000196557 001__ 196557
000196557 003__ CZ-ZdVUG
000196557 005__ 20231030121201.0
000196557 041__ $$aeng
000196557 040__ $$aABC039$$bcze
000196557 1001_ $$aHolota, Petr
000196557 24510 $$aGeneral curvilinear coordinates, Laplace’s operator with topography dependent coefficients and analysis of the iteration solution of the GBVP
000196557 5203_ $$aThe structure of the Laplace operator is relatively simple when expressed in terms of spherical or ellipsoidal coordinates. The physical surface of the Earth, however, substantially differs from a sphere or an oblate ellipsoid of revolution, even if optimally fitted. The same holds true for the solution domain and the exterior of a sphere or of an oblate ellipsoid of revolution. The situation is more convenient in a system of general curvilinear coordinates such that the physical surface of the Earth (smoothed to a certain degree) is imbedded in the family of coordinate surfaces. Therefore, a transformation of coordinates is applied in treating the geodetic boundary value problem. The transformation contains also an attenuation function. Subsequently, tensor calculus is used and the Laplace operator is expressed in the new coordinates. Its structure becomes more complicated now. Nevertheless, in a sense it represents the topography of the physical surface of the Earth. For this reason the Green’s function method is used together with the method of successive approximations in the solution of the geodetic boundary value problem expressed in terms of the new coordinates. The structure of iteration steps is analyzed and if possible, it is modified by means of integration by parts. The iteration steps and their convergence are discussed and interpreted, numerically as well as in terms of functional analysis. The approach is also compared with the method of analytical continuation.
000196557 655_4 $$aanotace
000196557 7001_ $$aNesvadba, Otakar
000196557 7730_ $$92022
000196557 85642 $$ahttps://www.isvavai.cz/riv?s=rozsirene-vyhledavani&ss=detail&n=0&h=RIV%2F00025615%3A_____%2F22%3AN0000031%21RIV23-MSM-00025615
000196557 910__ $$aABC039
000196557 980__ $$aclanky_vugtk
000196557 985__ $$aholota
000196557 985__ $$aanotace (J)
000196557 985__ $$ariv
000196557 985__ $$autvar24