Bibliografie VÚGTK
Domain Transformation and the Iteration Solution of the Linear Gravimetric Boundary Value Problem
Holota, Petr ; IAG General Assembly

Source: Proceedings of the IAG General Assembly, Prague, Springer, 2016 : (2016) ISSN: 0939-9585

Publication type: příspěvek ve sborníku
Extent6 stran

Annotation:
The aim of this paper is to discuss the solution of the simple gravimetric boundary value problem by means of the method of successive approximations. A transformation of coordinates is used to express the relation between the description of the boundary of the solution domain and the structure of Laplace’s operator. The solution domain is carried onto the exterior of a sphere and the original oblique derivative boundary condition is given the form of Neumann’s boundary condition. Laplace’s operator expressed in terms of new coordinates involves topography-dependent coefficients. Effects caused by the topography of the physical surface of the Earth are treated as perturbations. Their internal structure is analyzed and modified by using integration by parts. As a result of the transformation a spherical mathematical apparatus may be applied at each iteration step, including the spherical form of Green’s function of the second kind, i.e. Neumann’s function in the integral representation of the successive approximations.
Keywords: Earth’s gravity field ; boundary value problems ; Laplace’s operator ; transformation of coordinates ; Green’s function method ; method of successive approximations

Citation: HOLOTA, Petr. Domain Transformation and the Iteration Solution of the Linear Gravimetric Boundary Value Problem. In: 1-6. Praha: Springer, 2015. DOI: 10.1007/1345_2016_236.
[Odkaz do RIVu]

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Focus on VÚGTK > VÚGTK Departments > Geodesy and Geodynamics
Focus on VÚGTK > Researchers > Petr Holota
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