学术报告报告主题: A hierarchical splines-based h-adaptive isogeometric solver for all-electron Kohn--Sham equation
报 告 人: 况阳副教授
报告时间： 2025年 4月1日（星期二）下午15:30-17:00
报告地点： 腾讯会议（507-8644-4575）
邀 请 人: 姚文琦 副教授
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数学学院
2025年3月26日
报告摘要：
We present a novel h-adaptive isogeometric solver utilizing high-order hierarchical splines to solve the all-electron Kohn--Sham equation. In virtue of the smooth nature of Kohn--Sham wavefunctions across the domain, except at the nuclear positions, high-order globally regular basis functions such as B-splines are well suited for achieving high accuracy. To further handle the singularities in the external potential at the nuclear positions, an h-adaptive framework based on the hierarchical splines is presented with a specially designed residual-type error indicator, allowing for different resolutions on the domain. The generalized eigenvalue problem raising from the discretized Kohn--Sham equation is effectively solved by the locally optimal block preconditioned conjugate gradient (LOBPCG) method with an elliptic preconditioner, and it is found that the eigensolver's convergence is independent of the spline basis order. A series of numerical experiments confirm the effectiveness of the h-adaptive framework, with a notable experiment that the numerical accuracy 0.001 Hartree/particle in the all-electron simulation of a methane molecule is achieved using only 6355 degrees of freedom, demonstrating the competitiveness of our solver for the all-electron Kohn--Sham equation.
报告人介绍：
况阳，广东工业大学数学与统计学院特聘副教授。2019年于澳门大学获得哲学（数学）博士学位，2019-2021年在新加坡国立大学数学系从事博士后工作。主要研究方向是量子系统中偏微分方程的数值模拟，先后在SISC, SINUM, JCP, CICP, PRD等杂志发表十余篇学术论文，目前主持一项国家自然科学基金青年基金项目，一项国家自然科学基金数学天元访问基金项目，和一项广州市基金。