Algebraic multigrid methods for large scale finite element equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Linz
Trauner
2001
|
| Schriftenreihe: | Universität <Linz>: [Schriften der Johannes-Kepler-Universität Linz / C]
36 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IV, 117 S. Ill., graph. Darst. |
| ISBN: | 3854872593 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV013780974 | ||
| 003 | DE-604 | ||
| 005 | 20011127 | ||
| 007 | t | ||
| 008 | 010621s2001 ad|| m||| 00||| eng d | ||
| 020 | |a 3854872593 |9 3-85487-259-3 | ||
| 035 | |a (OCoLC)444710588 | ||
| 035 | |a (DE-599)BVBBV013780974 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-355 |a DE-29 |a DE-739 |a DE-703 |a DE-83 | ||
| 080 | |a 519.6 | ||
| 084 | |a SK 910 |0 (DE-625)143270: |2 rvk | ||
| 084 | |a SK 920 |0 (DE-625)143272: |2 rvk | ||
| 100 | 1 | |a Reitzinger, Stefan |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Algebraic multigrid methods for large scale finite element equations |c Stefan Reitzinger |
| 264 | 1 | |a Linz |b Trauner |c 2001 | |
| 300 | |a IV, 117 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Universität <Linz>: [Schriften der Johannes-Kepler-Universität Linz / C] |v 36 | |
| 502 | |a Zugl.: Linz, Univ., Diss., 2001 | ||
| 650 | 4 | |a matematika - numerična analiza - numerične metode - mrežne metode - eliptične diferencialne enačbe - linearni prostori - disertacije | |
| 650 | 0 | 7 | |a Algebraische Methode |0 (DE-588)4141841-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mehrgitterverfahren |0 (DE-588)4038376-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Finite-Elemente-Methode |0 (DE-588)4017233-8 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
| 689 | 0 | 0 | |a Mehrgitterverfahren |0 (DE-588)4038376-3 |D s |
| 689 | 0 | 1 | |a Finite-Elemente-Methode |0 (DE-588)4017233-8 |D s |
| 689 | 0 | 2 | |a Algebraische Methode |0 (DE-588)4141841-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 810 | 2 | |a C] |t Universität <Linz>: [Schriften der Johannes-Kepler-Universität Linz |v 36 |w (DE-604)BV009806089 |9 36 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009420533&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-009420533 | ||
Datensatz im Suchindex
| _version_ | 1804128602576388096 |
|---|---|
| adam_text | Contents
1 Introduction 1
2 Preliminaries 9
2.1 Sobolev Spaces 9
2.2 Classical Formulations 12
2.2.1 Maxwell Equations 12
2.2.2 Cauchy Navier Equations 14
2.2.3 Coupled Field Problems 11
2.3 Primal Variational Formulation 15
2.4 Finite Element Method 18
2.5 Iterative Solvers 20
3 General Approach to AMG Methods 25
3.1 Motivation for AMG Methods 25
3.2 Components of an AMG Method 26
3.2.1 Auxiliary Matrix ( virtual FE mesh ) 26
3.2.2 Coarsening Process 2!)
3.2.3 Prolongation Operators 30
3.2.4 Smoother and Coarse Grid Operator 32
3.3 Routines and Algorithms 33
3.4 Convergence Theory and Limitations 36
4 Special Algebraic Multigrid Methods 41
4.1 Symmetric JJ1 (fi) based Equations 41
4.2 Symmetric {Hl (tyY based Equations 43
4.3 Symmetric if (curl. H) based Equations 44
5 Element Preconditioning Technique 49
5.1 Motivation 49
5.2 Basic Concept 49
5.3 Optimization Procedure 51
5.4 Classification Strategy 59
6 A Parallel Version of AMG 61
6.1 A Unified Data Distribution Concept 61
6.1.1 Notations 61
i
ii CONTENTS
6.1.2 Vector and Matrix Types 62
6.1.3 Basic Operations 63
6.1.4 Basic Algorithms 64
6.2 The Parallel AMG Algorithm and Its Implementation 65
6.2.1 Communication Groups and Node Sets 65
6.2.2 Parallel Coarsening 67
6.2.3 Coarse Grid Matrix and Parallel Setup 68
6.2.4 Object Oriented Approach 68
7 AMG Software Package PEBBLES 71
7.1 Requirements and Implementation 71
7.2 Setup Phase 73
7.2.1 General Relations 73
7.2.2 Special Examples 75
7.3 Applications 77
8 Numerical Studies 79
8.1 Symmetric H1 (O) based Equations 80
8.1.1 Element Preconditioning Studies 80
8.1.2 Anisotropic Studies with an Auxiliary Matrix 84
8.1.3 Nonlinear Studies 85
8.1.4 Coupled Field Problems 89
8.1.5 Inverse Source Reconstruction 91
8.2 Symmetric (HL(Sl))p based Equations 93
8.2.1 Linear Elasticity Problems 93
8.2.2 Magnetic Field Equations in 3D with Nodal Elements .... 95
8.3 Symmetric /f(curl,fi) based Equations 98
8.3.1 Magnetic Field Equations in 3D with Edge Elements 98
8.3.2 FIT Discretization 100
8.4 Parallel Results 102
8.4.1 Symmetric Hl (Ji) based Equations 102
8.4.2 Symmetric H (curl, fi) based Equations 104
8.5 Other Comparisons 106
|
| any_adam_object | 1 |
| author | Reitzinger, Stefan |
| author_facet | Reitzinger, Stefan |
| author_role | aut |
| author_sort | Reitzinger, Stefan |
| author_variant | s r sr |
| building | Verbundindex |
| bvnumber | BV013780974 |
| classification_rvk | SK 910 SK 920 |
| ctrlnum | (OCoLC)444710588 (DE-599)BVBBV013780974 |
| discipline | Mathematik |
| format | Thesis Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02025nam a2200445 cb4500</leader><controlfield tag="001">BV013780974</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20011127 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">010621s2001 ad|| m||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3854872593</subfield><subfield code="9">3-85487-259-3</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)444710588</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV013780974</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield><subfield code="a">DE-29</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-83</subfield></datafield><datafield tag="080" ind1=" " ind2=" "><subfield code="a">519.6</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 910</subfield><subfield code="0">(DE-625)143270:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 920</subfield><subfield code="0">(DE-625)143272:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Reitzinger, Stefan</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Algebraic multigrid methods for large scale finite element equations</subfield><subfield code="c">Stefan Reitzinger</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Linz</subfield><subfield code="b">Trauner</subfield><subfield code="c">2001</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">IV, 117 S.</subfield><subfield code="b">Ill., graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Universität <Linz>: [Schriften der Johannes-Kepler-Universität Linz / C]</subfield><subfield code="v">36</subfield></datafield><datafield tag="502" ind1=" " ind2=" "><subfield code="a">Zugl.: Linz, Univ., Diss., 2001</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">matematika - numerična analiza - numerične metode - mrežne metode - eliptične diferencialne enačbe - linearni prostori - disertacije</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Algebraische Methode</subfield><subfield code="0">(DE-588)4141841-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mehrgitterverfahren</subfield><subfield code="0">(DE-588)4038376-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Finite-Elemente-Methode</subfield><subfield code="0">(DE-588)4017233-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)4113937-9</subfield><subfield code="a">Hochschulschrift</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Mehrgitterverfahren</subfield><subfield code="0">(DE-588)4038376-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Finite-Elemente-Methode</subfield><subfield code="0">(DE-588)4017233-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Algebraische Methode</subfield><subfield code="0">(DE-588)4141841-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="810" ind1="2" ind2=" "><subfield code="a">C]</subfield><subfield code="t">Universität <Linz>: [Schriften der Johannes-Kepler-Universität Linz</subfield><subfield code="v">36</subfield><subfield code="w">(DE-604)BV009806089</subfield><subfield code="9">36</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009420533&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-009420533</subfield></datafield></record></collection> |
| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV013780974 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:51:51Z |
| institution | BVB |
| isbn | 3854872593 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009420533 |
| oclc_num | 444710588 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-29 DE-739 DE-703 DE-83 |
| owner_facet | DE-355 DE-BY-UBR DE-29 DE-739 DE-703 DE-83 |
| physical | IV, 117 S. Ill., graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Trauner |
| record_format | marc |
| series2 | Universität <Linz>: [Schriften der Johannes-Kepler-Universität Linz / C] |
| spelling | Reitzinger, Stefan Verfasser aut Algebraic multigrid methods for large scale finite element equations Stefan Reitzinger Linz Trauner 2001 IV, 117 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universität <Linz>: [Schriften der Johannes-Kepler-Universität Linz / C] 36 Zugl.: Linz, Univ., Diss., 2001 matematika - numerična analiza - numerične metode - mrežne metode - eliptične diferencialne enačbe - linearni prostori - disertacije Algebraische Methode (DE-588)4141841-4 gnd rswk-swf Mehrgitterverfahren (DE-588)4038376-3 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Mehrgitterverfahren (DE-588)4038376-3 s Finite-Elemente-Methode (DE-588)4017233-8 s Algebraische Methode (DE-588)4141841-4 s DE-604 C] Universität <Linz>: [Schriften der Johannes-Kepler-Universität Linz 36 (DE-604)BV009806089 36 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009420533&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Reitzinger, Stefan Algebraic multigrid methods for large scale finite element equations matematika - numerična analiza - numerične metode - mrežne metode - eliptične diferencialne enačbe - linearni prostori - disertacije Algebraische Methode (DE-588)4141841-4 gnd Mehrgitterverfahren (DE-588)4038376-3 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| subject_GND | (DE-588)4141841-4 (DE-588)4038376-3 (DE-588)4017233-8 (DE-588)4113937-9 |
| title | Algebraic multigrid methods for large scale finite element equations |
| title_auth | Algebraic multigrid methods for large scale finite element equations |
| title_exact_search | Algebraic multigrid methods for large scale finite element equations |
| title_full | Algebraic multigrid methods for large scale finite element equations Stefan Reitzinger |
| title_fullStr | Algebraic multigrid methods for large scale finite element equations Stefan Reitzinger |
| title_full_unstemmed | Algebraic multigrid methods for large scale finite element equations Stefan Reitzinger |
| title_short | Algebraic multigrid methods for large scale finite element equations |
| title_sort | algebraic multigrid methods for large scale finite element equations |
| topic | matematika - numerična analiza - numerične metode - mrežne metode - eliptične diferencialne enačbe - linearni prostori - disertacije Algebraische Methode (DE-588)4141841-4 gnd Mehrgitterverfahren (DE-588)4038376-3 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| topic_facet | matematika - numerična analiza - numerične metode - mrežne metode - eliptične diferencialne enačbe - linearni prostori - disertacije Algebraische Methode Mehrgitterverfahren Finite-Elemente-Methode Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009420533&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009806089 |
| work_keys_str_mv | AT reitzingerstefan algebraicmultigridmethodsforlargescalefiniteelementequations |