COMPUTER METHODS IN PHYSICS
COMPUTER METHODS IN PHYSICS PHZ 3151
University of Central Florida
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This 10 page Class Notes was uploaded by Humberto Romaguera II on Thursday October 22, 2015. The Class Notes belongs to PHZ 3151 at University of Central Florida taught by Staff in Fall. Since its upload, it has received 11 views. For similar materials see /class/227504/phz-3151-university-of-central-florida in Physics 2 at University of Central Florida.
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Date Created: 10/22/15
Why computational physics Whywhen 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 eg 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 Important problemsapplications Large systems of coupled differential equations Examples Schrodinger s equation trajectories of many interacting particlesmasses Large systems of linear equations linear algebramatrices Examples Normal modes solutions to differential equations in a basis eigenvalueseigenvectors Nonlinear differential equations Examples Fluid dynamics plasma physics chaos Analysis of large amounts of data Examples Spectral methods fitting data to functions What tools are commonly usedavailable Ordinary desktoplaptop 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 doit yourself relatively cheap widely used What other tools might one use Software toolsnumerical libraries Tools for common numerical tasks eg 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 Where do we start Extremely broad topic all areas of physics let s start with ordinary differential equations Review of solutions of ordinary linear diff eq Pseudocode Independent of any computer language General outline of code Might not contain actual detailsalgorithm Declare variables and arrays Initialize variables Do the calclation implement algorithm Store output the results F ortran 77 and programming basics PROGRAM programname Define variables MPLC3T NONE constants arrays speCIfIcatIon part The program code execution part STOP 4 End the main program END subprogram part ubroutines eg matrix diagonalization Why computational physics Why computational physics Why computational physics