why is PhysDeriv not a linear function
******************* This email originates from outside Imperial. Do not click on links and attachments unless you recognise the sender. If you trust the sender, add them to your safe senders list https://spam.ic.ac.uk/SpamConsole/Senders.aspx to disable email stamping for this address. ******************* Hello, I am calling PhysDeriv from an Expansion Class Object. Why is this not linear? In the sense that if I call PhysDeriv for any linear combination of vectors it should be the same as computing the linear combination of the PhysDeriv of the vectors. Martin Hess -- -- Martin Hess, Ph.D., Post-doctoral research fellow SISSA mathLab, International School for Advanced Studies Office A-434 (4th floor), via Bonomea 265, I-34136 Trieste, Italy phone: +39 040 3787 491 email: mhess@sissa.it
Hi Martin, I think it should have been linear provided all vectors are in the polynomial space of your expansion. In your tests is everything in a resolved polynomial space since otherwise you are doing a collocation projections somewhere and this may not be linear. Cheers, Spencer.
On 17 Jun 2021, at 17:34, Martin Wilfried Hess <mhess@sissa.it> wrote:
******************* This email originates from outside Imperial. Do not click on links and attachments unless you recognise the sender. If you trust the sender, add them to your safe senders list https://spam.ic.ac.uk/SpamConsole/Senders.aspx to disable email stamping for this address. *******************
Hello,
I am calling PhysDeriv from an Expansion Class Object.
Why is this not linear?
In the sense that if I call PhysDeriv for any linear combination of vectors it should be the same as computing the linear combination of the PhysDeriv of the vectors.
Martin Hess
--
-- Martin Hess, Ph.D., Post-doctoral research fellow
SISSA mathLab, International School for Advanced Studies Office A-434 (4th floor), via Bonomea 265, I-34136 Trieste, Italy phone: +39 040 3787 491 email: mhess@sissa.it
_______________________________________________ Nektar-users mailing list Nektar-users@imperial.ac.uk https://mailman.ic.ac.uk/mailman/listinfo/nektar-users
thanks for the swift reply. I do expand a valid flowfield in a POD basis. So I collect a time trajectory in phys coordinates, compute the POD modes (similar to a truncated orthonormal basis of the time trajectory phys vectors, if POD basis is unfamiliar) and then expand the flowfield as a linear combination of the POD basis. If the flowfield was part of the sample data in the POD computation, then this is possible with negligible error ( less then 1e-14 relative error ). I can adapt this if necessary, but I am not sure what to do. Do I need to compute the POD basis in local or global coords and then go back to phys? Or maybe something else? Martin On 2021-06-17 18:43, Sherwin, Spencer J wrote:
Hi Martin,
I think it should have been linear provided all vectors are in the polynomial space of your expansion. In your tests is everything in a resolved polynomial space since otherwise you are doing a collocation projections somewhere and this may not be linear.
Cheers, Spencer.
On 17 Jun 2021, at 17:34, Martin Wilfried Hess <mhess@sissa.it> wrote:
******************* This email originates from outside Imperial. Do not click on links and attachments unless you recognise the sender. If you trust the sender, add them to your safe senders list https://spam.ic.ac.uk/SpamConsole/Senders.aspx to disable email stamping for this address. *******************
Hello,
I am calling PhysDeriv from an Expansion Class Object.
Why is this not linear?
In the sense that if I call PhysDeriv for any linear combination of vectors it should be the same as computing the linear combination of the PhysDeriv of the vectors.
Martin Hess
--
-- Martin Hess, Ph.D., Post-doctoral research fellow
SISSA mathLab, International School for Advanced Studies Office A-434 (4th floor), via Bonomea 265, I-34136 Trieste, Italy phone: +39 040 3787 491 email: mhess@sissa.it
_______________________________________________ Nektar-users mailing list Nektar-users@imperial.ac.uk https://mailman.ic.ac.uk/mailman/listinfo/nektar-users
HI Martin, The phys polynomial space is slightly richer than the local coefficient space and so it could be worth expressing the POD modes in local coifs and then going back to the phys space. Ideally the coefficient should also respect the global expansion and be C0 continuous. Cheers, Spencer.
On 17 Jun 2021, at 22:48, Martin Wilfried Hess <mhess@sissa.it> wrote:
thanks for the swift reply.
I do expand a valid flowfield in a POD basis. So I collect a time trajectory in phys coordinates, compute the POD modes (similar to a truncated orthonormal basis of the time trajectory phys vectors, if POD basis is unfamiliar) and then expand the flowfield as a linear combination of the POD basis. If the flowfield was part of the sample data in the POD computation, then this is possible with negligible error ( less then 1e-14 relative error ).
I can adapt this if necessary, but I am not sure what to do. Do I need to compute the POD basis in local or global coords and then go back to phys? Or maybe something else?
Martin
On 2021-06-17 18:43, Sherwin, Spencer J wrote:
Hi Martin, I think it should have been linear provided all vectors are in the polynomial space of your expansion. In your tests is everything in a resolved polynomial space since otherwise you are doing a collocation projections somewhere and this may not be linear. Cheers, Spencer.
On 17 Jun 2021, at 17:34, Martin Wilfried Hess <mhess@sissa.it> wrote: ******************* This email originates from outside Imperial. Do not click on links and attachments unless you recognise the sender. If you trust the sender, add them to your safe senders list https://spam.ic.ac.uk/SpamConsole/Senders.aspx to disable email stamping for this address. ******************* Hello, I am calling PhysDeriv from an Expansion Class Object. Why is this not linear? In the sense that if I call PhysDeriv for any linear combination of vectors it should be the same as computing the linear combination of the PhysDeriv of the vectors. Martin Hess -- -- Martin Hess, Ph.D., Post-doctoral research fellow SISSA mathLab, International School for Advanced Studies Office A-434 (4th floor), via Bonomea 265, I-34136 Trieste, Italy phone: +39 040 3787 491 email: mhess@sissa.it _______________________________________________ Nektar-users mailing list Nektar-users@imperial.ac.uk https://mailman.ic.ac.uk/mailman/listinfo/nektar-users
On 6/21/21 11:06 PM, Sherwin, Spencer J wrote:
HI Martin,
The phys polynomial space is slightly richer than the local coefficient space and so it could be worth expressing the POD modes in local coifs and then going back to the phys space. Ideally the coefficient should also respect the global expansion and be C0 continuous.
Yes, this works for a tiny test problem. Thanks. I will see how far this takes me. Martin
Cheers, Spencer.
On 17 Jun 2021, at 22:48, Martin Wilfried Hess <mhess@sissa.it> wrote:
thanks for the swift reply.
I do expand a valid flowfield in a POD basis. So I collect a time trajectory in phys coordinates, compute the POD modes (similar to a truncated orthonormal basis of the time trajectory phys vectors, if POD basis is unfamiliar) and then expand the flowfield as a linear combination of the POD basis. If the flowfield was part of the sample data in the POD computation, then this is possible with negligible error ( less then 1e-14 relative error ).
I can adapt this if necessary, but I am not sure what to do. Do I need to compute the POD basis in local or global coords and then go back to phys? Or maybe something else?
Martin
On 2021-06-17 18:43, Sherwin, Spencer J wrote:
Hi Martin, I think it should have been linear provided all vectors are in the polynomial space of your expansion. In your tests is everything in a resolved polynomial space since otherwise you are doing a collocation projections somewhere and this may not be linear. Cheers, Spencer.
On 17 Jun 2021, at 17:34, Martin Wilfried Hess <mhess@sissa.it> wrote: ******************* This email originates from outside Imperial. Do not click on links and attachments unless you recognise the sender. If you trust the sender, add them to your safe senders list https://spam.ic.ac.uk/SpamConsole/Senders.aspx to disable email stamping for this address. ******************* Hello, I am calling PhysDeriv from an Expansion Class Object. Why is this not linear? In the sense that if I call PhysDeriv for any linear combination of vectors it should be the same as computing the linear combination of the PhysDeriv of the vectors. Martin Hess -- -- Martin Hess, Ph.D., Post-doctoral research fellow SISSA mathLab, International School for Advanced Studies Office A-434 (4th floor), via Bonomea 265, I-34136 Trieste, Italy phone: +39 040 3787 491 email: mhess@sissa.it _______________________________________________ Nektar-users mailing list Nektar-users@imperial.ac.uk https://mailman.ic.ac.uk/mailman/listinfo/nektar-users
-- -- Martin Hess, Ph.D., Post-doctoral research fellow SISSA mathLab, International School for Advanced Studies Office A-434 (4th floor), via Bonomea 265, I-34136 Trieste, Italy phone: +39 040 3787 491 email: mhess@sissa.it
participants (2)
-
Martin Wilfried Hess
-
Sherwin, Spencer J