programming

iFEM

iFEM is is a collection of MATLAB subroutines contributed by all group members. For example, you are welcome to add your subroutines for convection diffusion problems or eigenvalue problems etc. It is different with Matlab Central or Matlab Database where you can find lots of existing packages for FEM computation. iFEM requries the code to be consistent with a simple data structure and certain programming style. Each subroutine can accept standard input arguments and is easy to modify to fit a specific problem. Please read the following references to get a feeling on the programming style.

• Principal: Ten digit, five seconds, and one page by Lloyd N. Trefethen.
• Programming style: MATLAB Programming style guidelines by Richard Johnson. Note: Due to Matlab convention, plotedge is better than plotEdge as suggested and used in C ++.
• Code Optimization:
  • Code Vectorization Guide by Mathwork.
  • Creating Sparse Finite-Element Matrices in MATLAB by Loren Shure.
• Data Structure: Basic and auxiliary data structure for trianglations by Long Chen.

Existing subroutines

Planned Subroutines

• ODTsmoothing.m: improve mesh quality using smoothing scheme based on ODT;
• bisection3.m: bisection in 3-D;
• coarsening3.m: coarsening in 3-D;
• quadraticFEM.m: quadratic finite element methods;
• quadraticFVM.m: quadratic finite volume methods.

Documentation

• Bisection. L. Chen. Short bisection implementation in MATLAB. Report, 2006.
• Coarsening. L. Chen and C.-S. Zhang. A coarsening algorithm and multilevel methods on adaptive grids by newest vertex bisection. Submitted.
• Preconditioner and Multigrid. L. Chen and C.-S. Zhang. A coarsening algorithm and multilevel methods on adaptive grids by newest vertex bisection. Submitted.
• Finite Element Methods. J. Alberty, C. Carstensen, and S. A. Funken. Remarks around 50 lines of Matlab: short finite element implementation. Numerical Algorithms,20:117--137, 1999.