# Error analysis of an asymptotic preserving dynamical low-rank integrator for the multi-scale radiative transfer equation

@article{Ding2019ErrorAO, title={Error analysis of an asymptotic preserving dynamical low-rank integrator for the multi-scale radiative transfer equation}, author={Zhiyan Ding and L. Einkemmer and Qin Li}, journal={ArXiv}, year={2019}, volume={abs/1907.04247} }

Dynamical low-rank algorithm are a class of numerical methods that compute low-rank approximations of dynamical systems. This is accomplished by projecting the dynamics onto a low-dimensional manifold and writing the solution directly in terms of the low-rank factors. The approach has been successfully applied to many types of differential equations. Recently, efficient dynamical low-rank algorithms have been applied to treat kinetic equations, including the Vlasov--Poisson and the Boltzmann… Expand

#### 6 Citations

A low-rank projector-splitting integrator for the Vlasov-Maxwell equations with divergence correction

- Physics, Mathematics
- J. Comput. Phys.
- 2020

This paper considers the Vlasov--Maxwell system and proposes a dynamic low-rank integrator based on Lagrange multipliers which enforces Gauss' law up to machine precision and achieves good behavior for a range of test problems. Expand

A reduced basis method for radiative transfer equation

- Computer Science, Mathematics
- ArXiv
- 2021

This work designs and test the angularspace reduced order model for the linear radiative transfer equation, the first such effort based on the celebrated reduced basis method (RBM), and indicates that the method is highly effective for computational cost reduction in a variety of regimes. Expand

A mass, momentum, and energy conservative dynamical low-rank scheme for the Vlasov equation

- Computer Science, Mathematics
- J. Comput. Phys.
- 2021

This paper proposes a dynamical low-rank algorithm that conserves mass, momentum, and energy as well as the corresponding continuity equations and shows how this approach can be combined with a conservative time and space discretization. Expand

An asymptotic-preserving dynamical low-rank method for the multi-scale multi-dimensional linear transport equation

- Computer Science, Mathematics
- J. Comput. Phys.
- 2021

A dynamical low-rank method to reduce the computational complexity for solving the multi-scale multi-dimensional linear transport equation based on a macro-micro decomposition of the equation is introduced. Expand

An efficient dynamical low-rank algorithm for the Boltzmann-BGK equation close to the compressible viscous flow regime

- Mathematics, Computer Science
- ArXiv
- 2021

This paper proposes an efficient dynamical low-rank integrator that can capture the fluid limit – the Navier-Stokes equations – of the Boltzmann-BGK model even in the compressible regime and has the advantage that the rank required to obtain accurate results is significantly reduced compared to the previous state of the art. Expand

A low-rank method for two-dimensional time-dependent radiation transport calculations

- Mathematics, Computer Science
- J. Comput. Phys.
- 2020

A dynamical low-rank approximation method is developed for the time-dependent radiation transport equation in 1-D and 2-D Cartesian geometries and it is shown that the low- rank algorithm can obtain high-fidelity results by increasing the number of basis functions while keeping the rank fixed. Expand

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