(untitled) (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 work of [24], the paper adopts a similar domain decomposition that the computational domain is first decomposed into a number of cuboid subdomains satisfying each nucleus is located in the center of one cube, in which a small ball element centered at the site of the nucleus is attached, and the remainder of the cube is further partitioned into six curvilinear hexahedrons. Specially designed Sobolev-orthogonal basis is adopted in each ball. Classic conforming spectral element approximations using mapped Jacobi polynomials are implemented on the curvilinear hexahedrons and the cuboid elements without 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 Coulomb singularities.