Improvements to a class of hybrid methods for radiation transport: Nyström reconstruction and defect correction methods

Crockatt, Michael; Christlieb, Andrew; Hauck, Cory D.

doi:10.1016/j.jcp.2020.109765

Cited by 9 publications

(4 citation statements)

References 60 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recent work on HOLO methods applied to the problem of thermal radiative transfer include applications where the high-order model is solved with continuum methods such as discrete ordinates (e.g., Park et al 2012Park et al , 2013Lou et al 2019) or Monte Carlo methods (e.g., Park et al 2014;Bolding et al 2017). We also point out related work on solving the linear transport equation (i.e., without nonlinear coupling to the material) with HOLO (or hybrid) methods by Hauck and McClarren (2013), Willert et al (2013); Willert et al (2015) and Crockatt et al (2017Crockatt et al ( , 2019Crockatt et al ( , 2020.…”

Section: Hybrid Methodsmentioning

confidence: 99%

Physical, numerical, and computational challenges of modeling neutrino transport in core-collapse supernovae

Mezzacappa

Endeve

Messer

2020

Living Rev Comput Astrophys

View full text Add to dashboard Cite

The proposal that core collapse supernovae are neutrino driven is still the subject of active investigation more than 50 years after the seminal paper by Colgate and White. The modern version of this paradigm, which we owe to Wilson, proposes that the supernova shock wave is powered by neutrino heating, mediated by the absorption of electron-flavor neutrinos and antineutrinos emanating from the proto-neutron star surface, or neutrinosphere. Neutrino weak interactions with the stellar core fluid, the theory of which is still evolving, are flavor and energy dependent. The associated neutrino mean free paths extend over many orders of magnitude and are never always small relative to the stellar core radius. Thus, neutrinos are never always fluid like. Instead, a kinetic description of them in terms of distribution functions that determine the number density of neutrinos in the six-dimensional phase space of position, direction, and energy, for both neutrinos and antineutrinos of each flavor, or in terms of angular moments of these neutrino distributions that instead provide neutrino number densities in the four-dimensional phase-space subspace of position and energy, is needed. In turn, the computational challenge is twofold: (i) to map the kinetic equations governing the evolution of these distributions or moments onto discrete representations that are stable, accurate, and, perhaps most important, respect physical laws such as conservation of lepton number and energy and the Fermi–Dirac nature of neutrinos and (ii) to develop efficient, supercomputer-architecture-aware solution methods for the resultant nonlinear algebraic equations. In this review, we present the current state of the art in attempts to meet this challenge.

show abstract

Section: Hybrid Methodsmentioning

confidence: 99%

Physical, numerical, and computational challenges of modeling neutrino transport in core-collapse supernovae

Mezzacappa

Endeve

Messer

2020

Living Rev Comput Astrophys

View full text Add to dashboard Cite

show abstract

“…Recent work on HOLO methods applied to the problem of thermal radiative transfer include applications where the high-order model is solved with continuum methods such as discrete ordinates (e.g., Park et al, 2012Park et al, , 2013Lou et al, 2019) or Monte Carlo methods (e.g., Park et al, 2014;Bolding et al, 2017). We also point out related work on solving the linear transport equation (i.e., without nonlinear coupling to the material) with HOLO (or hybrid) methods by Hauck and McClarren (2013); Willert et al (2013); Willert et al (2015); Crockatt et al (2017Crockatt et al ( , 2019Crockatt et al ( , 2020.…”

Section: Hybrid Methodsmentioning

confidence: 99%

Physical, numerical, and computational challenges of modeling neutrino transport in core-collapse supernovae

Mezzacappa,

Endeve,

Messer

et al. 2020

Preprint

View full text Add to dashboard Cite

The proposal that core collapse supernovae are neutrino driven is still the subject of active investigation more than fifty years after the seminal paper by Colgate and White. The modern version of this paradigm, which we owe to Wilson, proposes that the supernova shock wave is powered by neutrino heating, mediated by the absorption of electron-flavor neutrinos and antineutrinos emanating from the protoneutron star surface, or neutrinosphere. Neutrino weak interactions with the stellar core fluid, the theory of which is still evolving, are flavor and energy dependent. The associated neutrino mean free paths extend over many orders of magnitude and are never always small relative to the stellar core radius. Thus, neutrinos are never always fluid like. Instead, a kinetic description of them in terms of distribution functions that determine the number density of neutrinos in the six-dimensional phase space of position, direction, and energy, for both neutrinos and antineutrinos of each flavor, or in terms of angular moments of these neutrino distributions that instead provide neutrino

show abstract

“…Common discretization methods can be classified into two main approaches based on their semidiscretization in s. The spherical harmonics method [5,19,35] approximates the solution u by a truncated series of spherical harmonics, which allows for spectral convergence for smooth solutions. For non-smooth solutions, which is the generic situation, local approximations in s can be advantageous, which is achieved, e.g., by discrete ordinates methods [26,35,43,44,46], continuous Galerkin methods [7], the discontinuous Galerkin (DG) method [24,32,40], iteratively refined piecewise polynomial approximations [13], or hybrid methods [12,30].…”

Section: Related Workmentioning

confidence: 99%

“…As shown in [17], the even-parity formulation is a coercive, symmetric problem, which is well-posed by the Lax-Milgram lemma. Solving (12) for u + ∈ W + , we can retrieve u − ∈ V − by (11). In turn, (u…”

Section: Even-parity Formulationmentioning

confidence: 99%

On Robustly Convergent and Efficient Iterative Methods for Anisotropic Radiative Transfer

2022

View full text Add to dashboard Cite

This paper considers the iterative solution of linear systems arising from discretization of the anisotropic radiative transfer equation with discontinuous elements on the sphere. In order to achieve robust convergence behavior in the discretization parameters and the physical parameters we develop preconditioned Richardson iterations in Hilbert spaces. We prove convergence of the resulting scheme. The preconditioner is constructed in two steps. The first step borrows ideas from matrix splittings and ensures mesh independence. The second step uses a subspace correction technique to reduce the influence of the optical parameters. The correction spaces are build from low-order spherical harmonics approximations generalizing well-known diffusion approximations. We discuss in detail the efficient implementation and application of the discrete operators. In particular, for the considered discontinuous spherical elements, the scattering operator becomes dense and we show that $$\mathcal {H}$$ H - or $$\mathcal {H}^2$$ H 2 -matrix compression can be applied in a black-box fashion to obtain almost linear or linear complexity when applying the corresponding approximations. The effectiveness of the proposed method is shown in numerical examples.

show abstract

Improvements to a class of hybrid methods for radiation transport: Nyström reconstruction and defect correction methods

Cited by 9 publications

References 60 publications

Physical, numerical, and computational challenges of modeling neutrino transport in core-collapse supernovae

Physical, numerical, and computational challenges of modeling neutrino transport in core-collapse supernovae

Physical, numerical, and computational challenges of modeling neutrino transport in core-collapse supernovae

On Robustly Convergent and Efficient Iterative Methods for Anisotropic Radiative Transfer

Contact Info

Product

Resources

About