# A quadratic programming flux correction method for high-order DG discretizations of SN transport

@article{Yee2019AQP, title={A quadratic programming flux correction method for high-order DG discretizations of SN transport}, author={Ben C. Yee and Samuel S. Olivier and Terry S. Haut and M Holec and Vladimir Z. Tomov and Peter G. Maginot}, journal={J. Comput. Phys.}, year={2019}, volume={419}, pages={109696} }

## 9 Citations

### Meshless discretization of the discrete-ordinates transport equation with integration based on Voronoi cells

- Computer ScienceJ. Comput. Phys.
- 2022

### Data-driven acceleration of thermal radiation transfer calculations with the dynamic mode decomposition and a sequential singular value decomposition

- PhysicsJ. Comput. Phys.
- 2022

### A New Scheme for Solving High-Order DG Discretizations of Thermal Radiative Transfer using the Variable Eddington Factor Method

- Computer Science
- 2021

A new approach for solving high-order thermal radiative transfer (TRT) using the Variable Eddington Factor (VEF) method, which leverages the VEF equations to more efficiently compute the TRT solution for each time step.

### High-Order Mixed Finite Element Variable Eddington Factor Methods

- Computer ScienceJournal of Computational and Theoretical Transport
- 2023

Numerical results are presented that demonstrate high-order accuracy, compatibility with curved meshes, and robust and efficient convergence in iteratively solving the coupled transport-VEF system and in the preconditioned linear solvers used to invert the discretized VEF equations.

### A family of independent Variable Eddington Factor methods with efficient preconditioned iterative solvers

- Computer ScienceJ. Comput. Phys.
- 2023

### A Family of Independent Variable Eddington Factor Methods with Efficient Linear Solvers

- Computer ScienceArXiv
- 2021

Numerical results demonstrate that the VEF discretizations have arbitrary-order accuracy on curved meshes, preserve the thick diffusion limit, and are effective on a proxy problem from thermal radiative transfer in both outer transport iterations and inner preconditioned linear solver iterations.

### A variable Eddington factor method with different spatial discretizations for the radiative transfer equation and the hydrodynamics/radiation-moment equations

- PhysicsJ. Comput. Phys.
- 2021

### Enabling rapid COVID-19 small molecule drug design through scalable deep learning of generative models

- Computer ScienceInt. J. High Perform. Comput. Appl.
- 2021

The quality and time to produce machine learned models for use in small molecule antiviral design were improved and the time reduced.

## 35 References

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Newton’s method is used to solve fixed-source SN transport problems with negative-flux fixup, for which the analytic form of the Jacobian is shown to be nonsingular, demonstrating that Newton-Krylov can outperform SI, particularly for diffusive materials.

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A strictly nonnegative, nonlinear, Petrov-Galerkin finite element method that fully preserves the bilinear discontinuous spatial moments of the transport equation and is a more accurate solution than all the other methods considered.

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Out of the three DSA schemes derived, the modified interior penalty (MIP) scheme is stable and effective for realistic problems, even with distorted elements, but loses effectiveness for some highly heterogeneous configurations.

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This paper presents a general framework for high-order Lagrangian discretization of these compressible shock hydrodynamics equations using curvilinear finite elements for any finite dimensional approximation of the kinematic and thermodynamic fields.

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arbitrarily high order accurate DG schemes are constructed which preserve positivity of the radiative intensity in the simulation of both steady and unsteady radiative transfer equations in one- and two-dimensional geometry by using a combined technique of the scaling positivi...

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It is proved that performing two additional transport sweeps in between DSA steps yields the same theoretical conditioning of fixed-point iterations as in the cycle-free case, and also that the SIP DSA matrix is difficult to invert for small $\varepsilon$.

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Abstract We examine several mass matrix lumping techniques for the discrete ordinates (SN) particle transport equations spatially discretized with arbitrary order discontinuous finite elements in…