Generalized Finite Element Methods

 Lectures    M/R 2:00-3:20 pm, Carnegie 102

  Download Course Description

 

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 Instructor information  
 Professor Suvranu De
 Room JEC 5002
 Email:des_at_rpi_dot_edu
 Office Ph: X6096
 Office hrs: M  3:30-4:30 pm

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 Textbook:

  None required

  Lecture notes are posted here at the course website.

  Other reference texts: 

   1.      Numerical approximation of partial differential equations, A. Quarteroni and A. Valli, Springer-Verlag.

   2.      Meshfree particle methods, S. Li and W.K. Liu, Springer.

   3.      Finite element procedures, K. J. Bathe, Prentice Hall

   4.      Integral equations, W. Hackbusch, Birkhauser

  Blog: iMechanica

  Lecture Notes:

  Introduction ( lec1.ppt ) [1/24]
  Mathematical Preliminaries (lec2.ppt ) [1/27]  Polynomial interpolation (lec3.ppt ) [1/31, 2/03]
  Least squares and moving least squares approximations (lec4.ppt ) [2/07, 2/10] 
  Kernel estimates and partition of unity approximations (lec5.ppt ) [2/14]
  Strong formulation, minimization principle and the variational formulation (lec6.ppt ) [2/17] 
  Approximation techniques: Rayleigh-Ritz and Galerkin methods (lec7.ppt ) [2/24]
  Error analysis of Galerkin methods (lec8.ppt ) [2/28] 
  Other approximation schemes (lec9.ppt ) [3/03, 3/21]
  Local Galerkin weak forms (lec10.ppt ) [3/24]  Discontinuities (lec 11.ppt ) [3/24]
  Imposition of constraints (lec12.ppt ) [3/28, 3/31]  Introduction to integral equations(lec13.ppt) [04/04, 04/07]
  Discretization convergence theory for integral equation methods ( lec14.ppt ) [4/11]
  Numerical integration  (lec15.ppt) [4/14, 4/18]

  Homework

  Homework #1   due Feb 24        Homework #2    due Mar 31       
  Homework #3   due Apr   07   download gauss.m  Homework #4    due Apr 28