Publications

This is the user manual for EMPIRE, a simulation code for electromagnetics and plasma physics.

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The Unstructured Time-Domain ElectroMagnetics (UTDEM) portion of the EMPHASIS suite solves Maxwell's equations using finite-element techniques on unstructured meshes. This document provides user-specific information to facilitate the use of the code for applications of interest.

Lagrangian shock hydrodynamics simulations will fail to proceed past a certain time if the mesh is approaching tangling. A common solution is an Arbitrary Lagrangian Eulerian (ALE) form, in which the mesh is improved (remeshing) and the solution is remapped onto the improved mesh. The simplest remeshing techniques involve moving only the nodes of the mesh. More advanced remeshing techniques involve altering the mesh connectivity in portions of the domain in order to prevent tangling. Work has been done using Voronoi-based polygonal mesh generators and 2D quad/triangle mesh adaptation. Here, this paper presents the use of tetrahedral mesh adaptation methods as the remeshing step in an otherwise Lagrangian finite element shock hydrodynamics code called Alexa.

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We investigate the use of implicit time integrators for finite element time domain approximations of Maxwell's equations in vacuum. We discretize Maxwell's equations in time using Crank-Nicolson and in 3D space using compatible finite elements. We solve the system by taking a single step of Newton's method and inverting the Eddy-Current Schur complement allowing for the use of standard preconditioning techniques. This approach also generalizes to more complex material models that can include the Unsplit PML. We present verification results and demonstrate performance at CFL numbers up to 1000.

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Computational simulation of structures subjected to blast loadings requires integration of computational shock-physics for blast, and structural response with potential for pervasive failure. Current methodologies for this problem space are problematic in terms of efficiency and solution quality. This report details the development of several coupling algorithms for thin shells, with an emphasis on rigorous verification where possible and comparisons to existing methodologies in use at Sandia.

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We review the edge element formulation for describing the kinematics of hyperelastic solids. This approach is used to frame the problem of remapping the inverse deformation gradient for Arbitrary Lagrangian-Eulerian (ALE) simulations of solid dynamics. For hyperelastic materials, the stress state is completely determined by the deformation gradient, so remapping this quantity effectively updates the stress state of the material. A method, inspired by the constrained transport remap in electromagnetics, is reviewed, according to which the zero-curl constraint on the inverse deformation gradient is implicitly satisfied. Open issues related to the accuracy of this approach are identified. An optimization-based approach is implemented to enforce positivity of the determinant of the deformation gradient. The efficacy of this approach is illustrated with numerical examples.

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This article presents a generalized analysis on the significance of Galilean invariance in compressible flow computations with stabilized and variational multi-scale methods. The understanding of the key issues and the development of general approaches to Galilean-invariant stabilization are facilitated by the use of a matrix-operator description of Galilean transformations. The analysis of invariance for discontinuity capturing operators is also included. Published in 2010 by John Wiley & Sons, Ltd. This article is a U.S. Government work and is in the public domain in the U.S.A. Published in 2010 by John Wiley & Sons, Ltd.

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