@misc{KrauseFackeldeyKrause, author = {Krause, Dorian and Fackeldey, Konstantin and Krause, Rolf}, title = {A parallel multiscale simulation toolbox for coupling molecular dynamics and finite elements}, issn = {1438-0064}, doi = {10.1007/978-3-319-00786-1_14}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-42354}, abstract = {It is the ultimate goal of concurrent multiscale methods to provide computational tools that allow to simulation physical processes with the accuracy of micro-scale and the computational speed of macro-scale models. As a matter of fact, the efficient and scalable implementation of concurrent multiscale methods on clusters and supercomputers is a complicated endeavor. In this article we present the parallel multiscale simulation tool MACI which has been designed for efficient coupling between molecular dynamics and finite element codes. We propose a specification for a thin yet versatile interface for the coupling of molecular dynamics and finite element codes in a modular fashion. Further we discuss the parallelization strategy pursued in MACI, in particular, focusing on the parallel assembly of transfer operators and their efficient execution.}, 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}, series = {SIAM Multiscale Model. Simul.}, volume = {9}, journal = {SIAM Multiscale Model. Simul.}, doi = {/10.1137/100782097}, pages = {1459 -- 1494}, year = {2011}, language = {en} } @inproceedings{FackeldeyKrauseKrause2010, author = {Fackeldey, Konstantin and Krause, Dorian and Krause, Rolf}, title = {Numerical Validation of Constraints Based Multiscale Methods}, series = {Lecture Notes in Computational Science and Engineering}, booktitle = {Lecture Notes in Computational Science and Engineering}, editor = {Griebel, Michael and Schweitzer, M.}, pages = {141 -- 154}, year = {2010}, language = {en} } @inproceedings{FackeldeyKrauseKrause2008, author = {Fackeldey, Konstantin and Krause, Dorian and Krause, Rolf}, title = {Quadrature and Implementation of the Weak Coupling Method}, series = {MMM 2008: Proceedings of the 4th International Conference on Multiscale Materials Modelling, 27-31 October 2008, Tallahassee, Fla.}, 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}, series = {Proceedings of the third Inter. Confer. on Comp. Meth. for Coupled Problems in Science and Engrg}, booktitle = {Proceedings of the third Inter. Confer. on Comp. Meth. for Coupled Problems in Science and Engrg}, pages = {1023pp}, year = {2009}, language = {en} } @article{KrauseFackeldeyKrause2014, author = {Krause, Dorian and Fackeldey, Konstantin and Krause, Rolf}, title = {A Parallel Multiscale Simulation Toolbox for Coupling Molecular Dynamics and Finite Elements}, series = {Singular Phenomena and Scaling in Mathematical Models}, journal = {Singular Phenomena and Scaling in Mathematical Models}, editor = {Griebel, Michael}, publisher = {Springer International Publishing}, doi = {10.1007/978-3-319-00786-1_14}, pages = {327 -- 346}, year = {2014}, language = {en} } @misc{SanderKrause, author = {Sander, Oliver and Krause, Rolf}, title = {Automatic Construction of Boundary Parametrizations for Geometric Multigrid Solvers}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7240}, number = {03-02}, abstract = {We present an algorithm that constructs parametrizations of boundary and interface surfaces automatically. Starting with high-resolution triangulated surfaces describing the computational domains, we iteratively simplify the surfaces yielding a coarse approximation of the boundaries with the same topological type. While simplifying we construct a function that is defined on the coarse surface and whose image is the original surface. This function allows access to the correct shape and surface normals of the original surface as well as to any kind of data defined on it. Such information can be used by geometric multigrid solvers doing adaptive mesh refinement. Our algorithm runs stable on all types of input surfaces, including those that describe domains consisting of several materials. We have used our method with success in different fields and we discuss examples from structural mechanics and biomechanics.}, language = {en} } @misc{DeuflhardKrauseErtel, author = {Deuflhard, Peter and Krause, Rolf and Ertel, Susanne}, title = {A Contact-Stabilized Newmark Method for Dynamical Contact Problems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9361}, number = {06-42}, abstract = {The numerical integration of dynamical contact problems often leads to instabilities at contact boundaries caused by the non-penetration condition between bodies in contact. Even a recent energy dissipative modification due to Kane et al. (1999), which discretizes the non-penetration constraints implicitly, is not able to circumvent artificial oscillations. For this reason, the present paper suggests a contact stabilization which avoids artificial oscillations at contact interfaces and is also energy dissipative. The key idea of this contact stabilization is an additional \$L^2\$-projection at contact interfaces, which can easily be added to any existing time integration scheme. In case of a lumped mass matrix, this projection can be carried out completely locally, thus creating only negligible additional numerical cost. For the new scheme, an elementary analysis is given, which is confirmed by numerical findings in an illustrative test example (Hertzian two body contact).}, language = {en} } @misc{BornemannKrause, author = {Bornemann, Folkmar A. and Krause, Rolf}, title = {Classical and Cascadic Multigrid - A Methodical Comparison}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2368}, number = {SC-96-25}, abstract = {Using the full multigrid method {\em without} any coarse grid correction steps but with an a posteriori control of the number of smoothing iterations was shown by Bornemann and Deuflhard [1996] to be an optimal iteration method with respect to the energy norm. They named this new kind of multigrid iteration the {\em cascadic multigrid method}. However, numerical examples with {\em linear} finite elements raised serious doubts whether the cascadic multigrid method can be made optimal with respect to the {\em \$L^2\$-norm}. In this paper we prove that the cascadic multigrid method cannot be optimal for linear finite elements and show that the case might be different for higher order elements. We present a careful analysis of the two grid variant of the cascadic multigrid method providing a setting where one can understand the methodical difference between the cascadic multigrid method and the classical multigrid \$V\$-cycle almost immediately. As a rule of thumb we get that whenever the cascadic multigrid works the classical multigrid will work too but not vice versa.}, language = {en} } @article{DeuflhardKrauseErtel2007, author = {Deuflhard, Peter and Krause, Rolf and Ertel, Susanne}, title = {A Contact-Stabilized Newmark Method for Dynamical Contact Problems}, series = {International Journal for Numerical Methods in Engineering}, volume = {73}, journal = {International Journal for Numerical Methods in Engineering}, number = {9}, pages = {1274 -- 1290}, year = {2007}, language = {en} }