Sparse grid methods for the electronic Schrödinger equation and mesoscopic material models (A07)

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Solutions of the electronic Schrödinger equation are fundamentally important in numerous applications in materials science, but must be obtained numerically, which is prohibitively expensive at sufficient levels of accuracy in all but the simplest cases. In this project, we investigate the problem of estimating these solutions using a family of efficient dimension-adaptive algorithms based on sparse grid methods; this approach offers the potential for significant improvements in accuracy at greatly reduced computational cost. We further aim to incorporate these algorithms into modeling techniques which will enable the simulation of dynamics over the inherently long timescales involved in phenomena such as material ageing.