Class page for "Mathematical and numerical foundations of modeling and simulation using partial differential equations"
Part of the Program: French-Vietnam Master in Applied Mathematics
I will update this page regularly until the start of the class. My lectures will be simpler and shorter than the lecture notes provided below.
Background material (I will do a brief review at the beginning of the class).
Scientific content of the class.
Software that is useful to have on your laptop if possible (otherwise I can provide some licenses
you can share)
Lectures and projects.
1. Write your own code to calcuate the 6 FE matrices (M,K,A,Q,G,F) from the mesh quantities P, E, T and the coefficients of the PDE and the boundary condition.
2. Compute the computational time of your code to generate the 6 FE matrices
and compare with the computational time of the Matlab code.
3. What is the ratio between the time of your code and the time of the Matlab code.
4. How do the computational times and the ratio change as a function of the number of elements?
Note concerning the Matlab 2013 code given below:
the Matlab 2013 code defines the mass matrix as from the term a*u so I set a = 1 to get our mass matrix m_ij = int_Omega phi_i*phi_j (D_COEFF = 1 for us).
To get the "A" matrix, I just did A = A_COEFF*M, but this works only if A_coeff is a constant and does not depend on space variable (x,y).
Matlab 2016 files (Updated Monday Sept 18 at 10:38pm).
Matlab 2013 files (Updated Monday Sept 18 at 11:33pm).
Last modified: Tue Sep 19 14:58:37 GMT 2017