Difference between revisions of "JSG T.35"

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(Created page with "<big>'''JSG 0.22: High resolution harmonic analysis and synthesis of potential fields'''</big> Chair: ''Sten Claessens (Australia)''<br> Affiliation:''Comm. 2 and GGOS'' __T...")
 
 
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<big>'''JSG 0.22: High resolution harmonic analysis and synthesis of potential fields'''</big>
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<big>'''JSG T.35: Advanced numerical methods in physical geodesy'''</big>
  
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Chair: ''Sten Claessens (Australia)''<br>
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Chair: ''Robert Čunderlík (Slovakia)''<br>
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Affiliation:''Comm. 2 and GGOS''
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Affiliation:''Commission and GGOS''
  
 
__TOC__
 
__TOC__
  
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===Terms of Reference===
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===Introduction===
  
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The gravitational fields of the Earth and other celestial bodies in the Solar System are customarily represented by a series of spherical harmonic coefficients. The models made up of these harmonic coefficients are used widely in a large range of applications within geodesy. In addition, spherical harmonics are now used in many other areas of science such as geomagnetism, particle physics, planetary geophysics, biochemistry and computer graphics, but one of the first applications of spherical harmonics was related to the gravitational potential, and geodesists are still at the forefront of research into spherical harmonics. This holds true especially when it comes to the extension of spherical harmonic series to ever higher degree and order (d/o).
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Advanced numerical methods and high performance computing (HPC) facilities provide new opportunities in many applications in geodesy. The goal of this JSG is to apply such numerical methods to solve various problems of physical geodesy, mainly gravity field modelling, processing satellite observations, nonlinear data filtering or others. It focuses on a further development of approaches based on discretization numerical methods like the finite element method (FEM), finite volume method (FVM) and boundary element method (BEM) or the meshless collocation techniques like the method of fundamental solutions (MFS) or singular boundary method (SOR). Such approaches allow gravity field modelling in spatial domain while solving the geodetic boundary-value problems (GBVPs) directly on the discretized Earth’s surface. Their parallel implementations and large-scale parallel computations on clusters with distributed memory allow high-resolution numerical modelling.
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The maximum d/o of spherical harmonic series of the Earth’s gravitational potential has risen steadily over the past decades. The highest d/o models currently listed by the International Centre for Global Earth Models (ICGEM) have a maximum d/o of 2190. In recent years, spherical harmonic models of the topography and topographic potential to d/o 10,800 have been computed, and with ever-increasing computational prowess, expansions to even higher d/o are feasible. For comparison, the current highest-resolution global gravity model has a resolution of 7.2” in the space domain, which is roughly equivalent to d/o 90,000 in the frequency domain, while the highest-resolution global Digital Elevation Model has a resolution of 5 m, equivalent to d/o ~4,000,000.
 
  
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The increasing maximum d/o of harmonic models has posed and continues to pose both theoretical and practical challenges for the geodetic community. For example, the computation of associated Legendre functions of the first kind, which are required for spherical harmonic analysis and synthesis, is traditionally subject to numerical instabilities and underflow/overflow problems. Much progress has been made on this issue by selection of suitable recurrence relations, summation strategies, and use of extended range arithmetic, but further improvements to efficiency may still be achieved.
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The JSG is also open to new innovative approaches based for example on the computational fluid dynamics (CFD) techniques, spectral FEM, advection-diffusion equations, or similar approaches of scientific computing. It is also open for researchers dealing with classical approaches of gravity field modelling like the spherical or ellipsoidal harmonics that are using HPC facilities 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).
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There are further separate challenges in ultra-high d/o harmonic analysis (the forward harmonic transform) and synthesis (the inverse harmonic transform). Many methods for the forward harmonic transform exist, typically separated into least-squares and quadrature methods, and further comparison between the two at high d/o, including studying the influence of aliasing, is of interest. The inverse harmonic transform, including synthesis of a large variety of quantities, has received much interest in recent years. In moving towards higher d/o series, highly efficient algorithms for synthesis on irregular surfaces and/or in scattered point locations, are of utmost importance.  
 
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Another question that has occupied geodesists for many decades is whether there is a substantial benefit to the use of oblate ellipsoidal (or spheroidal) harmonics instead of spherical harmonics.  The limitations of the spherical harmonic series for use on or near the Earth’s surface are becoming more and more apparent as the maximum d/o of the harmonic series increase. There are still open questions about the divergence effect and the amplification of the omission error in spherical and spheroidal harmonic series inside the Brillouin surface.  
 
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The Hotine-Jekeli transformation between spherical and spheroidal harmonic coefficients has proven very useful, in particular for spherical harmonic analysis of data on a reference ellipsoid. It has recently been improved upon and extended, while alternatives using surface spherical harmonics have also been proposed, but the performance of the transformations at very high d/o may be improved further. Direct use of spheroidal harmonic series requires (ratios of) associated Legendre functions of the second kind, and their stable and efficient computation is also of ongoing interest.
 
  
 
===Objectives===
 
===Objectives===
  
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The objectives of this study group are to:
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* Design the FEM, BEM and FVM numerical models for solving GBVPs with the oblique derivative boundary conditions.
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* Create and compare stable and efficient methods for computation of ultra-high degree and order associated Legendre functions of the first and second kind (or ratios thereof), plus its derivatives and integrals.
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* Develop algorithms for a discretization of the Earth’s surface based on adaptive refinement procedures (the BEM approach).
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* Study the divergence effect of ultra-high degree spherical and spheroidal harmonic series inside the Brillouin sphere/spheroid.
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* Develop algorithms for an optimal construction of 3D unstructured meshes above the Earth’s topography (the FVM or FEM approaches).
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* Verify the numerical performance of transformations between spherical and spheroidal harmonic coefficients to ultra-high degree and order.
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* Design numerical models based on MFS or SBM for processing the GOCE gravity gradients in spatial domain.
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* Compare least-squares and quadrature approaches to very high-degree and order spherical and spheroidal harmonic analysis.
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* Design algorithms for 1D along track filtering of satellite data, e.g., from the GOCE satellite mission.
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* Study efficient methods for ultra-high degree and order harmonic analysis (the forward harmonic transform) for a variety of data types and boundary surfaces.
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* Develop numerical methods for nonlinear diffusion filtering of data on the Earth’s surface based on solutions of the nonlinear heat equations.
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* Study efficient methods for ultra-high degree and order harmonic synthesis (the inverse harmonic transform) of point values and area means of all potential quantities of interest on regular and irregular surfaces.
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* Investigate innovative approaches based on the computational fluid dynamics (CFD) techniques, spectral FEM or advection-diffusion equations.
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* Apply parallel algorithms using MPI procedures.
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* Apply large-scale parallel computations on clusters with distributed memory.
  
 
===Program of activities===
 
===Program of activities===
  
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* Providing a platform for increased cooperation between group members, facilitating and encouraging exchange of ideas and research results.
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* Active participation in major geodetic conferences.  
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* Creating and updating a bibliographic list of relevant publications from both the geodetic community as well as other disciplines for the perusal of group members.
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* Working meetings at international symposia.
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* Organizing working meetings at international symposia and presenting research results in the appropriate sessions.
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* Organization of a conference session.
  
 
===Membership===
 
===Membership===
  
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'' '''Sten Claessens (Australia), chair''' <br /> Hussein Abd-Elmotaal (Egypt) <br /> Oleh Abrykosov (Germany) <br /> Blažej Bucha (Slovakia) <br /> Toshio Fukushima (Japan) <br /> Thomas Grombein (Germany) <br /> Christian Gruber (Germany) <br /> Eliška Hamáčková (Czech Republic) <br /> Christian Hirt (Germany) <br /> Christopher Jekeli (USA) <br /> Otakar Nesvadba (Czech Republic) <br /> Moritz Rexer (Germany) <br /> Josef Sebera (Czech Republic) <br /> Kurt Seitz (Germany) <br />''
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'' '''Róbert Čunderlík (Slovakia), chair ''' <br /> Petr Holota (Czech Republic) <br /> Michal Kollár (Slovakia) <br /> Marek Macák (Slovakia) <br /> Matej Medľa (Austria) <br /> Karol Mikula (Slovakia) <br /> Zuzana Minarechová (Slovakia) <br /> Otakar Nesvadba (Czech Republic) <br /> Yoshiyuki Tanaka (Japan) <br /> Robert Tenzer (Hong Kong) <br /> Zhi Yin (Germany) <br />''

Latest revision as of 12:55, 10 June 2020

JSG T.35: Advanced numerical methods in physical geodesy

Chair: Robert Čunderlík (Slovakia)
Affiliation:Commission and GGOS

Introduction

Advanced numerical methods and high performance computing (HPC) facilities provide new opportunities in many applications in geodesy. The goal of this JSG is to apply such numerical methods to solve various problems of physical geodesy, mainly gravity field modelling, processing satellite observations, nonlinear data filtering or others. It focuses on a further development of approaches based on discretization numerical methods like the finite element method (FEM), finite volume method (FVM) and boundary element method (BEM) or the meshless collocation techniques like the method of fundamental solutions (MFS) or singular boundary method (SOR). Such approaches allow gravity field modelling in spatial domain while solving the geodetic boundary-value problems (GBVPs) directly on the discretized Earth’s surface. Their parallel implementations and large-scale parallel computations on clusters with distributed memory allow high-resolution numerical modelling.

The JSG is also open to new innovative approaches based for example on the computational fluid dynamics (CFD) techniques, spectral FEM, advection-diffusion equations, or similar approaches of scientific computing. It is also open for researchers dealing with classical approaches of gravity field modelling like the spherical or ellipsoidal harmonics that are using HPC facilities 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).

Objectives

  • Design the FEM, BEM and FVM numerical models for solving GBVPs with the oblique derivative boundary conditions.
  • Develop algorithms for a discretization of the Earth’s surface based on adaptive refinement procedures (the BEM approach).
  • Develop algorithms for an optimal construction of 3D unstructured meshes above the Earth’s topography (the FVM or FEM approaches).
  • Design numerical models based on MFS or SBM for processing the GOCE gravity gradients in spatial domain.
  • Design algorithms for 1D along track filtering of satellite data, e.g., from the GOCE satellite mission.
  • Develop numerical methods for nonlinear diffusion filtering of data on the Earth’s surface based on solutions of the nonlinear heat equations.
  • Investigate innovative approaches based on the computational fluid dynamics (CFD) techniques, spectral FEM or advection-diffusion equations.
  • Apply parallel algorithms using MPI procedures.
  • Apply large-scale parallel computations on clusters with distributed memory.

Program of activities

  • Active participation in major geodetic conferences.
  • Working meetings at international symposia.
  • Organization of a conference session.

Membership

Róbert Čunderlík (Slovakia), chair
Petr Holota (Czech Republic)
Michal Kollár (Slovakia)
Marek Macák (Slovakia)
Matej Medľa (Austria)
Karol Mikula (Slovakia)
Zuzana Minarechová (Slovakia)
Otakar Nesvadba (Czech Republic)
Yoshiyuki Tanaka (Japan)
Robert Tenzer (Hong Kong)
Zhi Yin (Germany)

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