A Hybrid Scheme for Fuzzy Dark Matter Simulations Combining the Schrödinger and Hamilton–Jacobi–Madelung Equations
Journal
The Astrophysical Journal Supplement Series
Journal Volume
279
Journal Issue
2
Start Page
39
ISSN
0067-0049
1538-4365
Date Issued
2025-07-22
Author(s)
Abstract
This paper introduces a hybrid numerical scheme for the fuzzy dark matter (FDM) model: it combines a wave-based approach to solve the Schrödinger equation using Fourier continuations with Gram polynomials and a fluid-based approach to solve the Hamilton-Jacobi-Madelung equations. This hybrid scheme facilitates zoom-in simulations for cosmological volumes beyond the capabilities of wave-based solvers alone and accurately simulates the full nonlinear dynamics of FDM. We detail the implementation of a Hamilton-Jacobi-Madelung solver, the methodology for phase matching at fluid-wave boundaries, the development of a local pseudospectral wave solver based on Fourier continuations, new grid refinement criteria for both fluid and wave solvers, an interpolation algorithm based on Fourier continuations, and the integration of these building blocks into the adaptive mesh refinement code GAMER. The superiority of the scheme is demonstrated through various performance and accuracy tests, tracking the linear power spectrum evolution in a 10 Mpc h-1 box, and a hybrid cosmological simulation in a 5.6 Mpc h-1 box. The corresponding code is published as part of the GAMER project on https://github.com/gamer-project/gamer.
Publisher
American Astronomical Society
Type
journal article