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Tensor-based methods for numerical homogenization from high-resolution images
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DOI：10.1016/j.cma.2012.10.012.png)
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摘要
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We present a complete numerical strategy based on tensor approximation techniques for the solution of numerical homogenization problems with geometrical data coming from high resolution images. We first introduce specific numerical treatments for the translation of image-based homogenization problems into a tensor framework. It includes the tensor approximations in suitable tensor formats of fields of material properties or indicator functions of multiple material phases recovered from segmented images. We then introduce some variants of proper generalized decomposition (PGD) methods for the construction of tensor decompositions in different tensor formats of the solution of boundary value problems. A new definition of PGD is introduced which allows the progressive construction of a Tucker decomposition of the solution. This tensor format is well adapted to the present application and improves convergence properties of tensor decompositions. Finally, we use a dual-based error estimator on quantities of interest which was recently introduced in the context of PGD. We exhibit its specificities when it is used for assessing the error on the homogenized properties of the heterogeneous material. We also provide a complete goal-oriented adaptive strategy for the progressive construction of tensor decompositions (of primal and dual solutions) yielding to predictions of homogenized quantities with a prescribed accuracy. (C) 2012 Elsevier B.V. All rights reserved.
Keyword:
Image-based computing
Numerical homogenization
Tensor methods
Proper generalized decomposition (PGD)
Model reduction
Goal-oriented error estimation
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7.3
论文数:
1.3W
被引数:
5.6W
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