Multilevel projection methods for partial differential equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Philadelphia, Pa.
Society for Industrial and Applied Mathematics
1992
|
| Series: | CBMS-NSF regional conference series in applied mathematics
62 |
| Subjects: | |
| Online Access: | TUM01 UBW01 UBY01 UER01 Volltext |
| Item Description: | Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader Includes bibliographical references and index Chapter 1. Fundamentals. Introduction; Notation and conventions; Prototype problems; Discretization by projections; Realizability and nodal representations; Interlevel transfer matrices; Error measures -- Chapter 2. Multilevel projections methods. Abstract framework: the Multilevel Projection method (PML); The Multigrid method (MG); the Fast Adaptive Composite grid method (FAC); Prototype problems; Relaxation; Coarse-level realizability and recursiveness; Parallelization: Asynchronous FAC (AFAC); Other practical matters; Summary -- Chapter 3. Unigrid. Basic Unigrid scheme; Multgrid simulation; FAC simulation; Performance assessment; Caveats -- Chapter 4. Paradigms. Rayleigh-Ritz 1: parameter estimation; Rayleigh-Ritz 2: transport equations: Galerkin 1: general Eigenvalue problems; Galerkin 2: Riccati equations; Petrov-Galerkin 1: the Finite Volume Element method (FVE); Petrov-Galerkin 2: image reconstruction -- Chapter 5. Perspectives -- References -- Appendix A. Simple Unigrid code -- Appendix B. More efficient Unigrid code -- Appendix C. Modification to Unigrid code for local refinement The multilevel projection method is a new formalism that provides a framework for the development of multilevel algorithms in a very general setting. This methodology guides the choices of all the major multilevel processes, including relaxation and coarsening, and it applies directly to global or locally-refined discretizations. This book was developed from lectures at the CBMS-NSF Regional Conference on Multigrid and Multilevel Adaptive Methods for Partial Differential Equations in June 1991, and is a supplement to Multilevel Adaptive Methods for Partial Differential Equations, also written by Stephen F. McCormick |
| Physical Description: | 1 Online-Ressource (vi, 114 Seiten) |
| ISBN: | 0898712920 9780898712926 |
| DOI: | 10.1137/1.9781611970098 |
Staff View
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| 500 | |a Chapter 1. Fundamentals. Introduction; Notation and conventions; Prototype problems; Discretization by projections; Realizability and nodal representations; Interlevel transfer matrices; Error measures -- Chapter 2. Multilevel projections methods. Abstract framework: the Multilevel Projection method (PML); The Multigrid method (MG); the Fast Adaptive Composite grid method (FAC); Prototype problems; Relaxation; Coarse-level realizability and recursiveness; Parallelization: Asynchronous FAC (AFAC); Other practical matters; Summary -- Chapter 3. Unigrid. Basic Unigrid scheme; Multgrid simulation; FAC simulation; Performance assessment; Caveats -- Chapter 4. Paradigms. Rayleigh-Ritz 1: parameter estimation; Rayleigh-Ritz 2: transport equations: Galerkin 1: general Eigenvalue problems; Galerkin 2: Riccati equations; Petrov-Galerkin 1: the Finite Volume Element method (FVE); Petrov-Galerkin 2: image reconstruction -- Chapter 5. Perspectives -- References -- Appendix A. Simple Unigrid code -- Appendix B. More efficient Unigrid code -- Appendix C. Modification to Unigrid code for local refinement | ||
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| id | DE-604.BV039747291 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:10:18Z |
| institution | BVB |
| isbn | 0898712920 9780898712926 |
| language | English |
| lccn | 91039536 |
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| publishDate | 1992 |
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| series2 | CBMS-NSF regional conference series in applied mathematics |
| spelling | McCormick, Stephen F. 1944- Verfasser (DE-588)142774065 aut Multilevel projection methods for partial differential equations Stephen F. McCormick Philadelphia, Pa. Society for Industrial and Applied Mathematics 1992 1 Online-Ressource (vi, 114 Seiten) txt rdacontent c rdamedia cr rdacarrier CBMS-NSF regional conference series in applied mathematics 62 Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader Includes bibliographical references and index Chapter 1. Fundamentals. Introduction; Notation and conventions; Prototype problems; Discretization by projections; Realizability and nodal representations; Interlevel transfer matrices; Error measures -- Chapter 2. Multilevel projections methods. Abstract framework: the Multilevel Projection method (PML); The Multigrid method (MG); the Fast Adaptive Composite grid method (FAC); Prototype problems; Relaxation; Coarse-level realizability and recursiveness; Parallelization: Asynchronous FAC (AFAC); Other practical matters; Summary -- Chapter 3. Unigrid. Basic Unigrid scheme; Multgrid simulation; FAC simulation; Performance assessment; Caveats -- Chapter 4. Paradigms. Rayleigh-Ritz 1: parameter estimation; Rayleigh-Ritz 2: transport equations: Galerkin 1: general Eigenvalue problems; Galerkin 2: Riccati equations; Petrov-Galerkin 1: the Finite Volume Element method (FVE); Petrov-Galerkin 2: image reconstruction -- Chapter 5. Perspectives -- References -- Appendix A. Simple Unigrid code -- Appendix B. More efficient Unigrid code -- Appendix C. Modification to Unigrid code for local refinement The multilevel projection method is a new formalism that provides a framework for the development of multilevel algorithms in a very general setting. This methodology guides the choices of all the major multilevel processes, including relaxation and coarsening, and it applies directly to global or locally-refined discretizations. This book was developed from lectures at the CBMS-NSF Regional Conference on Multigrid and Multilevel Adaptive Methods for Partial Differential Equations in June 1991, and is a supplement to Multilevel Adaptive Methods for Partial Differential Equations, also written by Stephen F. McCormick Differential equations, Partial / Numerical solutions Multigrid methods (Numerical analysis) Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Mehrgitterverfahren (DE-588)4038376-3 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Mehrgitterverfahren (DE-588)4038376-3 s DE-604 Partielle Differentialgleichung (DE-588)4044779-0 s Numerisches Verfahren (DE-588)4128130-5 s Erscheint auch als Druck-Ausgabe, Paperback 0898712920 Erscheint auch als Druck-Ausgabe, Paperback 9780898712926 CBMS-NSF regional conference series in applied mathematics 62 (DE-604)BV046682627 62 https://doi.org/10.1137/1.9781611970098 Verlag Volltext |
| spellingShingle | McCormick, Stephen F. 1944- Multilevel projection methods for partial differential equations CBMS-NSF regional conference series in applied mathematics Differential equations, Partial / Numerical solutions Multigrid methods (Numerical analysis) Partielle Differentialgleichung (DE-588)4044779-0 gnd Mehrgitterverfahren (DE-588)4038376-3 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4038376-3 (DE-588)4128130-5 |
| title | Multilevel projection methods for partial differential equations |
| title_auth | Multilevel projection methods for partial differential equations |
| title_exact_search | Multilevel projection methods for partial differential equations |
| title_full | Multilevel projection methods for partial differential equations Stephen F. McCormick |
| title_fullStr | Multilevel projection methods for partial differential equations Stephen F. McCormick |
| title_full_unstemmed | Multilevel projection methods for partial differential equations Stephen F. McCormick |
| title_short | Multilevel projection methods for partial differential equations |
| title_sort | multilevel projection methods for partial differential equations |
| topic | Differential equations, Partial / Numerical solutions Multigrid methods (Numerical analysis) Partielle Differentialgleichung (DE-588)4044779-0 gnd Mehrgitterverfahren (DE-588)4038376-3 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Differential equations, Partial / Numerical solutions Multigrid methods (Numerical analysis) Partielle Differentialgleichung Mehrgitterverfahren Numerisches Verfahren |
| url | https://doi.org/10.1137/1.9781611970098 |
| volume_link | (DE-604)BV046682627 |
| work_keys_str_mv | AT mccormickstephenf multilevelprojectionmethodsforpartialdifferentialequations |