Why doesn't FlexPDE find a solution to my PDE system?

Frequently Asked Questions about FlexPDE.

Why doesn't FlexPDE find a solution to my PDE system?

Postby mgnelson on Fri Mar 30, 2012 3:51 pm

FlexPDE is a very flexible solver which can be used in a wide variety of applications. We cannot be knowledgeable in all of these fields. Nor can we afford to invest the time necessary to deconstruct each user's script and determine whether it is correct for the desired application. The user must take responsibility for constructing a well-posed PDE system which accurately represents their desired model. We can answer questions regarding the features and use of FlexPDE and we provide a large number of examples which demonstrate the use of FlexPDE in various fields, but we cannot determine for the user the cause of any failure to reach a solution. It is very easy to pose PDE systems that have no solution, and in these cases FlexPDE will fail.

There are several steps a user can follow to try to resolve these issues:

1) Start with a basic formulation for which you know the exact solution. Once you have created a script that solves this system correctly, you will have a basis on which to build a more complex model. Be aware that incorrect boundary conditions can destroy an otherwise well-behaved model.

2) In many cases, a test problem can be constructed by assuming a solution expression, substituting it into the PDE and deriving source terms that will generate the assumed solution. This will help find errors in boundary conditions, parameters etc.

3) Replace any complex or non-linear coefficients with constant coefficients of similar size. This will help diagnose whether the non-linearity or complexity is the source of failure. Be sure that expressions used for coefficients remain well-behaved in regions far beyond the expected solutions, as these values may be sampled by FlexPDE during the solution process.

4) Add diagnostic plots of all variables and parameters, as well as validation relationships that may be of use in detecting incorrect formulations. This is most important when adding new components to an existing basic formulation.

5) Think about what the system you have posed means in terms of expected behavior, and inspect all components of your system looking for inconsistencies.
mgnelson
 
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