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DOE OSTI2018

FELIX-2.0: New version of the finite element solver for the time dependent generator coordinate method with the Gaussian overlap approximation

The time-dependent generator coordinate method (TDGCM) is a powerful method to study the largeamplitude collective motion of quantum many-body systems such as atomic nuclei. Under the GaussianOverlap Approximation (GOA), the TDGCM leads to a local, time-dependent Schrödinger equation in amulti-dimensional collective space. In this paper, we present the version 2.0 of the code FELIX that solvesthe collective Schrödinger equation in a finite element basis. This new version features: (i) the ability tosolve a generalized TDGCM+GOA equation with a metric term in the collective Hamiltonian, (ii) supportfor new kinds of finite elements and different types of quadrature to compute the discretized Hamiltonianand overlap matrices, (iii) the possibility to leverage the spectral element scheme, (iv) an explicit Krylovapproximation of the time propagator for time integration instead of the implicit Crank–Nicolson methodimplemented in the first version, (v) an entirely redesigned workflow. We benchmark this release on ananalytic problem as well as on realistic two-dimensional calculations of the low-energy fission of240Puand256Fm. Low to moderate numerical precision calculations are most efficiently performed with simplexelements with a degree 2 polynomial basis. Higher precision calculations should instead use the spectralelement method with a degree 4 polynomial basis. We emphasize that in a realistic calculation of fissionmass distributions of240Pu, FELIX-2.0 is about 20 times faster than its previous release (within a numericalprecision of a few percents).

Regnier, D.↗

DOE OSTI2021

The LISE package: solvers for static and time-dependent superfluid local density approximation equations in three dimensions

Nuclear implementation of the density functional theory (DFT) is at present the only microscopic framework applicable to the whole nuclear landscape. The extension of DFT to superfluid systems in the spirit of the Kohn-Sham approach, the superfluid local density approximation (SLDA) and its extension to time-dependent situations, time-dependent superfluid local density ap- proximation (TDSLDA), have been extensively used to describe various static and dynamical problems in nuclear physics, neutron star crust, and cold atom systems. In this paper, we present the codes that solve the static and time-dependent SLDA equations in three-dimensional coordinate space without any symmetry restriction. These codes are fully parallelized with the message passing interface (MPI) library and take advantage of graphic processing units (GPU) for accelerating execution. The dynamic codes have checkpoint/restart capabilities and for initial conditions one can use any generalized Slater determinant type of wave function. The code can describe a large number of physical problems: nuclear fission, collisions of heavy ions, the interaction of quantized vor- tices with nuclei in the nuclear star crust, excitation of superfluid fermion systems by time dependent external fields, quantum shock waves, domain wall generation and propagation, the dynamics of the Anderson-Bogoliubov-Higgs mode, dynamics of fragmented condensates, vortex rings dynamics, generation and dynamics of quantized vortices, their crossing and recombinations and the incipient phases of quantum turbulence.

Jin, Shi↗

DOE OSTI2014

Residual Monte Carlo high-order solver for Moment-Based Accelerated Thermal Radiative Transfer equations

In this article we explore the possibility of replacing Standard Monte Carlo (SMC) transport sweeps within a Moment-Based Accelerated Thermal Radiative Transfer (TRT) algorithm with a Residual Monte Carlo (RMC) formulation. Previous Moment-Based Accelerated TRT implementations have encountered trouble when stochastic noise from SMC transport sweeps accumulates over several iterations and pollutes the low-order system. With RMC we hope to significantly lower the build-up of statistical error at a much lower cost. First, we display encouraging results for a zero-dimensional test problem. Then, we demonstrate that we can achieve a lower degree of error in two one-dimensional test problems by employing an RMC transport sweep with multiple orders of magnitude fewer particles per sweep. We find that by reformulating the high-order problem, we can compute more accurate solutions at a fraction of the cost.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Second-order accurate interface- and discontinuity-aware diffusion solvers in two and three dimensions

A numerical scheme is developed for two- and three-dimensional time-dependent diffusion equations in numerical simulations involving mixed cells. The focus of the development is on the formulations for both transient and steady states, the property for large time steps, second-order accuracy in both space and time, the correct treatment of the discontinuity in material properties, and the handling of mixed cells. For a mixed cell, interfaces between materials are reconstructed within the cell so that each of resulting sub-cells contains only one material and the material properties of each sub-cell are known. Diffusion equations are solved on the resulting polyhedral mesh even if the original mesh is structured. The discontinuity of material properties between different materials is correctly treated based on governing physics principles. The treatment is exact for arbitrarily strong discontinuity. The formulae for effective diffusion coefficients across interfaces between materials are derived for general polyhedral meshes. The scheme is general in two and three dimensions. Since the scheme to be developed in this paper is intended for multi-physics code with adaptive mesh refinement (AMR), we present the scheme on mesh generated from AMR. The correctness and features of the scheme are demonstrated for transient problems and steady states in one-, two-, and three-dimensional simulations for heat conduction and radiation heat transfer. The test problems involve dramatically different materials.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Boltzmann equation solver adapted to emergent chemical non-equilibrium

We present a novel method to solve the spatially homogeneous and isotropic relativistic Boltzmann equation. We employ a basis set of orthogonal polynomials dynamically adapted to allow for emergence of chemical non-equilibrium. Two time dependent parameters characterize the set of orthogonal polynomials, the effective temperature T(t) and phase space occupation factor ϒ(t). In this first paper we address (effectively) massless fermions and derive dynamical equations for T(t) and ϒ(t) such that the zeroth order term of the basis alone captures the particle number density and energy density of each particle distribution. We validate our method and illustrate the reduced computational cost and the ability to easily represent final state chemical non-equilibrium by studying a model problem that is motivated by the physics of the neutrino freeze-out processes in the early Universe, where the essential physical characteristics include reheating from another disappearing particle component (e{sup ±}-annihilation)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017