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000193246 001__ 193246 000193246 003__ CZ-ZdVUG 000193246 005__ 20190524110747.0 000193246 041__ $$aeng 000193246 040__ $$aABC039$$bcze 000193246 1001_ $$aHolota, Petr 000193246 24510 $$aSmall Modifications of Curvilinear Coordinates and Successive Approximations Applied in Geopotential Determination 000193246 500__ $$aRIV: RIV/00025615:_____/16:N0000045 000193246 5203_ $$9eng$$aThe mathematical apparatus currently applied for geopotential determination is undoubtedly quite developed. This concerns numerical methods as well as methods based on classical analysis, equally as classical and weak solution concepts. Nevertheless, the nature of the real surface of the Earth has its specific features and is still rather complex. The aim of this paper is to consider these limits and to seek a balance between the performance of an apparatus developed for the surface of the Earth smoothed (or simplified) up to a certain degree and an iteration procedure used to bridge the difference between the real and smoothed topography. The approach is applied for the solution of the linear gravimetric boundary value problem in geopotential determination. Similarly as in other branches of engineering and mathematical physics a transformation of coordinates is used that offers a possibility to solve an alternative between the boundary complexity and the complexity of the coefficients of the partial differential equation governing the solution. As examples the use of modified ellipsoidal coordinates for the transformation of the solution domain is discussed. However, the complexity of the boundary is then reflected in the structure of Laplace’s operator. This effect is taken into account by means of successive approximations. The structure of the respective iteration steps is derived and analyzed. On the level of individual iteration steps the attention is paid to the representation of the solution in terms of Green’s function method. The convergence of the procedure and the efficiency of its use for geopotential determination is discussed. 000193246 655_4 $$aanotace 000193246 653_0 $$asuccessive approximations$$aGreen’s function method$$aLaplace’s operator$$atransformation of coordinates$$aboundary value problems$$aEarth’s gravity field 000193246 7001_ $$aNesvadba, Otakar 000193246 7730_ $$92016$$tonline 000193246 85640 $$uhttps://agu.confex.com/agu/fm16/meetingapp.cgi/Paper/189936 000193246 85642 $$uhttps://www.rvvi.cz/riv?s=rozsirene-vyhledavani&ss=detail&n=0&h=RIV%2F00025615%3A_____%2F16%3AN0000045%21RIV17-GA0-00025615 000193246 910__ $$aABC039 000193246 980__ $$aclanky_vugtk 000193246 985__ $$aholota 000193246 985__ $$aanotace 000193246 985__ $$aA 000193246 985__ $$autvar24 000193246 999C1 $$9CURATOR$$aGA14-34595S - Matematické metody pro studium tíhového pole Země (2014 - 2016)$$bGA ČR