Liebe Mitarbeiter des INS, am kommenden Montag wird Lei Zhang (Shanghai Jiao Tong University) im Rahmen unseres Forschungsseminars "Mathematics of Computation" zum Thema "Construction and analysis of consistent energy based atomistic/continuum coupling methods" vortragen. Der Vortrag findet am Montag, den 30.6. um 15:30 Uhr im Raum 5.002 WE6 statt. Kaffee, Tee und Gebäck stehen bereit. Mit den besten Grüßen Tino Ullrich und Daniel Peterseim Abstract: We discuss the construction and numerical analysis of energy based atomistic/continuum coupling methods (A/C Coupling) for modeling crystalline solids with defects, in particular, the issues of consistency (so-called 'ghost force removal') and stability of the coupling method. For general multi-body interactions on the 2D triangular lattice, we show that ghost force removal (patch test consistent) a/c methods can be constructed for arbitrary interface geometries[1]. Moreover, we prove that all methods within this class are first-order consistent at the atomistic/continuum interface and second-order consistent in the interior of the continuum region. The convergence and stability of the method is analyzed and justified with numerical experiments[2,3]. Development of optimal implementation for consistent methods is dicussed [3]. References: [1] Construction and sharp consistency estimates for atomistic/continuum coupling methods with general interfaces: a 2D model problem, C. Ortner, L. Zhang, SIAM Numerical Analysis. Volume 50, Issue 6, pp. 2940-2965 (2012). [2] (In-)Stability and Stabilisation of QNL-Type Atomistic-to-Continuum Coupling Methods, C. Ortner, A. Shapeev, L. Zhang, 2013, Accepted by SIAM Multiscale Model. Simul. [3] Implementation of Geometric Reconstruction Based Atomistic-to-Continuum Coupling, C. Ortner, L. Zhang, 2013, Accepted by Computer Methods in Applied Mechanics and Engineering _______________________________________________ Ins-mitarbeiter mailing list Ins-mitarbeiter@ins.uni-bonn.de https://mail.ins.uni-bonn.de/mailman/listinfo/ins-mitarbeiter