Publications

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

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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 e ffi ciency 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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Algorithmic properties of the midpoint predictor-corrector time integration algorithm are examined. In the case of a finite number of iterations, the errors in angular momentum conservation and incremental objectivity are controlled by the number of iterations performed. Exact angular momentum conservation and exact incremental objectivity are achieved in the limit of an infinite number of iterations. A complete stability and dispersion analysis of the linearized algorithm is detailed. The main observation is that stability depends critically on the number of iterations performed.

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