@misc{GalliatHuisingaDeuflhard1999, author = {Galliat, Tobias and Huisinga, Wilhelm and Deuflhard, Peter}, title = {Self-Organizing Maps Combined with Eigenmode Analysis for Automated Cluster Identification}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4279}, number = {SC-99-38}, year = {1999}, abstract = {One of the important tasks in Data Mining is automated cluster analysis. Self-Organizing Maps (SOMs) introduced by {\sc Kohonen} are, in principle, a powerful tool for this task. Up to now, however, its cluster identification part is still open to personal bias. The present paper suggests a new approach towards automated cluster identification based on a combination of SOMs with an eigenmode analysis that has recently been developed by {\sc Deuflhard et al.} in the context of molecular conformational dynamics. Details of the algorithm are worked out. Numerical examples from Data Mining and Molecular Dynamics are included.}, language = {en} } @misc{Deuflhard1990, author = {Deuflhard, Peter}, title = {Zuses Werk weiterdenken. (Vortrag)}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4717}, number = {TR-90-07}, year = {1990}, language = {de} } @misc{DeuflhardHuisingaFischeretal.1998, author = {Deuflhard, Peter and Huisinga, Wilhelm and Fischer, Alexander and Sch{\"u}tte, Christof}, title = {Identification of Almost Invariant Aggregates in Reversible Nearly Uncoupled Markov Chains}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3469}, number = {SC-98-03}, year = {1998}, abstract = {The topic of the present paper bas been motivated by a recent computational approach to identify chemical conformations and conformational changes within molecular systems. After proper discretization, the conformations show up as almost invariant aggregates in reversible nearly uncoupled Markov chains. Most of the former work on this subject treated the direct problem: given the aggregates, analyze the loose coupling in connection with the computation of the stationary distribution (aggregation/disaggregation techniques). In contrast to that the present paper focuses on the inverse problem: given the system as a whole, identify the almost invariant aggregates together with the associated transition probabilites. A rather simple and robust algorithm is suggested and illustrated by its application to the n-pentane molecule.}, language = {en} } @misc{SchuetteFischerHuisingaetal.1998, author = {Sch{\"u}tte, Christof and Fischer, Alexander and Huisinga, Wilhelm and Deuflhard, Peter}, title = {A Hybrid Monte Carlo Method for Essential Molecular Dynamics}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3474}, number = {SC-98-04}, year = {1998}, abstract = {Recently, a novel concept for the computation of essential features of Hamiltonian systems (such as those arising in molecular dynamics) has been proposed. The realization of that concept was based on subdivision techniques applied to the Frobenius--Perron operator for the dynamical system. The present paper suggests an alternative but related concept based on statistical mechanics, which allows to attack realistic molecular systems. In a first step, the frequency of conformational changes is characterized in statistical terms leading to the definition of some Markov operator \$T\$ that describes the corresponding transition probabilities within the canonical ensemble. In a second step, a discretization of \$T\$ via hybrid Monte Carlo techniques (based on short term subtrajectories only) is shown to lead to a stochastic matrix \$P\$. With these theoretical preparations, an identification algorithm for conformations is applicable (to be presented elsewhere). Numerical results for the n-pentane molecule are given and interpreted.}, language = {en} } @misc{DeuflhardFrieseSchmidt1997, author = {Deuflhard, Peter and Friese, Tilmann and Schmidt, Frank}, title = {A Nonlinear Multigrid Eigenproblem Solver for the Complex Helmholtz Equation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3240}, number = {SC-97-55}, year = {1997}, abstract = {The paper is motivated by the need for a fast robust adaptive multigrid method to solve complex Helmholtz eigenvalue problems arising from the design of optical chips. A nonlinear multigrid method is developed, which can be regarded as an extension of a previous adaptive Rayleigh quotient minimization method for selfadjoint Helmholtz eigenproblems. Since the complex Helmholtz operator is just a compact nonselfadjoint perturbation of a selfadjoint operator, linear algebra techniques like Schur decomposition can be extended from the finite dimensional case. The efficiency of the derived adaptive nonlinear multigrid method is illustrated by computations for a technologically relevant integrated optics component containing Multi Quantum Well Layers.}, language = {en} } @book{DeuflhardBornemann1994, author = {Deuflhard, Peter and Bornemann, Folkmar A.}, title = {Numerische Mathematik. II}, publisher = {De Gruyter Lehrbuch. Berlin: de Gruyter}, year = {1994}, language = {en} } @book{DeuflhardHohmann1993, author = {Deuflhard, Peter and Hohmann, Andreas}, title = {Numerische Mathematik I. Eine algorithmisch orientierte Einf{\"u}hrung.(Numerical mathematics I. An algorithmically oriented introduction)}, edition = {2}, publisher = {de Gruyter Lehrbuch. Berlin: Walter de Gruyter,}, year = {1993}, language = {en} } @article{WeiserDeuflhard2007, author = {Weiser, Martin and Deuflhard, Peter}, title = {Inexact central path following algorithms for optimal control problems}, volume = {46}, journal = {SIAM J. Control Opt.}, number = {3}, pages = {792 -- 815}, year = {2007}, language = {en} } @inproceedings{BaderNowakDeuflhard1985, author = {Bader, G. and Nowak, Ulrich and Deuflhard, Peter}, title = {An Advanced Simulation Package for Large Chemical Reaction Systems}, booktitle = {Stiff Computation. Proc. Intern. Conf. Park City, Utah/USA}, editor = {Aiken, R.}, publisher = {Oxford University Press}, year = {1985}, language = {en} } @inproceedings{BeckDeuflhardHegeetal.1997, author = {Beck, Rudolf and Deuflhard, Peter and Hege, Hans-Christian and Seebass, Martin and Stalling, Detlev}, title = {Numerical Algorithms and Visualization in Medical Treament Planning}, booktitle = {Visualization and Mathematics}, editor = {Hege, Hans-Christian and Polthier, Konrad}, publisher = {Springer-Verlag}, pages = {303 -- 328}, year = {1997}, language = {en} } @article{BeckDeuflhardHiptmairetal.1999, author = {Beck, Rudolf and Deuflhard, Peter and Hiptmair, Ralf and Hoppe, Ronald H. W. and Wohlmuth, Barbara}, title = {Adaptive multilevel methods for edge element discretizations of Maxwell's equations}, volume = {8}, journal = {Surv. Math. Ind.}, number = {3-4}, pages = {271 -- 312}, year = {1999}, language = {en} }