THE BIGGEST PROBLEM OF ALL: SWITCHING TO FINITE VOLUME DISCRETIZATION
SLOWES THE CONVERGENCE CONSIDERABLY.

I DISCOVERED WHY IS THAT PROBLEM. FOR FINITE VOLUME DISCRETZATON,
RESTRICTION SHOULD BE JUST ADDING THE FINE CELL VALUES. THESE ARE
INTEGRATED RESIDUALS!

I completely forgot to create/check copy constructors :-(


@ Grid1D
%%%%%%%%

Information on periodicity might get lost when dividing the grid :-(
Not any longer, I have introduced periodic1 and periodicN :-)


Strategical question about domain decomposition
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

I have to perform two things: grid coarsening and grid decomposition
for parallel processing. The question is: which one to make first.
If I first make coarsening, my algorithm for decomposition would not
be so flexible any longer.

So I have decided to make decomposition first (still automatic), and
then coarsen in each sub-grid (sub-domain). To achieve this, I need
to coarsen the grid to a certain extent and then take part of it.

For example, if I had this grid:

+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
 0 1 2         7              15

I know from the domain decomposition algorithm that proc 1 gets cells
0 - 7. So, for the level 1, I coarsen the grid by 2:

+---+---+---+---+---+---+---+---+
  0   1   2   3               7 

and take the sub-grid 0 - 3 from it. For the next level, I coarsen 
again the original grid by 4:

+-------+-------+-------+-------+
    0       1       2        3    

and take cells 0 and 1. I achieve that by writing specialized constructor
in Grid1D.

However, all of this is still a bit questionable, since I am not sure 
yet what will partitioning requirements result from parallel multigrid 
strategies.


Ravioli
%%%%%%%

Maybe they should be defined in the include file for the class they are
used for, rather than in separate directory. 

-> Maybe not. Some of them might be used in several classes.

-> Maybe those which are used inside one class only, could be defined
   (declared) in the header of that functions. Others, which are used
   in different places, could be in the separate directory.


Restriction & Interpolation
%%%%%%%%%%%%%%%%%%%%%%%%%%%

Is it parallelized? Does it take any care about periodicity?


@ Discretization
%%%%%%%%%%%%%%%%

Huge problem: when switching from FD to FV discretization in 2D, it
converges very poorly. Why?

I DISCOVERED WHY IS THAT PROBLEM. FOR FINITE VOLUME DISCRETZATON,
RESTRICTION SHOULD BE JUST ADDING THE FINE CELL VALUES. THESE ARE
INTEGRATED RESIDUALS!

Implementation of Aditive correction AC method:
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Step 1: Make AC from MG
        -  1D -> OK
        -  2D -> OK
        -  3D -> OK

Step 2: Embed AC algorithms into loops! -> OK

Step 3: Encapsulate AC and MG into one class.
        (I am not quite sure about this. Transport is quite cumbersome).
        (Maybe to separate Scalar from the Pressure)

Code duplication
%%%%%%%%%%%%%%%%

I have it a lot :-( For example, Level in MG and AC are almost identical,
I have gmv plotting of problem domains from Scalar3D and Domain3D. 

A cure to resolve this issue could be in abandoning 1D and 2D versions.
I do not think it has a lot of sense to contine the development of these
parts of the code.

OK, I DID IT. ABANDONED 1D AND 2D VERSIONS AND ALSO CREATED A SPECIALIZED
CLASS ONLY FOR PLOTTING!

How to make just one instance of the solver?
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
OK, I DID THAT AS WELL. NOT WITH STATIC METHOD, BUT BY PASSING IT AS
AN ARGUMENT.

I have to decide how to treat sources for variables. There is external
source, the one from boundary conditions, and internal (from time stepping
algorithm). So how to deal with all of this?

@ Discretization (04.11.2008)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Should I switch back to finite difference discretization? 
It is easier to define projection algorithm and immersed boundary methods.
Or should I keep both?

The discretization is performed in following 18 functions:

Centered/centered_advance.cpp                 - (A)
Centered/centered_convection.cpp              - (B)
Centered/centered_insert_bc.cpp               - (B)
Centered/centered_new_time_step.cpp           - (A)
Centered/centered_system_bnd.cpp              - (B)
Centered/centered_system_diffusive.cpp        - (A)
Centered/centered_system_innertial.cpp        - (A)
Centered/centered_system_obst.cpp             - (E)

Centered/LevelSet/levelset_sharpen.cpp        - (D)
Centered/LevelSet/levelset_tension.cpp        - (A)

Centered/Pressure/pressure_discretize.cpp     - (A)
Centered/Pressure/pressure_update_rhs.cpp     - (A)

Staggered/Momentum/momentum_bulk_ijk.cpp      - (C)
Staggered/Momentum/momentum_convection.cpp    - (B)
Staggered/Momentum/momentum_create_system.cpp - (A)
Staggered/Momentum/momentum_grad.cpp          - (A)
Staggered/Momentum/momentum_new_time_step.cpp - (A)
Staggered/Momentum/momentum_volf_bct.cpp      - (C)

(A) - could be done with: dV(i,j,k), dSi(i,j,k), dSj(i,j,k) dSk(i,j,k)

(B) - uses dV(i,j,k), dSi(i,j,k), dSj(i,j,k) dSk(i,j,k), 
      but it would require big modifications too.

(C) - has dV(i,j,k), dSi(i,j,k), dSj(i,j,k) dSk(i,j,k), 
      but they are just a hinderance.

(D) - big modifications are needed

(E) - it is not finished, anyway.

Total: 10 A  +  4 B  +  2 C  +  1 D  +  1 E

List them all:

Centered/centered_advance.cpp
Centered/centered_convection.cpp
Centered/centered_insert_bc.cpp
Centered/centered_new_time_step.cpp
Centered/centered_system_bnd.cpp
Centered/centered_system_diffusive.cpp
Centered/centered_system_innertial.cpp
Centered/centered_system_obst.cpp
Centered/LevelSet/levelset_sharpen.cpp
Centered/LevelSet/levelset_tension.cpp
Centered/Pressure/pressure_discretize.cpp
Centered/Pressure/pressure_update_rhs.cpp
Staggered/Momentum/momentum_bulk_ijk.cpp
Staggered/Momentum/momentum_convection.cpp
Staggered/Momentum/momentum_create_system.cpp
Staggered/Momentum/momentum_grad.cpp
Staggered/Momentum/momentum_new_time_step.cpp
Staggered/Momentum/momentum_volf_bct.cpp