A Mortar Spectral Element Method for Full-Potential Electronic Structure Calculations (Communications in Computational Physics, 2021)
In this paper, we propose an efficient mortar spectral element approximation scheme for full-potential electronic structure calculations. As a subsequent workof [24], the paper adopts a similar domain decomposition that the computational domain is first decomposed into a number of cuboid subdomains satisfying each nucleusis located in the center of one cube, in which a small ball element centered at the siteof the nucleus is attached, and the remainder of the cube is further partitioned into sixcurvilinear hexahedrons. Specially designed Sobolev-orthogonal basis is adopted ineach ball. Classic conforming spectral element approximations using mapped Jacobipolynomials are implemented on the curvilinear hexahedrons and the cuboid elementswithout nuclei. A mortar technique is applied to patch the different discretizations.Numerical experiments are carried out to demonstrate the efficiency of our scheme,especially the spectral convergence rates of the ground state approximations. Essentially the algorithm can be extended to general eigenvalue problems with the Coulombsingularities.
Keywords: Kohn-Sham equation; full-potential calculations; mortar spectral element method; exponential order of convergence.