查看完整版本: Contribution of nonlinear terms to natural

Contribution of nonlinear terms to natural

[size=2]Hello, I have equation with one term dx(U)*dxx(W), where U and W are both system variables. The natural BC for this term is given by integration by parts as
9u/aO*Ft!r0sb@ surface value of dx(U)*dx(W). Am I right? [/size]

[size=2]I ran a test, and it shows that the FlexPDE symbolic analyzer is not smart enough to split the term dx(U)*dxx(W).
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I think it's because it doesn't know which derivative is the variable defined by the equation, and doing it wrong caused trouble in tests. -NG
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So, in short, the term dx(U)*dx(W) does NOT appear in the NATURAL. /Kz/mpp}:BH ?@

} Tm%yH[+~9br1Y/i You can force it by writing %N%h6wlRBU
dx(dx(U)*dx(W))-dx(W)*dxx(U) F:Fh2Mn)Y
The leading dx() causes the term to be integrated by parts, and the -dx(W)*dxx(U) cancels the extra term from expanding the dx(..). ^'x$W$pU$`

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You can get FlexPDE to tell you what it is doing with the equations by use of
s.^4S%{1PCxu SELECT DEBUG(FORMULAS) 8U3W+u*]i/qvm/| f9E%u
This prints out a lot of computation trees for the equation processing. It's not easy to read, but it's there. v6z%Qn#J
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In particular, an equation F%APp3a5f*sC9Ct7L
c: dx(a)*dxx(c)+ ka*dxx(c) = 0 { where c is var 4 and a is var 2}
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GLA produces the following:
)VzD$T0j7XI:O =============================== TY^ ~;A6a`
EQUATION 4 C
e;^a
p
`-K b5F ===============================
+N5]/gx"G%v
0b E Vps!QAb%g7m REGION 1 SOURCE[4]
rg#oQt T#`y?-l | <v> | ZERO
M@W YO%f+bj%x ----------------------------------------
9C8K!i^Gpa.n 6N)VBv T"k5FW\
REGION 1 GALERKIN INTEGRAL[4]
d,I7?+x*qu;L3FM | - | <v>.X | * | 0.00500
8T2I9U'sT P$sV
jiY _____________| C.X c%N4m$kQ~0Z O9su
___| <v> | * | C.XX
-F"Eo(hHo ____________| A.X i.O_+z"v`5a8}*Nf*k
----------------------------------------
9l0bp9T;CacL y-s?8L6F2^D0s!rC$\1[
REGION 1 SURFACE GALERKIN[4] 2Gt;l r0@W
| <s>.X | * | 0.00500 !V/]g'W rlh
__________| C.X (i1O$n7S-QN
---------------------------------------- BX~]2U%R

&qS/z8C DK-_LeY k*dxx(c) has been integrated by parts, but dx(a)*dxx(c) has not. [/size]