Re: [petsc-users] Increasing norm with finer mesh
Amazing, right preconditioning fixes the problem. Thanks a lot!
On Tue, Oct 16, 2018 at 8:31 PM Dave May wrote:
>
>
> On Wed, 17 Oct 2018 at 03:15, Weizhuo Wang wrote:
>
>> I just tried both, neither of them make a difference. I got exactly the
>> same curve with either combination.
>>
>
> Try using right preconditioning.
>
>
> https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSPSetPCSide.html
>
>
> Use the options:
>
> -ksp_type gmres -ksp_pc_side right -ksp_rtol 1e-12
>
> Or;
>
> -ksp_type fgmres -ksp_rtol 1e-12
>
> Fgmres does right preconditioning my default
>
>
>
>> Thanks!
>>
>> Wang weizhuo
>>
>> On Tue, Oct 16, 2018 at 8:06 PM Matthew Knepley
>> wrote:
>>
>>> On Tue, Oct 16, 2018 at 7:26 PM Weizhuo Wang
>>> wrote:
>>>
>>>> Hello again!
>>>>
>>>> After some tweaking the code is giving right answers now. However it
>>>> start to disagree with MATLAB results ('traditional' way using matrix
>>>> inverse) when the grid is larger than 100*100. My PhD advisor and I
>>>> suspects that the default dimension of the Krylov subspace is 100 in the
>>>> test case we are running. If so, is there a way to increase the size of the
>>>> subspace?
>>>>
>>>
>>> 1) The default subspace size is 30, not 100. You can increase the
>>> subspace size using
>>>
>>>-ksp_gmres_restart n
>>>
>>> 2) The problem is likely your tolerance. The default solver tolerance is
>>> 1e-5. You can change it using
>>>
>>>-ksp_rtol 1e-9
>>>
>>> Thanks,
>>>
>>> Matt
>>>
>>>
>>>>
>>>> [image: Disagrees.png]
>>>>
>>>> Thanks!
>>>>
>>>> Wang Weizhuo
>>>>
>>>> On Tue, Oct 9, 2018 at 2:50 AM Mark Adams wrote:
>>>>
>>>>> To reiterate what Matt is saying, you seem to have the exact solution
>>>>> on a 10x10 grid. That makes no sense unless the solution can be
>>>>> represented
>>>>> exactly by your FE space (eg, u(x,y) = x + y).
>>>>>
>>>>> On Mon, Oct 8, 2018 at 9:33 PM Matthew Knepley
>>>>> wrote:
>>>>>
>>>>>> On Mon, Oct 8, 2018 at 9:28 PM Weizhuo Wang
>>>>>> wrote:
>>>>>>
>>>>>>> The code is attached in case anyone wants to take a look, I will try
>>>>>>> the high frequency scenario later.
>>>>>>>
>>>>>>
>>>>>> That is not the error. It is superconvergence at the vertices. The
>>>>>> real solution is trigonometric, so your
>>>>>> linear interpolants or whatever you use is not going to get the right
>>>>>> value in between mesh points. You
>>>>>> need to do a real integral over the whole interval to get the L_2
>>>>>> error.
>>>>>>
>>>>>> Thanks,
>>>>>>
>>>>>> Matt
>>>>>>
>>>>>>
>>>>>>> On Mon, Oct 8, 2018 at 7:58 PM Mark Adams wrote:
>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> On Mon, Oct 8, 2018 at 6:58 PM Weizhuo Wang
>>>>>>>> wrote:
>>>>>>>>
>>>>>>>>> The first plot is the norm with the flag -pc_type lu with respect
>>>>>>>>> to number of grids in one axis (n), and the second plot is the norm
>>>>>>>>> without
>>>>>>>>> the flag -pc_type lu.
>>>>>>>>>
>>>>>>>>
>>>>>>>> So you are using the default PC w/o LU. The default is ILU. This
>>>>>>>> will reduce high frequency effectively but is not effective on the low
>>>>>>>> frequency error. Don't expect your algebraic error reduction to be at
>>>>>>>> the
>>>>>>>> same scale as the residual reduction (what KSP measures).
>>>>>>>>
>>>>>>>>
>>>>>>>>>
>>>>>>>
>>>>>>> --
>>>>>>> Wang Weizhuo
>>>>>>>
>>>>>>
>>>>>>
>>>>>> --
>>>>>> What most experimenters take for granted before they begin their
>>>>>> experiments is infinitely more interesting than any results to which
>>>>>> their
>>>>>> experiments lead.
>>>>>> -- Norbert Wiener
>>>>>>
>>>>>> https://www.cse.buffalo.edu/~knepley/
>>>>>> <https://urldefense.proofpoint.com/v2/url?u=http-3A__www.cse.buffalo.edu_-7Eknepley_=DwMFaQ=OCIEmEwdEq_aNlsP4fF3gFqSN-E3mlr2t9JcDdfOZag=hsLktHsuxNfF6zyuWGCN8x-6ghPYxhx4cV62Hya47oo=EFM29ATgv4U8PjXEtfgMkuxKr5DGscMlH-j769W5W_4=grgSL2LaDCthvYvvFITmeOOWPCwgmNfYRPs94N8kmOs=>
>>>>>>
>>>>>
>>>>
>>>> --
>>>> Wang Weizhuo
>>>>
>>>
>>>
>>> --
>>> What most experimenters take for granted before they begin their
>>> experiments is infinitely more interesting than any results to which their
>>> experiments lead.
>>> -- Norbert Wiener
>>>
>>> https://www.cse.buffalo.edu/~knepley/
>>> <http://www.cse.buffalo.edu/~knepley/>
>>>
>>
>>
>> --
>> Wang Weizhuo
>>
>
--
Wang Weizhuo
Re: [petsc-users] Increasing norm with finer mesh
I just tried both, neither of them make a difference. I got exactly the
same curve with either combination.
Thanks!
Wang weizhuo
On Tue, Oct 16, 2018 at 8:06 PM Matthew Knepley wrote:
> On Tue, Oct 16, 2018 at 7:26 PM Weizhuo Wang
> wrote:
>
>> Hello again!
>>
>> After some tweaking the code is giving right answers now. However it
>> start to disagree with MATLAB results ('traditional' way using matrix
>> inverse) when the grid is larger than 100*100. My PhD advisor and I
>> suspects that the default dimension of the Krylov subspace is 100 in the
>> test case we are running. If so, is there a way to increase the size of the
>> subspace?
>>
>
> 1) The default subspace size is 30, not 100. You can increase the subspace
> size using
>
>-ksp_gmres_restart n
>
> 2) The problem is likely your tolerance. The default solver tolerance is
> 1e-5. You can change it using
>
>-ksp_rtol 1e-9
>
> Thanks,
>
> Matt
>
>
>>
>> [image: Disagrees.png]
>>
>> Thanks!
>>
>> Wang Weizhuo
>>
>> On Tue, Oct 9, 2018 at 2:50 AM Mark Adams wrote:
>>
>>> To reiterate what Matt is saying, you seem to have the exact solution on
>>> a 10x10 grid. That makes no sense unless the solution can be represented
>>> exactly by your FE space (eg, u(x,y) = x + y).
>>>
>>> On Mon, Oct 8, 2018 at 9:33 PM Matthew Knepley
>>> wrote:
>>>
>>>> On Mon, Oct 8, 2018 at 9:28 PM Weizhuo Wang
>>>> wrote:
>>>>
>>>>> The code is attached in case anyone wants to take a look, I will try
>>>>> the high frequency scenario later.
>>>>>
>>>>
>>>> That is not the error. It is superconvergence at the vertices. The real
>>>> solution is trigonometric, so your
>>>> linear interpolants or whatever you use is not going to get the right
>>>> value in between mesh points. You
>>>> need to do a real integral over the whole interval to get the L_2 error.
>>>>
>>>> Thanks,
>>>>
>>>> Matt
>>>>
>>>>
>>>>> On Mon, Oct 8, 2018 at 7:58 PM Mark Adams wrote:
>>>>>
>>>>>>
>>>>>>
>>>>>> On Mon, Oct 8, 2018 at 6:58 PM Weizhuo Wang
>>>>>> wrote:
>>>>>>
>>>>>>> The first plot is the norm with the flag -pc_type lu with respect to
>>>>>>> number of grids in one axis (n), and the second plot is the norm without
>>>>>>> the flag -pc_type lu.
>>>>>>>
>>>>>>
>>>>>> So you are using the default PC w/o LU. The default is ILU. This will
>>>>>> reduce high frequency effectively but is not effective on the low
>>>>>> frequency
>>>>>> error. Don't expect your algebraic error reduction to be at the same
>>>>>> scale
>>>>>> as the residual reduction (what KSP measures).
>>>>>>
>>>>>>
>>>>>>>
>>>>>
>>>>> --
>>>>> Wang Weizhuo
>>>>>
>>>>
>>>>
>>>> --
>>>> What most experimenters take for granted before they begin their
>>>> experiments is infinitely more interesting than any results to which their
>>>> experiments lead.
>>>> -- Norbert Wiener
>>>>
>>>> https://www.cse.buffalo.edu/~knepley/
>>>> <https://urldefense.proofpoint.com/v2/url?u=http-3A__www.cse.buffalo.edu_-7Eknepley_=DwMFaQ=OCIEmEwdEq_aNlsP4fF3gFqSN-E3mlr2t9JcDdfOZag=hsLktHsuxNfF6zyuWGCN8x-6ghPYxhx4cV62Hya47oo=EFM29ATgv4U8PjXEtfgMkuxKr5DGscMlH-j769W5W_4=grgSL2LaDCthvYvvFITmeOOWPCwgmNfYRPs94N8kmOs=>
>>>>
>>>
>>
>> --
>> Wang Weizhuo
>>
>
>
> --
> What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which their
> experiments lead.
> -- Norbert Wiener
>
> https://www.cse.buffalo.edu/~knepley/
> <http://www.cse.buffalo.edu/~knepley/>
>
--
Wang Weizhuo
Re: [petsc-users] Increasing norm with finer mesh
Hello again!
After some tweaking the code is giving right answers now. However it start
to disagree with MATLAB results ('traditional' way using matrix inverse)
when the grid is larger than 100*100. My PhD advisor and I suspects that
the default dimension of the Krylov subspace is 100 in the test case we are
running. If so, is there a way to increase the size of the subspace?
[image: Disagrees.png]
Thanks!
Wang Weizhuo
On Tue, Oct 9, 2018 at 2:50 AM Mark Adams wrote:
> To reiterate what Matt is saying, you seem to have the exact solution on a
> 10x10 grid. That makes no sense unless the solution can be represented
> exactly by your FE space (eg, u(x,y) = x + y).
>
> On Mon, Oct 8, 2018 at 9:33 PM Matthew Knepley wrote:
>
>> On Mon, Oct 8, 2018 at 9:28 PM Weizhuo Wang
>> wrote:
>>
>>> The code is attached in case anyone wants to take a look, I will try the
>>> high frequency scenario later.
>>>
>>
>> That is not the error. It is superconvergence at the vertices. The real
>> solution is trigonometric, so your
>> linear interpolants or whatever you use is not going to get the right
>> value in between mesh points. You
>> need to do a real integral over the whole interval to get the L_2 error.
>>
>> Thanks,
>>
>> Matt
>>
>>
>>> On Mon, Oct 8, 2018 at 7:58 PM Mark Adams wrote:
>>>
>>>>
>>>>
>>>> On Mon, Oct 8, 2018 at 6:58 PM Weizhuo Wang
>>>> wrote:
>>>>
>>>>> The first plot is the norm with the flag -pc_type lu with respect to
>>>>> number of grids in one axis (n), and the second plot is the norm without
>>>>> the flag -pc_type lu.
>>>>>
>>>>
>>>> So you are using the default PC w/o LU. The default is ILU. This will
>>>> reduce high frequency effectively but is not effective on the low frequency
>>>> error. Don't expect your algebraic error reduction to be at the same scale
>>>> as the residual reduction (what KSP measures).
>>>>
>>>>
>>>>>
>>>
>>> --
>>> Wang Weizhuo
>>>
>>
>>
>> --
>> What most experimenters take for granted before they begin their
>> experiments is infinitely more interesting than any results to which their
>> experiments lead.
>> -- Norbert Wiener
>>
>> https://www.cse.buffalo.edu/~knepley/
>> <https://urldefense.proofpoint.com/v2/url?u=http-3A__www.cse.buffalo.edu_-7Eknepley_=DwMFaQ=OCIEmEwdEq_aNlsP4fF3gFqSN-E3mlr2t9JcDdfOZag=hsLktHsuxNfF6zyuWGCN8x-6ghPYxhx4cV62Hya47oo=EFM29ATgv4U8PjXEtfgMkuxKr5DGscMlH-j769W5W_4=grgSL2LaDCthvYvvFITmeOOWPCwgmNfYRPs94N8kmOs=>
>>
>
--
Wang Weizhuo
Re: [petsc-users] Increasing norm with finer mesh
The code is attached in case anyone wants to take a look, I will try the high frequency scenario later. On Mon, Oct 8, 2018 at 7:58 PM Mark Adams wrote: > > > On Mon, Oct 8, 2018 at 6:58 PM Weizhuo Wang wrote: > >> The first plot is the norm with the flag -pc_type lu with respect to >> number of grids in one axis (n), and the second plot is the norm without >> the flag -pc_type lu. >> > > So you are using the default PC w/o LU. The default is ILU. This will > reduce high frequency effectively but is not effective on the low frequency > error. Don't expect your algebraic error reduction to be at the same scale > as the residual reduction (what KSP measures). > > >> -- Wang Weizhuo makefile Description: Binary data Helmholtz_demoV2C.cpp Description: Binary data
Re: [petsc-users] Increasing norm with finer mesh
I didn't specify a tolerance, it was using the default tolerance. Doesn't the asymptoting norm implies finer grid won't help to get finer solution? Mark Adams 于2018年10月2日周二 下午4:11写道： > > > On Tue, Oct 2, 2018 at 5:04 PM Weizhuo Wang wrote: > >> Yes I was using one norm in my Helmholtz code, the example code used 2 >> norm. But now I am using 2 norm in both code. >> >> /* >> Check the error >> */ >> ierr = VecAXPY(x,-1.0,u); CHKERRQ(ierr); >> ierr = VecNorm(x,NORM_1,); CHKERRQ(ierr); >> ierr = KSPGetIterationNumber(ksp,); CHKERRQ(ierr); >> ierr = PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g iterations >> %D\n",(double)norm/(m*n),its); CHKERRQ(ierr); >> >> I made a plot to show the increase: >> > > > FYI, this is asymptoting to a constant. What solver tolerance are > you using? > > >> >> [image: Norm comparison.png] >> >> Mark Adams 于2018年10月2日周二 下午2:27写道： >> >>> >>> >>> On Tue, Oct 2, 2018 at 2:24 PM Weizhuo Wang >>> wrote: >>> >>>> The example code and makefile are attached below. The whole thing >>>> started as I tried to build a Helmholtz solver, and the mean error >>>> (calculated by: sum( | numerical_sol - analytical_sol | / analytical_sol ) >>>> ) >>>> >>> >>> This is a one norm. If you use max (instead of sum) then you don't need >>> to scale. You do have to be careful about dividing by (near) zero. >>> >>> >>>> increases as I use finer and finer grids. >>>> >>> >>> What was the rate of increase? >>> >>> >>>> Then I looked at the example 12 (Laplacian solver) which is similar to >>>> what I did to see if I have missed something. The example is using 2_norm. >>>> I have made some minor modifications (3 places) on the code, you can search >>>> 'Modified' in the code to see them. >>>> >>>> If this helps: I configured the PETSc to use real and double precision. >>>> Changed the name of the example code from ex12.c to ex12c.c >>>> >>>> Thanks for all your reply! >>>> >>>> Weizhuo >>>> >>>> >>>> Smith, Barry F. >>>> >>>> >>>>>Please send your version of the example that computes the mean norm >>>>> of the grid; I suspect we are talking apples and oranges >>>>> >>>>>Barry >>>>> >>>>> >>>>> >>>>> > On Oct 1, 2018, at 7:51 PM, Weizhuo Wang >>>>> wrote: >>>>> > >>>>> > I also tried to divide the norm by m*n , which is the number of >>>>> grids, the trend of norm still increases. >>>>> > >>>>> > Thanks! >>>>> > >>>>> > Weizhuo >>>>> > >>>>> > Matthew Knepley >>>>> > On Mon, Oct 1, 2018 at 6:31 PM Weizhuo Wang >>>>> wrote: >>>>> > Hi! >>>>> > >>>>> > I'm recently trying out the example code provided with the KSP >>>>> solver (ex12.c). I noticed that the mean norm of the grid increases as I >>>>> use finer meshes. For example, the mean norm is 5.72e-8 at m=10 n=10. >>>>> However at m=100, n=100, mean norm increases to 9.55e-6. This seems >>>>> counter >>>>> intuitive, since most of the time error should decreases when using finer >>>>> grid. Am I doing this wrong? >>>>> > >>>>> > The norm is misleading in that it is the l_2 norm, meaning just the >>>>> sqrt of the sum of the squares of >>>>> > the vector entries. It should be scaled by the volume element to >>>>> approximate a scale-independent >>>>> > norm (like the L_2 norm). >>>>> > >>>>> > Thanks, >>>>> > >>>>> > Matt >>>>> > >>>>> > Thanks! >>>>> > -- >>>>> > Wang Weizhuo >>>>> > >>>>> > >>>>> > -- >>>>> > What most experimenters take for granted before they begin their >>>>> experiments is infinitely more interesting than any results to which their >>>>> experiments lead. >>>>> > -- Norbert Wiener >>>>> > >>>>> > https://www.cse.buffalo.edu/~knepley/ >>>>> <https://urldefense.proofpoint.com/v2/url?u=https-3A__www.cse.buffalo.edu_-7Eknepley_=DwMFaQ=OCIEmEwdEq_aNlsP4fF3gFqSN-E3mlr2t9JcDdfOZag=hsLktHsuxNfF6zyuWGCN8x-6ghPYxhx4cV62Hya47oo=KjmDEsZ6w8LEry7nlv3Bw7-pczqWbKGueFU59VoIWZg=tEv9-AHhL2CIlmmVos0gFa5PAY9oMG3aTQlnfi62ivA=> >>>>> > >>>>> > >>>>> > -- >>>>> > Wang Weizhuo >>>>> >>>>> >>>> >>>> -- >>>> Wang Weizhuo >>>> >>> >> >> -- >> Wang Weizhuo >> > -- Wang Weizhuo
Re: [petsc-users] Increasing norm with finer mesh
Yes I was using one norm in my Helmholtz code, the example code used 2 norm. But now I am using 2 norm in both code. /* Check the error */ ierr = VecAXPY(x,-1.0,u); CHKERRQ(ierr); ierr = VecNorm(x,NORM_1,); CHKERRQ(ierr); ierr = KSPGetIterationNumber(ksp,); CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g iterations %D\n",(double)norm/(m*n),its); CHKERRQ(ierr); I made a plot to show the increase: [image: Norm comparison.png] Mark Adams 于2018年10月2日周二 下午2:27写道： > > > On Tue, Oct 2, 2018 at 2:24 PM Weizhuo Wang wrote: > >> The example code and makefile are attached below. The whole thing started >> as I tried to build a Helmholtz solver, and the mean error (calculated by: >> sum( | numerical_sol - analytical_sol | / analytical_sol ) ) >> > > This is a one norm. If you use max (instead of sum) then you don't need to > scale. You do have to be careful about dividing by (near) zero. > > >> increases as I use finer and finer grids. >> > > What was the rate of increase? > > >> Then I looked at the example 12 (Laplacian solver) which is similar to >> what I did to see if I have missed something. The example is using 2_norm. >> I have made some minor modifications (3 places) on the code, you can search >> 'Modified' in the code to see them. >> >> If this helps: I configured the PETSc to use real and double precision. >> Changed the name of the example code from ex12.c to ex12c.c >> >> Thanks for all your reply! >> >> Weizhuo >> >> >> Smith, Barry F. >> >> >>>Please send your version of the example that computes the mean norm >>> of the grid; I suspect we are talking apples and oranges >>> >>>Barry >>> >>> >>> >>> > On Oct 1, 2018, at 7:51 PM, Weizhuo Wang >>> wrote: >>> > >>> > I also tried to divide the norm by m*n , which is the number of grids, >>> the trend of norm still increases. >>> > >>> > Thanks! >>> > >>> > Weizhuo >>> > >>> > Matthew Knepley >>> > On Mon, Oct 1, 2018 at 6:31 PM Weizhuo Wang >>> wrote: >>> > Hi! >>> > >>> > I'm recently trying out the example code provided with the KSP solver >>> (ex12.c). I noticed that the mean norm of the grid increases as I use finer >>> meshes. For example, the mean norm is 5.72e-8 at m=10 n=10. However at >>> m=100, n=100, mean norm increases to 9.55e-6. This seems counter intuitive, >>> since most of the time error should decreases when using finer grid. Am I >>> doing this wrong? >>> > >>> > The norm is misleading in that it is the l_2 norm, meaning just the >>> sqrt of the sum of the squares of >>> > the vector entries. It should be scaled by the volume element to >>> approximate a scale-independent >>> > norm (like the L_2 norm). >>> > >>> > Thanks, >>> > >>> > Matt >>> > >>> > Thanks! >>> > -- >>> > Wang Weizhuo >>> > >>> > >>> > -- >>> > What most experimenters take for granted before they begin their >>> experiments is infinitely more interesting than any results to which their >>> experiments lead. >>> > -- Norbert Wiener >>> > >>> > https://www.cse.buffalo.edu/~knepley/ >>> <https://urldefense.proofpoint.com/v2/url?u=https-3A__www.cse.buffalo.edu_-7Eknepley_=DwMFaQ=OCIEmEwdEq_aNlsP4fF3gFqSN-E3mlr2t9JcDdfOZag=hsLktHsuxNfF6zyuWGCN8x-6ghPYxhx4cV62Hya47oo=KjmDEsZ6w8LEry7nlv3Bw7-pczqWbKGueFU59VoIWZg=tEv9-AHhL2CIlmmVos0gFa5PAY9oMG3aTQlnfi62ivA=> >>> > >>> > >>> > -- >>> > Wang Weizhuo >>> >>> >> >> -- >> Wang Weizhuo >> > -- Wang Weizhuo
Re: [petsc-users] Increasing norm with finer mesh
The example code and makefile are attached below. The whole thing started
as I tried to build a Helmholtz solver, and the mean error (calculated by:
sum( | numerical_sol - analytical_sol | / analytical_sol ) ) increases as I
use finer and finer grids. Then I looked at the example 12 (Laplacian
solver) which is similar to what I did to see if I have missed something.
The example is using 2_norm. I have made some minor modifications (3
places) on the code, you can search 'Modified' in the code to see them.
If this helps: I configured the PETSc to use real and double precision.
Changed the name of the example code from ex12.c to ex12c.c
Thanks for all your reply!
Weizhuo
Smith, Barry F.
>Please send your version of the example that computes the mean norm of
> the grid; I suspect we are talking apples and oranges
>
>Barry
>
>
>
> > On Oct 1, 2018, at 7:51 PM, Weizhuo Wang wrote:
> >
> > I also tried to divide the norm by m*n , which is the number of grids,
> the trend of norm still increases.
> >
> > Thanks!
> >
> > Weizhuo
> >
> > Matthew Knepley
> > On Mon, Oct 1, 2018 at 6:31 PM Weizhuo Wang
> wrote:
> > Hi!
> >
> > I'm recently trying out the example code provided with the KSP solver
> (ex12.c). I noticed that the mean norm of the grid increases as I use finer
> meshes. For example, the mean norm is 5.72e-8 at m=10 n=10. However at
> m=100, n=100, mean norm increases to 9.55e-6. This seems counter intuitive,
> since most of the time error should decreases when using finer grid. Am I
> doing this wrong?
> >
> > The norm is misleading in that it is the l_2 norm, meaning just the sqrt
> of the sum of the squares of
> > the vector entries. It should be scaled by the volume element to
> approximate a scale-independent
> > norm (like the L_2 norm).
> >
> > Thanks,
> >
> > Matt
> >
> > Thanks!
> > --
> > Wang Weizhuo
> >
> >
> > --
> > What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which their
> experiments lead.
> > -- Norbert Wiener
> >
> > https://www.cse.buffalo.edu/~knepley/
> >
> >
> > --
> > Wang Weizhuo
>
>
--
Wang Weizhuo
static char help[] = "Solves a linear system in parallel with KSP.\n\
Input parameters include:\n\
-m: number of mesh points in x-direction\n\
-n: number of mesh points in y-direction\n\n";
/*T
Concepts: KSP^solving a system of linear equations
Concepts: KSP^Laplacian, 2d
Concepts: PC^registering preconditioners
Processors: n
T*/
/*
Demonstrates registering a new preconditioner (PC) type.
To register a PC type whose code is linked into the executable,
use PCRegister(). To register a PC type in a dynamic library use PCRegister()
Also provide the prototype for your PCCreate_XXX() function. In
this example we use the PETSc implementation of the Jacobi method,
PCCreate_Jacobi() just as an example.
See the file src/ksp/pc/impls/jacobi/jacobi.c for details on how to
write a new PC component.
See the manual page PCRegister() for details on how to register a method.
*/
/*
Include "petscksp.h" so that we can use KSP solvers. Note that this file
automatically includes:
petscsys.h - base PETSc routines petscvec.h - vectors
petscmat.h - matrices
petscis.h - index setspetscksp.h - Krylov subspace methods
petscviewer.h - viewers petscpc.h - preconditioners
*/
#include
PETSC_EXTERN PetscErrorCode PCCreate_Jacobi(PC);
int main(int argc,char **args)
{
Vecx,b,u; /* approx solution, RHS, exact solution */
MatA;/* linear system matrix */
KSPksp; /* linear solver context */
PetscReal norm; /* norm of solution error */
PetscInt i,j,Ii,J,Istart,Iend,m = 8,n = 7,its;
PetscErrorCode ierr;
PetscScalarv,one = 1.0;
PC pc; /* preconditioner context */
ierr = PetscInitialize(,,(char*)0,help);if (ierr) return ierr;
ierr = PetscOptionsGetInt(NULL,NULL,"-m",,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-n",,NULL);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Compute the matrix and right-hand-side vector that define
the linear system, Ax = b.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/*
Create parallel matrix, specifying only its global dimensions.
When using MatCreate(), the matrix format can be specified at
runtime. Also, the parallel partitioning of the matrix can be
determined by PETSc at runtime.
*/
ierr = MatCreate
Re: [petsc-users] Increasing norm with finer mesh
I also tried to divide the norm by m*n , which is the number of grids, the trend of norm still increases. Thanks! Weizhuo Matthew Knepley 于2018年10月1日周一 下午7:45写道： > On Mon, Oct 1, 2018 at 6:31 PM Weizhuo Wang wrote: > >> Hi! >> >> I'm recently trying out the example code provided with the KSP solver >> (ex12.c). I noticed that the mean norm of the grid increases as I use finer >> meshes. For example, the mean norm is 5.72e-8 at m=10 n=10. However at >> m=100, n=100, mean norm increases to 9.55e-6. This seems counter intuitive, >> since most of the time error should decreases when using finer grid. Am I >> doing this wrong? >> > > The norm is misleading in that it is the l_2 norm, meaning just the sqrt > of the sum of the squares of > the vector entries. It should be scaled by the volume element to > approximate a scale-independent > norm (like the L_2 norm). > > Thanks, > > Matt > > >> Thanks! >> -- >> Wang Weizhuo >> > > > -- > What most experimenters take for granted before they begin their > experiments is infinitely more interesting than any results to which their > experiments lead. > -- Norbert Wiener > > https://www.cse.buffalo.edu/~knepley/ > <http://www.cse.buffalo.edu/~knepley/> > -- Wang Weizhuo
[petsc-users] Increasing norm with finer mesh
Hi! I'm recently trying out the example code provided with the KSP solver (ex12.c). I noticed that the mean norm of the grid increases as I use finer meshes. For example, the mean norm is 5.72e-8 at m=10 n=10. However at m=100, n=100, mean norm increases to 9.55e-6. This seems counter intuitive, since most of the time error should decreases when using finer grid. Am I doing this wrong? Thanks! -- Wang Weizhuo
