Verification of high-order mixed FEM solution of transient Magnetic diffusion problems

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We develop and present high order mixed finite element discretizations of the time dependent electromagnetic diffusion equations for solving eddy current problems on 3D unstructured grids. The discretizations are based on high order H(grad), H(curl) and H(div) conforming finite element spaces combined with an implicit and unconditionally stable generalized Crank-Nicholson time differencing method. We develop three separate electromagnetic diffusion formulations, namely the E (electric field), H (magnetic field) and the A-{phi} (potential) formulations. For each formulation, we also provide a consistent procedure for computing the secondary variables F (current flux density) and B (magnetic flux density), as these fields are ... continued below

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Rieben, R & White, D A May 12, 2005.

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We develop and present high order mixed finite element discretizations of the time dependent electromagnetic diffusion equations for solving eddy current problems on 3D unstructured grids. The discretizations are based on high order H(grad), H(curl) and H(div) conforming finite element spaces combined with an implicit and unconditionally stable generalized Crank-Nicholson time differencing method. We develop three separate electromagnetic diffusion formulations, namely the E (electric field), H (magnetic field) and the A-{phi} (potential) formulations. For each formulation, we also provide a consistent procedure for computing the secondary variables F (current flux density) and B (magnetic flux density), as these fields are required for the computation of electromagnetic force and heating terms. We verify the error convergence properties of each formulation via a series of numerical experiments on canonical problems with known analytic solutions. The key result is that the different formulations are equally accurate, even for the secondary variables J and B, and hence the choice of which formulation to use depends mostly upon relevance of the Natural and Essential boundary conditions to the problem of interest. In addition, we highlight issues with numerical verification of finite element methods which can lead to false conclusions on the accuracy of the methods.

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PDF-file: 18 pages; size: 0 Kbytes

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  • Journal Name: IEEE Transaction on Magnetics; Journal Volume: 42; Journal Issue: 1

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  • Report No.: UCRL-JRNL-212411
  • Grant Number: W-7405-ENG-48
  • Office of Scientific & Technical Information Report Number: 884765
  • Archival Resource Key: ark:/67531/metadc892451

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Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

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  • May 12, 2005

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  • Sept. 23, 2016, 2:42 p.m.

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  • Dec. 9, 2016, 8:57 p.m.

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Rieben, R & White, D A. Verification of high-order mixed FEM solution of transient Magnetic diffusion problems, article, May 12, 2005; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc892451/: accessed October 18, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.