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JSG 0.12: Advanced computational methods for recovery of high-resolution gravity field models

Chairs: Robert Čunderlík (Slovakia)
Affiliation: Comm. 2 and GGOS



Efficient numerical methods and HPC (high performance computing) facilities provide new opportunities in many applications in geodesy. The goal of the JSG is to apply numerical methods and/or HPC techniques mostly for gravity field modelling and nonlinear filtering of various geodetic data. The discretization numerical methods like the finite element method (FEM), finite volume method (FVM) and boundary element method (BEM) or the meshless methods like the method of fundamental solutions (MFS) or singular boundary method (SOR) can be efficiently used to solve the geodetic boundary value problems and nonlinear diffusion filtering, or to process e.g. the GOCE observations. Their parallel implementations and large-scale parallel computations on clusters with distributed memory using the MPI (Message Passing Interface) standards allows to solve such problems in spatial domains while obtaining high-resolution numerical solutions.

Our JSG is also open for researchers dealing with the classical approaches of gravity field modelling (e.g. the spherical or ellipsoidal harmonics) that are using high performance computing to speed up their processing of enormous amount of input data. This includes large-scale parallel computations on massively parallel architectures as well as heterogeneous parallel computations using graphics processing units (GPUs).

Applications of the aforementioned numerical methods for gravity field modelling involve a detailed discretization of the real Earth’s surface considering its topography. It naturally leads to the oblique derivative problem that needs to be treated. In case of FEM or FVM, unstructured meshes above the topography will be constructed. The meshless methods like MFS or SBM that are based on the point-masses modelling can be applied for processing the gravity gradients observed by the GOCE satellite mission. To reach precise and high-resolution solutions, an elimination of far zones’ contributions is practically inevitable. This can be performed using the fast multipole method or iterative procedures. In both cases such an elimination process improves conditioning of the system matrix and a numerical stability of the problem. The aim of the JSG is also to investigate and develop nonlinear filtering methods that allow adaptive smoothing, which effectively reduces the noise while preserves main structures in data. The proposed approach is based on a numerical solution of partial differential equations using a surface finite volume method. It leads to a semi-implicit numerical scheme of the nonlinear diffusion equation on a closed surface where the diffusivity coefficients depend on a combination of the edge detector and a mean curvature of the filtered function. This will avoid undesirable smoothing of local extremes.


The main objectives of the study group are as follows:

  • to develop algorithms for detailed discretization of the real Earth’s surface including the possibility of adaptive refinement procedures,
  • to create unstructured meshes above the topography for the FVM or FEM approach,
  • to develop the FVM, BEM or FEM numerical models for solving the geodetic BVPs that will treat the oblique derivative problem,
  • to develop numerical models based on MFS or SBM for processing the GOCE observations,
  • to develop parallel implementations of algorithms using the standard MPI procedures,
  • to perform large-scale parallel computations on clusters with distributed memory,
  • to investigate and develop methods for nonlinear diffusion filtering of data on the Earth’s surface where the diffusivity coefficients depend on a combination of the edge detector and a mean curvature of the filtered function,
  • to derive the semi-implicit numerical schemes for the nonlinear diffusion equation on closed surfaces using the surface FVM,
  • and to apply the developed nonlinear filtering methods to real geodetic data.

Program of Activities

  • Active participation at major geodetic workshops and conferences.
  • Organization of group working meetings at main international symposia.
  • Organization of conference sessions.


Róbert Čunderlík (Slovakia), chair
Karol Mikula (Slovakia), vice-chair

Jan Martin Brockmann (Germany)
Walyeldeen Godah (Poland)
Petr Holota (Czech Republic)
Michal Kollár (Slovakia)
Marek Macák (Slovakia)
Zuzana Minarechová (Slovakia)
Otakar Nesvadba (Czech Republic)
Wolf-Dieter Schuh (Germany)

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