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Questions tagged [fast-multipoles]

For questions regarding the Fast Multipole Method (FMM). Useful in modeling forces in N-body problems with only O(N) scaling.

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Matrix Free alternatives in dealii

I am implementing a Fast Multipole Method (FMM) in deal ii. I do not want to store a dense matrix, but lower rank matrices and to use matrix free methods. By now, I store the elements of the low-rank ...
user90189's user avatar
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How to accelerate a convolution (laplace kernel) with FFT

I have the following computation I'm trying to program and accelerate with the FFT. $$ \phi(x) = \sum_{y \in Y} K(x, y) q(x), \> \> \forall x \in X $$ Where $X$ and $Y$ are sets of Cartesian ...
foobar's user avatar
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Clarification regarding 3D FMM translation operators

I am implementing an adaptive 3D FMM with the "basic" $O(p^4)$ translation operators. I am looking for clarification on the multipole-to-multipole (M2M) translation operator. I will explain my ...
Ariel Kellison's user avatar
1 vote
1 answer
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Need for translation theorem in Fast Multipole Method

I have rephrased my original question to be clearer: From my understanding, a multipole expansion is used to approximate the potential from a cluster of points, and can be evaluated at any point ...
Jeremy Adams's user avatar
4 votes
1 answer
258 views

Fast Multipole Method (FMM) 3D (Laplace)

While implementing the Multipole-to-Multipole translation (M2M) with the following equation, $$\phi(P) = \sum_{j=0}^\infty \sum_{k=-j}^j \frac{M_j^k}{r^{j+1}} Y_j^k(\theta,\phi)$$ where, $$M_j^k=\...
foobar's user avatar
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1 vote
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Multipole expansion for magneticfield intesity (magnetization)

I'm using the Barnes Hut method to calculate the magnetic vector potential induced by an applied current. Given as: $\begin{equation} A(r) = \frac{\mu_0}{4\pi} \int_V\frac{\bf{J(r')}}{|r-r'|}dV(r') \...
Noveel's user avatar
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1 answer
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Indexing Nested Loops in C [closed]

I am having trouble indexing correctly the below statement in C inside a function and then returning it as a pointer. The returning part should not be confusing - hopefully - however the indexing is a ...
debronee101's user avatar
4 votes
1 answer
628 views

Fast Multipole Method in 3D

I am writing a FMM (Fast Multipole Method) algorithm in 3D. I generated the mesh and, currently, I am developing the expansion and the three (M2M, M2L, L2L) translation operators using spherical ...
debronee101's user avatar