Abstract
The fixed gravimetric boundary-value problem (FGBVP) represents an exterior oblique derivative problem for the Laplace equation. The boundary element method and the collocation with linear basis functions are used to get a numerical solution of FGBVP in which the oblique derivative is treated by its decomposition into normal and tangential components to the Earth’s surface. The tangential components are expressed through the gradients of the linear basis functions.This new numerical approach to the solution of FGBVP is applied to global gravity field modelling. Input surface gravity disturbances as the oblique derivative boundary conditions are generated from the DNSC08 gravity field model. The obtained numerical solution with the resolution of 0.1∘ is compared with the EGM2008 geopotential model at collocation points. A contribution of the tangential components to the solution is presented and discussed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Andersen OB, Knudsen P, Berry P (2008) The DNSC08 ocean wide altimetry derived gravity field. Presented at EGU-2008, Vienna, Austria, April 2008
Aoyama Y, Nakano J (1999) RS/6000 SP: Practical MPI programming. IBM, Poughkeepsie
Balaš J, Sládek J, Sládek V (1989) Stress analysis by boundary element methods. Elsevier, Amsterdam
Barrett R, Berry M, Chan TF, Demmel J, Donato J, Dongarra J, Eijkhout V, Pozo R, Romine C, Van der Vorst H (1994) Templates for the solution of linear systems: Building blocks for iterative methods. http://www.netlib.org/templates/Templates.html
Becker JJ, Sandwell DT, Smith WHF, Braud J, Binder B, Depner J, Fabre D, Factor J, Ingalls S, Kim S-H, Ladner R, Marks K, Nelson S, Pharaoh A, Sharman G, Trimmer R, vonRosenburg J, Wallace G, Weatherall P (2009) Global bathymetry and elevation data at 30 arc seconds resolution: SRTM30_PLUS, revised for Marine Geodesy
Bjerhammar A, Svensson L (1983) On the geodetic boundary-value problem for a fixed boundary surface – satellite approach. Bull Géodes 57:382–393
Brebbia CA, Telles JCF, Wrobel LC (1984) Boundary element techniques, theory and applications in engineering. Springer, New York
Čunderlík R, Mikula K, Mojzeš M (2002) 3D BEM application to Neumann geodetic BVP using the collocation with linear basis functions. In: Proceedings of ALGORITMY 2002, conference on scientific computing, Podbanské: 268–275
Čunderlík R, Mikula K, Mojzeš M (2008) Numerical solution of the linearized fixed gravimetric boundary-value problem. J Geodes 82:15–29
Čunderlík R, Mikula K (2010) Direct BEM for high-resolution gravity field modeling. Stud Geophys Geodes, Vol. 54, No. 2, pp. 219–238
Grafarend EW (1989) The geoid and the gravimetric boundary-value problem. Rep 18 Dept Geod, The Royal Institute of Technology, Stockholm
Koch KR, Pope AJ (1972) Uniqueness and existence for the geodetic boundary value problem using the known surface of the earth. Bull Géod 46:467–476
Mayer-Gürr T (2007) ITG-Grace03s: The latest GRACE gravity field solution computed in Bonn. Presentation at GSTM+SPP, Potsdam, 15–17 Oct 2007
Nesvadba O, Holota P, Klees R (2007) A direct method and its numerical interpretation in the determination of the Earth’s gravity field from terrestrial data. In: Tregoning P, Rizos C (eds) Dynamic Planet. IAG Symposia, vol 130, Springer, New York, pp 370–376
Pavlis NK, Holmes SA, Kenyon SC, Factor JK (2008) An Earth gravitational model to degree 2,160: EGM2008, presented at the 2008 General Assembly of EGU, Vienna, Austria, April 13–18, 2008
Schatz AH, Thomée V, Wendland WL (1990) Mathematical theory of finite and boundary element methods. Birkhäuser, Basel
Acknowledgements
Authors gratefully thank to the financial support given by grants: VEGA 1/0269/09, APVV-LPP-0216–06 and APVV-0351–07.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Čunderlı́k, R., Mikula, K., Špir, R. (2012). An Oblique Derivative in the Direct BEM Formulation of the Fixed Gravimetric BVP. In: Sneeuw, N., Novák, P., Crespi, M., Sansò, F. (eds) VII Hotine-Marussi Symposium on Mathematical Geodesy. International Association of Geodesy Symposia, vol 137. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22078-4_34
Download citation
DOI: https://doi.org/10.1007/978-3-642-22078-4_34
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22077-7
Online ISBN: 978-3-642-22078-4
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)