Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient Fast Multipole Accelerated Boundary Elements via Recursive
  Computation of Multipole Expansions of Integrals   In boundary element methods (BEM) in $\mathbb{R}^3$, matrix elements and
right hand sides are typically computed via integration over line, triangle and
tetrahedral volume elements. When the problem size gets large, the resulting
linear systems are often solved iteratively via Krylov methods, with fast
multipole methods (FMM) used to accelerate the matrix vector products needed.
The integrals are often computed via numerical or analytical quadrature. When
FMM acceleration is used, most entries of the matrix never need be computed
explicitly - they are only needed in terms of their contribution to the
multipole expansion coefficients. Furthermore, the two parts of this resulting
algorithm - the integration and the FMM matrix vector product - are both
approximate, and their errors have to be matched to avoid wasteful
computations, or poorly controlled error. We propose a new fast method for
generation of multipole expansion coefficients for the fields produced by the
integration of the single and double layer potentials on surface triangles;
charge distributions over line segments; and regular functions over tetrahedra
in the volume; so that the overall method is well integrated into the FMM, with
controlled error. The method is based on recursive computations of the
multipole moments for $O(1)$ cost per moment with a low asymptotic constant.
The method is developed for the Laplace Green's function in ${\mathbb R}^3$.
The derived recursions are tested both for accuracy and performance.

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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: nlin
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The categories of this paper are: q-alg