<?xml version="1.0" encoding="utf-8"?>
<export-example>
  <doc>
    <id>5284</id>
    <completedYear/>
    <publishedYear>2003</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>4609</pageFirst>
    <pageLast>4640</pageLast>
    <pageNumber/>
    <edition/>
    <issue>41-42</issue>
    <volume>192</volume>
    <type>article</type>
    <publisherName>Elsevier</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Krylov subspace projection method for simultaneous solution of Helmholtz problems at multiple frequencies</title>
    <abstract language="eng">A Krylov subspace projection method which provides simultaneous solutions of the Helmholtz equation at multiple frequencies in one solution step is presented. The projector is obtained with an unsymmetric block Lanczos algorithm applied to a transfer function derived from a finite element discretization. This approach is equivalent to a matrix-valued Padé approximation of the transfer function. The proposed method is an extension of the formulation presented in [J. Comput. Acoust. 8 (2000) 223] to unsymmetric systems and allows the treatment of a much wider range of practical problems, including near-field and fluid–structure interaction computations</abstract>
    <parentTitle language="eng">Computer Methods in Applied Mechanics and Engineering</parentTitle>
    <identifier type="doi">10.1016/S0045-7825(03)00429-8</identifier>
    <enrichment key="opus.import.date">2022-08-20T07:06:56+00:00</enrichment>
    <enrichment key="opus.source">sword</enrichment>
    <enrichment key="opus.import.user">importuser</enrichment>
    <enrichment key="BegutachtungStatus">peer-reviewed</enrichment>
    <licence>Keine Lizenz - Es gilt das deutsche Urheberrecht: § 53 UrhG</licence>
    <author>Marcus Wagner</author>
    <author>Peter M. Pinsky</author>
    <author>Assad Oberai</author>
    <author>Manish Malhotra</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Multiple-frequency solution</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Krylov subspace</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Lanczos algorithm</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Padé approximation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Helmholtz equation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Dirichlet-to-Neumann map</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Acoustics</value>
    </subject>
    <collection role="institutes" number="FAKMB">Fakultät Maschinenbau</collection>
    <collection role="othpublikationsherkunft" number="">Externe Publikationen</collection>
    <collection role="othforschungsschwerpunkt" number="16316">Produktion und Systeme</collection>
  </doc>
  <doc>
    <id>5285</id>
    <completedYear/>
    <publishedYear>2003</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>313</pageFirst>
    <pageLast>319</pageLast>
    <pageNumber/>
    <edition/>
    <issue>1</issue>
    <volume>113</volume>
    <type>article</type>
    <publisherName>American Inst. of Physics</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Application of Padé via Lanczos approximations for efficient multifrequency solution of Helmholtz problems</title>
    <abstract language="eng">This paper addresses the efficient solution of acoustic problems in which the primary interest is obtaining the solution only on restricted portions of the domain but over a wide range of frequencies. The exterior acoustics boundary value problem is approximated using the finite element method in combination with the Dirichlet-to-Neumann (DtN) map. The restriction domain problem is formally posed in transfer function form based on the finite element solution. In order to obtain the solution over a range of frequencies, a matrix-valued Padé approximation of the transfer function is employed, using a two-sided block Lanczos algorithm. This approach provides a stable and efficient representation of the Padé approximation. In order to apply the algorithm, it is necessary to reformulate the transfer function due to the frequency dependency in the nonreflecting boundary condition. This is illustrated for the case of the DtN boundary condition, but there is no restriction on the approach which can also be applied to other radiation boundary conditions. Numerical tests confirm that the approach offers significant computational speed-up.</abstract>
    <parentTitle language="eng">Journal of the Acoustical Society of America</parentTitle>
    <identifier type="issn">1520-8524</identifier>
    <identifier type="issn">0001-4966</identifier>
    <identifier type="doi">10.1121/1.1514932</identifier>
    <enrichment key="opus.import.date">2022-08-20T07:06:56+00:00</enrichment>
    <enrichment key="opus.source">sword</enrichment>
    <enrichment key="opus.import.user">importuser</enrichment>
    <licence>Keine Lizenz - Es gilt das deutsche Urheberrecht: § 53 UrhG</licence>
    <author>Marcus Wagner</author>
    <author>Peter M. Pinsky</author>
    <author>Manish Malhotra</author>
    <collection role="institutes" number="FAKMB">Fakultät Maschinenbau</collection>
    <collection role="othpublikationsherkunft" number="">Externe Publikationen</collection>
    <collection role="othforschungsschwerpunkt" number="16316">Produktion und Systeme</collection>
    <collection role="institutes" number="">Labor Maschinendynamik und Strukturanalyse (LMS)</collection>
  </doc>
</export-example>
