): 4717-4725, 2007.
- Affine conjugate adaptive Newton methods for nonlinear elastomechanics.
Opt. Meth. Softw. 22
(3):
413-431,
2007.
- Abstract
- Preprint This is a preprint of an article submitted for consideration in the OPTIMIZATION METHODS AND SOFTWARE (C) 2006; OPTIMIZATION METHODS AND SOFTWARE is available online at http://journalsonline.tandf.co.uk/
- Journal Version
- DOI 10.1080/10556780600605129
- Inexact central path following algorithms for optimal control problems. SIAM J. Control Opt. 46 (3): 792-815, 2007.
- Comparison of MR-thermography and planning calculations in phantoms. Medical Physics 33: 3912-3920, 2006.
- Mathematics in Facial Surgery. Notices Amer. Math. Soc. 53: 1012-1016, 2006.
- SQP methods for parameter identification problems arising in hyperthermia. Opt. Meth. Softw., Special Issue on Parameter Estimation and Experimental Design 21 (6): 869-887, 2006.
- Asymptotic Mesh Independence of Newton's Method Revisited. SIAM J. Num. Anal. 42 (5): 1830-1845, 2005.
- Interior point methods in function space. SIAM J. Control Opt. 44 (5): 1766-1786, 2005.
- Fully Adaptive Propagation of the Quantum-Classical Liouville Equation. J. Chem. Phys. 120 (19): 8913-8923, 2004.
- Adaptive integration of molecular dynamics. J. Comput. Chem. 24 (15): 1921-1929, 2003.
- Affine Invariant Convergence Analysis for Inexact Augmented Lagrangian-SQP Methods. SIAM J. Control Opt. 41 (3): 875-899, 2002.
- A New Nonlinear Elliptic Multilevel FEM Applied to Regional Hyperthermia. Comput. Vis. Sci. 3 (3): 115-120, 2000.
- The View Template Library. In First Workshop on C++ Template Programming, Erfurt. 2000.
- Global inexact Newton multilevel FEM for nonlinear elliptic problems.
In
- W. Hackbusch
- G. Wittum
- Local inexact Newton multilevel FEM for nonlinear elliptic problems.
In
- M.-O. Bristeau
- G. Etgen
- W. Fitzgibbon
- J.-L. Lions
- J. Periaux
- M. Wheeler
Unrefereed Articles in Journals and Conference Proceedings
- Efficient numerical methods for simulating cardiac electrophysiology with cellular resolution. In 10th Int. Conf. Computational Methods for Coupled Problems in Science and Engineering 2023. 2023.
- A Bayesian Framework for Simulation-based Digital Twins of Bridges. ce/papers 6: 734-740, 2023.
- Evaluation of Model Bias Identification Approaches Based on Bayesian Inference and Applications to Digital Twins. In 5th International Conference on Uncertainty Quantification in Computational Sciences and Engineering. 2023.
- Wear testing of knee implants.
In
- H.-G. Bock
- K.-H. Küfer
- P. Maass
- A. Milde
- V. Schulz
- Solving inverse problems appearing in design and metrology of diffractive optical elements by using Bayesian optimization. In Proc. SPIE. pp. 1069407, 2018.
- Thermografie mit optimierter Anregung für die quantitative Untersuchung von Delaminationen in kohlenstofffaserverstärkten Kunststoffen. In NDT.net Proc. DGZfP 2017. 2017.
- Verbesserung und Qualifizierung der Ultraschallprüfung von Mischnähten im Primärkreis von KKW . In NDT.net Proc. DGZfP 2017. 2017.
- Quantifying parameter uncertainties in optical scatterometry using Bayesian inversion. In Proc. SPIE. pp. 10330, 2017.
- Quantitative Defect Reconstruction in Active Thermography for Fiber-Reinforced Composites. In Proceedings 19th World Conference on Non-Destructive Testing (WCNDT 2016). 2017.
- Ray Tracing Boundary Value Problems: Simulation and SAFT Reconstruction for Ultrasonic Testing. In Proceedings 19th World Conference on Non-Destructive Testing (WCNDT 2016). 2017.
- Adaptive Algorithms for Optimal Hip Implant Positioning . PAMM 17 (1): 203-204, 2017.
- Mathematics cures virtual patients.
In
- P. Deuflhard
- M. Grötschel
- D. Hömberg
- U. Horst
- J. Kramer
- V. Mehrmann
- K. Polthier
- F. Schmidt
- C. Schütte
- M. Skutella
- J. Sprekels
- Data Enhancement for Active Thermography.
In
- G. Cardone
- State Trajectory Compression in Optimal Control. PAMM 10 (1): 579-580, 2010.
- Delayed Residual Compensation for Bidomain Equations. AIP Conference Proceedings 1281 (1): 419-422, 2010.
- On Efficiency and Accuracy in Cardioelectric Simulation.
In
- E. Wilson
- A. Fitt
- H. Ockendon
- J. Norbury
- Benchmarking Solvers of the Monodomain Equation in Cardiac Electrophysiological Modeling.
Biomed. Engineer. 55:
99-102,
2010.
- DOI 10.1515/BMT.2010.712
- Optimization of clinical radiofrequency hyperthermia by use of MR-thermography in a hybrid system.
In
- O. Dössel
- W. Schlegel
- R. Magjarevic
- Advances in the Planning and Control of the MR-guided Regional Hyperthermia Applications. In pp. 1010-1013, Proc. Int. Conf. Electromagnetics in Advanced Applications, ICEAA 2007, Torino, Italy . 2007.
- Soft Tissue Prediction in Computer Assisted Maxillofacial
Surgery Planning: A Quantitative Evaluation of Histomechanical
Modeling using Pre- and Postoperative CT-Data.
In
- Y. Payan
- Function space interior point methods for PDE constrained optimization. PAMM 4 (1): 43-46, 2004.
- Views, A new form of container adaptors. C/C++ Users Journal 18 (4): 40-51, 2000.
Preprints
- Adaptive Gradient Enhanced Gaussian Process Surrogates for Inverse Problems. 2024.
- Model bias identification for Bayesian calibration of stochastic digital twins of bridges. 2023.
- Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods. submitted 2022.
- CINDy: Conditional gradient-based Identification of Non-linear Dynamics - Noise-robust recovery. arXiv:2101.02630 2021.
- Adaptive affine invariant Newton codes for discretized PDEs. ZIB Report 02-33, 2002.
- Linear convergence of an interior point method for linear control constrained optimal control problems. ZIB Report 02-13, 2002.
Theses
- Function Space Complementarity Methods for Optimal Control Problems. 2001.
- Newton-artige Iterationsverfahren zur Minimierung strikt konvexer Funktionale. Freie Universität Berlin 1995. P. Deuflhard
Popular Science Articles
- Molekülbillard.
In
- K. Biermann
- M. Grötschel
- B. Lutz-Westphal