Timeline for How to integrate polynomial expression over 3D 4-node element?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Oct 8, 2012 at 6:27 | history | edited | Geoff Oxberry | CC BY-SA 3.0 |
Corrected notation.
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| Oct 8, 2012 at 4:04 | comment | added | Ondřej Čertík | Geoff, that's correct. I put a simple general formula plus a worked out example here: theoretical-physics.net/dev/src/math/integration.html | |
| Oct 7, 2012 at 19:35 | comment | added | Geoff Oxberry | Your Jacobian matrix $\mathrm{D}\varphi$ should be 3 by 2, so $\mathrm{D}\varphi^{\mathrm{T}}\mathrm{D}\varphi$ should be a 2 by 2 matrix. | |
| Oct 7, 2012 at 17:49 | vote | accept | danny_23 | ||
| Oct 7, 2012 at 17:45 | comment | added | danny_23 | Thanks a lot. The book I'm reading covers only the case where a square (2 by 2) Jacobi matrix is involved to keep things simple. The expression above if I got it right makes it possible to use arbitrary sized (2 by 3) Jacobi matrices. Unfortunately I'm still getting $\det(\mathrm{D}\varphi^{\mathrm{T}}(x,y)\mathrm{D}\varphi(x,y))=0$ at the moment but it's much better than I had earlier. I'll create another thread on the proper choice of mapping function. Thanks again. | |
| Oct 7, 2012 at 8:52 | history | edited | Geoff Oxberry | CC BY-SA 3.0 |
Added some clarifying comments.
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| Oct 7, 2012 at 8:01 | history | answered | Geoff Oxberry | CC BY-SA 3.0 |