| Author | Message | ||
     Peter Cendula (cendo) Member Username: cendo Post Number: 4 Registered: 06-2007 |
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 surface value of dx(U)*dx(W). Am I right? Thanks, Peter | ||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 899 Registered: 06-2003 |
I ran a test, and it shows that the FlexPDE symbolic analyzer is not smart enough to split the term dx(U)*dxx(W). 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. So, in short, the term dx(U)*dx(W) does NOT appear in the NATURAL. You can force it by writing dx(dx(U)*dx(W))-dx(W)*dxx(U) 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(..). You can get FlexPDE to tell you what it is doing with the equations by use of SELECT DEBUG(FORMULAS) This prints out a lot of computation trees for the equation processing. It's not easy to read, but it's there. In particular, an equation c: dx(a)*dxx(c)+ ka*dxx(c) = 0 { where c is var 4 and a is var 2} produces the following: =============================== EQUATION 4 C =============================== REGION 1 SOURCE[4] | <v> | ZERO ---------------------------------------- REGION 1 GALERKIN INTEGRAL[4] | - | <v>.X | * | 0.00500 _____________| C.X ___| <v> | * | C.XX ____________| A.X ---------------------------------------- REGION 1 SURFACE GALERKIN[4] | <s>.X | * | 0.00500 __________| C.X ---------------------------------------- k*dxx(c) has been integrated by parts, but dx(a)*dxx(c) has not. |