Efficient solution of large-scale electromagnetic Eigenvalue problems using the implicity restarted Arnoldi method

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The authors are interested in determining the electromagnetic fields within closed perfectly conducting cavities that may contain dielectric or magnetic materials. The vector Helmholtz equation is the appropriate partial differential equation for this problem. It is well known that the electromagnetic fields in a cavity can be decomposed into distinct modes that oscillate in time at specific resonant frequencies. These modes are referred to as eigenmodes, and the frequencies of these modes are referred to as eigenfrequencies. The authors' present application is the analysis of linear accelerator components. These components may have a complex geometry; hence numerical methods are require ... continued below

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817 Kilobytes pages

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White, D. & Koning, J. October 21, 1999.

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The authors are interested in determining the electromagnetic fields within closed perfectly conducting cavities that may contain dielectric or magnetic materials. The vector Helmholtz equation is the appropriate partial differential equation for this problem. It is well known that the electromagnetic fields in a cavity can be decomposed into distinct modes that oscillate in time at specific resonant frequencies. These modes are referred to as eigenmodes, and the frequencies of these modes are referred to as eigenfrequencies. The authors' present application is the analysis of linear accelerator components. These components may have a complex geometry; hence numerical methods are require to compute the eigenmodes and the eigenfrequencies of these components. The Implicitly Restarted Arnoldi Method (IRAM) is a robust and efficient method for the numerical solution of the generalized eigenproblem Ax = {lambda}Bx, where A and B are sparse matrices, x is an eigenvector, and {lambda} is an eigenvalue. The IRAM is an iterative method for computing extremal eigenvalues; it is an extension of the classic Lanczos method. The mathematical details of the IRAM are too sophisticated to describe here; instead they refer the reader to [1]. A FORTRAN subroutine library that implements various versions of the IRAM is freely available, both in a serial version named ARPACK and parallel version named PARPACK. In this paper they discretize the vector Helmholtz equation using 1st order H(curl) conforming edge elements (also known as Nedelec elements). This discretization results in a generalized eigenvalue problem which can be solved using the IRAM. The question of so-called spurious modes is discussed, and it is shown that applying a spectral transformation completely eliminates these modes, without any need for an additional constraint equation. Typically they use the IRAM to compute a small set (n < 30) of eigenvalues and eigenmodes for a very large systems (N > 100,000).

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817 Kilobytes pages

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  • 16th Annual Review of Progress in Applied Naval Postgraduate School, Monterey, CA (US), 03/20/2000--03/25/2000

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  • Report No.: UCRL-JC-136069
  • Report No.: YN0100000
  • Grant Number: W-7405-ENG-48
  • Office of Scientific & Technical Information Report Number: 756955
  • Archival Resource Key: ark:/67531/metadc702124

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  • October 21, 1999

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  • Sept. 12, 2015, 6:31 a.m.

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  • Feb. 24, 2016, 4:21 p.m.

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White, D. & Koning, J. Efficient solution of large-scale electromagnetic Eigenvalue problems using the implicity restarted Arnoldi method, article, October 21, 1999; California. (digital.library.unt.edu/ark:/67531/metadc702124/: accessed October 22, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.