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Lecture 36a, Special discretization, non uniform 


We have arbitrarily scattered boundary points and DOF.
No structure is provided. The problem is to discretize
and build a system of equations, solve the equations,
and determine the values at the DOF.


Simple 1D demonstration

check_nuderiv.c just 6 points
check_nuderiv_c.out check solution
check_nuderiv.java just 6 points
check_nuderiv_java.out check solution

So far, only for 2D and 3D geometry, yet could be generalized.
The basic problem is avoiding singular matrices.
The worse case of arbitrarily scattered points is
when they are uniformly spaced.


The basic non uniform discretization:

nuderiv2d.c use all points
nuderiv2d.h
test_nuderiv2d.c
test_nuderiv2d_c.out
nuderiv2dg.c use good points, less singular
nuderiv2dg.h
test_nuderiv2dg.c
test_nuderiv2dg_c.out

nuderiv2d.java use all points
test_nuderiv2d.java
test_nuderiv2d_java.out
nuderiv2dg.java use good points, less singular
test_nuderiv2dg.java
test_nuderiv2dg_java.out


Now a corner geometry
test_nuderiv2dgc.c
test_nuderiv2dgc_c.out



The basic 3D non uniform discretization:

nuderiv3d.c use all points
nuderiv3d.h
test_nuderiv3d.c
test_nuderiv3d_c.out
nuderiv3dg.c use good points, less singular
nuderiv3dg.h
test_nuderiv3dg.c
test_nuderiv3dg_c.out

nuderiv3dg.java use good points, less singular
test_nuderiv3dg.java
test_nuderiv3dg_java.out


Applying non uniform discretization to a PDE






blivet.inp zero based, regular
blivet_nr.inp non regular

pde_blivet.c
pde_blivet_c.out
pde_blivet_nr_c.out
pde_blivet.java
pde_blivet_java.out
pde_blivet_nr_java.out


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