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Showing 2019 · math.NAShow all
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math.NA2019★ 4 cited
Quasi-Monte Carlo sampling for machine-learning partial differential equations
Jingrun Chen, Rui Du, Panchi Li +1
Solving partial differential equations in high dimensions by deep neural network has brought significant attentions in recent years. In many scenarios, the loss function is defined…
math.NA2019★ 24 cited
Two improved Gauss-Seidel projection methods for Landau-Lifshitz-Gilbert equation
Panchi Li, Changjian Xie, Rui Du +2
In this paper, we present two improved Gauss-Seidel projection methods with unconditional stability. The first method updates the gyromagnetic term and the damping term simultaneou…
math.NA2019
A multiscale reduced basis method for Schrödinger equation with multiscale and random potentials
Jingrun Chen, Dingjiong Ma, Zhiwen Zhang
The semiclassical Schrödinger equation with multiscale and random potentials often appears when studying electron dynamics in heterogeneous quantum systems. As time evolves, the wa…