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Spherical harmonic functions, vectors and tensors. Spectral approximation of data given on a sphere in terms of
generalized spherical harmonics. Application to solving PDF. Spectral solution of the following problems: Laplace-Poisson
equation for gravitational potential, deformation of a spherical elastic shall, thermal convection in a mantle, viscoelastic
relaxation of a spherical body, and the problem of electromagnetic induction.
Last update: T_KG (14.04.2008)
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Getting practice in application of spectral methods to solving basic geophysical problems in spherical geometry. Last update: T_KG (14.04.2008)
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Zkouška probíhá formou testu, v rámci kterého studenti vyřeší zadanou rovnici spektrální metodou. V případě nejasností následuje ústní zkouška. Last update: Čadek Ondřej, prof. RNDr., CSc. (06.10.2017)
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Jones M. N.: Spherical Harmonics and Tensors for Classical Field Theory, Research Studies Press Ltd., 1985 Last update: T_KG (14.04.2008)
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Basic principle of spectral methods. Basis functions. Fourier series. Spherical harmonic functions. Various definitions of vector and tensor spherical harmonics (SH). Approximation of geophysical quantities in terms of spherical harmonics. Products of SH series. Application of differential operators. Exercises.
Laplace-Poisson equation. Solution for gravitational potential and acceleration. Expression of centrifugal and tidal forces.
Deformation of an elastic shall with radially dependent material paremeters. Methods of including lateral variations of parameters. Elastic membrane.
Momentum and heat transport equations. Nonlinear terms. Degree 0 and 1.
Viscoelastic deformation of a spherical body, evaluation of the memory term. Compressibility and selfgravitation.
Maxwell equations. Problem of electromagnetic induction. Generation of magnetic field in the core. Last update: T_KG (14.04.2008)
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