Green’s Function Method Extended by Successive Approximations and Applied to Earth’s Gravity Field Recovery
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00025615%3A_____%2F18%3AN0000054" target="_blank" >RIV/00025615:_____/18:N0000054 - isvavai.cz</a>
Výsledek na webu
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DOI - Digital Object Identifier
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Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
Green’s Function Method Extended by Successive Approximations and Applied to Earth’s Gravity Field Recovery
Popis výsledku v původním jazyce
The aim of the paper is to implement the Green’s function method for the solution of the Linear Gravimetric Boundary Value Problem. The approach is iterative by nature. A transformation of spatial (ellipsoidal) coordinates is used that offers a possibility for an alternative between the boundary complexity and the complexity of the coefficients of Laplace’s partial differential equation governing the solution. The solution domain is carried onto the exterior of an oblate ellipsoid of revolution. Obviously, the structure of Laplace’s operator is more complex after the transformation. It was deduced by means of tensor calculus and in a sense it reflects the geometrical nature of the Earth’s surface. Nevertheless, the construction of the respective Green’s function is simpler for the solution domain transformed. It gives Neumann’s function (Green’s function of the 2nd kind) for the exterior of an oblate ellipsoid of revolution. In combination with successive approximations it enables to meet also Laplace’s partial differential equation expressed in the system of new (i.e. transformed) coordinates.
Název v anglickém jazyce
Green’s Function Method Extended by Successive Approximations and Applied to Earth’s Gravity Field Recovery
Popis výsledku anglicky
The aim of the paper is to implement the Green’s function method for the solution of the Linear Gravimetric Boundary Value Problem. The approach is iterative by nature. A transformation of spatial (ellipsoidal) coordinates is used that offers a possibility for an alternative between the boundary complexity and the complexity of the coefficients of Laplace’s partial differential equation governing the solution. The solution domain is carried onto the exterior of an oblate ellipsoid of revolution. Obviously, the structure of Laplace’s operator is more complex after the transformation. It was deduced by means of tensor calculus and in a sense it reflects the geometrical nature of the Earth’s surface. Nevertheless, the construction of the respective Green’s function is simpler for the solution domain transformed. It gives Neumann’s function (Green’s function of the 2nd kind) for the exterior of an oblate ellipsoid of revolution. In combination with successive approximations it enables to meet also Laplace’s partial differential equation expressed in the system of new (i.e. transformed) coordinates.
Klasifikace
Druh
O - Ostatní výsledky
CEP obor
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OECD FORD obor
10102 - Applied mathematics
Návaznosti výsledku
Projekt
<a href="/cs/project/LO1506" target="_blank" >LO1506: Podpora udržitelnosti centra NTIS - Nové technologie pro informační společnost</a><br>
Návaznosti
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Ostatní
Rok uplatnění
2018
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů