ANZIAM J.
48 (2006), 11-22
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Parallelisation of sparse grids for large scale data analysis
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Jochen Garcke
Centre for Mathematics and its Applications
Mathematical Sciences Institute
Australian National University
Canberra ACT 0200
Australia
jochen.garcke@anu.edu.au
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Markus Hegland
Centre for Mathematics and its Applications
Mathematical Sciences Institute
Australian National University
Canberra ACT 0200
Australia
markus.hegland@anu.edu.au
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Ole Nielsen
Centre for Mathematics and its Applications
Mathematical Sciences Institute
Australian National University
Canberra ACT 0200
Australia
ole.nielsen@ga.gov.au
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Abstract
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Sparse grids are the basis for efficient high
dimensional approximation and have recently been
applied successfully to predictive modelling.
They are spanned by a collection of simpler
function spaces represented by regular grids.
The sparse grid combination technique prescribes
how approximations on a collection of anisotropic
grids can be combined to approximate high
dimensional functions.
In this paper we study
the parallelisation of fitting data onto a sparse
grid. The computation can be done entirely by
fitting partial models on a collection of regular
grids. This allows parallelism over the
collection of grids. In addition, each of the
partial grid fits can be parallelised as well,
both in the assembly phase, where parallelism is
done over the data, and in the solution stage
using traditional parallel solvers for the
resulting PDEs. Using a simple timing model we
confirm that the most effective methods are
obtained when both types of parallelism are used.
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Australian Mathematical Publishing Association Inc.
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©
Australian MS
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