Generalized Finite Element Methods

We have made some exciting progress on the application of this technique. They include the following:

  1. Development of Scalar GFEM
  2. Development of Scalar GFEM-BI
  3. Development of Scalar GFEM-PML
  4. Imposition of different boundary conditions
  5. Demonstration of h and p Convergence
  6. Addressing condition number issues
  7. Development of vector basis functions in homogeneous media
  8. Mixture of different basis in different regions
  9. Development of vector basis functions for inhomogenieties
  10. Dispersion analysis
  11. Generalization to tetrahedra
  12. Integration with discontinuous Galerkin methods
  13. Integration with boundary integrals
  14. Application to a range of practical problems

Several of our recent presentation and papers (from 2005-2010) present solutions to these problems.