Hierarchy-Direction Selective Approach for Locally Adaptive Sparse Grids

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We consider the problem of multidimensional adaptive hierarchical interpolation. We use sparse grids points and functions that are induced from a one dimensional hierarchical rule via tensor products. The classical locally adaptive sparse grid algorithm uses an isotropic refinement from the coarser to the denser levels of the hierarchy. However, the multidimensional hierarchy provides a more complex structure that allows for various anisotropic and hierarchy selective refinement techniques. We consider the more advanced refinement techniques and apply them to a number of simple test functions chosen to demonstrate the various advantages and disadvantages of each method. While there is no ... continued below

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Stoyanov, Miroslav K September 1, 2013.

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We consider the problem of multidimensional adaptive hierarchical interpolation. We use sparse grids points and functions that are induced from a one dimensional hierarchical rule via tensor products. The classical locally adaptive sparse grid algorithm uses an isotropic refinement from the coarser to the denser levels of the hierarchy. However, the multidimensional hierarchy provides a more complex structure that allows for various anisotropic and hierarchy selective refinement techniques. We consider the more advanced refinement techniques and apply them to a number of simple test functions chosen to demonstrate the various advantages and disadvantages of each method. While there is no refinement scheme that is optimal for all functions, the fully adaptive family-direction-selective technique is usually more stable and requires fewer samples.

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  • Report No.: ORNL/TM-2013/384
  • Grant Number: DE-AC05-00OR22725
  • DOI: 10.2172/1097490 | External Link
  • Office of Scientific & Technical Information Report Number: 1097490
  • Archival Resource Key: ark:/67531/metadc863854

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  • September 1, 2013

Added to The UNT Digital Library

  • Sept. 16, 2016, 12:32 a.m.

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  • Oct. 31, 2016, 4:28 p.m.

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Stoyanov, Miroslav K. Hierarchy-Direction Selective Approach for Locally Adaptive Sparse Grids, report, September 1, 2013; [Tennessee]. (digital.library.unt.edu/ark:/67531/metadc863854/: accessed December 13, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.