<?xml version="1.0" encoding="utf-8"?>
<export-example>
  <doc>
    <id>429</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1999-12-06</completedDate>
    <publishedDate>1999-12-06</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Algebraic Multigrid by Component Splitting for Edge Elements on Simplicial Triangulations</title>
    <abstract language="eng">Our focus is on Maxwell's equations in the low frequency range; two specific applications we aim at are time-stepping schemes for eddy current computations and the stationary double-curl equation for time-harmonic fields. We assume that the computational domain is discretized by triangles or tetrahedrons; for the finite element approximation we choose N\'{e}d\'{e}lec's $H(curl)$-conforming edge elements of the lowest order. For the solution of the arising linear equation systems we devise an algebraic multigrid preconditioner based on a spatial component splitting of the field. Mesh coarsening takes place in an auxiliary subspace, which is constructed with the aid of a nodal vector basis. Within this subspace coarse grids are created by exploiting the matrix graphs. Additionally, we have to cope with the kernel of the $curl$-operator, which comprises a considerable part of the spectral modes on the grid. Fortunately, the kernel modes are accessible via a discrete Helmholtz decomposition of the fields; they are smoothed by additional algebraic multigrid cycles. Numerical experiments are included in order to assess the efficacy of the proposed algorithms.</abstract>
    <identifier type="serial">SC-99-40</identifier>
    <identifier type="opus3-id">429</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-4290</identifier>
    <author>Rudolf Beck</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-99-40</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Algebraic multigrid</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>mesh coarsening</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>edge elements</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>N\'{e}d\'{e}lec spaces</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Maxwell's equations</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="35Q60">PDEs in connection with optics and electromagnetic theory</collection>
    <collection role="msc" number="65-XX">NUMERICAL ANALYSIS</collection>
    <collection role="msc" number="65F10">Iterative methods for linear systems [See also 65N22]</collection>
    <collection role="msc" number="65N30">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="msc" number="65N55">Multigrid methods; domain decomposition</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/429/SC-99-40.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/429/SC-99-40.pdf</file>
  </doc>
</export-example>
