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    An effective method for parameter estimation with pde constraints with multiple right-hand sides

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    Downloads: 1453
    Date
    2012
    Author
    Haber, Eldad
    Chung, Matthias
    Herrmann, Felix
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    Abstract
    Often, parameter estimation problems of parameter-dependent PDEs involve multiple right-hand sides. The computational cost and memory requirements of such problems increase linearly with the number of right-hand sides. For many applications this is the main bottleneck of the computation. In this paper we show that problems with multiple right-hand sides can be reformulated as stochastic programming problems by combining the right-hand sides into a few "simultaneous" sources. This effectively reduces the cost of the forward problem and results in problems that are much cheaper to solve. We discuss two solution methodologies: namely sample average approximation and stochastic approximation. To illustrate the effectiveness of our approach we present two model problems, direct current resistivity and seismic tomography.
    URI
    http://hdl.handle.net/10919/48152
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    • Scholarly Works, Department of Mathematics [269]

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