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Title: The Crank Nicolson Time Integrator for EMPHASIS

Abstract

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.

Authors:
 [1];  [1];  [1]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1432597
Report Number(s):
SAND-2018-2994
661971
DOE Contract Number:  
AC04-94AL85000
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English

Citation Formats

McGregor, Duncan Alisdair Odum, Love, Edward, and Kramer, Richard Michael Jack. The Crank Nicolson Time Integrator for EMPHASIS. United States: N. p., 2018. Web. doi:10.2172/1432597.
McGregor, Duncan Alisdair Odum, Love, Edward, & Kramer, Richard Michael Jack. The Crank Nicolson Time Integrator for EMPHASIS. United States. doi:10.2172/1432597.
McGregor, Duncan Alisdair Odum, Love, Edward, and Kramer, Richard Michael Jack. Thu . "The Crank Nicolson Time Integrator for EMPHASIS". United States. doi:10.2172/1432597. https://www.osti.gov/servlets/purl/1432597.
@article{osti_1432597,
title = {The Crank Nicolson Time Integrator for EMPHASIS},
author = {McGregor, Duncan Alisdair Odum and Love, Edward and Kramer, Richard Michael Jack},
abstractNote = {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.},
doi = {10.2172/1432597},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Thu Mar 01 00:00:00 EST 2018},
month = {Thu Mar 01 00:00:00 EST 2018}
}

Technical Report:

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