Here is my new website of my Open source software projects

Hello,


Here is my new website of my Open source software projects:

I have just converted my website from the classic Google sites
to new Google Sites, and i have pointed the web link for downloading my 
zip files to the google drive, also i have just changed the theme of
my website, and all the new web links of my website pages are the same 
to the previous web link of my old website pages, so please look at my 
new website here:

https://sites.google.com/site/scalable68/


I am a white arab, and i think i am smart since i have invented many 
scalable algorithms..

About SOR and Conjugate gradient mathematical methods..

I have just looked at SOR(Successive Overrelaxation Method),
and i think it is much less powerful than Conjugate gradient method,
read the following to notice it:

COMPARATIVE PERFORMANCE OF THE CONJUGATE GRADIENT AND SOR METHODS
FOR COMPUTATIONAL THERMAL HYDRAULICS

https://inis.iaea.org/collection/NCLCollectionStore/_Public/19/055/19055644.pdf?r=1&r=1


This is why i have implemented in both C++ and Delphi my Parallel 
Conjugate Gradient Linear System Solver Library that scales very well, 
read my following thoughts about it to understand more:


About the convergence properties of the conjugate gradient method

The conjugate gradient method can theoretically be viewed as a direct 
method, as it produces the exact solution after a finite number of 
iterations, which is not larger than the size of the matrix, in the 
absence of round-off error. However, the conjugate gradient method is 
unstable with respect to even small perturbations, e.g., most directions 
are not in practice conjugate, and the exact solution is never obtained. 
Fortunately, the conjugate gradient method can be used as an iterative 
method as it provides monotonically improving approximations to the 
exact solution, which may reach the required tolerance after a 
relatively small (compared to the problem size) number of iterations. 
The improvement is typically linear and its speed is determined by the 
condition number κ(A) of the system matrix A: the
larger is κ(A), the slower the improvement.

Read more here:

http://pages.stat.wisc.edu/~wahba/stat860public/pdf1/cj.pdf


So i think my Conjugate Gradient Linear System Solver Library
that scales very well is still very useful, read about it
in my writing below:

Read the following interesting news:

The finite element method finds its place in games

Read more here:

https://translate.google.com/translate?hl=en&sl=auto&tl=en&u=https%3A%2F%2Fhpc.developpez.com%2Factu%2F288260%2FLa-methode-des-elements-finis-trouve-sa-place-dans-les-jeux-AMD-propose-la-bibliotheque-FEMFX-pour-une-simulation-en-temps-reel-des-deformations%2F

But you have to be aware that finite element method uses Conjugate 
Gradient Method for Solution of Finite Element Problems, read here to 
notice it:

Conjugate Gradient Method for Solution of Large Finite Element Problems 
on CPU and GPU

https://pdfs.semanticscholar.org/1f4c/f080ee622aa02623b35eda947fbc169b199d.pdf


This is why i have also designed and implemented my Parallel Conjugate 
Gradient Linear System Solver library that scales very well,
here it is:

My Parallel C++ Conjugate Gradient Linear System Solver Library
that scales very well version 1.76 is here..

Author: Amine Moulay Ramdane

Description:

This library contains a Parallel implementation of Conjugate Gradient 
Dense Linear System Solver library that is NUMA-aware and cache-aware 
that scales very well, and it contains also a Parallel implementation of 
Conjugate Gradient Sparse Linear System Solver library that is 
cache-aware that scales very well.

Sparse linear system solvers are ubiquitous in high performance 
computing (HPC) and often are the most computational intensive parts in 
scientific computing codes.  A few of the many applications relying on 
sparse linear solvers include fusion energy simulation, space weather 
simulation, climate modeling, and environmental modeling, and finite 
element method, and large-scale reservoir simulations to enhance oil 
recovery by the oil and gas industry.

Conjugate Gradient is known to converge to the exact solution in n steps 
for a matrix of size n, and was historically first seen as a direct 
method because of this. However, after a while people figured out that 
it works really well if you just stop the iteration much earlier - often 
you will get a very good approximation after much fewer than n steps. In 
fact, we can analyze how fast Conjugate gradient converges. The end 
result is that Conjugate gradient is used as an iterative method for 
large linear systems today.

Please download the zip file and read the readme file inside the zip to 
know how to use it.

You can download it from:

https://sites.google.com/site/scalable68/scalable-parallel-c-conjugate-gradient-linear-system-solver-library

Language: GNU C++ and Visual C++ and C++Builder

Operating Systems: Windows, Linux, Unix and Mac OS X on (x86)

-- 

As you have noticed i have just written above about my Parallel C++ 
Conjugate Gradient Linear System Solver Library that scales very well, 
but here is my Parallel Delphi and Freepascal Conjugate Gradient Linear 
System Solvers Libraries that scale very well:

Parallel implementation of Conjugate Gradient Dense Linear System solver 
library that is NUMA-aware and cache-aware that scales very well

https://sites.google.com/site/scalable68/scalable-parallel-implementation-of-conjugate-gradient-dense-linear-system-solver-library-that-is-numa-aware-and-cache-aware

PARALLEL IMPLEMENTATION OF CONJUGATE GRADIENT SPARSE LINEAR SYSTEM 
SOLVER LIBRARY THAT SCALES VERY WELL

https://sites.google.com/site/scalable68/scalable-parallel-implementation-of-conjugate-gradient-sparse-linear-system-solver


Thank you,
Amine Moulay Ramdane.