The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Hong Wang - One of the best experts on this subject based on the ideXlab platform.
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a preconditioned fast parareal finite Difference Method for space time fractional partial differential equation
Journal of Scientific Computing, 2019Co-Authors: Hong WangAbstract:We develop a fast parareal finite Difference Method for space-time fractional partial differential equation. The Method properly handles the heavy tail behavior in the numerical discretization, while retaining the numerical advantages of conventional parareal algorithm. At each time step, we explore the structure of the stiffness matrix to develop a matrix-free preconditioned fast Krylov subspace iterative solver for the finite Difference Method without resorting to any lossy compression. Consequently, the Method has significantly reduced computational complexity and memory requirement. Numerical experiments show the strong potential of the Method.
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a fast finite Difference Method for three dimensional time dependent space fractional diffusion equations with fractional derivative boundary conditions
Journal of Scientific Computing, 2018Co-Authors: Meng Zhao, Hong Wang, Aijie ChengAbstract:We develop a fast finite Difference Method for time-dependent variable-coefficient space-fractional diffusion equations with fractional derivative boundary-value conditions in three dimensional spaces. Fractional differential operators appear in both of the equation and the boundary conditions. Because of the nonlocal nature of the fractional Neumann boundary operator, the internal and boundary nodes are strongly coupled together in the coupled linear system. The stability and convergence of the finite Difference Method are discussed. For the implementation, the development of the fast Method is based upon a careful analysis and delicate decomposition of the structure of the coefficient matrix. The fast Method has approximately linear computational complexity per Krylov subspace iteration and an optimal-order memory requirement. Numerical results are presented to show the utility of the Method.
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an o n log2n alternating direction finite Difference Method for two dimensional fractional diffusion equations
Journal of Computational Physics, 2011Co-Authors: Hong Wang, Kaixin WangAbstract:Fractional diffusion equations model phenomena exhibiting anomalous diffusion that cannot be modeled accurately by the second-order diffusion equations. Because of the nonlocal property of fractional differential operators, the numerical Methods for fractional diffusion equations often generate dense or even full coefficient matrices. Consequently, the numerical solution of these Methods often require computational work of O(N^3) per time step and memory of O(N^2) for where N is the number of grid points. In this paper we develop a fast alternating-direction implicit finite Difference Method for space-fractional diffusion equations in two space dimensions. The Method only requires computational work of O(N log^2N) per time step and memory of O(N), while retaining the same accuracy and approximation property as the regular finite Difference Method with Gaussian elimination. Our preliminary numerical example runs for two dimensional model problem of intermediate size seem to indicate the observations: To achieve the same accuracy, the new Method has a significant reduction of the CPU time from more than 2 months and 1 week consumed by a traditional finite Difference Method to 1.5h, using less than one thousandth of memory the standard Method does. This demonstrates the utility of the Method.
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a direct o nlog2n finite Difference Method for fractional diffusion equations
Journal of Computational Physics, 2010Co-Authors: Hong Wang, Kaixin Wang, Treena SircarAbstract:Fractional diffusion equations model phenomena exhibiting anomalous diffusion that can not be modeled accurately by the second-order diffusion equations. Because of the nonlocal property of fractional differential operators, the numerical Methods have full coefficient matrices which require storage of O(N^2) and computational cost of O(N^3) where N is the number of grid points. In this paper we develop a fast finite Difference Method for fractional diffusion equations, which only requires storage of O(N) and computational cost of O(Nlog^2N) while retaining the same accuracy and approximation property as the regular finite Difference Method. Numerical experiments are presented to show the utility of the Method.
Mehdi Dehghan - One of the best experts on this subject based on the ideXlab platform.
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a compact split step finite Difference Method for solving the nonlinear schrodinger equations with constant and variable coefficients
Computer Physics Communications, 2010Co-Authors: Mehdi Dehghan, Ameneh TaleeiAbstract:Abstract We propose a compact split-step finite Difference Method to solve the nonlinear Schrodinger equations with constant and variable coefficients. This Method improves the accuracy of split-step finite Difference Method by introducing a compact scheme for discretization of space variable while this improvement does not reduce the stability range and does not increase the computational cost. This Method also preserves some conservation laws. Numerical tests are presented to confirm the theoretical results for the new numerical Method by using the cubic nonlinear Schrodinger equation with constant and variable coefficients and Gross–Pitaevskii equation.
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chebyshev finite Difference Method for fredholm integro differential equation
International Journal of Computer Mathematics, 2008Co-Authors: Mehdi Dehghan, Abbas SaadatmandiAbstract:A Chebyshev finite Difference Method has been proposed in order to solve linear and nonlinear second-order Fredholm integro-differential equations. The approach consists of reducing the problem to a set of algebraic equations. This Method can be regarded as a nonuniform finite Difference scheme. Some numerical results are also given to demonstrate the validity and applicability of the presented technique.
Ameneh Taleei - One of the best experts on this subject based on the ideXlab platform.
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a compact split step finite Difference Method for solving the nonlinear schrodinger equations with constant and variable coefficients
Computer Physics Communications, 2010Co-Authors: Mehdi Dehghan, Ameneh TaleeiAbstract:Abstract We propose a compact split-step finite Difference Method to solve the nonlinear Schrodinger equations with constant and variable coefficients. This Method improves the accuracy of split-step finite Difference Method by introducing a compact scheme for discretization of space variable while this improvement does not reduce the stability range and does not increase the computational cost. This Method also preserves some conservation laws. Numerical tests are presented to confirm the theoretical results for the new numerical Method by using the cubic nonlinear Schrodinger equation with constant and variable coefficients and Gross–Pitaevskii equation.
B Wu - One of the best experts on this subject based on the ideXlab platform.
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stability of central Difference Method for dynamic real time substructure testing
Earthquake Engineering & Structural Dynamics, 2009Co-Authors: B Wu, L. Deng, X. YangAbstract:This paper studies the stability of the central Difference Method (CDM) for real-time substructure test considering specimen mass. Because the standard CDM is implicit in terms of acceleration, to avoid iteration, an explicit acceleration formulation is assumed for its implementation in real-time dynamic substructure testing. The analytical work shows that the stability of the algorithm decreases with increasing specimen mass if the experimental substructure is a pure inertia specimen. The algorithm becomes unstable however small the time integration interval is, when the mass of specimen equal or greater than that of its numerical counterpart. For the case of dynamic specimen, the algorithm is unstable when there is no damping in the whole test structure; a damping will make the algorithm stable conditionally. Part of the analytical results is validated through an actual test. Copyright © 2009 John Wiley & Sons, Ltd.
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stability and accuracy analysis of the central Difference Method for real time substructure testing
Earthquake Engineering & Structural Dynamics, 2005Co-Authors: B Wu, Jinping Ou, S. TianAbstract:The central Difference Method (CDM) that is explicit for pseudo-dynamic testing is also believed to be explicit for real-time substructure testing (RST). However, to obtain the correct velocity dependent restoring force of the physical substructure being tested, the target velocity is required to be calculated as well as the displacement. The standard CDM provides only explicit target displacement but not explicit target velocity. This paper investigates the required modification of the standard central Difference Method when applied to RST and analyzes the stability and accuracy of the modified CDM for RST. Copyright © 2005 John Wiley & Sons, Ltd.
Kaixin Wang - One of the best experts on this subject based on the ideXlab platform.
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an o n log2n alternating direction finite Difference Method for two dimensional fractional diffusion equations
Journal of Computational Physics, 2011Co-Authors: Hong Wang, Kaixin WangAbstract:Fractional diffusion equations model phenomena exhibiting anomalous diffusion that cannot be modeled accurately by the second-order diffusion equations. Because of the nonlocal property of fractional differential operators, the numerical Methods for fractional diffusion equations often generate dense or even full coefficient matrices. Consequently, the numerical solution of these Methods often require computational work of O(N^3) per time step and memory of O(N^2) for where N is the number of grid points. In this paper we develop a fast alternating-direction implicit finite Difference Method for space-fractional diffusion equations in two space dimensions. The Method only requires computational work of O(N log^2N) per time step and memory of O(N), while retaining the same accuracy and approximation property as the regular finite Difference Method with Gaussian elimination. Our preliminary numerical example runs for two dimensional model problem of intermediate size seem to indicate the observations: To achieve the same accuracy, the new Method has a significant reduction of the CPU time from more than 2 months and 1 week consumed by a traditional finite Difference Method to 1.5h, using less than one thousandth of memory the standard Method does. This demonstrates the utility of the Method.
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a direct o nlog2n finite Difference Method for fractional diffusion equations
Journal of Computational Physics, 2010Co-Authors: Hong Wang, Kaixin Wang, Treena SircarAbstract:Fractional diffusion equations model phenomena exhibiting anomalous diffusion that can not be modeled accurately by the second-order diffusion equations. Because of the nonlocal property of fractional differential operators, the numerical Methods have full coefficient matrices which require storage of O(N^2) and computational cost of O(N^3) where N is the number of grid points. In this paper we develop a fast finite Difference Method for fractional diffusion equations, which only requires storage of O(N) and computational cost of O(Nlog^2N) while retaining the same accuracy and approximation property as the regular finite Difference Method. Numerical experiments are presented to show the utility of the Method.
