Daubechies Wavelet

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Zhangzhi Cen - One of the best experts on this subject based on the ideXlab platform.

  • A meshless method based on Daubechies Wavelet for 2-D elastoplaticity problems
    2020
    Co-Authors: Yanan Liu, Yinghua Liu, Zhangzhi Cen
    Abstract:

    Summary In this paper, a Daubechies(DB) Wavelet-based meshless method is proposed to analyze 2-D elastoplasticity problems. Using DB Wavelet scaling functions and Wavelet functions as basis functions to approximate the unknown field functions, there is no need to construct the shape functions costly as done in FEM and conventional meshless methods. Incremental formulations are established for solution of 2-D elastoplasticity problems. In addition, the property of DB Wavelet is used to make the method concise in formulations, flexible in applications and easy to realize. Due to the lack of Kroneker delta properties in scaling functions and Wavelet functions, the penalty method is used to impose the essential boundary condition in this work. Numerical examples of two dimensional elastoplasticity problems illustrate that this method is very efficient and stable

  • multi scale Daubechies Wavelet based method for 2 d elastic problems
    Finite Elements in Analysis and Design, 2011
    Co-Authors: Yanan Liu, Yinghua Liu, Zhangzhi Cen
    Abstract:

    In this paper, the multi-scale Daubechies (DB) Wavelet method is used for solution of 2-D plain elastic problems. Unlike the single scale Wavelet method, the DB Wavelet functions are also used in function approximation for solving problems with local complicated deformation in the multi-scale method. Using the ideas of some meshless methods and Galerkin methods, the solution formulations for two dimensional elastic problems in multi-scale approach are established. In order to treat general boundaries and improve the efficiency and accuracy of solution, a method for evaluation of integrals in general region is proposed. Numerical examples of 2-D elastic problems illustrate that this multi-scale Daubechies Wavelet method is effective and stable.

  • a Daubechies Wavelet based method for elastic problems
    Engineering Analysis With Boundary Elements, 2010
    Co-Authors: Yanan Liu, Feifei Qin, Yinhua Liu, Zhangzhi Cen
    Abstract:

    Abstact In this paper, Daubechies (DB) Wavelet is used for solution of 2-D plain elastic problems. Because the DB Wavelet scaling functions are directly used in function approximation, neither nodes nor meshes are needed in this method. Using the ideas of some meshless methods, the solution formulations for two-dimensional elastic problems are established. In order to treat general boundaries and improve the efficiency and accuracy in solution, a method for evaluation of integrals is proposed. Numerical examples of 2-D elastic problems illustrate that this method is effective and stable and it is promising to solve more complicated problems in solid mechanics.

  • the 2d large deformation analysis using Daubechies Wavelet
    Computational Mechanics, 2010
    Co-Authors: Yanan Liu, Yinghua Liu, Fei Qin, Zhangzhi Cen
    Abstract:

    In this paper, Daubechies (DB) Wavelet is used for solution of 2D large deformation problems. Because the DB Wavelet scaling functions are directly used as basis function, no meshes are needed in function approximation. Using the DB Wavelet, the solution formulations based on total Lagrangian approach for two-dimensional large deformation problems are established. Due to the lack of Kroneker delta properties in Wavelet scaling functions, Lagrange multipliers are used for imposition of boundary condition. Numerical examples of 2D large deformation problems illustrate that this method is effective and stable.

  • Daubechies Wavelet meshless method for 2 d elastic problems
    Tsinghua Science & Technology, 2008
    Co-Authors: Yanan Liu, Yinghua Liu, Zhangzhi Cen
    Abstract:

    Abstract This paper introduces a meshless method based on Daubechies (DB) Wavelets for 2-D elastic problems. The scaling and Wavelet functions of the DB Wavelet are used as basis functions to approximate the unknown field functions, so there is no need to construct costly shape functions as in the finite element method (FEM) and other meshless methods. In addition, the properties of the DB Wavelets facilitate implementation of the method. The new method is used to analyze the elastic problem of a plain plate with a circle hole, and the numerical results agree well with the FEM. This method is effective and can be extended to solve complicated two or three dimensional problems.

Yanan Liu - One of the best experts on this subject based on the ideXlab platform.

  • A meshless method based on Daubechies Wavelet for 2-D elastoplaticity problems
    2020
    Co-Authors: Yanan Liu, Yinghua Liu, Zhangzhi Cen
    Abstract:

    Summary In this paper, a Daubechies(DB) Wavelet-based meshless method is proposed to analyze 2-D elastoplasticity problems. Using DB Wavelet scaling functions and Wavelet functions as basis functions to approximate the unknown field functions, there is no need to construct the shape functions costly as done in FEM and conventional meshless methods. Incremental formulations are established for solution of 2-D elastoplasticity problems. In addition, the property of DB Wavelet is used to make the method concise in formulations, flexible in applications and easy to realize. Due to the lack of Kroneker delta properties in scaling functions and Wavelet functions, the penalty method is used to impose the essential boundary condition in this work. Numerical examples of two dimensional elastoplasticity problems illustrate that this method is very efficient and stable

  • multi scale Daubechies Wavelet based method for 2 d elastic problems
    Finite Elements in Analysis and Design, 2011
    Co-Authors: Yanan Liu, Yinghua Liu, Zhangzhi Cen
    Abstract:

    In this paper, the multi-scale Daubechies (DB) Wavelet method is used for solution of 2-D plain elastic problems. Unlike the single scale Wavelet method, the DB Wavelet functions are also used in function approximation for solving problems with local complicated deformation in the multi-scale method. Using the ideas of some meshless methods and Galerkin methods, the solution formulations for two dimensional elastic problems in multi-scale approach are established. In order to treat general boundaries and improve the efficiency and accuracy of solution, a method for evaluation of integrals in general region is proposed. Numerical examples of 2-D elastic problems illustrate that this multi-scale Daubechies Wavelet method is effective and stable.

  • a Daubechies Wavelet based method for elastic problems
    Engineering Analysis With Boundary Elements, 2010
    Co-Authors: Yanan Liu, Feifei Qin, Yinhua Liu, Zhangzhi Cen
    Abstract:

    Abstact In this paper, Daubechies (DB) Wavelet is used for solution of 2-D plain elastic problems. Because the DB Wavelet scaling functions are directly used in function approximation, neither nodes nor meshes are needed in this method. Using the ideas of some meshless methods, the solution formulations for two-dimensional elastic problems are established. In order to treat general boundaries and improve the efficiency and accuracy in solution, a method for evaluation of integrals is proposed. Numerical examples of 2-D elastic problems illustrate that this method is effective and stable and it is promising to solve more complicated problems in solid mechanics.

  • the 2d large deformation analysis using Daubechies Wavelet
    Computational Mechanics, 2010
    Co-Authors: Yanan Liu, Yinghua Liu, Fei Qin, Zhangzhi Cen
    Abstract:

    In this paper, Daubechies (DB) Wavelet is used for solution of 2D large deformation problems. Because the DB Wavelet scaling functions are directly used as basis function, no meshes are needed in function approximation. Using the DB Wavelet, the solution formulations based on total Lagrangian approach for two-dimensional large deformation problems are established. Due to the lack of Kroneker delta properties in Wavelet scaling functions, Lagrange multipliers are used for imposition of boundary condition. Numerical examples of 2D large deformation problems illustrate that this method is effective and stable.

  • Daubechies Wavelet meshless method for 2 d elastic problems
    Tsinghua Science & Technology, 2008
    Co-Authors: Yanan Liu, Yinghua Liu, Zhangzhi Cen
    Abstract:

    Abstract This paper introduces a meshless method based on Daubechies (DB) Wavelets for 2-D elastic problems. The scaling and Wavelet functions of the DB Wavelet are used as basis functions to approximate the unknown field functions, so there is no need to construct costly shape functions as in the finite element method (FEM) and other meshless methods. In addition, the properties of the DB Wavelets facilitate implementation of the method. The new method is used to analyze the elastic problem of a plain plate with a circle hole, and the numerical results agree well with the FEM. This method is effective and can be extended to solve complicated two or three dimensional problems.

Yinghua Liu - One of the best experts on this subject based on the ideXlab platform.

  • A meshless method based on Daubechies Wavelet for 2-D elastoplaticity problems
    2020
    Co-Authors: Yanan Liu, Yinghua Liu, Zhangzhi Cen
    Abstract:

    Summary In this paper, a Daubechies(DB) Wavelet-based meshless method is proposed to analyze 2-D elastoplasticity problems. Using DB Wavelet scaling functions and Wavelet functions as basis functions to approximate the unknown field functions, there is no need to construct the shape functions costly as done in FEM and conventional meshless methods. Incremental formulations are established for solution of 2-D elastoplasticity problems. In addition, the property of DB Wavelet is used to make the method concise in formulations, flexible in applications and easy to realize. Due to the lack of Kroneker delta properties in scaling functions and Wavelet functions, the penalty method is used to impose the essential boundary condition in this work. Numerical examples of two dimensional elastoplasticity problems illustrate that this method is very efficient and stable

  • multi scale Daubechies Wavelet based method for 2 d elastic problems
    Finite Elements in Analysis and Design, 2011
    Co-Authors: Yanan Liu, Yinghua Liu, Zhangzhi Cen
    Abstract:

    In this paper, the multi-scale Daubechies (DB) Wavelet method is used for solution of 2-D plain elastic problems. Unlike the single scale Wavelet method, the DB Wavelet functions are also used in function approximation for solving problems with local complicated deformation in the multi-scale method. Using the ideas of some meshless methods and Galerkin methods, the solution formulations for two dimensional elastic problems in multi-scale approach are established. In order to treat general boundaries and improve the efficiency and accuracy of solution, a method for evaluation of integrals in general region is proposed. Numerical examples of 2-D elastic problems illustrate that this multi-scale Daubechies Wavelet method is effective and stable.

  • the 2d large deformation analysis using Daubechies Wavelet
    Computational Mechanics, 2010
    Co-Authors: Yanan Liu, Yinghua Liu, Fei Qin, Zhangzhi Cen
    Abstract:

    In this paper, Daubechies (DB) Wavelet is used for solution of 2D large deformation problems. Because the DB Wavelet scaling functions are directly used as basis function, no meshes are needed in function approximation. Using the DB Wavelet, the solution formulations based on total Lagrangian approach for two-dimensional large deformation problems are established. Due to the lack of Kroneker delta properties in Wavelet scaling functions, Lagrange multipliers are used for imposition of boundary condition. Numerical examples of 2D large deformation problems illustrate that this method is effective and stable.

  • Daubechies Wavelet meshless method for 2 d elastic problems
    Tsinghua Science & Technology, 2008
    Co-Authors: Yanan Liu, Yinghua Liu, Zhangzhi Cen
    Abstract:

    Abstract This paper introduces a meshless method based on Daubechies (DB) Wavelets for 2-D elastic problems. The scaling and Wavelet functions of the DB Wavelet are used as basis functions to approximate the unknown field functions, so there is no need to construct costly shape functions as in the finite element method (FEM) and other meshless methods. In addition, the properties of the DB Wavelets facilitate implementation of the method. The new method is used to analyze the elastic problem of a plain plate with a circle hole, and the numerical results agree well with the FEM. This method is effective and can be extended to solve complicated two or three dimensional problems.

Khan A. Wahid - One of the best experts on this subject based on the ideXlab platform.

  • area and power efficient design of Daubechies Wavelet transforms using folded aiq mapping
    IEEE Transactions on Circuits and Systems Ii-express Briefs, 2010
    Co-Authors: Ashraful Islam, Khan A. Wahid
    Abstract:

    In this brief, we present an efficient design of a shared architecture to compute two 8-point Daubechies Wavelet transforms. The architecture is based on a two-level folded mapping technique that is developed on the factorization and decomposition of transform matrices exploiting the symmetrical structure. The chip occupies a 2.08-mm2 silicon area, runs at 100 MHz, and consumes 4.51 mW of power in 0.18-m CMOS technology.

  • VLSI ARCHITECTURES OF Daubechies Wavelet TRANSFORMS USING ALGEBRAIC INTEGERS
    Journal of Circuits Systems and Computers, 2004
    Co-Authors: Khan A. Wahid, Vassil S. Dimitrov, Graham A. Jullien
    Abstract:

    Two-Dimensional Wavelet Transforms have proven to be highly effective tools for image analysis. In this paper, we present a VLSI implementation of four- and six-coefficient Daubechies Wavelet Transforms using an algebraic integer encoding representation for the coefficients. The Daubechies filters (DAUB4 and DAUB6) provide excellent spatial and spectral locality, properties which make it useful in image compression. In our algorithm, the algebraic integer representation of the Wavelet coefficients provides error-free calculations until the final reconstruction step. This also makes the VLSI architecture simple, multiplication-free and inherently parallel. Compared to other DWT algorithms found in the literature, such as embedded zero-tree, recursive or semi-recursive, linear systolic arrays and conventional fixed-point binary architectures, it has reduced hardware cost, lower power dissipation and optimized data-bus utilization. The architecture is also cascadable for computation of one- or multi-dimensional Daubechies Discrete Wavelet Transforms.

  • an analysis of Daubechies discrete Wavelet transform based on algebraic integer encoding scheme
    Third International Workshop on Digital and Computational Video 2002. DCV 2002. Proceedings., 2002
    Co-Authors: Khan A. Wahid, V S Dimitrov, G A Jullien, W Badawy
    Abstract:

    A new and novel encoding scheme of Daubechies Wavelet coefficients for implementing discrete Wavelet transform based on algebraic integer is proposed. This encoding technique eliminates the requirements to approximate the transformation matrix elements. Instead of approximating the matrix coefficients, we are able to obtain the exact representations for them. As a result, we achieve error-free calculations up to the final reconstruction step where we can choose an approximate substitution precision based on hardware/accuracy trade-off. A comparison between Daubechies 4 and 6 coefficients is also performed. The last part demonstrates that the new encoding technique offers better performance compared to the classical binary (fixed-point binary) design and it is also very well suited for high-speed VLSI implementation.

  • an algebraic integer based encoding scheme for implementing Daubechies discrete Wavelet transforms
    Asilomar Conference on Signals Systems and Computers, 2002
    Co-Authors: Khan A. Wahid, V S Dimitrov, G A Jullien, W Badawy
    Abstract:

    A novel approach for implementing a discrete Wavelet transform (DWT), based on algebraic integer encoding of Daubechies Wavelet coefficients is proposed. These encoding techniques eliminate the requirement to approximate the matrix element; rather they use algebraic 'placeholders' for them. Using these mapping techniques, we were able to obtain error-free calculations up to the final reconstruction step, where we can choose an appropriate approximate substitution precision based on hardware/accuracy trade-offs. This paper also demonstrate the new encoding technique offers better performance compared to classical fixed-point binary designs and that it is well suited for high-speed VLSI implementation.

  • on algebraic integer encoding scheme
    2002
    Co-Authors: Khan A. Wahid, V S Dimitrov, G A Jullien, W Badawy
    Abstract:

    In this paper a new and novel encoding scheme of Daubechies Wavelet coeflcients for implementing Discrete Wavelet Transform based on algebraic integer is proposed. This encoding technique eliminates the requirements to approximate the transformation matrix elements. Instead of approximating the matrix coefficients, we are able to obtain the exact representations for them. As a result, we achieve error-free calculations up to the final reconstruction step where we can choose an approximate substitution precision based on hardware/accuracy trade-ofl A comparison between Daubechies 4 and 6 coef- ficients is also performed. The last part of this paper demonstrates that the new encod- ing technique oflers better performance compared to the classical binary Cfured-point binary) design and it is also very well suited for high-speed VLSI implementation.

Victoria Vampa - One of the best experts on this subject based on the ideXlab platform.

  • Daubechies Wavelet beam and plate finite elements
    Finite Elements in Analysis and Design, 2009
    Co-Authors: Lilliam Alvarez Díaz, María Teresa Martín, Victoria Vampa
    Abstract:

    In the last few years, Wavelets analysis application has called the attention of researchers in a wide variety of practical problems, particularly for the numerical solutions of partial differential equations using different methods such as finite differences, semi-discrete techniques or finite element method. In some mathematical models in mechanics of continuous media, the solutions may have local singularities and it is necessary to approximate with interpolatory functions having good properties or capacities to efficiently localize those non-regular zones. Due to their excellent properties of orthogonality and minimum compact support, Daubechies Wavelets can be useful and convenient, providing guaranty of convergence and accuracy of the approximation in a wide variety of situations. In this work, we show the feasibility of a hybrid scheme using Daubechies Wavelet functions and the finite element method to obtain numerical solutions of some problems in structural mechanics. Following this scheme, the formulations of an Euler-Bernoulli beam element and a Mindlin-Reisner plate element are derived. The accuracy of this approach is investigated in some numerical test cases.

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