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

电子薛定谔方程和介观材料模型的稀疏网格方法 (A07)

• 批准号: 233524792
• 金额: --
• 依托单位: Institut für Numerische Simulation
• 依托单位国家: 德国
• 项目类别: Collaborative Research Centres
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/233524792?language=en
• 关键词: Sparse; grid; methods; electronic; Schr

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.

电子薛定谔方程的解在材料科学中的许多应用中都是非常重要的，但必须通过数值获得，除了最简单的情况外，在足够的精度水平下，数值求解的成本都高得令人望而却步。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；这种方法在极大地降低计算成本的情况下提供了显著提高精度的潜力。我们的进一步目标是将这些算法整合到建模技术中，从而能够在材料老化等现象所涉及的固有的长时间尺度上模拟动力学。