[Nek5000-users] How to obtain spectral coefficients and basis

[nek5000-users at lists.mcs.anl.gov]

Nek is based on a Gauss-Legendre-Lobatto(GLL) quadrature, so the grids are GLL points. The basis polynomials are Lagrange polynomials.

Oana
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From: nek5000-users-bounces at lists.mcs.anl.gov [nek5000-users-bounces at lists.mcs.anl.gov] on behalf of nek5000-users at lists.mcs.anl.gov [nek5000-users at lists.mcs.anl.gov]
Sent: Monday, December 14, 2015 12:35 PM
To: nek5000-users at lists.mcs.anl.gov
Subject: Re: [Nek5000-users] How to obtain spectral coefficients and basis

Andrew,

Thanks for the reply. And can you please confirm that the polynomials used are Chebyshev?

On 12/8/2015 11:26 AM, nek5000-users at lists.mcs.anl.gov<mailto:nek5000-users at lists.mcs.anl.gov> wrote:
Hello,

If I've understood you propely, you can see all the collocation points and weights in the file coef.f (subroutine genwz).

Andrew

2015-12-07 4:23 GMT+01:00 <nek5000-users at lists.mcs.anl.gov<mailto:nek5000-users at lists.mcs.anl.gov>>:
Hello,

I'm trying to represent the solution, either velocity or temperature, in terms of spectral basis, i.e.

$u=\Sigma a_i \phi_i $ with $\phi_i$ as the basis and $a_i$ as the coefficients.

I have two questions:

1) (a naive one!) Which basis is being used in Nek5000? I assume it is Chebyshev polynomials. Is that true? If not, what is the basis?

2) How can I retrieve the coefficients $a_i$? Also, is there a way to access such coefficients during the solution, say by writing them to a file?

I really appreciate the responses. As a side note, I'd like to use DNS data for model reduction.

Many thanks,
Saleh
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