"A Differential Variational Inequality Approach for the Simulation of Heterogeneous Materials"
L. Wang, J. Lee, M. Anitescu, A. El Azab, L. C. McInnes, T. Munson, and B. Smith
Proc. SciDAC2011 Conference, Denver, CO, . Also Preprint ANL/MCS-P1895-0511
Preprint Version: [pdf]
The phase-field method has recently emerged as a powerful computational approach for modeling and predicting mesoscale morphological and microstructure evolution in materials. While differential variational inequalities (DVIs) arise naturally in the phase-field method, the prevailing approach replaces these by smooth approximations that result in equations that are typically very stiff and limit the efficiency and accuracy of the numerical methods applied. This paper discusses initial work in formulating the phase-field equations as a DVI, which is equivalent to a complementarity problem. We solve the system with newly developed nonlinear algebraic solvers for variational inequalities, and we demonstrate that this DVI approach is accurate and efficient for the resolution of heterogeneous materials problems.