000196570 001__ 196570 000196570 003__ CZ-ZdVUG 000196570 005__ 20231123101711.0 000196570 041__ $$aeng 000196570 040__ $$aABC039$$bcze 000196570 1001_ $$aHolota, Petr 000196570 24510 $$aStructure of the Laplace operator, geometry of the Earth’s surface and successive approximations in the solution of the geodetic boundary value problem 000196570 300__ $$a1 strana 000196570 5203_ $$aThe Laplace operator has a relatively simple structure in terms of spherical or ellipsoidal coordinates which are frequently used in geodesy. However, in treating the geodetic boundary value problem the physical surface of the Earth substantially differs from a sphere or an oblate ellipsoid of revolution, even if optimally approximated. Therefore, an alternative between the boundary complexity and the complexity of the coefficients of the Laplace partial differential equation governing the solution is discussed. The situation is more convenient in a system of general curvilinear coordinates such that the physical surface of the Earth (smoothed to a certain degree) is imbedded in the family of coordinate surfaces. The idea is close to concepts followed also in other branches of engineering and mathematical physics. A transformation of coordinates is applied. Subsequently, tensor calculus is used to express the Laplace operator in the system of new coordinates. The structure of the Laplacian is more complicated now, but in a sense it represents the topography of the physical surface of the Earth. Finally, the Green’s function method together with the method of successive approximations is used for the solution of the geodetic boundary value problem expressed in terms of the new coordinates. The structure of iteration steps is analyzed and where useful and possible, modified by means of integration by parts. The iteration steps and their convergence are discussed and interpreted, numerically and in terms of functional analyses. 000196570 655_4 $$aanotace 000196570 7001_ $$aNesvadba, Otakar 000196570 7730_ $$92022 000196570 85642 $$ahttps://www.isvavai.cz/riv?s=rozsirene-vyhledavani&ss=detail&n=1&h=RIV%2F00025615%3A_____%2F22%3AN0000028%21RIV23-MSM-00025615 000196570 910__ $$aABC039 000196570 980__ $$aclanky_vugtk 000196570 985__ $$aholota 000196570 985__ $$aanotace (J) 000196570 985__ $$ariv 000196570 985__ $$autvar24