Treecode-accelerated Green iteration for Kohn-Sham density functional theory. (English) Zbl 07506532
Summary: We present a real-space computational method called treecode-accelerated Green Iteration (TAGI) for all-electron Kohn-Sham Density Functional Theory. TAGI is based on a reformulation of the Kohn-Sham equations in which the eigenvalue problem in differential form is converted into a fixed-point problem in integral form by convolution with the modified Helmholtz Green’s function. In each self-consistent field (SCF) iteration, the fixed-points are computed by Green Iteration, where the discrete convolution sums are efficiently evaluated by a GPU-accelerated barycentric Lagrange treecode. Other techniques used in TAGI include a-priori adaptive mesh refinement, Fejér quadrature, singularity subtraction, gradient-free eigenvalue update, and Anderson mixing to accelerate convergence of the SCF and Green Iterations. Ground state energy computations of several atoms (Li, Be, O) and small molecules (\(\mathrm{H}_2\), CO, \(\mathrm{C_6H}_6\)) demonstrate TAGI’s ability to efficiently achieve chemical accuracy.
MSC:
| 65Nxx | Numerical methods for partial differential equations, boundary value problems |
| 65Dxx | Numerical approximation and computational geometry (primarily algorithms) |
| 78Axx | General topics in optics and electromagnetic theory |
Keywords:
all-electron Kohn-Sham density functional theory; real-space integral equation; Green iteration; a-priori adaptive mesh refinement; barycentric Lagrange treecode; GPU accelerationReferences:
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