Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Communication Complexity of the Fast Multipole Method and its Algebraic
  Variants   A combination of hierarchical tree-like data structures and data access
patterns from fast multipole methods and hierarchical low-rank approximation of
linear operators from H-matrix methods appears to form an algorithmic path
forward for efficient implementation of many linear algebraic operations of
scientific computing at the exascale. The combination provides asymptotically
optimal computational and communication complexity and applicability to large
classes of operators that commonly arise in scientific computing applications.
A convergence of the mathematical theories of the fast multipole and H-matrix
methods has been underway for over a decade. We recap this mathematical
unification and describe implementation aspects of a hybrid of these two
compelling hierarchical algorithms on hierarchical distributed-shared memory
architectures, which are likely to be the first to reach the exascale. We
present a new communication complexity estimate for fast multipole methods on
such architectures. We also show how the data structures and access patterns of
H-matrices for low-rank operators map onto those of fast multipole, leading to
an algebraically generalized form of fast multipole that compromises none of
its architecturally ideal properties.

31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
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The categories of this paper are: q-fin