Solving the linear transport equation by a deep neural network approach
In this paper, we study the linear transport model by adopting the deep learning method, in
particular the deep neural network (DNN) approach. While the interest of using DNN to study …
particular the deep neural network (DNN) approach. While the interest of using DNN to study …
An asymptotic preserving discontinuous Galerkin method for a linear Boltzmann semiconductor model
VP DeCaria, CD Hauck, SR Schnake - SIAM Journal on Numerical Analysis, 2024 - SIAM
A key property of the linear Boltzmann semiconductor model is that as the collision
frequency tends to infinity, the phase space density converges to an isotropic function, called …
frequency tends to infinity, the phase space density converges to an isotropic function, called …
A collision-based hybrid method for the BGK equation
We apply the collision-based hybrid method introduced by Hauck and McClarren [1] to the
Boltzmann equation with the BGK operator and a hyperbolic scaling. An implicit treatment of …
Boltzmann equation with the BGK operator and a hyperbolic scaling. An implicit treatment of …
Anderson acceleration with approximate calculations: applications to scientific computing
ML Pasini, MP Laiu - arXiv preprint arXiv:2206.03915, 2022 - arxiv.org
We provide rigorous theoretical bounds for Anderson acceleration (AA) that allow for
efficient approximate residual calculations in AA, which in turn reduce computational time …
efficient approximate residual calculations in AA, which in turn reduce computational time …
Anderson acceleration with approximate calculations: Applications to scientific computing
M Lupo Pasini, MP Laiu - Numerical Linear Algebra with …, 2022 - Wiley Online Library
We provide rigorous theoretical bounds for Anderson acceleration (AA) that allow for
approximate calculations when applied to solve linear problems. We show that, when the …
approximate calculations when applied to solve linear problems. We show that, when the …