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math.NA2025
Time-asymptotic behavior of the Boltzmann equation with random inputs in whole space and its stochastic Galerkin approximation
Shi Jin, Qi Shao, Haitao Wang
We consider the Boltzmann equation with random uncertainties arising from the initial data and collision kernel in the {\it whole space}, along with their stochastic Galerkin (SG)…
math.NA2025
Quantum simulation of Helmholtz equations via Schr{ö}dingerization
Anjiao Gu, Shi Jin, Chuwen Ma
The Helmholtz equation is a prototypical model for time-harmonic wave propagation. Numerical solutions become increasingly challenging as the wave number grows, due to the equa…
math.NA2025
Asymptotic uniform estimate of random batch method with replacement for the Cucker-Smale model
Shi Jin, Yuelin Wang, Yuliang Wang
The Random Batch Method (RBM) [S. Jin, L. Li and J.-G. Liu, Random Batch Methods (RBM) for interacting particle systems, J. Comput. Phys. 400 (2020) 108877] is not only an efficien…