6 papers
An hp-version time stepping spectral Monte Carlo method for semi-linear parabolic equations
Jiaying Feng, Zhiyuan Hui, Changtao Sheng +1
In this paper, we present an -version time-stepping spectral Monte Carlo method for solving semi-linear parabolic equations. The key innovation lies in constructing an exponent…
A modified projected walk on spheres method for elliptic equations on high-dimensional embedded manifolds: algorithm and error estimates
Zhiyuan Hui, Changtao Sheng, Bihao Su +1
In this paper, we propose a modified projected Walk on Spheres method (MPWoS) for screened Poisson equations on embedded manifolds. The method employs local extensions together wit…
FNWoS: Fractional Neural Walk-on-Spheres Methods for High-Dimensional PDEs Driven by -stable Lévy Process on Irregular Domains
Ling Guo, Mingxin Qin, Changtao Sheng +2
In this paper, we develop a highly parallel and derivative-free fractional neural walk-on-spheres method (FNWoS) for solving high-dimensional fractional Poisson equations on irregu…
A derivative-free localized stochastic method for very high-dimensional semilinear parabolic PDEs
Shuixin Fang, Changtao Sheng, Bihao Su +1
We develop a mesh-free, derivative-free, matrix-free, and highly parallel localized stochastic method for high-dimensional semilinear parabolic PDEs. The efficiency of the proposed…
Efficient implicit-explicit sparse stochastic method for high dimensional semi-linear nonlocal diffusion equations
Changtao Sheng, Bihao Su, Chenglong Xu
In this paper, we present a sparse grid-based Monte Carlo method for solving high-dimensional semi-linear nonlocal diffusion equations with volume constraints. The nonlocal model i…
Exponentially accurate spectral Monte Carlo method for linear PDEs and their error estimates
Jiaying Feng, Changtao Sheng, Chenglong Xu
This paper introduces a spectral Monte Carlo iterative method (SMC) for solving linear Poisson and parabolic equations driven by -stable Lévy process with , which…