193407
20181127114100.0
Boundary Complexity and Kernel Functions in Classical and Variational Concepts of Solving Geodetic Boundary Value Problems
https://www.rvvi.cz/riv?s=jednoduche-vyhledavani&ss=detail&h=RIV%2F00025615%3A_____%2F17%3AN0000038%21RIV18-GA0-00025615
2017
Cham, Springer, 2017
Proceedings of the Joint Scientific Assembly of the International Association of Geodesy and the International Association of Seismology and Physics of the Earth’s Interior (IAG-IASPEI 2017)
0939-9585
10 stran
clanky_vugtk
Nesvadba, Otakar
RIV:D
anotace
riv
holota
anotace
eng
In gravity field studies the complex structure of the Earth’s surface makes the solution of geodetic boundary value problems quite challenging. This equally concerns classical methods of potential theory as well as modern methods often based on a (variational or) weak solution concept. Aspects of this nature are reflected in the content of the paper. In case of a spherical Neumann problem the focus is on the classical Green’s function method and on the use of reproducing kernel and elementary potentials in generating function bases for Galerkin’s approximations. Similarly, the use of reproducing kernel and elementary potentials is also highlighted for Galerkin’s approximations to the solution of Neumann’s problem in the exterior of an oblate ellipsoid of revolution. In this connection the role of elliptic integrals is pointed out. Finally, two concepts applied to the solution of the linear gravimetric boundary value problem are mentioned. They represent an approach based on variational methods and on the use of a transformation of coordinates offering an alternative between the boundary complexity and the complexity of the coefficients of the partial differential equation governing the solution. Successive approximations are involved in both the cases.
Green’s function
Galerkin’s system
reproducing kernel
elliptic integrals
Laplace’s operator
transformation of coordinates
Holota, Petr
eng