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

05/13/2020
by   Lukas Einkemmer, et al.
0

We introduce a dynamical low-rank method to reduce the computational complexity for solving the multi-scale multi-dimensional linear transport equation. The method is based on a macro-micro decomposition of the equation. The proposed numerical method uses the low rank approximation only for the micro part of the solution. The time and spatial discretizations are done properly so that the overall scheme is second order accurate and asymptotic-preserving (AP); that is, in the diffusive regime, the scheme becomes a macroscopic solver for the limiting diffusion equation and is automatically low rank. We demonstrate the accuracy and efficiency of the proposed low rank method by a number of two-dimensional examples.

READ FULL TEXT

page 18

page 21

page 22

page 23

page 24

10/06/2021

Robust Multi-dimensional Model Order Estimation Using LineAr Regression of Global Eigenvalues (LaRGE)

The efficient estimation of an approximate model order is very important...
12/22/2022

Asymptotic–preserving and energy stable dynamical low-rank approximation

Radiation transport problems are posed in a high-dimensional phase space...
11/09/2022

A micro-macro decomposed reduced basis method for the time-dependent radiative transfer equation

Kinetic transport equations are notoriously difficult to simulate becaus...
11/13/2021

A robust collision source method for rank adaptive dynamical low-rank approximation in radiation therapy

Deterministic models for radiation transport describe the density of rad...
09/18/2019

Asymptotic preserving P_N methods for haptotaxis equations

The so-called haptotaxis equation is a special class of transport equati...
04/22/2022

Efficient dynamical low-rank approximation for the Vlasov-Ampère-Fokker-Planck system

Kinetic equations are difficult to solve numerically due to their high d...

Please sign up or login with your details

Forgot password? Click here to reset