scholarly journals Computational optimization in solving the geodetic boundary value problems

2018 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
Marek Macák ◽  
◽  
Róbert Čunderlík ◽  
Karol Mikula ◽  
Zuzana Minarechová
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Computational Optimization ◽  
Geodetic Boundary

Uniquely and overdetermined geodetic boundary value problems by least squares

1989 ◽  
Vol 63 (1) ◽  
pp. 1-33 ◽  
Author(s):  
R. Rummel ◽  
P. Teunissen ◽  
M. Gelderen
Keyword(s):  
Least Squares ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Geodetic Boundary

Laplacian structure, solution domain geometry and successive approximations in gravity field studies

2020 ◽  
Author(s):  
Petr Holota ◽  
Otakar Nesvadba
Keyword(s):  
Boundary Value Problems ◽  
Gravity Field ◽  
Laplace Operator ◽  
Boundary Value ◽  
Field Studies ◽  
Successive Approximations ◽  
Physical Surface ◽  
The Earth ◽  
Geodetic Boundary ◽  
The Laplace Operator

<p>When treating geodetic boundary value problems in gravity field studies, the geometry of the physical surface of the Earth may be seen in relation to the structure of the Laplace operator. 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. The Laplace operator has a relatively simple structure in terms of spherical or ellipsoidal coordinates which are frequently used in geodesy. However, the physical surface of the Earth substantially differs from a sphere or an oblate ellipsoid of revolution, even if these are optimally fitted. The situation may be more convenient in a system of general curvilinear coordinates such that the physical surface of the Earth is imbedded in the family of coordinate surfaces. The structure of the Laplace operator, however, is more complicated in this case and in a sense it represents the topography of the physical surface of the Earth. The Green’s function method together with the method of successive approximations is used for the solution of geodetic boundary value problems expressed in terms of new coordinates. The structure of iteration steps is analyzed and if useful, it is modified by means of the integration by parts. Subsequently, the individual iteration steps are discussed and interpreted.</p>

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