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Finite-Volumen- Und Mehrgitter-Verfahren Für Elliptische Randwertprobleme by Jürgen Bey

Finite-Volumen- Und Mehrgitter-Verfahren Für Elliptische Randwertprobleme

by Jürgen Bey
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Book cover type: Paperback
  • ISBN13: 9783519027416
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Vieweg+teubner Verlag
  • Publisher Imprint: Vieweg+teubner Verlag
  • Publication Date:
  • Pages: 356
  • Original Price: EUR 46.72
  • Language: German
  • Edition: 1998
  • Item Weight: 572 grams
  • BISAC Subject(s): Engineering (General)

Zum Kontext dieses Buches Die numerische Behandlung partieller Differentialgleichungen beinhaltet im allgemeinen die L�sung gro er bis sehr gro er Gleichungssysteme. Bei dreidimensionalen Problemen z. B. sind mehrere Millionen Unbekannte keine Seltenheit, und obwohl die Rechenleistung der st�rksten Computer in den letzten Jahrzehnten exponentiell angestiegen ist, k�nnten viele praxis- relevante Probleme heute nicht gel�st werden, w�ren die Numeriker nicht bei der Entwicklung effizienter Algorithmen �hnlich erfolgreich gewesen. Zu den bemerkenswertesten Fortschritten auf diesem Gebiet z�hlt die Entwicklung adaptiver Mehrgitter-und Multilevelverfahren, deren Erfolg auf der Verschmelzung zweier leistungsf�higer Konzepte beruht: der Kombination adaptiver Diskretisierungstechniken mit schnellen Mehrgitter- bzw. Multilevell�sern. Die Anwendung adaptiver Diskretisierungstechniken dient zun�chst dazu, die Anzahl der Unbekannten und damit die Dimension des zu l�senden Gleichungssystems m�glichst gering zu halten. Wurden fr�her zur Diskretisierung partieller Differentialgleichungen in erster Linie gleichm� ig strukturierte Rechteckgitter verwendet, so ist man heute durch den Einsatz ge- eigneter Fehlersch�tzer in der Lage, die Diskretisierung - ausgehend von einem relativ groben Anfangsgitter und einer entsprechend groben N�herungsl�sung - schrittweise an die aktuel- le N�herungsl�sung anzupassen, bis die gew�nschte Genauigkeit erreicht ist. �blicherweise wird dazu das aktuelle Diskretisierungsgitter lokal verfeinert, und zwar an solchen Stellen, wo aufgrund entsprechender Fehlerabsch�tzungen eine h�here Genauigkeit zu erwarten ist, z. B. in der N�he von Singularit�ten, Grenzschichten, einspringenden Ecken, etc. Bereiche, in denen die L�sung sichals hinreichend glatt herausstellt, bleiben unverfeinert oder k�nne- etwa bei zeit abh�ngigen Anwendungen - sogar wieder vergr�bert werden.

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