cours NM406 In english.

Year: 2015-16

F. Hecht.

Version 8 dec  2015

Tutorial  C++  in room 16-26 401  with X. Claeys Friday 8h30 to 10h30.

week 1:  19 / 25 October.

presentation of the EU.

Remark on numerics:

Series  of one and numerical derivative

plot of abs(cos(1)-(sin(1+x)-sin(1))/x)

with gunplay

gnuplot> set logscale xy

gnuplot> plot [1e-20:1] abs(cos(1)-(sin(1+x)-sin(1))/x)

Weak formulation of the Poisson Problem,

conformal Mesh

Basic Affine continious Finite Element (call P1 Lagrange Finite Element)

Barycentric coordinate,

computation of barycentric coordinate and this garden

Finite element method,

see chapter 2 section 2.1 to section 2.5.

week 2:  26  October. (O. Pironneau)

Lesson of freefem++ to valid your projet.

week 3 : 2 November

Explanation on to build finite element matrix

Code algo section 7.7

warning exchange alpha , beta.

I have put all tool in w3 directory w3  or   w3.zip

the work is try to code the AddMatMult method.

week 4; 9 November

Finish the code to solve Possion see directory s4 or s4.zip

introduction of quadrature formulas see section ( 2.4 Quadrature formular of NotesdeCoursMN406-GB.pdf)

to compute Lp error

For introduction  of sparse matrix see https://en.wikipedia.org/wiki/Sparse_matrix

week 5: 16 November

Introduction of Sparse matrix,

format COO, CSR,CSR, ..

Use the map and Hash-coding to build space matrix.

see HashMatrix.cpp or HashMatrix.hpp

Do the algorithmic part (section algorithmique)

have put all tool in w5 directory

week 6: 27 November

Explai of Hight ordre finite element P2, P3, \$

Continuous the  algorithmic part  to computing

the numbering for degree of freedom.

Explain howto to compile an use the umfpack solver ..

have put all tool in w6  directory

week 7: 30 November

Presentation of algorithme to solve no linear problem.

Fixe point, Gradient method, Newton method.

Explain how to to compute Differential ,

And explain what the difference between Gradient and Differential in case de minimization problem

see section Problème non linear (not translate).

have put all tool in w7 directory

FreeFem++ example for  minimal surface problem.

week 8: 7 December

Choose the projet

Explain how to automate the building of matrix un right hand side

Given, some quadrature formula in 1d, 2d, 3d.

To day the code will be solve la Stokes problem with stabilise method.

No valide today.in progess.