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Wave phenomena and spectral analysis methods: Waves and oscillations in physics, the Fourier and Laplace transforms, discretization, DFT, FFT, implementation, stability analysis, duration analysis, code optimization, hardware acceleration
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Gravitation, electrostatics and computational procedures: gravitation problems and Coulomb‘s law, periodic systems and convergence, Ewald summation, error analysis, Particle Mesh Ewald, efficient implementation, hardware acceleration
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Thermal conductivity equation, Poisson’s equation and solution methods: thermal conductivity equation, Poisson’s equation, parabolic PDEs, PDEs, analytical solutions for special cases, domain decomposition / finite element approximation, solution using algebraic methods, implementation, convergence analysis, code optimization, hardware acceleration
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Data analysis and dimensional reduction: examples of correlated high-dimensional signals, Rayleigh quotient and optimality principle, eigenvalue problem, singular value decomposition and usual solution methods, Nystro¨m approximation and sparse sampling, efficient implementation