Adaptive application of the operator exponential
In this article an inherently parallel algorithm to approximate the operator exponential is presented. The construction is based on the integral representation of the operator exponential and allows arbitrarily large time steps constituting a major advantage compared to classical schemes. The algori...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Jürgens, M. [verfasserIn] |
|---|
| Format: |
E-Artikel |
|---|
| Erschienen: |
Genthiner Strasse 1310875 BerlinGermany: Walter de Gruyter ; 2006 |
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| Schlagwörter: |
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| Anmerkung: |
Copyright 2006, Walter de Gruyter |
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| Umfang: |
30 |
| Reproduktion: |
Walter de Gruyter Online Zeitschriften |
|---|---|
| Übergeordnetes Werk: |
Enthalten in: Journal of numerical mathematics - Berlin : de Gruyter, 2002, 14, 3, Seite 217-246 |
| Übergeordnetes Werk: |
volume:14 ; number:3 ; pages:217-246 ; extent:30 |
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| DOI / URN: |
10.1515/156939506778658311 |
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| 520 | |a In this article an inherently parallel algorithm to approximate the operator exponential is presented. The construction is based on the integral representation of the operator exponential and allows arbitrarily large time steps constituting a major advantage compared to classical schemes. The algorithm rests on the efficient solution of several elliptic problems depending on a complex parameter. We prove Besov regularity of the solutions to these elliptic problems. This result implies the efficiency of adaptive methods applied to the elliptic problems and leads to a complexity estimate for the complete algorithm. In the numerical experiments the efficiency of the new scheme is demonstrated by comparison to a single step method of second order. | ||
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10.1515/156939506778658311 doi artikel_Grundlieferung.pp (DE-627)NLEJ246225637 DE-627 ger DE-627 rakwb Jürgens, M. verfasserin aut Adaptive application of the operator exponential Genthiner Strasse 1310875 BerlinGermany Walter de Gruyter 2006 30 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Copyright 2006, Walter de Gruyter In this article an inherently parallel algorithm to approximate the operator exponential is presented. The construction is based on the integral representation of the operator exponential and allows arbitrarily large time steps constituting a major advantage compared to classical schemes. The algorithm rests on the efficient solution of several elliptic problems depending on a complex parameter. We prove Besov regularity of the solutions to these elliptic problems. This result implies the efficiency of adaptive methods applied to the elliptic problems and leads to a complexity estimate for the complete algorithm. In the numerical experiments the efficiency of the new scheme is demonstrated by comparison to a single step method of second order. Walter de Gruyter Online Zeitschriften operator exponential, approximation, Besov regularity, complexity Enthalten in Journal of numerical mathematics Berlin : de Gruyter, 2002 14, 3, Seite 217-246 (DE-627)NLEJ248236172 (DE-600)2095674-5 1569-3953 nnns volume:14 number:3 pages:217-246 extent:30 https://doi.org/10.1515/156939506778658311 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 14 3 217-246 30 |
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10.1515/156939506778658311 doi artikel_Grundlieferung.pp (DE-627)NLEJ246225637 DE-627 ger DE-627 rakwb Jürgens, M. verfasserin aut Adaptive application of the operator exponential Genthiner Strasse 1310875 BerlinGermany Walter de Gruyter 2006 30 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Copyright 2006, Walter de Gruyter In this article an inherently parallel algorithm to approximate the operator exponential is presented. The construction is based on the integral representation of the operator exponential and allows arbitrarily large time steps constituting a major advantage compared to classical schemes. The algorithm rests on the efficient solution of several elliptic problems depending on a complex parameter. We prove Besov regularity of the solutions to these elliptic problems. This result implies the efficiency of adaptive methods applied to the elliptic problems and leads to a complexity estimate for the complete algorithm. In the numerical experiments the efficiency of the new scheme is demonstrated by comparison to a single step method of second order. Walter de Gruyter Online Zeitschriften operator exponential, approximation, Besov regularity, complexity Enthalten in Journal of numerical mathematics Berlin : de Gruyter, 2002 14, 3, Seite 217-246 (DE-627)NLEJ248236172 (DE-600)2095674-5 1569-3953 nnns volume:14 number:3 pages:217-246 extent:30 https://doi.org/10.1515/156939506778658311 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 14 3 217-246 30 |
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10.1515/156939506778658311 doi artikel_Grundlieferung.pp (DE-627)NLEJ246225637 DE-627 ger DE-627 rakwb Jürgens, M. verfasserin aut Adaptive application of the operator exponential Genthiner Strasse 1310875 BerlinGermany Walter de Gruyter 2006 30 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Copyright 2006, Walter de Gruyter In this article an inherently parallel algorithm to approximate the operator exponential is presented. The construction is based on the integral representation of the operator exponential and allows arbitrarily large time steps constituting a major advantage compared to classical schemes. The algorithm rests on the efficient solution of several elliptic problems depending on a complex parameter. We prove Besov regularity of the solutions to these elliptic problems. This result implies the efficiency of adaptive methods applied to the elliptic problems and leads to a complexity estimate for the complete algorithm. In the numerical experiments the efficiency of the new scheme is demonstrated by comparison to a single step method of second order. Walter de Gruyter Online Zeitschriften operator exponential, approximation, Besov regularity, complexity Enthalten in Journal of numerical mathematics Berlin : de Gruyter, 2002 14, 3, Seite 217-246 (DE-627)NLEJ248236172 (DE-600)2095674-5 1569-3953 nnns volume:14 number:3 pages:217-246 extent:30 https://doi.org/10.1515/156939506778658311 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 14 3 217-246 30 |
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10.1515/156939506778658311 doi artikel_Grundlieferung.pp (DE-627)NLEJ246225637 DE-627 ger DE-627 rakwb Jürgens, M. verfasserin aut Adaptive application of the operator exponential Genthiner Strasse 1310875 BerlinGermany Walter de Gruyter 2006 30 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Copyright 2006, Walter de Gruyter In this article an inherently parallel algorithm to approximate the operator exponential is presented. The construction is based on the integral representation of the operator exponential and allows arbitrarily large time steps constituting a major advantage compared to classical schemes. The algorithm rests on the efficient solution of several elliptic problems depending on a complex parameter. We prove Besov regularity of the solutions to these elliptic problems. This result implies the efficiency of adaptive methods applied to the elliptic problems and leads to a complexity estimate for the complete algorithm. In the numerical experiments the efficiency of the new scheme is demonstrated by comparison to a single step method of second order. Walter de Gruyter Online Zeitschriften operator exponential, approximation, Besov regularity, complexity Enthalten in Journal of numerical mathematics Berlin : de Gruyter, 2002 14, 3, Seite 217-246 (DE-627)NLEJ248236172 (DE-600)2095674-5 1569-3953 nnns volume:14 number:3 pages:217-246 extent:30 https://doi.org/10.1515/156939506778658311 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 14 3 217-246 30 |
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10.1515/156939506778658311 doi artikel_Grundlieferung.pp (DE-627)NLEJ246225637 DE-627 ger DE-627 rakwb Jürgens, M. verfasserin aut Adaptive application of the operator exponential Genthiner Strasse 1310875 BerlinGermany Walter de Gruyter 2006 30 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Copyright 2006, Walter de Gruyter In this article an inherently parallel algorithm to approximate the operator exponential is presented. The construction is based on the integral representation of the operator exponential and allows arbitrarily large time steps constituting a major advantage compared to classical schemes. The algorithm rests on the efficient solution of several elliptic problems depending on a complex parameter. We prove Besov regularity of the solutions to these elliptic problems. This result implies the efficiency of adaptive methods applied to the elliptic problems and leads to a complexity estimate for the complete algorithm. In the numerical experiments the efficiency of the new scheme is demonstrated by comparison to a single step method of second order. Walter de Gruyter Online Zeitschriften operator exponential, approximation, Besov regularity, complexity Enthalten in Journal of numerical mathematics Berlin : de Gruyter, 2002 14, 3, Seite 217-246 (DE-627)NLEJ248236172 (DE-600)2095674-5 1569-3953 nnns volume:14 number:3 pages:217-246 extent:30 https://doi.org/10.1515/156939506778658311 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 14 3 217-246 30 |
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Adaptive application of the operator exponential |
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In this article an inherently parallel algorithm to approximate the operator exponential is presented. The construction is based on the integral representation of the operator exponential and allows arbitrarily large time steps constituting a major advantage compared to classical schemes. The algorithm rests on the efficient solution of several elliptic problems depending on a complex parameter. We prove Besov regularity of the solutions to these elliptic problems. This result implies the efficiency of adaptive methods applied to the elliptic problems and leads to a complexity estimate for the complete algorithm. In the numerical experiments the efficiency of the new scheme is demonstrated by comparison to a single step method of second order. Copyright 2006, Walter de Gruyter |
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In this article an inherently parallel algorithm to approximate the operator exponential is presented. The construction is based on the integral representation of the operator exponential and allows arbitrarily large time steps constituting a major advantage compared to classical schemes. The algorithm rests on the efficient solution of several elliptic problems depending on a complex parameter. We prove Besov regularity of the solutions to these elliptic problems. This result implies the efficiency of adaptive methods applied to the elliptic problems and leads to a complexity estimate for the complete algorithm. In the numerical experiments the efficiency of the new scheme is demonstrated by comparison to a single step method of second order. Copyright 2006, Walter de Gruyter |
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In this article an inherently parallel algorithm to approximate the operator exponential is presented. The construction is based on the integral representation of the operator exponential and allows arbitrarily large time steps constituting a major advantage compared to classical schemes. The algorithm rests on the efficient solution of several elliptic problems depending on a complex parameter. We prove Besov regularity of the solutions to these elliptic problems. This result implies the efficiency of adaptive methods applied to the elliptic problems and leads to a complexity estimate for the complete algorithm. In the numerical experiments the efficiency of the new scheme is demonstrated by comparison to a single step method of second order. Copyright 2006, Walter de Gruyter |
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