boundary issue in derivatives with bsplines

[fbischoff]

The derivative using the b-spline method gives artifacts at the boundaries, while abgv does not

factor_derivative_abgv.pdf
factor.pdf
factor_derivative_bspline.pdf

[robertjharrison]

Correct ... it just has central differences right now. When I get back from Japan (2 weeks) we can chat about what boundary conditions are readily doable. Assuming the function and its derivatives are zero beyond the boundary is readily done. Anything else is going to require work. In the meantime mask the input function to ensure it (and its derivatives) are zero at the boundary.

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On Wed, May 15, 2019 at 9:47 AM fbischoff ***@***.***> wrote: The derivative using the b-spline method gives artifacts at the boundaries, while abgv does not factor_derivative_abgv.pdf <https://github.com/m-a-d-n-e-s-s/madness/files/3182775/factor_derivative_abgv.pdf> factor.pdf <https://github.com/m-a-d-n-e-s-s/madness/files/3182776/factor.pdf> factor_derivative_bspline.pdf <https://github.com/m-a-d-n-e-s-s/madness/files/3182777/factor_derivative_bspline.pdf> — You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub <#311?email_source=notifications&email_token=ABZSAPMHGMMIB7RZZB4NDSTPVQH6ZA5CNFSM4HNDPTVKYY3PNVWWK3TUL52HS4DFUVEXG43VMWVGG33NNVSW45C7NFSM4GT5YIPQ>, or mute the thread <https://github.com/notifications/unsubscribe-auth/ABZSAPOZGA2NL4IHTH4KQQTPVQH6ZANCNFSM4HNDPTVA> .

-- Robert J. Harrison tel: 865-274-8544

[fbischoff]

The assumption that the function goes to zero at the boundarie should definitely be good enough. It would be nice if all derivatives behave the same. I always thought that the agbv derivatives also use the central differences, and I am pleased to see they can handle non-zero functions at the boundaries. Florian Bischoff Humboldt-Universitaet zu Berlin, Institut fuer Chemie Unter den Linden 6, 10099 Berlin phone: +49-30-2093-7140 [email protected]

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On 15. May 2019, at 17:07, Robert J. Harrison ***@***.***> wrote: Correct ... it just has central differences right now. When I get back from Japan (2 weeks) we can chat about what boundary conditions are readily doable. Assuming the function and its derivatives are zero beyond the boundary is readily done. Anything else is going to require work. In the meantime mask the input function to ensure it (and its derivatives) are zero at the boundary. On Wed, May 15, 2019 at 9:47 AM fbischoff ***@***.***> wrote: > The derivative using the b-spline method gives artifacts at the > boundaries, while abgv does not > > factor_derivative_abgv.pdf > <https://github.com/m-a-d-n-e-s-s/madness/files/3182775/factor_derivative_abgv.pdf> > factor.pdf > <https://github.com/m-a-d-n-e-s-s/madness/files/3182776/factor.pdf> > factor_derivative_bspline.pdf > <https://github.com/m-a-d-n-e-s-s/madness/files/3182777/factor_derivative_bspline.pdf> > > — > You are receiving this because you are subscribed to this thread. > Reply to this email directly, view it on GitHub > <#311?email_source=notifications&email_token=ABZSAPMHGMMIB7RZZB4NDSTPVQH6ZA5CNFSM4HNDPTVKYY3PNVWWK3TUL52HS4DFUVEXG43VMWVGG33NNVSW45C7NFSM4GT5YIPQ>, > or mute the thread > <https://github.com/notifications/unsubscribe-auth/ABZSAPOZGA2NL4IHTH4KQQTPVQH6ZANCNFSM4HNDPTVA> > . > -- Robert J. Harrison tel: 865-274-8544 — You are receiving this because you authored the thread. Reply to this email directly, view it on GitHub, or mute the thread.

[robertjharrison]

The default derivative operator in MADNESS uses central differences in the volume and at the edge enforces a zero boundary condition using left/right differences. There are also non-zero (and even non-constant) Dirichlet and Neumann boundary conditions implemented. However, the smoother derivatives only have central differences which will work at the boundary only if the input function is both smooth and zero there.

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On Wed, May 15, 2019 at 3:04 PM fbischoff ***@***.***> wrote: The assumption that the function goes to zero at the boundarie should definitely be good enough. It would be nice if all derivatives behave the same. I always thought that the agbv derivatives also use the central differences, and I am pleased to see they can handle non-zero functions at the boundaries. Florian Bischoff Humboldt-Universitaet zu Berlin, Institut fuer Chemie Unter den Linden 6, 10099 Berlin phone: +49-30-2093-7140 ***@***.*** > On 15. May 2019, at 17:07, Robert J. Harrison ***@***.***> wrote: > > Correct ... it just has central differences right now. > > When I get back from Japan (2 weeks) we can chat about what boundary > conditions are readily doable. Assuming the function and its derivatives > are zero beyond the boundary is readily done. Anything else is going to > require work. > > In the meantime mask the input function to ensure it (and its derivatives) > are zero at the boundary. > > On Wed, May 15, 2019 at 9:47 AM fbischoff ***@***.***> wrote: > > > The derivative using the b-spline method gives artifacts at the > > boundaries, while abgv does not > > > > factor_derivative_abgv.pdf > > < https://github.com/m-a-d-n-e-s-s/madness/files/3182775/factor_derivative_abgv.pdf > > > factor.pdf > > <https://github.com/m-a-d-n-e-s-s/madness/files/3182776/factor.pdf> > > factor_derivative_bspline.pdf > > < https://github.com/m-a-d-n-e-s-s/madness/files/3182777/factor_derivative_bspline.pdf > > > > > — > > You are receiving this because you are subscribed to this thread. > > Reply to this email directly, view it on GitHub > > < #311?email_source=notifications&email_token=ABZSAPMHGMMIB7RZZB4NDSTPVQH6ZA5CNFSM4HNDPTVKYY3PNVWWK3TUL52HS4DFUVEXG43VMWVGG33NNVSW45C7NFSM4GT5YIPQ >, > > or mute the thread > > < https://github.com/notifications/unsubscribe-auth/ABZSAPOZGA2NL4IHTH4KQQTPVQH6ZANCNFSM4HNDPTVA > > > . > > > > > -- > Robert J. Harrison > tel: 865-274-8544 > — > You are receiving this because you authored the thread. > Reply to this email directly, view it on GitHub, or mute the thread. > — You are receiving this because you commented. Reply to this email directly, view it on GitHub <#311?email_source=notifications&email_token=ABZSAPKTRRM2M4NT5ESPZLLPVRNEJA5CNFSM4HNDPTVKYY3PNVWWK3TUL52HS4DFVREXG43VMVBW63LNMVXHJKTDN5WW2ZLOORPWSZGODVPUPMA#issuecomment-492783536>, or mute the thread <https://github.com/notifications/unsubscribe-auth/ABZSAPPFVTUPF2BH4WJCT3TPVRNEJANCNFSM4HNDPTVA> .

-- Robert J. Harrison tel: 865-274-8544