Application of linear multifrequency-grey acceleration to preconditioned Krylov iterations for thermal radiation transport

Till, Andrew; Warsa, James S.; Morel, Jim E.

doi:10.1016/j.jcp.2018.06.017

Cited by 7 publications

(4 citation statements)

References 10 publications

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“…(1), which leads to coupled systems that are difficult to solve due to memory and convergence issues. Associated with the multigroup approximation [11,12] or spectral models [13,14], monochromatic RTE solvers are a stepping stone for designing multi-frequency RTE solvers in different scientific communities, e.g., combustion [15,16].…”

Section: Introductionmentioning

confidence: 99%

Deterministic radiative transfer equation solver on unstructured tetrahedral meshes: Efficient assembly and preconditioning

Jolivet

Badri

Favennec

2021

Journal of Computational Physics

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Section: Introductionmentioning

confidence: 99%

Deterministic radiative transfer equation solver on unstructured tetrahedral meshes: Efficient assembly and preconditioning

Jolivet

Badri

Favennec

2021

Journal of Computational Physics

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“…( 13) efficiently by closely following earlier work. [8][9][10][11]16 Here, we cast the previous work more explicitly as operations within a standard Newton iteration so that it is easier to see the modifications that applying nonlinear elimination makes to the iteration scheme, shown in Sec. IV.…”

Section: Newton Iteration Formulationmentioning

confidence: 99%

“…II. We then proceed with a review of a method that closely follows previous methods 8,11,16 in Sec. III but cast it more explicitly in terms of a standard Newton iteration in order to apply the nonlinear elimination more easily.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Elimination Applied to Radiation Diffusion

Brunner

Haut

Nowak

2020

Nuclear Science and Engineering

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We apply a nonlinearly preconditioned, quasi-Newton framework to accelerate the numerical solution of the thermal radiative transfer (TRT) equations. This framework was inspired by the unpublished method that has existed for years in Teton, Lawrence Livermore National Laboratory's deterministic TRT code. In this paper, we cast this iteration scheme within a formal nonlinear preconditioning framework and compare its performance against other iteration schemes in the framework. With proper choices of iteration controls for the various levels of the solver, we can recover the standard linearized one-step method, a full nonlinear Newton scheme, as well as the method in Teton.In brief, the nonlinear preconditioning TRT scheme formally eliminates the material temperature equation from the nonlinear system in a nonlinear analog of a Schur complement. This nonlinear elimination step involves solving a decoupled nonlinear equation for each spatial degree of freedom and is therefore inexpensive. By applying a quasi-Newton iteration scheme on the new system, we obtain a three-level iteration scheme that is at least as efficient as commonly used TRT schemes. The new method allows full convergence to the nonlinear backward Euler time-discretized system, increasing accuracy and robustness, while using a similar number of linear iterations as the more common linearized one-step methods.

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“…The discretized equations are solved for the I n+1 m,g at every spatial degree of freedom in the problem, then used to compute φ n+1 g , and stored for the next time step. A Krylov iterative method preconditioned with linear multi-frequency gray acceleration (Till et al 2018) is used to calculate the solution. This in turn is substituted into (5) to find ∆t ne and then T n+1 e = T n e + δT e .…”

Section: Radiation Hydrodynamics Simulationsmentioning

confidence: 99%

The Role of Inhomogeneities in Supernova Shock Breakout Emission

Fryer,

Fontes,

Warsa

et al. 2020

Preprint

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The breakout of a supernova blast wave from its progenitor star provides strong constraints on the star and its immediate surroundings. These surroundings are shaped by mass loss from the star and can include a wide variety of inhomogeneities. Here we present results of multi-dimensional radiation-hydrodynamics calculations of the interactions of the supernova blast wave with inhomogeneities in the immediate surroundings of a massive Wolf-Rayet star, calculating the effect these interactions have on the shock breakout signal from supernovae.

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Application of linear multifrequency-grey acceleration to preconditioned Krylov iterations for thermal radiation transport

Cited by 7 publications

References 10 publications

Deterministic radiative transfer equation solver on unstructured tetrahedral meshes: Efficient assembly and preconditioning

Deterministic radiative transfer equation solver on unstructured tetrahedral meshes: Efficient assembly and preconditioning

Nonlinear Elimination Applied to Radiation Diffusion

The Role of Inhomogeneities in Supernova Shock Breakout Emission

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