A sweep-based low-rank method for the discrete ordinate transport equation

Peng, Zhuogang; McClarren, Ryan G.

doi:10.1016/j.jcp.2022.111748

Cited by 11 publications

(6 citation statements)

References 30 publications

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“…Dynamical low-rank approximation of time-dependent matrices [37] has proven to be an efficient model order reduction technique for applications from widely varying fields including plasma physics [24,26,20,8,22,14,27,15,23,56], radiation transport [49,16,47,41,48,57,21,4], radiation therapy [40], chemical kinetics [32,50,25], wave propagation [31,58], kinetic shallow water models [38], uncertainty quantification [51,3,28,43,44,46,39,33,17,2], and machine learning [54,59,52,53]. These problems can be written as a prohibitively large matrix differential equation for A(t) ∈ R m×n , .…”

Section: Introductionmentioning

confidence: 99%

A rank-adaptive robust integrator for dynamical low-rank approximation

2022

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A rank-adaptive integrator for the dynamical low-rank approximation of matrix and tensor differential equations is presented. The fixed-rank integrator recently proposed by two of the authors is extended to allow for an adaptive choice of the rank, using subspaces that are generated by the integrator itself. The integrator first updates the evolving bases and then does a Galerkin step in the subspace generated by both the new and old bases, which is followed by rank truncation to a given tolerance. It is shown that the adaptive low-rank integrator retains the exactness, robustness and symmetry-preserving properties of the previously proposed fixed-rank integrator. Beyond that, up to the truncation tolerance, the rank-adaptive integrator preserves the norm when the differential equation does, it preserves the energy for Schrödinger equations and Hamiltonian systems, and it preserves the monotonic decrease of the functional in gradient flows. Numerical experiments illustrate the behaviour of the rank-adaptive integrator. Keywordsdynamical low-rank approximation • rank adaptivity • structurepreserving integrator • matrix and tensor differential equations Mathematics Subject Classification (2000) 65L05 • 65L20 • 65L70 • 15A69

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Section: Introductionmentioning

confidence: 99%

A rank-adaptive robust integrator for dynamical low-rank approximation

2022

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“…The PGD has been used to seperate variables in the BTE solution in several geometries [51,52,53]. A low-rank manifold projection technique has been used in constructing ROMs for time-dependent problems [54,55,56,57]. Surrogate models for the BTE have been created using the DMD [58] and various neural network architectures [59,60,61].…”

Section: Introductionmentioning

confidence: 99%

“…A new approach based on data-driven reduced-order models (ROMs) has been gaining popularity in recent years which make use of data-based methodologies to dimensionality reduction. Data-driven models have been developed for (i) linear particle transport problems [29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48] (ii) nonlinear RT problems [49,50,51,52,53,54,55,56,57,58,59,60], and (iii) various problems in nuclear reactor-physics [61,62,63,64,65,66,67,68,69,70,71]. The fundamental idea behind these ROMs is to leverage databases of solutions to their problems of interest (known a-priori) to develop some reduction in the dimensionality for their involved equations.…”

Section: Introductionmentioning

confidence: 99%

Reduced order models for thermal radiative transfer problems based on moment equations and data-driven approximations of the Eddington tensor

Coale

Anistratov

2023

Journal of Quantitative Spectroscopy and Radiative Transfer

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“…DLRA's core idea is to represent and evolve the solution on the low-rank manifold of rank r functions. Past work in the area of radiative transfer has focused on asymptotic-preserving schemes [9,8], mass conservation [29], stable discretizations [18], imposing boundary conditions [19,15] and implicit time discretizations [30]. A discontinuous Galerkin discretization of the DLRA evolution equations for thermal radiative transfer has been proposed in [4].…”

Section: Introductionmentioning

confidence: 99%

Adaptation of the urban climate model PALM-4U for Wuerzburg, Germany

Baumann¹,

Paeth²

2021

Preprint

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The European Union-funded research project 'BigData@Geo &#173;&#173;&#173;&#173;&#173;&#173;&#173;&#173;- Advanced Environmental Technologies using AI on the Web' is dedicated to researching connections and interactions in the natural regional environmental system. This includes the development of a high-resolution regional earth system model for modelling climate change in Northern Bavaria, Germany.This research aims to run an urban climate model based on the Parallelized Large-Eddy Simulation Model for Urban Applications (PALM-4U) for Lower Franconia and thus to simulate the Main Valley with a focus on Wuerzburg in a high resolution of up to one meter. As part of this, PALM-4U is coupled to the regional climate model REMO to use generated dynamic input data in addition to static data, for example relating to buildings, roads, waterways, bridges, roof greening etc. in the simulation. The effects of variable development and the influence of green spaces and vegetation &#8211; especially also of street trees &#8211; on the urban climate are thereby considered, taking into account climate change in the 21st century. Furthermore, changes in the boundary conditions, topography and land use are also part of the research and compared using historical, current and future scenarios.First results of the coupled model, its urban climate components and of applied approaches such as nesting will be shown. Besides possibilities for their evaluation, possible further steps are also presented.&#160;

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A sweep-based low-rank method for the discrete ordinate transport equation

Cited by 11 publications

References 30 publications

A rank-adaptive robust integrator for dynamical low-rank approximation

A rank-adaptive robust integrator for dynamical low-rank approximation

Reduced order models for thermal radiative transfer problems based on moment equations and data-driven approximations of the Eddington tensor

Adaptation of the urban climate model PALM-4U for Wuerzburg, Germany

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