Place: 4th GAMM Seminar for Multiscale Material Modelling, Bochum, Germany
Alexander Stukowski, Technical University Darmstadt, Darmstadt, Germany
The focus of this contribution is on energy minimisation in concurrent multiscale methods which bridge the scales from atomic to continuum via coarse-graining. Our point of departure is an optimisation algorithm which was originally introduced for purely atomistic models and methods . We propose an adaption of this algorithm to the setting of the quasicontinuum method as a prominent example of an atomistic finite-element method with adaptive resolution. The novel minimiser called FIRE for Fast Inertial Relaxation Engine can be understood as a modification of the Steepest Descent (SD) method. It improves SD by accelerating the system in the direction of the force, making the minimisation more aggressive. FIRE takes dynamical steps and resets velocity if the force and velocity are in opposite directions. In representative examples of nano-to-micro multiscale materials simulation we assess the performance of FIRE with respect to efficiency and stability. We test it against well-established optimization methods like SD, the conjugate gradient (CG) and L-BFGS methods.
 Bitzek E., Koskinen P., Gähler F., Moseler M., Gumbsch P. PRL 97, 170201 (2006).