We develop and implement efficient techniques to solve our model numerically. These techniques include an incremental minimization scheme for the time evolution of the system, routines for the nonconvex mimimization and wavelet-based norm equivalences for a fast evalutation of the nonlocal higher-order contributions.
[1] | M. Arndt, M. Griebel, V. Novák, T. Roubícek, P. Šittner. Martensitic Transformation in NiMnGa Single Crystals: Numerical Simulation and Experiments. Technical Report, University of Bonn, 2005. |
[2] | M. Arndt. Upscaling from Atomistic Models to Higher Order Gradient Continuum Models for Crystalline Solids. Dissertation, Institute for Numerical Simulation, University of Bonn, 2004. |
[3] | M. Arndt, M. Griebel and T. Roubícek. Modelling and numerical simulation of martensitic transformation in shape memory alloys. Contin. Mech. Thermodyn. 15(5):463-485, 2003. |
[4] | M. Arndt. Modelling and numerical simulation of martensitic transformation. In: W. L. Wendland, M. Efendiev (eds.), Analysis and Simulation of Multifield Problems. Proceedings of the International Conference on Multifield Problems 2002, Stuttgart. Springer, 2003. |
[5] | M. Arndt. Upscaling Technique for the Atomistic-Continuum Simulation of Shape Memory Alloys with the EAM Potential. Proceedings of the Sixth World Congress on Computational Mechanics (WCCM 6), Beijing, 2004. |