lecture1 - Examples Fluid dynamics plasma physics chaos...

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Why computational physics? • Why/when computers instead of analytical (exact) approach? Answer: When it is impractical or impossible to find an analytical solution! (Not when it’s just hard to do!) • When an precise theory exists (e.g. Newton’s laws, Schrodinger Eq., statistical mechanics, electrodynamics), typically the “exactly solvable” applications are very few. • To find solutions that can be tested against experiments, numerical methods become an important (or even essential) approach.
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Important problems/applications • Large systems of coupled differential equations • Large systems of linear equations (linear algebra/matrices) • Nonlinear differential equations • Analysis of large amounts of data Examples: Schrodinger’s equation, trajectories of many interacting particles/masses Examples: Spectral methods, fitting data to functions Examples: Normal modes, solutions to differential equations in a basis, eigenvalues/eigenvectors
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Unformatted text preview: Examples: Fluid dynamics, plasma physics, chaos What tools are commonly used/available? • Ordinary desktop/laptop Convenient, cheap, limited in power, serial • Supercomputer facility Extremely powerful, usually parallel machines, run by experts, funded by govt. agencies, competitive grants. National Center for Supercomputer App. (NCSA), NERSC, etc. • Beowulf computer Large parallel machine built from desktops,“do-it-yourself”, relatively cheap, widely used What other tools might one use? • Software tools/numerical libraries Tools for common numerical tasks, e.g. manipulation of large matrices in linear algebra • Software for specific applications Fluid dynamics, electronic structure of molecules and crystals, modeling thermodynamics of alloys, etc. • As computational methods continue to become more widespread, strong chance of “reinventing the wheel”....
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