Timeline for Reveal the formal PDE of FiniteElement
Current License: CC BY-SA 4.0
23 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 16, 2022 at 7:17 | comment | added | user21 | @xzczd, yeah, would be nice but it's not easy to get and I'd rather spend my time fixing more serious issues. Thanks for checking this again and also for reporting it. | |
| Aug 15, 2022 at 11:41 | comment | added | xzczd♦ | Oops, I see, it's indeed not wrong. (It's $\nabla \color{orange}{\cdot} (-\alpha u)$ v.s. $\beta \color{orange}{\cdot} \nabla u$. ) But still, I'd argue if $−c∇u−αu+γ$ is in a single $\nabla \cdot$, the output will be much easier to follow. | |
| Aug 15, 2022 at 11:22 | comment | added | user21 | OK, thanks I'll look at that a bit later. | |
| Aug 15, 2022 at 11:19 | comment | added | xzczd♦ |
Yeah, but when Times is Inactived, the situation is different, I elaborate the issue in this answer: mathematica.stackexchange.com/a/271385/1871
|
|
| Aug 15, 2022 at 11:14 | comment | added | user21 |
@xzczd, this should be equivalent: Inactive[ Div][-c . Inactive[Grad][u[x], {x}] - \[Alpha]* u[x] + \[Gamma], {x}] == Inactive[Div][-c . Inactive[Grad][u[x], {x}], {x}] + Inactive[Div][-\[Alpha]*u[x], {x}] + Inactive[Div][\[Gamma], {x}] == NeumannValue
|
|
| Aug 15, 2022 at 11:09 | comment | added | user21 | @xzczd, there should not be any difference. | |
| Aug 15, 2022 at 11:05 | comment | added | xzczd♦ |
Well, I disagree. Though the PDEs are mathematically equivalent, the corresponding NeumannValues are different, and one of the most important usage of GetInactivePDE (in my view) is helping one to decide the correct NeumannValue.
|
|
| Aug 15, 2022 at 10:56 | comment | added | user21 | @xzczd, I had a look. The fact that GetInactivePDE returns a divergence for each term is not wrong per se. No matter how I implement this, there will always be forms where the output is mathematically equivalent but different from what was given on input. I don't think this is a major problem. Do you disagree? | |
| Jul 28, 2022 at 12:14 | comment | added | user21 | @xzczd, I'll have a look once I'm back from vacation. | |
| Jul 28, 2022 at 5:12 | comment | added | xzczd♦ |
Just notice an improper behavior of GetInactivePDE: c = IdentityMatrix[2]; α = {x, y}; γ = {y, x^2}; ipde = Inactive[Div][Inactive[Plus][-c . Inactive[Grad][u[x, y], {x, y}], Inactive[Times][-α, u[x, y]], γ], {x, y}] == 0; {state} = NDSolve`ProcessEquations[{ipde, DirichletCondition[u[x, y] == 0, True]}, u, {x, y} ∈ Disk[]]; NDSolve`FEM`GetInactivePDE@state, the $(-c ∇u-α u+γ)$ term should be placed in a single $∇·$.
|
|
| May 18, 2022 at 9:47 | comment | added | Ulrich Neumann |
@user21 Thank you, in this question Understanding NeumannValue I 'm trying, in vain, to verify this result. Please read my question.
|
|
| May 17, 2022 at 11:22 | comment | added | user21 |
@UlrichNeumann, yes, whatever is in the Div part defines NeumannValue.
|
|
| May 16, 2022 at 14:08 | comment | added | Ulrich Neumann |
@user21 Looking at the inactive form of the pde: The Div-part defines the NeumannValue (-{{x, 0}, {0, 1}} . Grad [U[x, y], {x, y}]) . Is this conclusion correct? Thanks!
|
|
| Apr 30, 2021 at 13:25 | comment | added | xzczd♦ |
I take the liberty to add a line making GetInactivePDE in this post handle NDSolve`StateData, feel free to roll back if you don't like it :) .
|
|
| Apr 30, 2021 at 13:23 | history | edited | xzczd♦ | CC BY-SA 4.0 |
added 72 characters in body
|
| Apr 29, 2021 at 15:21 | history | edited | user21 | CC BY-SA 4.0 |
edited body
|
| Apr 29, 2021 at 10:53 | history | edited | user21 | CC BY-SA 4.0 |
added 84 characters in body
|
| Apr 29, 2021 at 6:21 | comment | added | xzczd♦ |
Side note: NDSolve`FEM`GetInactivePDE is built-in in v12.2. (There's no separate document page for it though. )
|
|
| Jul 14, 2020 at 7:57 | vote | accept | xzczd♦ | ||
| Jul 13, 2020 at 10:49 | history | edited | xzczd♦ | CC BY-SA 4.0 |
deleted 9 characters in body
|
| Jul 13, 2020 at 7:43 | history | edited | user21 | CC BY-SA 4.0 |
added 391 characters in body
|
| Jul 13, 2020 at 7:11 | history | edited | user21 | CC BY-SA 4.0 |
added 74 characters in body
|
| Jul 13, 2020 at 7:02 | history | answered | user21 | CC BY-SA 4.0 |