<div dir="ltr"><div class="gmail_extra"><div class="gmail_quote">On Fri, Jun 1, 2018 at 12:07 PM, Samuel Lanthaler <span dir="ltr"><<a href="mailto:s.lanthaler@gmail.com" target="_blank">s.lanthaler@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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<div class="m_3362958314088522262moz-cite-prefix">On 06/01/2018 03:42 PM, Matthew Knepley
wrote:<br>
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<div class="gmail_quote">On Fri, Jun 1, 2018 at 9:21 AM,
Samuel Lanthaler <span dir="ltr"><<a href="mailto:s.lanthaler@gmail.com" target="_blank">s.lanthaler@gmail.com</a>></span>
wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">Hi,<br>
<br>
I was wondering what the most efficient way to use MatPtAP
would be in the following situation: I am discretizing a
PDE system. The discretization yields a matrix A that has
a band structure (with k upper and lower bands, say). In
order to implement the boundary conditions, I use a
transformation matrix P which is essentially the unit
matrix, except for the entries P_{ij} where i,j<k and
n-i,n-j<k, so<br>
<br>
P = [ B, 0, 0, 0, ..., 0, 0 ]<br>
[ 0, 1, 0, 0, ..., 0, 0 ]<br>
[ ]<br>
[ ]<br>
[ ..., 1, 0 ]<br>
[ 0, 0, 0, 0, ..., 0, C ]<br>
<br>
with B,C are (k-by-k) matrices.<br>
Right now, I'm simply constructing A, P and calling<br>
<br>
CALL MatPtAP(petsc_matA,petsc_matP,<wbr>MAT_INITIAL_MATRIX,PETSC_DEFAU<wbr>LT_REAL,petsc_matPtAP,ierr)<br>
<br>
where I haven't done anything to pestc_matPtAP, prior to
this call. Is this the way to do it?<br>
<br>
I'm asking because, currently, setting up the matrices A
and P takes very little time, whereas the operation
MatPtAP is taking quite long, which seems very odd... The
matrices are of type MPIAIJ. In my problem, the total
matrix dimension is around 10'000 and the matrix blocks
(B,C) are of size ~100.<br>
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<div>Are you sure this is what you want to do? Usually BC
are local, since by definition PDE are local, and</div>
<div>are applied pointwise. What kind of BC do you have
here?</div>
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<br>
The boundary conditions are a mixture of Dirichlet and Neumann; in
my case, the PDE is a system involving 8 variables on a disk, where
the periodic direction is discretized using a Fourier series
expansion, the radial direction uses B-splines. <br>
<br>
In reality, I have two matrices A,B, and want to solve the
eigenvalue problem \lambda*B*x = A*x. <br>
I found it quite convenient to use a transformation P to a different
set of variables y, such that x=P*y and x satisfies the BC iff
certain components of y are 0. The latter is enforced by inserting
spurious eigenvalues at the relevant components of y in the
transformed eigenvalue problem \lambda*Pt*B*P*y=Pt*A*P*y. After
solving the EVP in terms of y, I get back x=P*y.<br>
Is this an inherently bad/inefficient way of enforcing BC's? Thanks.<br></div></blockquote><div><br></div><div>I cannot quite see what is happening. However it appears that you are coupling all the unknowns on a boundary to enforce the boundary condition.</div><div>If this is true, its pretty expensive. For example, in 2D you have N^2 unknowns for N boundary unknowns. However, dense coupling on the boundary</div><div>produces N^2 storage and N^3 computation, which is not great. Am I missing something? Its fine to do this for some sizes (2D BEM guys do it all</div><div>the time), but for bigger stuff it gets untenable.</div><div><br></div><div> Thanks,</div><div><br></div><div> Matt</div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div bgcolor="#FFFFFF" text="#000000">
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<div> Thanks,</div>
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<div> Matt</div>
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Thanks in advance for any ideas.<br>
<br>
Cheers,<br>
Samuel<br>
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-- <br>
<div class="m_3362958314088522262gmail_signature" data-smartmail="gmail_signature">
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<div>What most experimenters take for granted before
they begin their experiments is infinitely more
interesting than any results to which their
experiments lead.<br>
-- Norbert Wiener</div>
<div><br>
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<div><a href="http://www.caam.rice.edu/%7Emk51/" target="_blank">https://www.cse.buffalo.edu/~<wbr>knepley/</a><br>
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</blockquote></div><br><br clear="all"><div><br></div>-- <br><div class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><div><div dir="ltr"><div>What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>-- Norbert Wiener</div><div><br></div><div><a href="http://www.caam.rice.edu/~mk51/" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><br></div></div></div></div></div>
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