IC SG7

JSG 0.7: Computational methods for high-resolution gravity field modelling and nonlinear dif-fusion filtering

Chairs: R. Čunderlík (Slovakia), K. Mikula (Slovakia)
Affiliation: Comm. 2, 3 and GGOS

Introduction

Efficient numerical methods and HPC (High Performance Computing) facilities provide new opportunities in many applications in geodesy. The goal of the IC SG is to apply numerical methods like the finite element method (FEM), finite volume method (FVM), boundary element method (BEM) and others mostly for gravity field modelling and non-linear filtering of data on the Earth’s surface. An advantage is that such numerical methods use finite elements as basis functions with local supports. Therefore a refinement of the discretization is very straightforward allowing adaptive refinement procedures as well.

In case of gravity field modelling, a parallelization of algorithms using the standard MPI (Message Passing Interface) procedures and computations on clusters with distributed memory allows to achieve global or local gravity field models of very high-resolution, where a level of the discretization practically depends on capacity of available HPC facilities. The aforementioned numerical methods allow a detailed discretization of the real Earth’s surface considering its topography. To get precise numerical solution to the geodetic boundary-value problems (BVPs) on such complicated surface it is also necessary handle problems like the oblique derivative. Data filtering occurs in many applications of geosciences. A quality of filtering is essential for correct interpretations of obtained results. In geodesy we usually use methods based on the Gaussian filtering that corresponds to a linear diffusion. Such filtering has a uniform smoothing effect, which also blurs “edges” representing important structures in the filtered data. In contrary, a nonlinear diffusion allows adaptive smoothing that can preserve main structures in data, while a noise is effectively reduced. In image processing there are known at least two basic nonlinear diffusion models; (i) the regularized Perona-Malik model, where the diffusion coefficient depends on an edge detector, and (ii) the geodesic mean curvature flow model based on a geometrical diffusion of level-sets of the image intensity.

The aim of the JSG is to investigate and develop nonlinear filtering methods that would be useful for a variety of geodetic data, e.g., from satellite missions, satellite altimetry and others. A choice of an appropriate numerical technique is open to members of the JSG. An example of 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.

Objectives

• to develop numerical models for solving the geodetic BVPs using numerical methods like FEM, FVM, BEM and others,
• to investigate the problem of oblique derivative,
• to implement parallelization of numerical algorithms using the standard MPI procedures,
• to perform large-scale parallel computations on clusters with distributed memory,
• to investigate methods for nonlinear filtering of data on closed surfaces using the regularized Perona-Malik model or mean curvature flow model,
• to derive fully-implicit and semi-implicit numerical schemes for the linear and nonlinear diffusion equation on closed surfaces using the surface FVM,
• to develop algorithms for the nonlinear filtering of data on the Earth’s surface,
• to summarize the developed methods and achieved numerical results in journal papers.

Program of activities

Active participation in major geodetic conferences, working meetings at international symposia, organization of a conference session.

Members

Róbert Čunderlík (Slovakia), chair
Karol Mikula (Slovakia), chair
Ahmed Abdalla, (New Zealand)
Michal Beneš (Czech Republic)
Zuzana Fašková (Slovakia)
Marek Macák (Slovakia)
Otakar Nesvadba (Czech Republic)
Róbert Špir (Slovakia)
Róbert Tenzer (New Zealand)