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Large-scale applications of energy density functional (EDF) methods depend onfast and reliable algorithms to solve the associated non-linearself-consistency problem. When dealing with large single-particle variationalspaces, existing solvers can become very slow, and their performance dependenton manual fine-tuning of numerical parameters. In addition, convergence cansensitively depend on particularities of the EDF's parametrisation underconsideration. Using the widely-used Skyrme EDF as an example, we investigatethe impact of the parametrisation of the EDF, both in terms of the operatorstructures present and the size of coupling constants, on the convergence ofnumerical solvers. We focus on two aspects of the self-consistency cycle, whichare the diagonalisation of a fixed single-particle Hamiltonian on one hand andthe evolution of the mean-field densities and potentials on the other.Throughout the article we use a coordinate-space representation, for which thebehaviour of algorithms can be straightforwardly analysed. We propose twoalgorithmic improvements that are easily implementable in existing solvers,heavy-ball dynamics and potential preconditioning. We demonstrate that thesemethods can be made virtually parameter-free, requiring no manual fine-tuningto achieve near-optimal performance except for isolated cases. The combinationof both methods decreases substantially the CPU time required to obtainconverged results. The improvements are illustrated for the MOCCa code thatsolves the self-consistent HFB problem in a 3d coordinate space representationfor parametrisations of the standard Skyrme EDF at next-to-leading order ingradients and its extension to next-to-next-to-leading order.

Iterative approaches to the self-consistent nuclear energy density functional problem. Heavy ball dynamics and potential preconditioning