# Numerical methods

(Difference between revisions)
 Revision as of 20:34, 14 December 2005 (view source)Tsaad (Talk | contribs)← Older edit Revision as of 20:35, 14 December 2005 (view source)Tsaad (Talk | contribs) Newer edit → Line 25: Line 25: # Linear systems of equations # Linear systems of equations ## [[Introduction and need]] ## [[Introduction and need]] - ## Matrix Related + - ### [[Matrix factorisation]] + - #### [[Incomplete LU factorization - ILU]] + - #### [[Incomplete Cholesky factorization]] + ## Direct methods ## Direct methods ### [[Gaussian elimination]] ### [[Gaussian elimination]] Line 34: Line 31: ### Direct solution to tridiagonal matrix ### Direct solution to tridiagonal matrix #### [[Thomas algorithm]] #### [[Thomas algorithm]] + ## Iterative methods ## Iterative methods ### [[Basic concept of iterative solutions]] ### [[Basic concept of iterative solutions]] Line 45: Line 43: #### [[Biconjugate gradient method]] #### [[Biconjugate gradient method]] #### [[Biconjugate gradient stabilized method]] #### [[Biconjugate gradient stabilized method]] + + ## Matrix factorization and preconditioning + ### [[Incomplete LU factorization - ILU]] + ### [[Incomplete Cholesky factorization]] + ## [[Multigrid methods]] ## [[Multigrid methods]] ### [[Geometric multigrid]] ### [[Geometric multigrid]]

## Numerical Aspects of CFD

This section covers the numerical soul of CFD.

1. Linear systems of equations
1. Introduction and need
1. Direct methods
1. Gaussian elimination
2. LU decomposition method
3. Direct solution to tridiagonal matrix
1. Thomas algorithm
1. Iterative methods
1. Matrix factorization and preconditioning