Publications – Numerical methods for geodetic boundary value problems

List of selected publications of our team:

2025

R. Čunderlík, M. Macák, M. Kollár, Z. Minarechová, K. Mikula. 3D high-resolution numerical modelling of altimetry-derived marine gravity data. Journal of Geodesy, Vol. 99, 33 (2025). (pdf file) (link to the paper)
X. Li, R. Čunderlík, M. Macák, D. J. Caccamise II, Z. Minarechová, P. Zahorec, J. Papčo, D. R. Roman, J. Krcmaric, M. Lin. Finite volume method: a good match to airborne gravimetry? Journal of Geodesy, Vol. 99, 4 (2025). (pdf file) (link to the paper)

2024

M.Macák, K.Mikula, Z.Minarechová, R.Čunderlík. Solving the gradiometric boundary value problem by the finite element method. Proceedings Of The Conference Algoritmy, 2024, 26 - 35. (pdf file) (link to the paper)

2023

M.Macák, Z.Minarechová, R.Čunderlík, K.Mikula. A gravity field modelling in mountainous areas by solving the nonlinear satellite-fixed geodetic boundary value problem with the finite element method. Acta Geodaetica et Geophysica (2023). https://doi.org/10.1007/s40328-023-00418-7 (pdf file) (link to the paper)
M. Macák, Z. Minarechová, L. Tomek, R. Čunderlík, K. Mikula. Solving the fixed gravimetric boundary value problem by the finite element method using mapped infinite elements. Computational Geosciences (2023). https://doi.org/10.1007/s10596-023-10224-3 (pdf file) (link to the paper)

2021

Z.Minarechová, M.Macák, R.Čunderlík, K.Mikula. On the finite element method for solving the oblique derivative boundary value problems and its application in local gravity field modelling. Journal of Geodesy, Vol. 95, 70 (2021). (pdf file) (link to the paper)
M.Macák, R.Čunderlík, K.Mikula, Z.Minarechová,Computational optimization in solving the geodetic boundary value problems, Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 987-999. (link to the paper)

2020

M.Macák, Z.Minarechová, R.Čunderlík, K.Mikula. The finite element method as a tool to solve the oblique derivative boundary value problem in geodesy (2020) TMMP, Vol 75, Issue 1 (pdf file) (link to the paper)

2018

R.Čunderlík, K.Mikula, Z.Minarechová, M.Macák. Numerical Methods for Solving the Oblique Derivative Boundary Value Problems in Geodesy, In: Freeden W., Rummel R. (eds) Handbuch der Geodäsie. Springer Reference Naturwissenschaften. Springer Spektrum, Berlin, Heidelberg, pp. 1-48. (pdf file) (link to the paper)
R.Čunderlík, M.Macák, M.Medľa, K.Mikula, Z.Minarechová. Computational Methods for High-Resolution Gravity Field Modeling, In: Grafarend E. (eds) Encyclopedia of Geodesy. Encyclopedia of Earth Sciences Series. Springer, Cham, 2018, ISBN: 978-3-319-02370-0 (pdf file) (link to the paper)

2016

M.Macák, K.Mikula, Z.Minarechová, R.Čunderlík. On an iterative approach to solving the nonlinear satellite-fixed geodetic boundary-value problem, VIII Hotine-Marussi Symposium on Mathematical Geodesy, Volume 142 of the series International Association of Geodesy Symposia, pp 185-192, 2016 (pdf file) (link to the paper)
L. Sanchez, R. Čunderlík, N. Dayoub, K. Mikula, Z. Minarechová, Z. Šíma, V. Vatrt, M. Vojtišková. A conventional value for the geoid reference potential W0, Journal of Geodesy, Vol. 90, Issue 9 (2016) pp. 815–835 ( pdf file ) (link to the paper)

2015

M.Macák, R.Čunderlík, K.Mikula, Z.Minarechová. An upwind-based scheme for solving the oblique derivative boundary-value problem related to physical geodesy, Journal of Geodetic Sciences, Vol. 5 (2015) pp. 180-188 (pdf file) (link to the paper)
Z. Minarechová, M.Macák, R.Čunderlík, K.Mikula. High-resolution global gravity field modelling by the finite volume method, Studia Geophysica et Geodaetica, Vol. 59 (2015) pp. 1-20 (pdf file) (link to the paper)

R. Čunderlík, Determination of W0 from the GOCE measurements using the method of fundamental solutions (Download PDF)
M.Macák, Z.Minarechová, K.Mikula. A novel scheme for solving the oblique derivative boundary-value problem, Studia Geophysica et Geodaetica, Vol. 58 (2014) pp. 556-570 (pdf file) (link to the paper)
J. Janák, M. Pitoňák, Z. Minarechová. Regional quasigeoid from GOCE and terrestrial measurements, Studia geophysica et geodaetica, Vol. 58, no. 4 (2014), s. 626-649. ISSN 0039-3169 (pdf file) (link to the paper)
L. Sanchez, N. Dayoub, R. Čunderlík, Z. Minarechová, K. Mikula, V. Vatrt, M. Vojtišková, Z. Šíma. W0 estimates in the frame od the GGOS working group on vertical Datum Standardisation (2014) International Association of Geodesy Symposia, 141, 203-210 (link to the paper)
R. Čunderlík, Z. Minarechová, K. Mikula. Realization of WHS based on the static gravity field observed by GOGE (2014) International Association of Geodesy Symposia, 141, 211-220 (link to the paper)

Z. Fašková, R. Čunderlík, K. Mikula, R. Tenzer, Influence of Vertical Datum Inconsistencies on Gravity Field Modelling. Influence of vertical datum inconsistencies on gravity field modelling. In Reference Frames for Applications in Geosciences : Proceedings of the Symposium. Marne-La-Vallée,4.-8.10.2010. International Association of Geodesy Symposia, Vol. 138, Berlin: Springer Verlag, 2013, s. 205--213.

R. Čunderlík, K.Mikula, M.Tunega, Nonlinear diffusion filtering of data on the Earth's surface, Journal of Geodesy, 2012, DOI 10.1007/s00190-012-0587-y (Download PDF).

M.Šprlák, Z.Fašková, K.Mikula, On the application of the coupled finite-infinite element method to the geodetic boundary value problem, Studia Geophysica et Geodaetica, Vol. 55 (2011) pp. 479-487 (Download PDF).

R. Čunderlík, K.Mikula, Direct BEM for high-resolution gravity field modelling, Studia Geophysica et Geodetica, Vol. 54, No. 2 (2010) pp. 219-238 (Download PDF).
Z.Fašková, R. Čunderlík, K.Mikula, Finite element method for solving geodetic boundary value problems, Journal of Geodesy, Vol. 84, Issue 2 (2010) pp 135-144 (Download PDF).

R. Čunderlík, K.Mikula, M.Mojzeš, Numerical solution of the linearized fixed gravimetric boundary value problem, Journal of Geodesy, Vol. 82, No. 1 (2008) pp. 15-29 (Download PDF).

Z.Fašková, R. Čunderlík, J.Janák, K.Mikula, M.Šprlák, Gravimetric quasigeoid in Slovakia by the finite element method, Kybernetika, Vol. 43, No. 6(2007) pp. 789-796 (Download PDF).

R. Čunderlík, M.Mojzeš, K.Mikula, A comparison of the variational solution of the Neumann geodetic boundary value problem with the geopotential model EGM-96, Contributions to Geophysics and Geodesy, Vol. 34, No. 3 (2004) pp. 209-225 (Download PDF).

R. Čunderlík, K.Mikula, M.Mojzeš, The boundary element method applied to the determination of the global quasigeoid, ALGORITMY 2000, Conference on Scientific Computing, Vysoke Tatry-Podbanske, Slovakia, September 10-15, 2000, Proceedings of contributed papers and posters (2000) 301-308 (Download DOC file).