| Author | Message | ||
     Mahir Celik (mahir) Junior Member Username: mahir Post Number: 3 Registered: 06-2003 |
Hello Mr. Nelson, in FlexPDE I can define naturalboundary condition for injected currents.This is then a "Neumann boundary problem" which can be solved, when the Value of Potential at a Point is known.Is this considered by FlexPDE? or have I to determine at a point at the Boundary the Value of Potential? Thanks for your Help Sincerely Mahir Celik | ||
| Robert G. Nelson (rgnelson) New member Username: rgnelson Post Number: 4 Registered: 06-2003 |
If all the boundary conditions are Neumann conditions, there is a possibility that the system is ill-posed, and has many solutions. However, if there are internal sources or sinks that are balanced by boundary fluxes, the solution will usually be unique. So the answer to your question depends on more than merely the statement that the boundary conditions are all derivative conditions. It is usually not effective to impose a value at a single point. Many systems, Laplace's equation in particular, admit of 1/r or ln(1/r) solutions around poles. FlexPDE will frequently interpret a point value as a pole, which is not what you want. The finite element equations are all based on integrals over mesh cells, and it is best wherever possible to impose distributed conditions, either values along a segment of the boundary, or integral constraints, or distributed sources and sinks. |