Summer of Code - Getting Started: Difference between revisions

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=== Incomplete sparse factorizations ichol, ilu ===
=== Incomplete sparse factorizations ichol, ilu ===


Implement incomplete Cholesky and LU factorization for sparse matrices. These functions are [http://www.mathworks.it/it/help/matlab/matrix-decomposition.html available in Matlab] as cholinc/ichol and luinc/ilu. Incomplete factorizations are useful as preconditioners
Octave still lacks of an incomplete Cholesky and LU factorization for sparse matrices. These functions are [http://www.mathworks.com/help/matlab/matrix-decomposition.html available in Matlab] as ichol and ilu. Incomplete factorizations are useful as preconditioners for iterative solvers such as [http://hg.savannah.gnu.org/hgweb/octave/file/812162c34a93/scripts/sparse/gmres.m gmres] or [http://hg.savannah.gnu.org/hgweb/octave/file/812162c34a93/scripts/sparse/pcg.m pcg].
for iterative solvers such as [http://hg.savannah.gnu.org/hgweb/octave/file/119ce9f5e1a3/scripts/sparse/gmres.m gmres] and
 
[http://hg.savannah.gnu.org/hgweb/octave/file/119ce9f5e1a3/scripts/sparse/gmres.m gmres] or [http://hg.savannah.gnu.org/hgweb/octave/file/119ce9f5e1a3/scripts/sparse/pcg.m pcg].
Good introductions to the math behind these factorizations are:
The classic book [http://netlib.org/linalg/html_templates/node81.html Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods] has a [http://netlib.org/linalg/html_templates/node100.html#SECTION00933000000000000000 chapter] describing the
* [http://netlib.org/linalg/html_templates/node81.html Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods] especially [http://netlib.org/linalg/html_templates/node100.html#SECTION00933000000000000000 this chapter]  
ILU algorithm in detail, though the algorithm described there should be adapted to Octave's internal Sparse Matrix file format which is [http://netlib.org/linalg/html_templates/node92.html#SECTION00931200000000000000 CCS] rather than [http://netlib.org/linalg/html_templates/node91.html#SECTION00931100000000000000 CRS]. The implementation of ILU in Octave has been recently discussed in the maintainers list and initial implementations were posted in this [http://octave.1599824.n4.nabble.com/Ilu-function-tp4648677.html thread]. In another [http://octave.1599824.n4.nabble.com/Re-Octave-maintainers-Digest-Vol-80-Issue-15-tp4646303.html thread] it was suggested to implement the ILU by interfacing Octave to [http://www-users.cs.umn.edu/~saad/software/ITSOL/ ITSOL]. Compared to other  
* [http://www-users.cs.umn.edu/~saad/IterMethBook_2ndEd.pdf Iterative Methods for Sparse Linear Systems (2nd Edition)] chapter 10 (also available as textbook)
projects in this section this one might require more knowledge of C++.
 
One should also familiarize with Octave's internal sparse matrix format which is [http://netlib.org/linalg/html_templates/node92.html#SECTION00931200000000000000 CCS] rather than [http://netlib.org/linalg/html_templates/node91.html#SECTION00931100000000000000 CRS], which is used in the listed textbooks. In the past GSoC a solution using [http://www-users.cs.umn.edu/~saad/software/ITSOL/ ITSOL] has been created. This work needs several improvements before it can be integrated into the Octave core. Read more about the past GSoC project in [http://siko1056-gsoc.blogspot.de/ this blog]. A [http://siko1056-gsoc.blogspot.de/p/getting-my-work.html demo implementation] is also available from there.
 
Compared to other projects in this section this one might require more knowledge of C++ and mathematical software. But this project doesn't need to be started from scratch and can be continued from the previous approach, if desired. For more information feel free to contact <k.ohlhus@gmail.com>.


=== General purpose Finite Element library ===
=== General purpose Finite Element library ===
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