Acceleration of material-dominated calculations via phase-space simplicial subdivision and interpolation
We develop an acceleration method for material-dominated calculations based on phase-space simplicial interpolation of the relevant material-response functions. This process of interpolation constitutes an approximation scheme by which an exact material-response function is replaced by a sequence of approximating response functions. The terms in the sequence are increasingly accurate, thus ensuring the convergence of the overall solution. The acceleration ratio depends on the dimensionality, the complexity of the deformation, the time-step size, and the fineness of the phase-space interpolation. We ascertain these trade-offs analytically and by recourse to selected numerical tests. The numerical examples with piecewise-quadratic interpolation in phase space confirm the analytical estimates.
© 2015 John Wiley & Sons, Ltd. Received 2 October 2014; Revised 8 January 2015; Accepted 8 January 2015. Financial support for B. K. from the Alexander von Humboldt Foundation, Germany, is gratefully acknowledged. M. O. gratefully acknowledges support from the US Army Research Laboratory (ARL) through the Materials in Extreme Dynamic Environments (MEDE) Collaborative Research Alliance (CRA) under Award Number W911NF-11-R-0001.