Multilevel correction adaptive finite element method for Hartree–Fock equation

This paper presents an efficient Hartree–Fock solver that combines multilevel correction with adaptive refinement for enhanced computational efficiency, integrating an optimized framework for streamlined implementation. This framework solves linearized boundary value problems and refines their solutions via small-scale Hartree–Fock equations in low-dimensional correction spaces. The correction space comprises a coarse space and the solution to the linearized boundary value problem, enabling high accuracy while preserving low-dimensional characteristics. The approach avoids direct handling of large-scale nonlinear eigenvalue systems and dense matrix operations. Furthermore, optimization techniques based on precomputations within the correction space render the total computational workload nearly independent of the number of self-consistent field iterations. This approach significantly accelerates the solution process of the Hartree–Fock equation, effectively mitigating the traditional quadratic scaling demands on computational resources while maintaining precision.