Validating jacobian calculations

[rebpoli]

Hi

Does libmesh have some tool to validate jacobian calculation and linearization derivatives? Like routines to systematically compare the residual response after small variations to the jacobian at the same state or so.

Thanks,
Renato

[roystgnr]

I'm afraid I'm not sure I understand the question. You're referring to the Jacobian J≡dF/du for residual F(u) when solving F(ū)=0, right? But you're not talking about perturbing u, but about perturbing J to see what it does to F? That honestly doesn't make sense to me; J is a function of F but F is not a function of J ... unless you're talking about how Fᵢ would change from perturbing Jᵢ₋₁ in a Newton-Raphson solver iteration?

[rebpoli]

Sorry, let me try again. This is the system I am trying to solve using NR J \Delta U = F(U) , where J = dF/du . Obtaining an analytical expression for J is typically cumbersome and error prone - while obtaining F is more straightforward (typically). I want to check if the final J calculation is correct. So, if I perturbate U and calculate F(U+\epsilon), I can estimate J numerically (at least for some cases). That would give me confidence that the system is well derived and implemented. Makes sense? Renato

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On Fri, Feb 21, 2025 at 3:30 PM roystgnr ***@***.***> wrote: I'm afraid I'm not sure I understand the question. You're referring to the Jacobian J≡dF/du for residual F(u) when solving F(ū)=0, right? But you're not talking about perturbing u, but about perturbing J to see what it does to F? That honestly doesn't make sense to me; J is a function of F but F is not a function of J ... unless you're talking about how Fᵢ would change from perturbing Jᵢ₋₁ in a Newton-Raphson solver iteration? — Reply to this email directly, view it on GitHub <#4086 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AMOVERYNB3MG5OFAHR776ZT2Q6LH3AVCNFSM6AAAAABXSHILFOVHI2DSMVQWIX3LMV43URDJONRXK43TNFXW4Q3PNVWWK3TUHMYTEMRYGE3TAMY> . You are receiving this because you authored the thread.Message ID: ***@***.***>

[roystgnr]

That makes perfect sense, yes, and it's a very good idea. If you're using the FEMSystem framework, there's a verify_analytic_jacobians setting you can use there. If you're using PETSc's SNES, there's a -snes_test_jacobian command line option for that. If you're using both then you have both options, and if you're using neither then you might be out of luck.

[rebpoli]

Thank you!