| Author | Message | ||
     Steve Strand (srstrand) New member Username: srstrand Post Number: 1 Registered: 02-2006 |
For a problem in r and z, I need to use in the equations a definite integral over r of a field variable at z locations. How can this be done? i.e. dz(U * C) = ... U = surf_integral(g(C)) over r at z The U variable is an average value over r instead of a mesh-point variable. | ||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 554 Registered: 06-2003 |
Define a boundary at the path you want to integrate (use a named FEATURE). Then include U = surf_integral(g(c), <path_name>) in your Definitions section. See for example "Backstrom_Books | Fields_of_Physics | b_Electricity | elec14a.pde" Or "Samples | Misc | Constraints | Bdry_Constraint.pde" | ||
| Steve Strand (srstrand) New member Username: srstrand Post Number: 2 Registered: 02-2006 |
This problem requires a value of the integral over r at every z point. It doesn't sound like this capability exists in FlexPDE. Another way to do this problem is to differentiate the integral equation to yield a new differential equation. We would then need the value of the integrated function at the boundaries as a continous function in z. So what is needed is the ability to write an expression that includes the value of one of the field variables as a function, not just at a point. The VAL and EVAl functions allow sampling of a field variable at a point. Is there a capability for continuous sampling of the field variable along a boundary for use in the differential equations? | ||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 558 Registered: 06-2003 |
An integral is the inverse of a derivative. If I=R_Integral(g(c)) then dr(I)=g(c). This can be posed as a PDE. Make I a variable and give it the equation above. Integrating differential equations is what FlexPDE does. |