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Mapping attempt in PeriodicBoundaryConditions ends in failure.

Posted 1 month ago
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Hello,

I am a Mathematica beginner, currently trying to solve a basic 3D cylindrical heat diffusion equation, but I am greeted with a failure to generate a list of mapped coordinates for my periodic boundary conditions. I get an error like this NDSolve::fempbcmf: Applying the mapping TransformationFunction[{{1,0,0,0,0},{0,1,0,0,0},{0,0,1,0,2 \[Pi]},{0,0,0,1,0},{0,0,0,0,1}}] of the periodic boundary condition PeriodicBoundaryCondition[u,\[Theta]==0,TransformationFunction[{{1,0,0,0,0},{0,1,0,0,0},{0,0,1,0,2 \[Pi]},{0,0,0,1,0},{0,0,0,0,1}}]] to the coordinates {{0.5,0.,0.},{0.5,0.,0.0714286},{0.571429,0.,0.0714286},{0.571429,0.,0.},{0.5,0.,0.0357143},{0.535714,0.,0.0714286},{0.571429,0.,0.0357143},{0.535714,0.,0.},{0.5,0.,0.142857},{0.571429,0.,0.142857},<<31>>,{0.535714,0.,0.571429},{0.571429,0.,0.535714},{0.5,0.,0.642857},{0.571429,0.,0.642857},{0.5,0.,0.607143},{0.535714,0.,0.642857},{0.571429,0.,0.607143},{0.5,0.,0.714286},{0.571429,0.,0.714286},<<287>>} did not result in a list of mapped coordinates.

According to the PeriodicBoundaryCondition document which can be found here : https://reference.wolfram.com/language/ref/PeriodicBoundaryCondition.html

There shouldn't be any issue with TranslationTransform in the PBC, as I wrote something similar to the example in "Scope" and then "3D Problems". And yet I have this error.

I did not really see a solution to this particular error whether it was on this site or mathematica.stackexchange so I do not really know what to do.

Could you guys help me? Thank you kindly.

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POSTED BY: Andy M
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2 Replies

I noticed your use of TranslationTransform[{0, 0, 2*Pi, 0}]] is to translate 4 variables, but your equations use 3 spacial variables + time. I believe NDSolve is expecting only 3 spacial variables to be transformed.

The result of using 3 seems to resolve the complaint but another arises: "NDSolve: DirichletCondition can not be present on the target boundary of a PeriodicBoundaryConditon.". I have no time at the moment to understand the problem dynamics so as to rewrite the problem to be solved. I believe Help for PeriodicBoundaryCondition has a similar problems in one and two dimensions to compare with.

Posted 1 month ago

Indeed, it solved the mapping issue. Thank kindly you for your answer.

POSTED BY: Andy M
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