Multilevel solution of the time harmonic Maxwell's equations based on edge elements:
Abstract: "A widely used approach for the computation of time- harmonic electromagnetic fields is based on the well-known double-curl equation for either E[right arrow] or H[right arrow]. An appealing choice for finite element discretizations are edge elements, the lowest order variant of a H(c...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Konrad-Zuse-Zentrum für Informationstechnik
1996
|
| Schriftenreihe: | Preprint SC / Konrad-Zuse-Zentrum für Informationstechnik Berlin
1996,51 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "A widely used approach for the computation of time- harmonic electromagnetic fields is based on the well-known double-curl equation for either E[right arrow] or H[right arrow]. An appealing choice for finite element discretizations are edge elements, the lowest order variant of a H(curl)-conforming family of finite elements. However, the large nullspace of the curl-operator gives rise to serious difficulties. It comprises a considerable part of all spectral modes on the finite element grid, tending to pollute the solution with non-physical contributions and crippling standard multilevel solvers. We tackle these problems by an adaptive multilevel algorithm. After every standard V- cycle with respect to the canonical basis of edge elements, the non- physical contributions are removed by a projection step. It requires the solution of Poisson's equation, augmented by certain boundary terms, in the nullspace, which can be carried out efficiently by an inner multilevel iteration. The whole scheme yields convergence rates independent of the refinement level of the mesh. Furthermore, a simple criterion for meshes is derived which can resolve all field modes corresponding to negative eigenvalues. This requirement is essential to guarantee both stability and efficiency of an iterative multilevel solver for indefinite systems. For controlling adaptive mesh refinement we have devised an a posteriori error indicator based on stress recovery. Numerical experiments demonstrate the efficiency of the method for the simulation of waveguides." |
| Beschreibung: | 21 S. |
Internformat
MARC
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| 049 | |a DE-703 | ||
| 100 | 1 | |a Beck, Rudolf |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Multilevel solution of the time harmonic Maxwell's equations based on edge elements |c Rudolf Beck ; Ralf Hiptmair |
| 264 | 1 | |a Berlin |b Konrad-Zuse-Zentrum für Informationstechnik |c 1996 | |
| 300 | |a 21 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Preprint SC / Konrad-Zuse-Zentrum für Informationstechnik Berlin |v 1996,51 | |
| 520 | 3 | |a Abstract: "A widely used approach for the computation of time- harmonic electromagnetic fields is based on the well-known double-curl equation for either E[right arrow] or H[right arrow]. An appealing choice for finite element discretizations are edge elements, the lowest order variant of a H(curl)-conforming family of finite elements. However, the large nullspace of the curl-operator gives rise to serious difficulties. It comprises a considerable part of all spectral modes on the finite element grid, tending to pollute the solution with non-physical contributions and crippling standard multilevel solvers. We tackle these problems by an adaptive multilevel algorithm. After every standard V- cycle with respect to the canonical basis of edge elements, the non- physical contributions are removed by a projection step. It requires the solution of Poisson's equation, augmented by certain boundary terms, in the nullspace, which can be carried out efficiently by an inner multilevel iteration. The whole scheme yields convergence rates independent of the refinement level of the mesh. Furthermore, a simple criterion for meshes is derived which can resolve all field modes corresponding to negative eigenvalues. This requirement is essential to guarantee both stability and efficiency of an iterative multilevel solver for indefinite systems. For controlling adaptive mesh refinement we have devised an a posteriori error indicator based on stress recovery. Numerical experiments demonstrate the efficiency of the method for the simulation of waveguides." | |
| 650 | 4 | |a Electromagnetic fields | |
| 650 | 4 | |a Maxwell equations | |
| 650 | 4 | |a Scattering (Physics) | |
| 650 | 4 | |a Wave guides | |
| 700 | 1 | |a Hiptmair, Ralf |e Verfasser |4 aut | |
| 810 | 2 | |a Konrad-Zuse-Zentrum für Informationstechnik Berlin |t Preprint SC |v 1996,51 |w (DE-604)BV004801715 |9 1996,51 | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-010359106 | |
Datensatz im Suchindex
| _version_ | 1820882503734394880 |
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| adam_text | |
| any_adam_object | |
| author | Beck, Rudolf Hiptmair, Ralf |
| author_facet | Beck, Rudolf Hiptmair, Ralf |
| author_role | aut aut |
| author_sort | Beck, Rudolf |
| author_variant | r b rb r h rh |
| building | Verbundindex |
| bvnumber | BV017188054 |
| classification_rvk | SS 4777 |
| ctrlnum | (OCoLC)37991484 (DE-599)BVBBV017188054 |
| discipline | Informatik |
| format | Book |
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| id | DE-604.BV017188054 |
| illustrated | Not Illustrated |
| indexdate | 2025-01-10T17:07:56Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010359106 |
| oclc_num | 37991484 |
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| owner | DE-703 |
| owner_facet | DE-703 |
| physical | 21 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Konrad-Zuse-Zentrum für Informationstechnik |
| record_format | marc |
| series2 | Preprint SC / Konrad-Zuse-Zentrum für Informationstechnik Berlin |
| spelling | Beck, Rudolf Verfasser aut Multilevel solution of the time harmonic Maxwell's equations based on edge elements Rudolf Beck ; Ralf Hiptmair Berlin Konrad-Zuse-Zentrum für Informationstechnik 1996 21 S. txt rdacontent n rdamedia nc rdacarrier Preprint SC / Konrad-Zuse-Zentrum für Informationstechnik Berlin 1996,51 Abstract: "A widely used approach for the computation of time- harmonic electromagnetic fields is based on the well-known double-curl equation for either E[right arrow] or H[right arrow]. An appealing choice for finite element discretizations are edge elements, the lowest order variant of a H(curl)-conforming family of finite elements. However, the large nullspace of the curl-operator gives rise to serious difficulties. It comprises a considerable part of all spectral modes on the finite element grid, tending to pollute the solution with non-physical contributions and crippling standard multilevel solvers. We tackle these problems by an adaptive multilevel algorithm. After every standard V- cycle with respect to the canonical basis of edge elements, the non- physical contributions are removed by a projection step. It requires the solution of Poisson's equation, augmented by certain boundary terms, in the nullspace, which can be carried out efficiently by an inner multilevel iteration. The whole scheme yields convergence rates independent of the refinement level of the mesh. Furthermore, a simple criterion for meshes is derived which can resolve all field modes corresponding to negative eigenvalues. This requirement is essential to guarantee both stability and efficiency of an iterative multilevel solver for indefinite systems. For controlling adaptive mesh refinement we have devised an a posteriori error indicator based on stress recovery. Numerical experiments demonstrate the efficiency of the method for the simulation of waveguides." Electromagnetic fields Maxwell equations Scattering (Physics) Wave guides Hiptmair, Ralf Verfasser aut Konrad-Zuse-Zentrum für Informationstechnik Berlin Preprint SC 1996,51 (DE-604)BV004801715 1996,51 |
| spellingShingle | Beck, Rudolf Hiptmair, Ralf Multilevel solution of the time harmonic Maxwell's equations based on edge elements Electromagnetic fields Maxwell equations Scattering (Physics) Wave guides |
| title | Multilevel solution of the time harmonic Maxwell's equations based on edge elements |
| title_auth | Multilevel solution of the time harmonic Maxwell's equations based on edge elements |
| title_exact_search | Multilevel solution of the time harmonic Maxwell's equations based on edge elements |
| title_full | Multilevel solution of the time harmonic Maxwell's equations based on edge elements Rudolf Beck ; Ralf Hiptmair |
| title_fullStr | Multilevel solution of the time harmonic Maxwell's equations based on edge elements Rudolf Beck ; Ralf Hiptmair |
| title_full_unstemmed | Multilevel solution of the time harmonic Maxwell's equations based on edge elements Rudolf Beck ; Ralf Hiptmair |
| title_short | Multilevel solution of the time harmonic Maxwell's equations based on edge elements |
| title_sort | multilevel solution of the time harmonic maxwell s equations based on edge elements |
| topic | Electromagnetic fields Maxwell equations Scattering (Physics) Wave guides |
| topic_facet | Electromagnetic fields Maxwell equations Scattering (Physics) Wave guides |
| volume_link | (DE-604)BV004801715 |
| work_keys_str_mv | AT beckrudolf multilevelsolutionofthetimeharmonicmaxwellsequationsbasedonedgeelements AT hiptmairralf multilevelsolutionofthetimeharmonicmaxwellsequationsbasedonedgeelements |