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Adaptive and stochastic algorithms for EIT and DC resistivity problems with piecewise constant
 

Summary: Adaptive and stochastic algorithms for EIT and DC
resistivity problems with piecewise constant
solutions and many measurements
Kees van den Doel and Uri M. Ascher
September 28, 2011
Abstract
This article develops fast numerical methods for the practical solution of
the famous EIT and DC-resistivity problems in the presence of discontinuities
and potentially many experiments or data. Based on a Gauss-Newton (GN)
approach coupled with preconditioned conjugate gradient (PCG) iterations,
we propose two algorithms. One determines adaptively the number of inner
PCG iterations required to stably and effectively carry out each GN iteration.
The other algorithm, useful especially in the presence of many experiments,
employs a randomly chosen subset of experiments at each GN iteration that is
controlled using a cross validation approach. Numerical examples demonstrate
the efficacy of our algorithms.
1 Introduction
The elliptic PDE
((x) u) = q(x), x , (1)
where IRd

  

Source: Ascher, Uri M. - Department of Computer Science, University of British Columbia
van den Doel, Kees - Department of Computer Science, University of British Columbia

 

Collections: Computer Technologies and Information Sciences