appendices:a19
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| * $\varepsilon$: tolerance coefficient | * $\varepsilon$: tolerance coefficient | ||
| * restol: residual threshold | * restol: residual threshold | ||
| + | |||
| + | ===== ILUT Preconditionners ===== | ||
| + | Preconditioning is a technique to reach quicker the convergence. The convergence depends on the distribution and the value of the eigenvalues of the stiffness matrix, $[K]$. \\ | ||
| + | Suppose that $[M]$ is symmetric, positive-definite matrix that approximates $[K]$, but easier to invert. The equation system can be indirectly solved by solving: \[ [M]^{-1}[K]\underline{x}=[M]^{-1}\underline{F}\] | ||
| + | If the set of eigenvalue of $[M]^{-1}[K]$ is lower and better clustered than the set of $[K]$, then the | ||
| + | number of iterations to solve without iteration will be lower than the number of iterations with preconditioning. \\ | ||
| + | The simplest ways of defining a preconditioner is to perform an incomplete LU factorization of the original matrix $[K]$. This entails a decomposition of the form: \[[K]=[L]_k[U]_k-[R]\] | ||
| + | where $[L]_k$ and $[U]_k$ have nonzero structure as the lower part and upper parts of $[K]$ respectively and $[R]$ is the residual error of the factorization therefore $[M]=[L]_k[U]_k$. \\ | ||
| + | The fill-in depends on the geometrical tolerance to avoid too large bandwidth for $[L]_k$ and $[U]_k$. The fill-in depends if the component, which does not belong to the diagonal is not inferior to a tolerance value. | ||
| + | The preconditioning required two parameters: | ||
| + | * lfil: degree of fill in | ||
| + | * droptol: acceptance limit for the value of the components which are out of the diagonal of the stiffness matrix. | ||
| + | |||
| + | ===== Guideline to using GMRES method ===== | ||
| + | KNSYM must be equal to 6 at the 1st line and the 15th column in the [[:lagamex|loading file]]. Then the parameters for the iterative method must be entered on the second line (this line is added in the loading file) with the following format: | ||
| + | ^Format^Name^Description^Use^Default value^ | ||
| + | | I5 | IM |size of the Krylov subspace (must be inferior to 1000)|GMRES parameter|20| | ||
| + | | I5 | MAXITS |Maximum of iterations allowed |GMRES parameters|5000| | ||
| + | | I5 | LFIL | Fill-in tolerance parameter |Preconditioning parameters|50| | ||
| + | | I5 | IOUT | Output unit number for printing intermediate results (=1 printing, =0 no printing)|GMRES parameters| 0| | ||
| + | | G10.0 | EPS | Tolerance for stopping criterion |GMRES parameter|10<sup>-4</sup>| | ||
| + | | G10.0 | DROPTOL |Sets the threshold for dropping small terms in the factorization|Preconditioning parameters| 10<sup>-8</sup>| | ||
| + | | G10.0 | RESTOL |Sets the threshold value of the residual which consider the convergence|GMRES parameters|10<sup>-8</sup>| | ||
| + | |||
| + | ===== Example of parameters as function of number of DOF ===== | ||
| + | === Example 1 === | ||
| + | ^DOF^IM^EPS^LFIL^DROPTOL^ | ||
| + | |26392 |2000 |1.10<sup>-4</sup>| 50| 1.10<sup>-6</sup>| | ||
| + | |14637| 500 |1.10<sup>-4</sup> |100 |5.10<sup>-3</sup>| | ||
| + | |||
| + | === Example 2 === | ||
| + | ^DOF^IM^MAXITS^LFIL^EPS^DROPTOL^ | ||
| + | |42700|20|5000|15|10<sup>-4</sup>|10<sup>-2</sup>| | ||
| + | |58483|175|5000|200|10<sup>-5</sup>|10<sup>-6</sup>| | ||
| + | |||
| + | ===== Effect of the parameters on the convergence ===== | ||
| + | |||
| + | * Higher are IM and LFIL, lower the number of iterations before convergence is. However the memory cost is more important. | ||
| + | * Higher EPS is, lower the number of iterations before convergence for the iterative solver is. However if the residual is not enough low, the out-of-balanced forces diminish slower and the Newton-Raphson can converge slower. | ||
| + | * Higher DROTOL is, lower the memory cost of the preconditioning matrix is. However the number of iterations before convergence for the iterative solver increases. | ||
appendices/a19.1561648476.txt.gz ยท Last modified: 2020/08/25 15:33 (external edit)
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