Robust algebraic multilevel methods and algorithms:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
<<de>> Gruyter
2009
|
| Series: | Radon series on computational and applied mathematics
5 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 237 - 244 |
| Physical Description: | X, 246 S. graph. Darst. 25 cm |
| ISBN: | 9783110193657 |
Staff View
MARC
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| 100 | 1 | |a Kraus, Johannes |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Robust algebraic multilevel methods and algorithms |c Johannes Kraus ; Svetozar Margenov |
| 264 | 1 | |a Berlin [u.a.] |b <<de>> Gruyter |c 2009 | |
| 300 | |a X, 246 S. |b graph. Darst. |c 25 cm | ||
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Record in the Search Index
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| adam_text | CONTENTS PREFACE V 1 INTRODUCTION 1 1.1 FINITE ELEMENT METHOD (FEM) 1
1.1.1 THE ELLIPTIC MODEL PROBLEM 1 1.1.2 CONFORMING DISCRETIZATIONS 4
1.1.3 NONCONFORMING DISCRETIZATIONS 5 1.1.4 STRUCTURE AND PROPERTIES OF
THE STIFFNESS MATRIX 8 1.2 ILL-CONDITIONED PROBLEMS 10 1.2.1 ANISOTROPIE
PROBLEMS 10 1.2.2 PROBLEMS WITH HIGHLY VARYING COEFFICIENTS 10 1.2.3
ELASTIC DEFORMATION OF ALMOST INCOMPRESSIBLE MATERIALS . . 11 1.2.4
HIGH-REYNOLDS-NUMBER FLOW 12 1.3 PRELIMINARIES ON ITERATIVE METHODS 13
1.3.1 STATIONARY METHODS 13 1.3.2 POLYNOMIAL ACCELERATION 15 1.4
CONJUGATE GRADIENTS (CG) 18 1.4.1 FROM STEEPEST DESCENT TO CONJUGATE
GRADIENTS 18 1.4.2 CONVERGENCE ANALYSIS OF THE CG METHOD 20 1.4.3
PRECONDITIONED CONJUGATE GRADIENT (PCG) METHOD 24 1.4.4 GENERALIZED
CONJUGATE GRADIENT (GCG) METHOD 26 2 ALGEBRAIC MULTILEVEL ITERATION
METHODS 29 2.1 BLOCK-FACTORIZATION: SCHUR COMPLEMENT 29 2.2 LOCAL
ESTIMATES OF THE CBS CONSTANT 31 2.3 TWO-LEVEL PRECONDITIONING METHODS
34 2.3.1 ALGEBRAIC TWO-LEVEL METHODS 34 2.3.2 TWO-LEVEL PRECONDITIONERS
FOR FEM SYSTEMS 37 2.4 LINEAR AMLI METHODS 38 2.5 NONLINEAR AMLI METHODS
43 2.6 OPTIMALITY CONDITIONS 48 2.7 ROBUSTNESS OF THE AMLI METHODS 51
2.7.1 LOCAL ANALYSIS OF THE MODEL PROBLEM 51 2.7.2 ROBUST
PRECONDITIONING STRATEGY 53 2.7. BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/997081279 DIGITALISIERT DURCH VIII CONTENTS 3 ROBUST
AMLI ALGORITHMS: CONFORMING LINEAR FINITE ELEMENTS . . . . 57 3.1 SOME
BASIC RELATIONS 57 3.2 UNIFORM ESTIMATES OF THE CONSTANT IN THE
STRENGTHENED CBS INEQUALITY 62 3.3 ADDITIVE PRECONDITIONING OF THE PIVOT
BLOCK 66 3.4 MULTIPLICATIVE PRECONDITIONING OF THE PIVOT BLOCK 69 3.5
LOCALLY IMPROVED ESTIMATES OF THE AMLI PARAMETERS 72 3.6 OPTIMAL
COMPLEXITY SOLUTION ALGORITHMS FOR SYSTEMS WITH C ... 73 3.6.1 A MODEL
PROBLEM 73 3.6.2 ADDITIVE ALGORITHM 74 3.6.3 MULTIPLICATIVE ALGORITHM 74
4 ROBUST AMLI ALGORITHMS: NONCONFORMING LINEAR FINITE ELEMENTS . . 77
4.1 CROUZEIX-RAVIART FINITE ELEMENTS 77 4.2 TWO-LEVEL SPLITTINGS: FIRST
REDUCE AND DIFFERENCES AND AGGRE- GATES 79 4.3 UNIFORM ESTIMATES OF
THE CBS CONSTANT IN CASE OF NON-NESTED SPACES 81 4.4 PRECONDITIONING OF
THE PIVOT BLOCK 95 4.5 NUMERICAL RESULTS 98 4.5.1 CONCLUDING REMARKS 100
5 SCHUR COMPLEMENT BASED MULTILEVEL PRECONDITIONERS 102 5.1 HIERARCHICAL
VERSUS STANDARD NODAL-BASIS 102 5.2 A GENERAL TWO-LEVEL PRECONDITIONER
102 5.3 INCOMPLETE FACTORIZATION BASED ON EXACT LOCAL FACTORIZATION . .
. . 107 5.4 LOCAL SCHUR COMPLEMENTS 112 5.5 NUMERICAL RESULTS 114 6
ALGEBRAIC MULTIGRID (AMG) 11 CONTENTS IX 6.6 SMOOTHED AGGREGATION AND
ADAPTIVE AMG METHODS 132 6.7 UTILIZING AMG COMPONENTS IN AMLI 134 7
PRECONDITIONING OF RANNACHER-TUREK NONCONFORMING FE SYSTEMS . 136 7.1
RANNACHER-TUREK NONCONFORMING FE SYSTEMS 136 7.1.1 THE NONCONFORMING FE
PROBLEM 136 7.1.2 ROTATED BILINEAR ELEMENTS 137 7.1.3 ROTATED TRILINEAR
ELEMENTS 138 7.2 HIERARCHICAL TWO-LEVEL SPLITTINGS: 2D CASE 140 7.2.1
FIRST REDUCE TWO-LEVEL SPLITTING 140 7.2.2 TWO-LEVEL SPLITTING BY
DIFFERENCES AND AGGREGATES 143 7.2.3 UNIFORM ESTIMATES OF THE CBS
CONSTANT FOR THE 2D SPLITTINGS 144 7.3 HIERARCHICAL TWO-LEVEL
SPLITTINGS: 3D CASE 147 7.3.1 FIRST REDUCE TWO-LEVEL SPLITTING 147 7.3.2
TWO-LEVEL SPLITTING BY DIFFERENCES AND AGGREGATES 150 7.3.3 UNIFORM
ESTIMATES OF THE CBS CONSTANT FOR THE 3D SPLITTINGS 152 7.4 MULTILEVEL
PRECONDITIONING 155 7.5 NUMERICAL TESTS 158 7.5.1 ADDITIVE AND
MULTIPLICATIVE AMLI PRECONDITIONERS IN 2D . 158 7.5.2 PROBLEMS WITH
JUMPING COEFFICIENTS IN 3D 159 8 AMLI ALGORITHMS FOR DISCONTINUOUS
GALERKIN FE PROBLEMS 164 8.1 INTRODUCTION TO DISCONTINUOUS GALERKIN FEM
164 8.2 ELEMENT-BASED APPROACH: BILINEAR DG SYSTEMS 166 8.3 FACE-BASED
APPROACH: ROTATED BILINEAR DG SYSTEMS 177 8.4 TWO-LEVEL METHOD AND AMLI
PRECONDITIONING OF GRAPH-LAPLACIANS 186 9 AMLI METHODS FOR COUPLED
PROBLEMS 196 9. X CONTENTS 10 PRACTICAL ISSUES 219 10.1 LINEAR AMLI
ALGORITHM 219 10.2 NONLINEAR AMLI ALGORITHM 223 10.3 CASE STUDY:
INTEGRATING OF NEW AMLI SOLVERS 225 10.3.1 CROUZEIX-RAVIART FE
DISCRETIZATION OF 3D PURE DISPLACE- MENT ELASTICITY PROBLEMS 226 10.3.2
COMPOSITE FR ALGORITHM 228 10.3.3 NUMERICAL TESTS: TOWARDS /XFEM
ANALYSIS OF BONE STRUCTURES 232 BIBLIOGRAPHY 237 INDEX 245
|
| any_adam_object | 1 |
| author | Kraus, Johannes Margenov, Svetozar |
| author_GND | (DE-588)123357764 |
| author_facet | Kraus, Johannes Margenov, Svetozar |
| author_role | aut aut |
| author_sort | Kraus, Johannes |
| author_variant | j k jk s m sm |
| building | Verbundindex |
| bvnumber | BV035829858 |
| callnumber-first | Q - Science |
| callnumber-label | QA184 |
| callnumber-raw | QA184.2 |
| callnumber-search | QA184.2 |
| callnumber-sort | QA 3184.2 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 500 SK 540 SK 910 SK 920 |
| ctrlnum | (OCoLC)198757366 (DE-599)DNB997081279 |
| dewey-full | 518.43 515.35 518.64 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis 515 - Analysis |
| dewey-raw | 518.43 515.35 518.64 |
| dewey-search | 518.43 515.35 518.64 |
| dewey-sort | 3518.43 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV035829858 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:05:36Z |
| institution | BVB |
| isbn | 9783110193657 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018688449 |
| oclc_num | 198757366 |
| open_access_boolean | |
| owner | DE-83 DE-634 DE-824 DE-11 DE-29T |
| owner_facet | DE-83 DE-634 DE-824 DE-11 DE-29T |
| physical | X, 246 S. graph. Darst. 25 cm |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | <<de>> Gruyter |
| record_format | marc |
| series | Radon series on computational and applied mathematics |
| series2 | Radon series on computational and applied mathematics |
| spelling | Kraus, Johannes Verfasser aut Robust algebraic multilevel methods and algorithms Johannes Kraus ; Svetozar Margenov Berlin [u.a.] <<de>> Gruyter 2009 X, 246 S. graph. Darst. 25 cm txt rdacontent n rdamedia nc rdacarrier Radon series on computational and applied mathematics 5 Literaturverz. S. 237 - 244 Datenverarbeitung Algebras, Linear Data processing Lineares Gleichungssystem (DE-588)4035826-4 gnd rswk-swf Multi-level-Verfahren (DE-588)4344428-3 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Iteration (DE-588)4123457-1 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Finite-Elemente-Methode (DE-588)4017233-8 s Lineares Gleichungssystem (DE-588)4035826-4 s Iteration (DE-588)4123457-1 s Multi-level-Verfahren (DE-588)4344428-3 s DE-604 Margenov, Svetozar Verfasser (DE-588)123357764 aut Radon series on computational and applied mathematics 5 (DE-604)BV023335470 5 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018688449&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kraus, Johannes Margenov, Svetozar Robust algebraic multilevel methods and algorithms Radon series on computational and applied mathematics Datenverarbeitung Algebras, Linear Data processing Lineares Gleichungssystem (DE-588)4035826-4 gnd Multi-level-Verfahren (DE-588)4344428-3 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Iteration (DE-588)4123457-1 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4035826-4 (DE-588)4344428-3 (DE-588)4017233-8 (DE-588)4123457-1 (DE-588)4044779-0 |
| title | Robust algebraic multilevel methods and algorithms |
| title_auth | Robust algebraic multilevel methods and algorithms |
| title_exact_search | Robust algebraic multilevel methods and algorithms |
| title_full | Robust algebraic multilevel methods and algorithms Johannes Kraus ; Svetozar Margenov |
| title_fullStr | Robust algebraic multilevel methods and algorithms Johannes Kraus ; Svetozar Margenov |
| title_full_unstemmed | Robust algebraic multilevel methods and algorithms Johannes Kraus ; Svetozar Margenov |
| title_short | Robust algebraic multilevel methods and algorithms |
| title_sort | robust algebraic multilevel methods and algorithms |
| topic | Datenverarbeitung Algebras, Linear Data processing Lineares Gleichungssystem (DE-588)4035826-4 gnd Multi-level-Verfahren (DE-588)4344428-3 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Iteration (DE-588)4123457-1 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Datenverarbeitung Algebras, Linear Data processing Lineares Gleichungssystem Multi-level-Verfahren Finite-Elemente-Methode Iteration Partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018688449&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV023335470 |
| work_keys_str_mv | AT krausjohannes robustalgebraicmultilevelmethodsandalgorithms AT margenovsvetozar robustalgebraicmultilevelmethodsandalgorithms |