Speaker
Description
The solution of the three-dimensional Schrödinger equations for large systems, without any symmetry, requires efficient and robust numerical algorithms due to the large-scale nature of the resulting eigenvalue problem. Conventional methods suffer from slow convergence and require careful tuning depending on the spatial discretization.
Gradient methods combined with preconditioning have been proposed to accelerate the convergence of symmetry-unrestricted Skyrme energy density functionals (EDFs); however, their effectiveness depends on the design of the preconditioner. In this work, we introduce the generalized conjugate gradient (GCG) method for the self-consistent solution of the Hartree--Fock--Bogoliubov equations, which eliminates the need for problem-dependent preconditioning and improves the convergence speed of currently available methods.
The performance of the proposed algorithm is demonstrated on representative nuclear systems, showing improved convergence behavior compared to standard approaches.
The GCG method ultimately provides a promising tool for systematic studies of superheavy, strongly deformed, and drip-line nuclei, where fully three-dimensional calculations are essential for accurate modeling.