ELUCID-DESI I: A Parallel MPI Implementation of the Initial Condition Solver for Large-Scale Reconstruction Simulations

We present a highly scalable, MPI-parallelized framework for reconstructing the initial cosmic density field, designed to meet the computational demands of next-generation cosmological simulations, particularly the upcoming ELUCID-DESI simulation based on DESI BGS data. Building upon the Hamiltonian Monte Carlo approach and the FastPM solver, our code employs domain decomposition to efficiently distribute memory between nodes. Although communication overhead increases the per-step runtime of the MPI version by roughly a factor of eight relative to the shared-memory implementation, our scaling tests-spanning different particle numbers, core counts, and node layouts-show nearly linear scaling with respect to both the number of particles and the number of CPU cores. Furthermore, to significantly reduce computational costs during the initial burn-in phase, we introduce a novel ``guess'' module that rapidly generates a high-quality initial density field. The results of the simulation test confirm substantial efficiency gains: for $256^3$ particles, 53 steps ($\sim$ 54 core hours) are saved, accelerating convergence by a factor of $\sim$ 18; for $1024^3$, 106 steps ($\sim$7500 core hours), achieving a speedup factor of $\sim$ 3. The total core hour gain grows with the number of particles, rendering large-volume reconstructions computationally practical for upcoming surveys, including our planned ELUCID-DESI reconstruction simulation with $4096^3$ particles. We estimate that achieving convergence for this scale (targeting DESI-BGS data) requires about 800 HMCMC steps ($\sim$ 5 million core hours). Our initial guess module will save approximately 360 steps ($\sim$2.3 million core hours), reducing the total computational time by about 45\%.