Missing BEM potentials

[CarolinePascal]

Hi everyone !

I am opening an issue concerning the BEM plugin, and especially the BemPotential class implementation. It appears that several BEM potentials , namely the transpose double layer potential and hypersingular potential, were not implemented, despite being mentioned in the comments in plugin/mpi/bem.hpp :

Would it be possible to add these potentials in an upcoming release ?

Thank you in advance for your help a consideration !

Caroline.

[PierreMarchand20]

Hello Caroline :-)

I think there is a slight confusion about the terminology:

• there are two potentials, the single and double layers potentials, convolutions with the green function and its normal derivative respectively
• there are four operators which are the Dirichlet and Neumann traces of the two potentials.

Note that potentials take traces and return functions in the volume, while operators take traces and return traces.

In particular, you can use the transpose double layer operator and the hypersingular operator as follows:

BemKernel TransposedDoubleLayerOperator("TDL",k=k);
BemKernel HyperSingularOperator("HS",k=k);

I guess the comment in the code you showed is a copy paste from the part defining the operators. You can checkout these examples for more details:

• https://github.com/FreeFem/FreeFem-sources/blob/master/examples/mpi/Helmholtz_circle_Dirichlet.edp
• https://github.com/FreeFem/FreeFem-sources/blob/master/examples/mpi/Helmholtz_circle_Neumann.edp