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

电子薛定谔方程的解在材料科学的许多应用中非常重要，但必须通过数值计算来获得，这在除了最简单的情况之外的所有情况下都是非常昂贵的。在这个项目中，我们调查的问题，估计这些解决方案使用一个家庭的有效的尺寸自适应算法的基础上稀疏网格方法，这种方法提供了显着提高精度的潜力，大大降低了计算成本。我们进一步的目标是将这些算法纳入建模技术，这将使在固有的长时间尺度的动态模拟所涉及的现象，如材料老化。

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.