Math 503 (Math modeling)

Computer project web page

By Nasser Abbasi

 

  1. This is the project description handout. It describes the problem to solve. PDF

 

  1. This is the report for the analytical part of the project (part 1). HTML  PDF

  2. This report: HTML  PDF  is the report for the Finite Elements and Finite difference method, where I did the Finite Elements implementation using symbolic method. It is nicer to see the set of equations being build as N increases. But this is slower ofcourse than the direct method where the A matrix (in Ax=b) is build offline and one just computes the solution.

 

  1. This is a Mathematica notebook which has the project report, and also implements the above method. It is also has a Manipulate GUI to simulate it. This is a Screen shot of the Mathematica GUI

    This is the Mathematica notebook which only has the Manipulate code (without the rest of the report). solutionV2_improved_MANIPULATE.nb

 

  1. This report HTML  PDF is the derivation of the A matrix for the finite element method based on the weak form we are solving for. This generate the entries in the A matrix from the parameters of the problem itself. Hence no need to symbolically solve the equation inline as in the first report I did. This method ofcourse is much faster.

 

  1. This is the Mathematica notebook which solve the Finite Element method based on the above direct method. It contains a Manipulate simulation program for the solution as N changes.  This is a screen shot of the GUI

    This is an Ada implementation of the above as well. It is written in Ada 2005 using gnat 2007 free compiler.  [ SOURCE_CODE     PDF  ]

    This is a Maple 11 implementation of the above.[ SOURCE_CODE  HTML ]

 

  1. This is a small movie showing the simulation.