Adaptive Linienmethoden für nichtlineare parabolische Systeme in einer Raumdimension:
Abstract: "A new method for the numerical solution of highly nonlinear, coupled systems of parabolic differential equations in one space dimension is presented. The approach is based on a classical method of lines treatment. Time discretization is done by means of the semi-implicit Euler discre...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English German |
| Veröffentlicht: |
Berlin
Konrad-Zuse-Zentrum für Informationstechnik Berlin
1993
|
| Schriftenreihe: | Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Technical report
1993,14 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | Abstract: "A new method for the numerical solution of highly nonlinear, coupled systems of parabolic differential equations in one space dimension is presented. The approach is based on a classical method of lines treatment. Time discretization is done by means of the semi-implicit Euler discretization. Space discretization is done with finite differences on non-uniform grids. Both basic discretizations are coupled with extrapolation techniques. With respect to time the extrapolation is of variable order whereas just one extrapolation step is done in space. Based on local error estimates for both, the time and the space discretization error, the accuracy of the numerical approximation is controlled and the discretization stepsizes are adapted automatically and simultaneously Besides the local adaptation of the space grids after each integration step (static regridding), the grid may even move within each integration step (dynamic regridding). Thus, the whole algorithm has a high degree of adaptivity. Due to this fact, challenging problems from applications can be solved in an efficient and robust way. |
| Beschreibung: | Zugl.: Berlin, Freie Univ., Diss., 1993 |
| Beschreibung: | III, 177 S. graph. Darst. |
Internformat
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| 100 | 1 | |a Nowak, Ulrich |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Adaptive Linienmethoden für nichtlineare parabolische Systeme in einer Raumdimension |c U. Nowak |
| 264 | 1 | |a Berlin |b Konrad-Zuse-Zentrum für Informationstechnik Berlin |c 1993 | |
| 300 | |a III, 177 S. |b graph. Darst. | ||
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| 490 | 1 | |a Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Technical report |v 1993,14 | |
| 500 | |a Zugl.: Berlin, Freie Univ., Diss., 1993 | ||
| 520 | 3 | |a Abstract: "A new method for the numerical solution of highly nonlinear, coupled systems of parabolic differential equations in one space dimension is presented. The approach is based on a classical method of lines treatment. Time discretization is done by means of the semi-implicit Euler discretization. Space discretization is done with finite differences on non-uniform grids. Both basic discretizations are coupled with extrapolation techniques. With respect to time the extrapolation is of variable order whereas just one extrapolation step is done in space. Based on local error estimates for both, the time and the space discretization error, the accuracy of the numerical approximation is controlled and the discretization stepsizes are adapted automatically and simultaneously | |
| 520 | 3 | |a Besides the local adaptation of the space grids after each integration step (static regridding), the grid may even move within each integration step (dynamic regridding). Thus, the whole algorithm has a high degree of adaptivity. Due to this fact, challenging problems from applications can be solved in an efficient and robust way. | |
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| 650 | 0 | 7 | |a Linienmethode |0 (DE-588)4324233-9 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1814895913801351168 |
|---|---|
| adam_text |
INHALTSVERZEICHNIS
1
EINLEITUNG
1
2
NICHTUNIFORME
DISKRETISIERUNGEN
6
2.1
GENAUE
PROBLEMFORMULIERUNG
.
6
2.2
ORTSDISKRETISIERUNG
MIT
FINITEN
DIFFERENZEN
.
8
2.2.1
UNTERSUCHUNG
EINES
MODELLPROBLEMS
.
9
2.2.2
DER
ALLGEMEINE
FALL
.
15
2.2.3
ZUSAMMENFASSUNG
.
23
2.3
ZEITDISKRETISIERUNG
MIT
SEMI-IMPLIZITEM
EULER
.
26
2.3.1
GEWOEHNLICHE
DIFFERENTIALGLEICHUNGEN
.
27
2.3.2
DIFFERENTIELL-ALGEBRAISCHE
SYSTEME
.
31
2.3.3
BASISDISKRETISIERUNG
DES
GESAMTVERFAHRENS
.
36
2.3.4
ANGENOMMENE
ASYMPTOTISCHE
ENTWICKLUNG
DES
GLOBA
LEN
FEHLERS
.
38
2.3.5
EIN
NUMERISCHES
EXPERIMENT
-
TEIL
I
.
39
3
STATISCHE
GITTERERNEUERUNG
47
3.1
GEKOPPELTE
EXTRAPOLATION
IN
RAUM
UND
ZEIT
.
47
3.1.1
2-D-POLYNOMEXTRAPOLATION
.
49
3.1.2
EIN
NUMERISCHES
EXPERIMENT
-
TEIL
II
.
54
3.2
FEHLERSCHAETZUNG
.
60
3.3
ADAPTIVE
WAHL
VON
ZEITSCHRITTWEITE
UND
RAUMGITTER
.
65
3.3.1
SIMULTANE
BESTIMMUNG
DER
GRUNDSCHRITTWEITEN
.
65
3.3.2
KONSEQUENZEN
AUS
GITTERWECHSEL
.
69
3.3.3
DAS
INTERPOLATIONSPROBLEM
.
71
3.3.4
LOKALE
GITTERANPASSUNG
.
77
3.4
GESAMTALGORITHMUS
.
81
4
MITBEWEGTES
GITTER
86
4.1
TRANSFORMATION
DER
GLEICHUNG
.
87
4.1.1
EIN
MODELLPROBLEM
.
87
4.1.2
DER
ALLGEMEINE
FALL
.
89
4.1.3
A
PRIORI
BESTIMMUNG
DES
GITTERS
.
90
4.2
GLEICHUNGEN
ZUR
GITTERANKOPPLUNG
.
91
4.2.1
MINIMIERUNG
EINES
ZIELFUNKTIONALS
.
91
4.2.2
DAS
PROBLEM
DER
KNOTENUEBERKREUZUNG
.
93
4.2.3
WEITERE
REGULARISIERUNG
DER
GITTERGLEICHUNGEN
.
94
4.2.4
ZWEI
ALLGEMEIN
VERWENDBARE
GITTERGLEICHUNGEN
.
96
4.2.5
ANALYSE
UND
VERGLEICH
.
99
4.2.6
SPEZIELLE
GITTERBEWEGUNGSVARIANTEN
.
104
4.3
EINBINDUNG
IN
DAS
GESAMTVERFAHREN
.
107
4.3.1
DIE
SEMI-DISKRETEN
GLEICHUNGEN
.
107
4.3.2
FEHLERKONTROLLE
.
108
4.3.3
ILLUSTRATION
.
109
5
PROGRAMMPAKET
PDEX1M
112
5.1
DETAILS
DER
ALGORITHMISCHEN
REALISIERUNG
.
112
5.1.1
WAHL
DER
NORM
UND
INTERNE
SKALIERUNG
.
112
5.1.2
LINEARE
ALGEBRA
.
114
5.1.3
BERECHNUNG
DER
JACOBIMATRIX
.
115
5.2
PROGRAMMSTRUKTUR
.
116
5.2.1
ALLGEMEINES
.
116
5.2.2
STANDARD-BENUTZERSCHNITTSTELLE
.
117
6
NUMERISCHE
ERGEBNISSE
123
6.1
EIN
EFFIZIENZVERGLEICH
.
124
6.2
VERHALTEN
AN
TYPISCHEN
TESTPROBLEMEN
.
129
6.2.1
DIE
BEISPIELE
VON
SINCOVEC/MADSEN
.
130
6.2.2
WANDERNDE
FRONTEN
.
143
6.3
EIN
PROBLEM
AUS
DER
PRAXIS
.
152
ZUSAMMENFASSUNG
169
LITERATURVERZEICHNIS
170
III |
| any_adam_object | 1 |
| author | Nowak, Ulrich |
| author_facet | Nowak, Ulrich |
| author_role | aut |
| author_sort | Nowak, Ulrich |
| author_variant | u n un |
| building | Verbundindex |
| bvnumber | BV009682912 |
| ctrlnum | (OCoLC)31400032 (DE-599)BVBBV009682912 |
| format | Book |
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| genre_facet | Hochschulschrift |
| id | DE-604.BV009682912 |
| illustrated | Illustrated |
| indexdate | 2024-11-05T15:13:38Z |
| institution | BVB |
| language | English German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006402974 |
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| owner_facet | DE-12 |
| physical | III, 177 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Konrad-Zuse-Zentrum für Informationstechnik Berlin |
| record_format | marc |
| series | Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Technical report |
| series2 | Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Technical report |
| spelling | Nowak, Ulrich Verfasser aut Adaptive Linienmethoden für nichtlineare parabolische Systeme in einer Raumdimension U. Nowak Berlin Konrad-Zuse-Zentrum für Informationstechnik Berlin 1993 III, 177 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Technical report 1993,14 Zugl.: Berlin, Freie Univ., Diss., 1993 Abstract: "A new method for the numerical solution of highly nonlinear, coupled systems of parabolic differential equations in one space dimension is presented. The approach is based on a classical method of lines treatment. Time discretization is done by means of the semi-implicit Euler discretization. Space discretization is done with finite differences on non-uniform grids. Both basic discretizations are coupled with extrapolation techniques. With respect to time the extrapolation is of variable order whereas just one extrapolation step is done in space. Based on local error estimates for both, the time and the space discretization error, the accuracy of the numerical approximation is controlled and the discretization stepsizes are adapted automatically and simultaneously Besides the local adaptation of the space grids after each integration step (static regridding), the grid may even move within each integration step (dynamic regridding). Thus, the whole algorithm has a high degree of adaptivity. Due to this fact, challenging problems from applications can be solved in an efficient and robust way. Differential equations, Parabolic Nichtlineares System (DE-588)4042110-7 gnd rswk-swf Mehrgitterverfahren (DE-588)4038376-3 gnd rswk-swf Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd rswk-swf Linienmethode (DE-588)4324233-9 gnd rswk-swf Adaptives Gitter (DE-588)4333769-7 gnd rswk-swf Parabolische Differentialgleichung (DE-588)4173245-5 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Parabolische Differentialgleichung (DE-588)4173245-5 s Nichtlineare Differentialgleichung (DE-588)4205536-2 s Linienmethode (DE-588)4324233-9 s Adaptives Gitter (DE-588)4333769-7 s DE-604 Nichtlineares System (DE-588)4042110-7 s 1\p DE-604 Mehrgitterverfahren (DE-588)4038376-3 s 2\p DE-604 Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Technical report 1993,14 (DE-604)BV005567559 1993,14 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006402974&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Nowak, Ulrich Adaptive Linienmethoden für nichtlineare parabolische Systeme in einer Raumdimension Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Technical report Differential equations, Parabolic Nichtlineares System (DE-588)4042110-7 gnd Mehrgitterverfahren (DE-588)4038376-3 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd Linienmethode (DE-588)4324233-9 gnd Adaptives Gitter (DE-588)4333769-7 gnd Parabolische Differentialgleichung (DE-588)4173245-5 gnd |
| subject_GND | (DE-588)4042110-7 (DE-588)4038376-3 (DE-588)4205536-2 (DE-588)4324233-9 (DE-588)4333769-7 (DE-588)4173245-5 (DE-588)4113937-9 |
| title | Adaptive Linienmethoden für nichtlineare parabolische Systeme in einer Raumdimension |
| title_auth | Adaptive Linienmethoden für nichtlineare parabolische Systeme in einer Raumdimension |
| title_exact_search | Adaptive Linienmethoden für nichtlineare parabolische Systeme in einer Raumdimension |
| title_full | Adaptive Linienmethoden für nichtlineare parabolische Systeme in einer Raumdimension U. Nowak |
| title_fullStr | Adaptive Linienmethoden für nichtlineare parabolische Systeme in einer Raumdimension U. Nowak |
| title_full_unstemmed | Adaptive Linienmethoden für nichtlineare parabolische Systeme in einer Raumdimension U. Nowak |
| title_short | Adaptive Linienmethoden für nichtlineare parabolische Systeme in einer Raumdimension |
| title_sort | adaptive linienmethoden fur nichtlineare parabolische systeme in einer raumdimension |
| topic | Differential equations, Parabolic Nichtlineares System (DE-588)4042110-7 gnd Mehrgitterverfahren (DE-588)4038376-3 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd Linienmethode (DE-588)4324233-9 gnd Adaptives Gitter (DE-588)4333769-7 gnd Parabolische Differentialgleichung (DE-588)4173245-5 gnd |
| topic_facet | Differential equations, Parabolic Nichtlineares System Mehrgitterverfahren Nichtlineare Differentialgleichung Linienmethode Adaptives Gitter Parabolische Differentialgleichung Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006402974&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005567559 |
| work_keys_str_mv | AT nowakulrich adaptivelinienmethodenfurnichtlineareparabolischesystemeineinerraumdimension |