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

电子Schrödinger方程的解在材料科学的许多应用中都是至关重要的，但必须通过数值方法获得，除了最简单的情况外，在足够的精度水平下，这是非常昂贵的。在这个项目中，我们研究了使用基于稀疏网格方法的一系列有效的维度自适应算法来估计这些解的问题；这种方法在大大降低计算成本的情况下提供了显著提高精度的潜力。我们进一步的目标是将这些算法纳入建模技术，这将使在材料老化等现象所涉及的固有长时间尺度上的动力学模拟成为可能。

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.