Jim E. Morel
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View article: A Second Moment Method for <i>k</i> -Eigenvalue Acceleration with Continuous Diffusion and Discontinuous Transport Discretizations
A Second Moment Method for <i>k</i> -Eigenvalue Acceleration with Continuous Diffusion and Discontinuous Transport Discretizations Open
The second moment method is a linear acceleration technique that couples the transport equation to a diffusion equation with transport-dependent additive closures. The resulting low-order diffusion equation can be discretized independent o…
View article: A Second Moment Method for k-Eigenvalue Acceleration with Continuous Diffusion and Discontinuous Transport Discretizations
A Second Moment Method for k-Eigenvalue Acceleration with Continuous Diffusion and Discontinuous Transport Discretizations Open
The second moment method is a linear acceleration technique which couples the transport equation to a diffusion equation with transport-dependent additive closures. The resulting low-order diffusion equation can be discretized independent …
View article: Neutron source reconstruction using a generalized expectation–maximization algorithm on one-dimensional neutron images from the Z facility
Neutron source reconstruction using a generalized expectation–maximization algorithm on one-dimensional neutron images from the Z facility Open
Magnetized Liner Inertial Fusion experiments have been performed at the Z facility at Sandia National Laboratories. These experiments use deuterium fuel, which produces 2.45 MeV neutrons on reaching thermonuclear conditions. To study the s…
View article: A forward/adjoint transport formalism for sensitivity studies
A forward/adjoint transport formalism for sensitivity studies Open
We describe a formalism for efficiently estimating the sensitivity of radiative transfer solutions to perturbations in the absorption and scattering properties of the transport medium assuming a fixed material temperature distribution. Thi…
View article: Diffusion-accelerated solution of the 2-D S{sub n} equations with bilinear-discontinuous differencing
Diffusion-accelerated solution of the 2-D S{sub n} equations with bilinear-discontinuous differencing Open
A new diffusion-synthetic acceleration scheme is developed for solving the 2-D S{sub n} equations in X-Y geometry with bilinear- discontinuous finite-element spatial discretization. This method differs from previous methods in that it is u…
View article: DETERMINISTIC TRANSPORT METHODS AND CODES AT LOS ALAMOS
DETERMINISTIC TRANSPORT METHODS AND CODES AT LOS ALAMOS Open
The purposes of this paper are to: Present a brief history of deterministic transport methods development at Los Alamos National Laboratory from the 1950's to the present; Discuss the current status and capabilities of deterministic transp…
View article: Krylov Subspace Iterations for the Calculation of K-Eigenvalues with sn Transport Codes
Krylov Subspace Iterations for the Calculation of K-Eigenvalues with sn Transport Codes Open
We apply the Implicitly Restarted Arnoldi Method (IRAM), a Krylov subspace iterative method, to the calculation of k-eigenvalues for criticality problems. We show that the method can be implemented with only modest changes to existing powe…
View article: Krylov iterative methods applied to multidimensional S[sub n] calculations in the presence of material discontinuities
Krylov iterative methods applied to multidimensional S[sub n] calculations in the presence of material discontinuities Open
We show that a Krylov iterative meihod, preconditioned with DSA, can be used to efficiently compute solutions to diffusive problems with discontinuities in material properties. We consider a lumped, linear discontinuous discretization of t…
View article: Anomalous Behavior of Newtonian Hydrodynamics Coupled with Radiation Transport
Anomalous Behavior of Newtonian Hydrodynamics Coupled with Radiation Transport Open
This study shows that Newtonian hydrodynamics coupled with radiation transport, using a wide range of methods for treating the material-motion corrections, results in anomalous behavior. In particular, the flow of infinite-medium equilibra…
View article: Reduced-Memory Methods for Linear Discontinuous Discretization of the Time-Dependent Boltzmann Transport Equation
Reduced-Memory Methods for Linear Discontinuous Discretization of the Time-Dependent Boltzmann Transport Equation Open
In this paper, new implicit methods with reduced memory are developed for solving the time-dependent Boltzmann transport equation (BTE). One-group transport problems in 1D slab geometry are considered. The reduced-memory methods are formul…
View article: Asymptotic Diffusion-Limit Accuracy of Sn Angular Differencing Schemes
Asymptotic Diffusion-Limit Accuracy of Sn Angular Differencing Schemes Open
In a previous paper, Morel and Montry used a Galerkin-based diffusion analysis to define a particular weighted diamond angular discretization for S{sub n}n calculations in curvilinear geometries. The weighting factors were chosen to ensure…
View article: Accelerating PDE-constrained Inverse Solutions with Deep Learning and Reduced Order Models
Accelerating PDE-constrained Inverse Solutions with Deep Learning and Reduced Order Models Open
Inverse problems are pervasive mathematical methods in inferring knowledge from observational and experimental data by leveraging simulations and models. Unlike direct inference methods, inverse problem approaches typically require many fo…
View article: Parallel Approximate Ideal Restriction Multigrid for Solving the S$_N$ Transport Equations
Parallel Approximate Ideal Restriction Multigrid for Solving the S$_N$ Transport Equations Open
The computational kernel in solving the $S_N$ transport equations is the parallel sweep, which corresponds to directly inverting a block lower triangular linear system that arises in discretizations of the linear transport equation. Existi…
View article: Nonlinear Diffusion Acceleration of the Least-Squares Transport Equation in Geometries with Voids
Nonlinear Diffusion Acceleration of the Least-Squares Transport Equation in Geometries with Voids Open
In this paper we show the extension of the Nonlinear-Diffusion Acceleration (NDA) to geometries containing small voids using a weighted least-squares (WLS) high order equation. Even though the WLS equation is well defined in voids, the low…
View article: A Weighted Least-Squares Transport Equation Compatible with Source Iteration and Voids
A Weighted Least-Squares Transport Equation Compatible with Source Iteration and Voids Open
We present that second-order forms of the transport equation allow the use of continuous finite elements (CFEMs). This can be desired in multiphysics calculations where other physics require CFEM discretizations. Second-order transport ope…
View article: Comparison of Two Galerkin Quadrature Methods
Comparison of Two Galerkin Quadrature Methods Open
Here, we compare two methods for generating Galerkin quadratures. In method 1, the standard SN method is used to generate the moment-to-discrete matrix and the discrete-to-moment matrix is generated by inverting the moment-to-discrete matr…