Abstract
The simulation of events on the atomistic scale is even with the increasing computer power still beyond the means. Thus in the last decades multiscale methods have been developed in order to cope with these problems. Here we present two different multiscale methods. The first method bridges multiscale phenomena in solids (e.g. cracks) from atomistic to continuum by assigning a partition of unity to the atoms. The second method copes with time steps in biomolecular simulations (drug design) by using a conformation dynamics approach.
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References
Deuflhard, P.: From molecular dynamics to conformation dynamics in drug design. In: Kirkilionis, M., Krömker, S., Rannacher, R., Toni, F. (eds.) Trends in Nonlinear Analysis, pp. 269–288. Springer, New York (2003)
Deuflhard, P., Dellnitz, M., Junge, O., Schütte, C.: Computation of essential molecular dynamics by subdivision techniques. In: Deuflhard, P., Hermans, J., Leimkuhler, B., Mark, A., Reich, S., Skeel, R. (eds.) Computational Molecular Dynamics: Challenges, Methods, Ideas., LNCSE, vol. 4, pp. 98–115. Springer, New York (1998)
Deuflhard, P., Schütte, C.: Molecular conformation dynamics and computational drug design. In: Hill, J., Moore, R. (eds.) Applied Mathematics Entering the 21st Century, Invited Talks from the ICIAM 2003 Congress, Sydney, Australia, pp. 91–119 (2004)
Deuflhard, P., Weber, M.: Robust Perron Cluster Analysis in Conformation Dynamics . Lin. Alg. App. 398c, 161–184 (2005)
Fackeldey, K.: The weak coupling method for coupling continuum mechanics with molecular dynamics. Ph.D. thesis, Universität Bonn (2009)
Fackeldey, K., Krause, D., Krause, R.: Concepts and implementation of the weak coupling method. In: Proceedings of 4th International Conference on Multiscale Materials Modeling 2008, pp. 62–65 (2008)
Fackeldey, K., Krause, R.: Multiscale coupling in function space - weak coupling between moelcular dynamics and continuum mechanics. Int. J. Num. Meth. Engrg, 79(12), 1517–1535 (2008)
Hughes, T., Feijoo, G., Mazzei, J., Quincy, J.: The variational mutiscale method - a paradigm for computational mechanics. Comput. Meth. Appl. Mech. 166, 3–24 (1998)
Schütte, C.: Conformational dynamics: Modelling, theory, algorithm, and application to biomolecules. habilitation thesis (1999)
Schütte, C., Fischer, A., Huisinga, W., Deuflhard, P.: A direct approach to conformational dynamics based on hybrid Monte Carlo. J. Comput. Phys. 151, 146–169 (1999)
Schweitzer, M.: A Parallel Multilevel Partition of Unity Method for Elliptic Partial Differential Equations. No. 29 in LNCSE. Springer, New York (2003)
Wagner, G., Liu, W.: Coupling of atomistic and continuum simulations using a bridging scale decomposition. J. Comp. Phy. 190, 1261–1289 (2003)
Weber, M.: Meshless methods in conformation dynamics. Ph.D. thesis, Freie Universität Berlin (2006)
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Fackeldey, K. (2012). Multiscale Methods in Time and Space. In: Günther, M., Bartel, A., Brunk, M., Schöps, S., Striebel, M. (eds) Progress in Industrial Mathematics at ECMI 2010. Mathematics in Industry(), vol 17. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25100-9_72
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DOI: https://doi.org/10.1007/978-3-642-25100-9_72
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