| Author | Message | ||
     mclc (mclc) New member Username: mclc Post Number: 2 Registered: 05-2006 |
Hi, I have a solution of simple diffusion equation for U(x,y) in 2D rectangular domain (0<x<1, 0<y<1): DIV(-GRAD(U))+DT(U)=0 Is it somehow possible to calculate within FlexPDE the following quantity: F(x)=Integral[U(x,y), y=0..1]? Thanks for any help. | ||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 605 Registered: 06-2003 |
FlexPDE integral operators must be applied to region volumes or declared bounding paths. So you can't use an integral statement to compute a family of integrals over a single coordinate. However, if F=y_integral(u) then dy(F)=u. This is a legal PDE, so you can declare a variable F and give it the equation dy(F)=u. You can then plot the field over your domain. This equation will require one value boundary condition along the bottom boundary. You may also need to add a small diffusion term to couple the solution in X. This will damp oscillations in X that arise from the finite element method computing integrals in X as part of the discretization. With no x coupling, the equations will accept solutions that are oscillatory in x. | ||
| mclc (mclc) Junior Member Username: mclc Post Number: 3 Registered: 05-2006 |
Thank you for advice! And how can I define zero value boundary condition only along the bottom boundary? Say, I have: REGION "domain" START (0,0) LINE TO (1,0) TO (1,1) TO (0,1) TO CLOSE If I write here: START (0,0) VALUE(F)=0 LINE TO (1,0) TO ... then zero value boundary condition will be prescribed at the all boundaries of "domain", but I need to give it only at bottom line. | ||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 608 Registered: 06-2003 |
See "Problem Descriptor Reference | The Sections of a Descriptor | Boundaries | Boundary Conditions" in the Help Contents for a description of boundary condition statements. See also all the example problems, which show the way boundary conditions are set. See also the User Guide, which shows how to build FlexPDE scripts. Boundary conditions apply to all segments of a path until they are explicitly changed. NATURAL(F) specifies a generalized surface source, and NATURAL(F)=0 specifies NO source. For a first-order equation, there is no integration by parts, so the NATURAL(F) is undefined. The effect is NO boundary condition. (See "Natural Boundary Conditions" in the Help Index). NOBC(F) specifically says NO boundary condition. It is the same as NATURAL(F)=0 in your case. (See NOBC in the Help Index) So you can say START(0,0) VALUE(F)=0 LINE TO (L,0) NOBC(F) LINE TO (L,H) TO (0,H) TO CLOSE |