Subjects of Research
- special functions of mathematical (geo)physics (in particular orthogonal polynomials, (scalar, vectorial, tensorial) spherical harmonics, Bessel and Hankel functions, etc.)
- partial differential equations (potential theory, elasticity, electromagnetism, fluid dynamics, refraction, geothermal flow)
- constructive approximation (in particular radial basis functions, finite elements, splines, wavelets etc.), integral transforms
- numerical methods ("scientific computing", particularly of georelevant problems in potential theory, elasticity and electromagnetic theory)
- inverse problems in geophysics, geodesy and satellite technology (e.g., geomagnetics, gravimetry, satellite to satellite tracking, satellite gradiometry, seismics, etc.)
- mathematics in industry: transfer of mathematical know how into (geo)practice, in particular in geothermal research
Curriculum Vitae
1948 born in Kaldenkirchen (nowadays Nettetal)
1971 Diplom in Mathematics
1972 State examination
1975 Ph.D. at RWTH Aachen University
1979 Habilitation atRWTH Aachen University
1982 Research Associate Professor at Ohio State Univ.
1984 Professor at RWTH Aachen University
1989 Professor at University of Kaiserslautern
2015 retired
Ph.D. students / Habilitations
- R. Reuter (1982): "Über Integralformeln der Einheitssphäre und harmonische Splinefunktionen".
- H. Schaffeld (1988): "Finite-Elemente-Methoden und ihre Anwendung zur Erstellung von Digitalen Geländemodellen".
- M. Schreiner (1994): "Tensor Spherical Harmonics and Their Application in Satellite Gradiometry".
- J. Cui (1995): "Finite Pointset Methods on the Sphere and Their Application in Physical Geodesy".
- U. Windheuser (1995): "Sphärische Wavelets: Theorie und Anwendungen in der Physikalischen Geodäsie."
- M. Tücks (1996): "Navier-Splines und ihre Anwendung in der Deformationanalyse".
- F. Schneider (1997): "Inverse Problems in Satellite Geodesy and Their Approximate Solution by Splines and Wavelets".
- V. Michel (1999): "A Multiscale Method for the Gravimetry Problem: Theoretical and Numerical Aspects of Harmonic and Anharmonic Modelling".
- M. Bayer (1999): "Geomagnetic Field Modelling From Satellite Data by First and Second Generation Wavelets".
- S. Beth (2000): "Multiscale Approximation by Vector Radial Basis Functions on the Sphere".
- O. Glockner (2001): "On Numerical Aspects of Gravitational Field Modelling from SST and SGG by Harmonic Splines and Wavelets (With Application to CHAMP Data)".
- H. Nutz (2001): "A Unified Setup of Gravitational Field Observables".
- R. Litzenberger (2001): "Pyramid Schemes for Harmonic Wavelets in Boundary--Value Problems".
- T. Maier (2002): "Multiscale Geomagnetic Field Modelling From Satellite Data: Theoretical Aspects and Numerical Applications".
- K. Hesse (2003): "Domain Decomposition Methods in Multiscale Geopotential Determination from SST and SGG".
- M.K. Abeyratne (2003): "Cauchy-Navier Wavelet Solvers and Their Application in Deformation Analysis".
- C. Mayer (2003): "Wavelet Modelling of Ionospheric Currents and Induced Magnetic Fields From Satellite Data".
- F. Bauer (2004): "An Alternative Approach to the Oblique Derivative Problem in Potential Theory".
- M. J. Fengler (2005): "Vector Spherical Harmonic and Vector Wavelet Based Non-Linear Galerkin Schemes for Solving the Incompressible Navier-Stokes Equation on the Sphere".
- D. Michel (2006): "Framelet Based Multiscale Operator Decomposition".
- S. Gramsch (2006): "Integralformeln und Wavelets auf regulären Gebieten der Sphäre".
- A. Amirbekyan (2007): "The Application of Reproducing Kernel Based Spline Approximation to Seismic Surface and Body Wave Tomography: Theoretical Aspects and Numerical Results".
- A. Luther (2007): "Vector Field Approximation on Regular Surfaces in Terms of Outer Harmonic Representations".
- M. Gutting (2007): "Fast Multipole Methods for Oblique Derivative Problems".
- A. Moghiseh (2007): "Fast Wavelet Transform by Biorthogonal Locally Supported Radial Bases Functions on Fixed Spherical Grids".
- O. Schulte (2009): "Euler Summation Oriented Spline Interpolation".
- T. Fehlinger (2009): "Multiscale Formulations for the Disturbing Potential and the Deflections of the Vertical in Locally Reflected Physical Geodesy".
- K. Wolf (2009): "Multiscale Modeling of Classical Boundary Value Problems in Physical Geodesy by Locally Supported Wavelets".
- A. Kohlhaas (2010): "Multiscale Methods on Regular Surfaces and their Application to Physical Geodesy".
- C. Gerhards (2011): "Spherical Multiscale Methods in Terms of Locally Supported Wavelets: Theory and Application to Geomagnetic Modeling".
- I. Ostermann (2011): "Modeling heat transport in deep geothermal systems by radial basis functions".
- M. Ilyasov (2011): "A Tree Algorithm for Helmholtz Potential Wavelets on Non-smooth Surfaces: Theoretical Background and Application to Seismic Data Processing".
- E. Kotevska (2011): "Real Earth Oriented Gravitational Potential Determination".
- S. Möhringer (2014): "Decorrelation of Gravimetric Data".
- M. Klug (2014): "Integral Formulas and Discrepancy Estimates Using the Fundamental Solution to the Beltrami Operator on Regular Surfaces".
- S. Eberle (2014): "Forest Fire Determination: Theory and Numerical Aspects".
- M. Augustin (2015): "A Method of Fundamental Solutions in Poroelasticity to Model the Stress Field in Geothermal Reservoirs".
- C. Blick (2015): "Multiscale Potential Methods in Geothermal Research: Decorrelation reflected Post-Processing and Locally Based Inversion".
- Volker Michel: "A Multiscale Approximation for Operator Equations in Separable Hilbert Space — Case Study: Reconstruction and Description of the Earth's Interior". Habilitation Thesis, University of Kaiserslautern, Geomathematics Group. Shaker, Aachen, 2002.
- Michael Schreiner: "Wavelet Approximation by Spherical Up Functions".
Habilitation Thesis, University of Kaiserslautern, Geomathematics Group, 2003. - Carsten Mayer: "Wavelet Modelling of the Stokes Problem".
Habilitation Thesis, University of Kaiserslautern, Geomathematics Group, 2007.