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Volume 2, Issue 2
The Partition of Unity Method for High-Order Finite Volume Schemes Using Radial Basis Functions Reconstruction

Serena Morigi & Fiorella Sgallari

Numer. Math. Theor. Meth. Appl., 2 (2009), pp. 153-179.

Published online: 2009-02

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  • Abstract

This paper introduces the use of partition of unity method for the development of a high order finite volume discretization scheme on unstructured grids for solving diffusion models based on partial differential equations. The unknown function and its gradient can be accurately reconstructed using high order optimal recovery based on radial basis functions. The methodology proposed is applied to the noise removal problem in functional surfaces and images. Numerical results demonstrate the effectiveness of the new numerical approach and provide experimental order of convergence.

  • Keywords

Finite volume discretization, radial basis functions, optimal recovery, regularization, image and surface denoising.

  • AMS Subject Headings

65N99, 68U10, 65F22

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-2-153, author = {Serena Morigi and Fiorella Sgallari}, title = {The Partition of Unity Method for High-Order Finite Volume Schemes Using Radial Basis Functions Reconstruction}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2009}, volume = {2}, number = {2}, pages = {153--179}, abstract = {

This paper introduces the use of partition of unity method for the development of a high order finite volume discretization scheme on unstructured grids for solving diffusion models based on partial differential equations. The unknown function and its gradient can be accurately reconstructed using high order optimal recovery based on radial basis functions. The methodology proposed is applied to the noise removal problem in functional surfaces and images. Numerical results demonstrate the effectiveness of the new numerical approach and provide experimental order of convergence.

}, issn = {2079-7338}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/nmtma/6020.html} }
TY - JOUR T1 - The Partition of Unity Method for High-Order Finite Volume Schemes Using Radial Basis Functions Reconstruction AU - Serena Morigi & Fiorella Sgallari JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 153 EP - 179 PY - 2009 DA - 2009/02 SN - 2 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/nmtma/6020.html KW - Finite volume discretization, radial basis functions, optimal recovery, regularization, image and surface denoising. AB -

This paper introduces the use of partition of unity method for the development of a high order finite volume discretization scheme on unstructured grids for solving diffusion models based on partial differential equations. The unknown function and its gradient can be accurately reconstructed using high order optimal recovery based on radial basis functions. The methodology proposed is applied to the noise removal problem in functional surfaces and images. Numerical results demonstrate the effectiveness of the new numerical approach and provide experimental order of convergence.

Serena Morigi and Fiorella Sgallari. (2009). The Partition of Unity Method for High-Order Finite Volume Schemes Using Radial Basis Functions Reconstruction. Numerical Mathematics: Theory, Methods and Applications. 2 (2). 153-179. doi:
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