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<p style="margin-bottom: 0in;">Dear all,</p>
<p style="margin-bottom: 0in;">I think that the GMRES ILU(p)
preconditioner in my program is consuming too much memory. I just
would like to check if it is correct or not and compare this
experience with other PETSc users.<br>
For a quite small sparse matrix
(dimension = 3500 and 2.5 Mb) the memory consumed while the
preconditioner is created is more or less:</p>
<p style="margin-bottom: 0in;">ILU
level approximate increase of
memory waste (Mb) </p>
<p style="margin-bottom: 0in;">4
9<br>
8
26<br>
12
43<br>
16
53<br>
20
68<br>
</p>
<p style="margin-bottom: 0in;">Moreover a fast convergence is reached
suddenly (i.e. for ILU level 25 convergence is not reached after 3000
iterations but for ILU level 30 the convergence is reached in 7
iterations).<br>
I suppose that some of the problems are
caused by the large condition number of the matrix but in any case I
guess that the memory used by the preconditioner is too large.<br>
I have tried to improve the performance
using:<font size="3"> PCFactorSetFill, PCFa</font>ctorSetAllowDiagonalFill
and PCFactorSetUseDropTolerance but I have not succeed.
</p>
<p style="margin-bottom: 0in;">
</p>
<p style="margin-bottom: 0in;">I would also like to know how to
estimate a priori the memory required for a PETSc sparse matrix if
the non null entries are known. Is the following rule: 1
double/complex<double> and 2 integers per non null coefficient,
a good approximation (taking into account PETSc implementation)? Is
the same rule valid for the case of the preconditioner?</p>
<p style="margin-bottom: 0in;">I will give some details on the
particular situation being solved:<br>
------------------------------------------------------------------------------------------------------------</p>
<p style="margin-bottom: 0in;">Type of matrix: FEM resolution of an
structural dynamic problem</p>
<p style="margin-bottom: 0in;">(K + w*w*M) | L^T</p>
<p style="margin-bottom: 0in;">------------------------- = System
matrix
</p>
<p style="margin-bottom: 0in;">L | 0</p>
<p style="margin-bottom: 0in;"><br>
</p>
<p style="margin-bottom: 0in;">K == stiffness matrix (square banded)<br>
M == consistent mass matrix (square
banded, and same nonzero pattern than K)<br>
w == pulsation of the problem (scalar)<br>
L == Lagrange multipliers matrix
(rectangular sparse)<br>
</p>
<p style="margin-bottom: 0in;">The matrix is in general ill
conditioned and non positive definite.
</p>
<p style="margin-bottom: 0in;">
------------------------------------------------------------------------------------------------------------</p>
<p style="margin-bottom: 0in;">
</p>
<p style="margin-bottom: 0in;">And my use of PETSc functions is as
follows:</p>
<p style="margin-bottom: 0in;"> <font style="font-size: 8pt;" size="1"> ierr
= KSPCreate(PETSC_COMM_WORLD,&MyKsp);CHKERRQ(ierr);</font></p>
<p style="margin-bottom: 0in;"><font style="font-size: 8pt;" size="1">ierr
= KSPSetType(MyKsp, KSPGMRES);CHKERRQ(ierr);</font></p>
<p style="margin-bottom: 0in;"> <font style="font-size: 8pt;" size="1"> ierr
= KSPSetOperators(MyKsp,MyMat,MyMat,DIFFERENT_NONZERO_PATTERN);
CHKERRQ(ierr);</font></p>
<p style="margin-bottom: 0in;"><br>
</p>
<p style="margin-bottom: 0in;"> <font style="font-size: 8pt;" size="1"> ierr
= KSPGetPC(MyKsp,&(MyPc));CHKERRQ(ierr);</font></p>
<p style="margin-bottom: 0in;"> <font style="font-size: 8pt;" size="1"> </font></p>
<p style="margin-bottom: 0in;"><font style="font-size: 8pt;" size="1"> </font></p>
<p style="margin-bottom: 0in;"><font style="font-size: 8pt;" size="1"> ierr
= PCSetType(MyPc,PCILU);CHKERRQ(ierr);</font></p>
<p style="margin-bottom: 0in;"><font style="font-size: 8pt;" size="1"> ierr
= PCFactorSetLevels(MyPc, LevelNumber);CHKERRQ(ierr);</font></p>
<p style="margin-bottom: 0in;"><br>
</p>
<p style="margin-bottom: 0in;"><font style="font-size: 8pt;" size="1"> PetscReal
realshift = 1.0;</font></p>
<p style="margin-bottom: 0in;"><font style="font-size: 8pt;" size="1"> ierr
= PCFactorSetShiftNonzero(MyPc, realshift); CHKERRQ(ierr); //With and
without this line</font></p>
<p style="margin-bottom: 0in;"><br>
</p>
<p style="margin-bottom: 0in;"><font style="font-size: 8pt;" size="1"> ierr
=
KSPSetTolerances(MyKsp,tol,PETSC_DEFAULT,PETSC_DEFAULT,itmax);CHKERRQ(ierr);</font></p>
<p style="margin-bottom: 0in;"><font style="font-size: 8pt;" size="1"> ierr
= KSPSetInitialGuessNonzero(MyKsp,PETSC_TRUE);CHKERRQ(ierr);</font></p>
<p style="margin-bottom: 0in;"><br>
</p>
<p style="margin-bottom: 0in;"><font style="font-size: 8pt;" size="1"> ierr
= KSPGMRESSetRestart(MyKsp, max_steps_restart); CHKERRQ(ierr); //With
and without this line</font></p>
<p style="margin-bottom: 0in;"><br>
</p>
<p style="margin-bottom: 0in;"> <font style="font-size: 8pt;" size="1"> ierr
= KSPSetFromOptions(MyKsp);CHKERRQ(ierr);</font></p>
<p style="margin-bottom: 0in;">
</p>
<p style="margin-bottom: 0in;"> <font style="font-size: 8pt;" size="1"> ierr
= KSPSolve(MyKsp,MyVector,x);CHKERRQ(ierr); </font>
</p>-----------------------------------------------------------------------------------------------------------
<p style="margin-bottom: 0in;">Thank you very much in advance,</p>
<p style="margin-bottom: 0in;"><br>
Jordi Poblet Puig</p>
<p style="margin-bottom: 0in;"><br>
</p>
<p style="margin-bottom: 0in;"><br>
</p>