@misc{BujotzekSchuettNielsenetal.2013, author = {Bujotzek, Alexander and Sch{\"u}tt, Ole and Nielsen, Adam and Fackeldey, Konstantin and Weber, Marcus}, title = {Efficient Conformational Analysis by Partition-of-Unity Coupling}, journal = {Math Chem}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-42570}, year = {2013}, abstract = {Obtaining a sufficient sampling of conformational space is a common problem in molecular simulation. We present the implementation of an umbrella-like adaptive sampling approach based on function-based meshless discretization of conformational space that is compatible with state of the art molecular dynamics code and that integrates an eigenvector-based clustering approach for conformational analysis and the computation of inter-conformational transition rates. The approach is applied to three example systems, namely n-pentane, alanine dipeptide, and a small synthetic host-guest system, the latter two including explicitly modeled solvent.}, language = {en} } @misc{WeberFackeldeySchuette2017, author = {Weber, Marcus and Fackeldey, Konstantin and Sch{\"u}tte, Christof}, title = {Set-free Markov State Building}, issn = {1438-0064}, doi = {10.1063/1.4978501}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-62167}, year = {2017}, abstract = {Molecular dynamics (MD) simulations face challenging problems since the timescales of interest often are much longer than what is possible to simulate and even if sufficiently long simulation are possible the complex nature of the resulting simulation data makes interpretation difficult. Markov State Models (MSMs) help to overcome these problems by making experimentally relevant timescales accessible via coarse grained representations that also allows for convenient interpretation. However, standard set-based MSMs exhibit some caveats limiting their approximation quality and statistical significance. One of the main caveats results from the fact that typical MD trajectories repeatedly re-cross the boundary between the sets used to build the MSM which causes statistical bias in estimating the transition probabilities between these sets. In this article, we present a set-free approach to MSM building utilizing smooth overlapping ansatz functions instead of sets and an adaptive refinement approach. This kind of meshless discretization helps to overcome the recrossing problem and yields an adaptive refinement procedure that allows to improve the quality of the model while exploring state space and inserting new ansatz functions into the MSM.}, language = {en} } @incollection{DurmazFackeldeyWeber2011, author = {Durmaz, Vedat and Fackeldey, Konstantin and Weber, Marcus}, title = {A rapidly Mixing Monte Carlo Method for the Simulation of Slow Molecular Processes}, booktitle = {Applications of Monte Carlo Methods in Biology, Medicine and Other Fields of Science}, editor = {Mode, Ch.}, publisher = {InTech}, year = {2011}, language = {en} } @inproceedings{FackeldeyKrauseKrause2008, author = {Fackeldey, Konstantin and Krause, Dorian and Krause, Rolf}, title = {Quadrature and Implementation of the Weak Coupling Method}, booktitle = {MMM 2008: Proceedings of the 4th International Conference on Multiscale Materials Modelling, 27-31 October 2008, Tallahassee, Fla.}, pages = {62 -- 65}, year = {2008}, language = {en} } @inproceedings{FackeldeyKrauseKrause2009, author = {Fackeldey, Konstantin and Krause, Dorian and Krause, Rolf}, title = {Weak Coupling Algorithms in Multiscale Simulations}, booktitle = {Proceedings of the third Inter. Confer. on Comp. Meth. for Coupled Problems in Science and Engrg}, pages = {1023pp}, year = {2009}, language = {en} } @inproceedings{FackeldeyKrauseKrause2010, author = {Fackeldey, Konstantin and Krause, Dorian and Krause, Rolf}, title = {Numerical Validation of Constraints Based Multiscale Methods}, booktitle = {Lecture Notes in Computational Science and Engineering}, editor = {Griebel, Michael and Schweitzer, M.}, pages = {141 -- 154}, year = {2010}, language = {en} } @article{FackeldeyKrauseKrauseetal.2011, author = {Fackeldey, Konstantin and Krause, Dorian and Krause, Rolf and Lenzen, Christoph}, title = {Coupling Molecular Dynamics and Continua with Weak Constraints}, volume = {9}, journal = {SIAM Multiscale Model. Simul.}, doi = {/10.1137/100782097}, pages = {1459 -- 1494}, year = {2011}, language = {en} } @inproceedings{FackeldeyKrauseSchweitzer2008, author = {Fackeldey, Konstantin and Krause, Rolf and Schweitzer, M.}, title = {Stability of Energy Transfer in the Weak Coupling Method}, volume = {65}, booktitle = {Meshfree Methods for Partial Differential Equations IV}, editor = {Griebel, Michael and Schweitzer, M.}, pages = {111 -- 121}, year = {2008}, language = {en} } @article{Fackeldey2011, author = {Fackeldey, Konstantin}, title = {Coupling Meshbased and Meshfree Methods by a Transfer Operator Approach}, volume = {69}, journal = {IJPAM}, number = {2}, pages = {185 -- 202}, year = {2011}, language = {en} } @article{FackeldeyKrause2009, author = {Fackeldey, Konstantin and Krause, Rolf}, title = {Multiscale Coupling in Function Space - Weak Coupling between Molecular Dynamics and Continuum Mechanics}, volume = {79}, journal = {International Journal for Numerical Methods in Engineering}, number = {12}, doi = {10.1002/nme.2626}, pages = {1517 -- 1535}, year = {2009}, language = {en} } @phdthesis{Fackeldey2009, author = {Fackeldey, Konstantin}, title = {The Weak Coupling Method for Coupling Continuum Mechanics with Molecular Dynamics}, year = {2009}, language = {en} } @inproceedings{FackeldeyKrause2007, author = {Fackeldey, Konstantin and Krause, Rolf}, title = {Solving Frictional Contact Problems with Multigrid Efficiency}, volume = {50}, booktitle = {Proc.of the 16th International Conference on Domain Decomposition Methods}, editor = {Widlund, Olof}, pages = {547 -- 554}, year = {2007}, language = {en} } @inproceedings{FackeldeyKrause2007, author = {Fackeldey, Konstantin and Krause, Rolf}, title = {Weak coupling in function space}, volume = {7}, booktitle = {Proc. Appl. Math. Mech.}, number = {1}, pages = {2020113pp}, year = {2007}, language = {en} } @inproceedings{FackeldeyKrause2008, author = {Fackeldey, Konstantin and Krause, Rolf}, title = {CM/MD Coupling - A Function Space Oriented Multiscale-Coupling Approach}, volume = {8}, booktitle = {Proc. Appl. Math. Mech.}, number = {1}, pages = {10495pp}, year = {2008}, language = {en} } @inproceedings{FackeldeyBujotzekWeber2012, author = {Fackeldey, Konstantin and Bujotzek, Alexander and Weber, Marcus}, title = {A meshless discretization method for Markov state models applied to explicit water peptide folding simulations}, volume = {89}, booktitle = {Meshfree Methods for Partial Differential Equations VI}, publisher = {Springer}, pages = {141 -- 154}, year = {2012}, language = {en} }