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by  Robertnsimpson    on 11.04.2013 - 20:28

Dear FMM forum,

I'm a researcher currently working on isogeometric boundary element methods in which we use CAD discretisations (NURBS, T-splines etc. ) to approximate both geometry and the unknown fields. We've got some code running in 3D for potential, elasticity and helmholtz problems. But now we're looking to move forward with acceleration strategies that would allow us to solve large problems quickly, and the FMM seems to be the natural method of choice for this.

Looking around the literature there appears to be quite a few variants of the original work proposed by Greengard and Rokhlin. For someone starting out in this field, it is difficult to comprehend what technologies are considered state-of-the-art and which would be worth considering for our application. Our plan is to implement FMM in a potential context to get a feel for the method. We then have plans to move forward into Helmholtz and electromagnetic problems. I understand that the latter two problems need to be considered in a different way when applying the FMM due to the oscillatory nature of the solution.

So my first question is what represents the latest FMM technology that would be applicable for potential problems and elasticity. And likewise, what is the latest FMM technology for Helmholtz problems? Anything that would speed up my learning process would be greatly appreciated.

Thanks for your time.

Rob Simpson

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