Shape Function

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Peng-zhi Pan - One of the best experts on this subject based on the ideXlab platform.

  • a new dual reciprocity hybrid boundary node method based on shepard and taylor interpolation method and chebyshev polynomials
    Engineering Analysis With Boundary Elements, 2016
    Co-Authors: Fei Yan, Xia-ting Feng, Peng-zhi Pan
    Abstract:

    Abstract A new dual reciprocity hybrid boundary node method (DHBNM) is proposed in this paper, in which the Shepard and Taylor interpolation method (STIM) and Chebyshev polynomials interpolation are proposed. Firstly, the Shepard interpolation is used to construct zero level Shape Function, and the high-power Shape Functions are constructed through the Taylor expansion, and through those two methods, no inversion is needed in the whole process of the Shape Function construction. Besides, Chebyshev polynomials are used as the basis Functions for particular solution interpolation instead of the conical Function, radial basis Functions, and the analytical solutions of the basic form of particular solutions related to Chebyshev polynomials for elasticity are obtained, by means of this method, no internal node is needed, and interpolation coefficients can be given as explicit Functions, so no inversion is needed for particular solution interpolation, which costs a large amount of computational expense for the traditional method. Based on those two methods, a new dual reciprocity hybrid boundary node method is developed, compared to the traditional DHBNM, no inversion is needed for both Shape Function construction and particular solution interpolation, which greatly improves the computational efficiency, and no internal node is needed for particular solution interpolation. Numerical examples are given to illustrate that the present method is accurate and effective.

  • a new hybrid boundary node method based on taylor expansion and the shepard interpolation method
    International Journal for Numerical Methods in Engineering, 2015
    Co-Authors: Fei Yan, Xia-ting Feng, Peng-zhi Pan
    Abstract:

    Summary A novel meshless method based on the Shepard and Taylor interpolation method (STIM) and the hybrid boundary node method (HBNM) is proposed. Based on the Shepard interpolation method and Taylor expansion, the STIM is developed to construct the Shape Function of the HBNM. In the STIM, the Shepard Shape Function is used as the basic Function, which is the zero-level Shape Function, and the high-power basic Functions are constructed through Taylor expansion. Four advantages of the STIM are the interpolation property, the arbitrarily high-order consistency, the absence of inversion for the whole process of Shape Function construction, and the low computational expense. These properties are desirable in the implementation of meshless methods. By combining the STIM and the HBNM, a much more effective meshless method is proposed to solve the elasticity problems. Compared with the traditional HBNM, the STIM can improve accuracy because of the use of high-power basic Functions and can also improve the computational efficiency because there is no inversion for the Shape Function construction process. Numerical examples are given to demonstrate the accuracy and efficiency of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.

Julia A Segre - One of the best experts on this subject based on the ideXlab platform.

  • biogeography and individuality Shape Function in the human skin metagenome
    Nature, 2014
    Co-Authors: Allyson L Byrd, Clay Deming, Sean Conlan, Nisc Comparative Sequencing Program, Heidi H Kong, Julia A Segre
    Abstract:

    The varied topography of human skin offers a unique opportunity to study how the body's microenvironments influence the Functional and taxonomic composition of microbial communities. Phylogenetic marker gene-based studies have identified many bacteria and fungi that colonize distinct skin niches. Here metagenomic analyses of diverse body sites in healthy humans demonstrate that local biogeography and strong individuality define the skin microbiome. We developed a relational analysis of bacterial, fungal and viral communities, which showed not only site specificity but also individual signatures. We further identified strain-level variation of dominant species as heterogeneous and multiphyletic. Reference-free analyses captured the uncharacterized metagenome through the development of a multi-kingdom gene catalogue, which was used to uncover genetic signatures of species lacking reference genomes. This work is foundational for human disease studies investigating inter-kingdom interactions, metabolic changes and strain tracking, and defines the dual influence of biogeography and individuality on microbial composition and Function.

  • biogeography and individuality Shape Function in the human skin metagenome
    Nature, 2014
    Co-Authors: Allyso L Yrd, Clay Deming, Nisc Comparative Sequencing Program, Heidi H Kong, Sea Conla, Julia A Segre
    Abstract:

    The varied topography of human skin offers a unique opportunity to study how the body’s microenvironments influence the Functional and taxonomic composition of microbial communities. Phylogenetic marker gene-based studies have identified many bacteria and fungi that colonize distinct skin niches. Here metagenomic analyses of diverse body sites in healthy humans demonstrate that local biogeography and strong individuality define the skin microbiome. We developed a relational analysis of bacterial, fungal and viral communities, which showed not only site specificity but also individual signatures. We further identified strain-level variation of dominant species as heterogeneous and multiphyletic. Reference-free analyses captured the uncharacterized metagenome through the development of a multi-kingdom gene catalogue, which was used to uncover genetic signatures of species lacking reference genomes. This work is foundational for human disease studies investigating inter-kingdom interactions, metabolic changes and strain tracking, and defines the dual influence of biogeography and individuality on microbial composition and Function. Previous work has shown that human skin is home to a rich and varied microbiota; here a metagenomic approach for samples from physiologically diverse body sites illuminates that the skin microbiota, including bacterial, fungal and viral members, is Shaped by the local biogeography and yet marked by strong individuality. Previous work based on taxonomic marker genes has shown that human skin is home to a rich and varied microbiota. Here Julia Segre and colleagues report a large-scale shotgun sequencing study of the healthy human skin microbiome using samples from 18 body sites from 15 healthy individuals. Their metagenomic approach reveals surprising taxonomic and Functional diversity, as well as both site-specificity and individual signatures. Samples from skin have markedly higher viral and fungal representation than reported for other body sites, including the gut. This work has also generated a reference catalogue of nearly 6 million genes that can be used to identify the genetic signatures for skin microbiota species for which no reference genome exists.

Fei Yan - One of the best experts on this subject based on the ideXlab platform.

  • a new dual reciprocity hybrid boundary node method based on shepard and taylor interpolation method and chebyshev polynomials
    Engineering Analysis With Boundary Elements, 2016
    Co-Authors: Fei Yan, Xia-ting Feng, Peng-zhi Pan
    Abstract:

    Abstract A new dual reciprocity hybrid boundary node method (DHBNM) is proposed in this paper, in which the Shepard and Taylor interpolation method (STIM) and Chebyshev polynomials interpolation are proposed. Firstly, the Shepard interpolation is used to construct zero level Shape Function, and the high-power Shape Functions are constructed through the Taylor expansion, and through those two methods, no inversion is needed in the whole process of the Shape Function construction. Besides, Chebyshev polynomials are used as the basis Functions for particular solution interpolation instead of the conical Function, radial basis Functions, and the analytical solutions of the basic form of particular solutions related to Chebyshev polynomials for elasticity are obtained, by means of this method, no internal node is needed, and interpolation coefficients can be given as explicit Functions, so no inversion is needed for particular solution interpolation, which costs a large amount of computational expense for the traditional method. Based on those two methods, a new dual reciprocity hybrid boundary node method is developed, compared to the traditional DHBNM, no inversion is needed for both Shape Function construction and particular solution interpolation, which greatly improves the computational efficiency, and no internal node is needed for particular solution interpolation. Numerical examples are given to illustrate that the present method is accurate and effective.

  • a new hybrid boundary node method based on taylor expansion and the shepard interpolation method
    International Journal for Numerical Methods in Engineering, 2015
    Co-Authors: Fei Yan, Xia-ting Feng, Peng-zhi Pan
    Abstract:

    Summary A novel meshless method based on the Shepard and Taylor interpolation method (STIM) and the hybrid boundary node method (HBNM) is proposed. Based on the Shepard interpolation method and Taylor expansion, the STIM is developed to construct the Shape Function of the HBNM. In the STIM, the Shepard Shape Function is used as the basic Function, which is the zero-level Shape Function, and the high-power basic Functions are constructed through Taylor expansion. Four advantages of the STIM are the interpolation property, the arbitrarily high-order consistency, the absence of inversion for the whole process of Shape Function construction, and the low computational expense. These properties are desirable in the implementation of meshless methods. By combining the STIM and the HBNM, a much more effective meshless method is proposed to solve the elasticity problems. Compared with the traditional HBNM, the STIM can improve accuracy because of the use of high-power basic Functions and can also improve the computational efficiency because there is no inversion for the Shape Function construction process. Numerical examples are given to demonstrate the accuracy and efficiency of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.

Weng Cho Chew - One of the best experts on this subject based on the ideXlab platform.

Xia-ting Feng - One of the best experts on this subject based on the ideXlab platform.

  • a new dual reciprocity hybrid boundary node method based on shepard and taylor interpolation method and chebyshev polynomials
    Engineering Analysis With Boundary Elements, 2016
    Co-Authors: Fei Yan, Xia-ting Feng, Peng-zhi Pan
    Abstract:

    Abstract A new dual reciprocity hybrid boundary node method (DHBNM) is proposed in this paper, in which the Shepard and Taylor interpolation method (STIM) and Chebyshev polynomials interpolation are proposed. Firstly, the Shepard interpolation is used to construct zero level Shape Function, and the high-power Shape Functions are constructed through the Taylor expansion, and through those two methods, no inversion is needed in the whole process of the Shape Function construction. Besides, Chebyshev polynomials are used as the basis Functions for particular solution interpolation instead of the conical Function, radial basis Functions, and the analytical solutions of the basic form of particular solutions related to Chebyshev polynomials for elasticity are obtained, by means of this method, no internal node is needed, and interpolation coefficients can be given as explicit Functions, so no inversion is needed for particular solution interpolation, which costs a large amount of computational expense for the traditional method. Based on those two methods, a new dual reciprocity hybrid boundary node method is developed, compared to the traditional DHBNM, no inversion is needed for both Shape Function construction and particular solution interpolation, which greatly improves the computational efficiency, and no internal node is needed for particular solution interpolation. Numerical examples are given to illustrate that the present method is accurate and effective.

  • a new hybrid boundary node method based on taylor expansion and the shepard interpolation method
    International Journal for Numerical Methods in Engineering, 2015
    Co-Authors: Fei Yan, Xia-ting Feng, Peng-zhi Pan
    Abstract:

    Summary A novel meshless method based on the Shepard and Taylor interpolation method (STIM) and the hybrid boundary node method (HBNM) is proposed. Based on the Shepard interpolation method and Taylor expansion, the STIM is developed to construct the Shape Function of the HBNM. In the STIM, the Shepard Shape Function is used as the basic Function, which is the zero-level Shape Function, and the high-power basic Functions are constructed through Taylor expansion. Four advantages of the STIM are the interpolation property, the arbitrarily high-order consistency, the absence of inversion for the whole process of Shape Function construction, and the low computational expense. These properties are desirable in the implementation of meshless methods. By combining the STIM and the HBNM, a much more effective meshless method is proposed to solve the elasticity problems. Compared with the traditional HBNM, the STIM can improve accuracy because of the use of high-power basic Functions and can also improve the computational efficiency because there is no inversion for the Shape Function construction process. Numerical examples are given to demonstrate the accuracy and efficiency of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.