IJPAM: Volume 41, No. 9 (2007)

SCIENTIFIC VISUALIZATION FOR PDES OF 2ND ORDER II:
COMPARATIVE VISUALIZATION OF THE GREEN'S
FUNCTIONS FOR ELLIPTIC, PARABOLIC
AND HYPERBOLIC CASES

Lubomir Dechevsky$^1$, Joakim Gundersen$^2$
$^{1,2}$R&D Group for Mathematical Modelling
Numerical Simulation and Computer Visualization
Institute for Information, Energy and Space Technology
Narvik University College
2, Lodve Lange's St., P.O. Box 385, Narvik, N-8505, NORWAY
$^1$e-mail: ltd@hin.no
$^1$url: https://ansatte.hin.no/ltd/
$^2$e-mail: joag@hin.no
$^2$url: https://ansatte.hin.no/joag/


Abstract.This work is continuation of [#!PDEpaperA!#]. Two types of graphical comparison is made for the Green's functions of the initial-value and boundary-value problems for 2nd order parabolic, hyperbolic and elliptic PDEs, as formulated in [#!PDEpaperA!#]. The first type of scientific visualization technique is via isocurves and isosurfaces in 3D, similar to the type of visualization in [#!ODEpaper!#]. The second type of scientific visualization technique is via the wavelet-based colour (mode 3) mapping introduced in [#!LtdJGPre:2004!#], [#!Dechevsky2006i!#]; see also Section 2 of [#!PDEpaperA!#]. The graphical results of both types of visualization and properties of the Green's function for the three types are compared and analyzed. All graphical images are obtained via the in-house software developed as part of the work on [#!GundersenPhD!#].

Received: November 11, 2007

AMS Subject Classification: 35E05, 65T60, 68U05, 35A40, 35J25, 35K05, 35K15, 35K20, 35L05, 35L20, 68U10

Key Words and Phrases: scientific visualization, comparative, partial, differential equation, parabolic, hyperbolic, elliptic, initial value, boundary value, fundamental solution, Green's function, isocurve, isosurface, wavelet, colour map, computational geometry, computer-aided-geometic design, computer graphics, multidimensional

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 41
Issue: 9