UNIVERSITÄTSBIBLIOTHEK

Time-Dependent Cauchy-Navier Splines and their Application to Seismic Wave Front Propagation

  • In this paper a known orthonormal system of time- and space-dependent functions, that were derived out of the Cauchy-Navier equation for elastodynamic phenomena, is used to construct reproducing kernel Hilbert spaces. After choosing one of the spaces the corresponding kernel is used to define a function system that serves as a basis for a spline space. We show that under certain conditions there exists a unique interpolating or approximating, respectively, spline in this space with respect to given samples of an unknown function. The name "spline" here refers to its property of minimising a norm among all interpolating functions. Moreover, a convergence theorem and an error estimate relative to the point grid density are derived. As numerical example we investigate the propagation of seismic waves.

Volltext Dateien herunterladen

Metadaten exportieren

Weitere Dienste

Teilen auf Twitter Suche bei Google Scholar
Metadaten
Verfasserangaben:Paula Kammann, Volker Michel
URN (Permalink):urn:nbn:de:hbz:386-kluedo-14373
Schriftenreihe (Bandnummer):Schriften zur Funktionalanalysis und Geomathematik (26)
Dokumentart:Preprint
Sprache der Veröffentlichung:Englisch
Jahr der Fertigstellung:2006
Jahr der Veröffentlichung:2006
Veröffentlichende Institution:Technische Universität Kaiserslautern
Datum der Publikation (Server):23.08.2006
Freies Schlagwort / Tag:Cauchy-Navier-Gleichung; reproduzierender Kern
Cauchy-Navier equation; reproducing kernel; seismic wave; sphere; spline
GND-Schlagwort:Approximation; Elastizität; Seismische Welle; Sphäre; Spline; Zeitabhängigkeit
Fachbereiche / Organisatorische Einheiten:Fachbereich Mathematik
DDC-Sachgruppen:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Klassifikation (Mathematik):41-XX APPROXIMATIONS AND EXPANSIONS (For all approximation theory in the complex domain, see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical approximation, see 65Dxx) / 41Axx Approximations and expansions / 41A05 Interpolation [See also 42A15 and 65D05]
41-XX APPROXIMATIONS AND EXPANSIONS (For all approximation theory in the complex domain, see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical approximation, see 65Dxx) / 41Axx Approximations and expansions / 41A15 Spline approximation
41-XX APPROXIMATIONS AND EXPANSIONS (For all approximation theory in the complex domain, see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical approximation, see 65Dxx) / 41Axx Approximations and expansions / 41A52 Uniqueness of best approximation
65-XX NUMERICAL ANALYSIS / 65Dxx Numerical approximation and computational geometry (primarily algorithms) (For theory, see 41-XX and 68Uxx) / 65D07 Splines
86-XX GEOPHYSICS [See also 76U05, 76V05] / 86Axx Geophysics [See also 76U05, 76V05] / 86A17 Global dynamics, earthquake problems
Lizenz (Deutsch):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011