Solution of boundary-element problems using the fast-inertial-relaxation-engine method

Abstract

The fast-inertial-relaxation engine (FIRE) has proven to efficiently find local minima of potential energies or related penalty functions although its implementation requires only few, additional lines of code in a molecular-dynamics or steepest-descent program. So far, FIRE has been predominantly applied to particle-based or low-dimensional problems. In this work, we demonstrate that it can also benefit the solution of boundary-value problems. Towards this end, we study the mechanical contact between an elastic body and a rigid indenter of varying complexity by augmenting Green's function molecular dynamics (GFMD) with FIRE. We find a rather remarkable speedup, which can be further enhanced when choosing the masses associated with the eigenmodes of the free elastic solid appropriately. For the investigated adhesive and randomly rough indenter with typical system size, 100 mass-weighted FIRE-GFMD iterations suffice to relax the excess energy to 10−3 of its original value. The standard GFMD method needs 25 times more iterations. For the investigated problems, FIRE-GFMD even appears to slightly outperform conjugate-gradient based optimization.