Measure transformation and efficient quadrature in reduced-dimensional stochastic modeling of coupled problems

in International Journal for Numerical Methods in Engineering (2012), 92

Coupled problems with various combinations of multiple physics, scales, and domains are found in numerous areas of science and engineering. A key challenge in the formulation and implementation of ... [more ▼]

Coupled problems with various combinations of multiple physics, scales, and domains are found in numerous areas of science and engineering. A key challenge in the formulation and implementation of corresponding coupled numerical models is to facilitate the communication of information across physics, scale, and domain interfaces, as well as between the iterations of solvers used for response computations. In a probabilistic context, any information that is to be communicated between subproblems or iterations should be characterized by an appropriate probabilistic representation. Although the number of sources of uncertainty can be expected to be large in most coupled problems, our contention is that exchanged probabilistic information often resides in a considerably lower-dimensional space than the sources themselves. In this work, we thus propose to use a dimension reduction technique for obtaining the representation of the exchanged information, and we propose a measure transformation technique that allows subproblem implementations to exploit this dimension reduction to achieve computational gains. The effectiveness of the proposed dimension reduction and measure transformation methodology is demonstrated through a multiphysics problem relevant to nuclear engineering. [less ▲]

Dimension Reduction and Measure Transformation in Stochastic Multiphysics Modeling

Conference (2012, April 02)

We present a computational framework based on stochastic expansion methods for the efficient propagation of uncertainties through multiphysics models. The framework leverages an adaptation of the Karhunen ... [more ▼]

We present a computational framework based on stochastic expansion methods for the efficient propagation of uncertainties through multiphysics models. The framework leverages an adaptation of the Karhunen-Loeve decomposition to extract a low-dimensional representation of information passed from component to component in a stochastic coupled model. After a measure transformation, the reduced-dimensional interface thus created enables a more efficient solution in a reduced-dimensional space. We demonstrate the proposed approach on an illustration problem from nuclear engineering [less ▲]

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