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Fast Multipole Methods (CTP)


original Fast Multipole Method in 3D


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by  Mengfzcn    on 24.07.2013 - 16:19

Dear Professor Huang,

Currently I am working on the implementation of the original Fast Multipole Method without using the exponential expansion to speed up the code. It is the second method mentioned in the paper by Greengard and Rokhlin. The title of the paper is "a New version of the Fast Multipole Method for the Laplace Equation in three dimensions".

My code gives me a good results when the number of level of the Oct-tree is 3. When I change the number of levels of the Oct-tree to 4, then the error between the FMM solution and the direct solution is very big. So the code is wrong in this case. My question is what can make things wrong?

When I'm debugging the code, I found out when the level is 3, then the Multipole to Multipole translation(M2M) function and the local to local translation (L2L) function are not being called. This is also correct according to the paper. But still I think M2M and L2L function is wrong.

Could you please give me a hint about how to find the problem?

Thanks you very much

Best regards

Fanzhong Meng

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