```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