The Experts below are selected from a list of 228 Experts worldwide ranked by ideXlab platform
Xinlong Feng - One of the best experts on this subject based on the ideXlab platform.
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Stability and Error Estimate of the Operator Splitting Method for the Phase Field Crystal Equation
Journal of Scientific Computing, 2021Co-Authors: Shuying Zhai, Zhifeng Weng, Xinlong FengAbstract:In this paper, we propose a second-order fast Explicit Operator splitting method for the phase field crystal equation. The basic idea lied in our method is to split the original problem into linear and nonlinear parts. The linear subproblem is numerically solved using the Fourier spectral method, which is based on the exact solution and thus has no stability restriction on the time-step size. The nonlinear one is solved via second-order strong stability preserving Runge–Kutta method. The stability and convergence are discussed in $$L^2$$ -norm. Numerical experiments are performed to validate the accuracy and efficiency of the proposed method. Moreover, energy degradation and mass conservation are also verified.
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fast Explicit Operator splitting method and time step adaptivity for fractional non local allen cahn model
Applied Mathematical Modelling, 2016Co-Authors: Shuying Zhai, Zhifeng Weng, Xinlong FengAbstract:The main purpose of this paper is to solve the fractional non-local Allen–Cahn model via a super fast Explicit Operator splitting spectral (FEOSS) method, which is based on the Strang splitting scheme for time discretization and the Fourier spectral method for space discretization. For a problem of size N, this method reduces the amount of storage from O(N2) to O(N) and cuts down the computational cost from O(N3) to O(Nlog2N). Moreover, significant computational gains can be obtained by applying a new adaptive time-stepping algorithm based on the local error method. This allows accessing time-scales that vary by several orders of magnitude. Numerical results demonstrate that the FEOSS method with adaptive time-stepping algorithm achieves a remarkable resolution and accuracy in a very efficient manner.
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Fast Explicit Operator splitting method and time-step adaptivity for fractional non-local Allen–Cahn model ☆
Applied Mathematical Modelling, 2016Co-Authors: Shuying Zhai, Zhifeng Weng, Xinlong FengAbstract:The main purpose of this paper is to solve the fractional non-local Allen–Cahn model via a super fast Explicit Operator splitting spectral (FEOSS) method, which is based on the Strang splitting scheme for time discretization and the Fourier spectral method for space discretization. For a problem of size N, this method reduces the amount of storage from O(N2) to O(N) and cuts down the computational cost from O(N3) to O(Nlog2N). Moreover, significant computational gains can be obtained by applying a new adaptive time-stepping algorithm based on the local error method. This allows accessing time-scales that vary by several orders of magnitude. Numerical results demonstrate that the FEOSS method with adaptive time-stepping algorithm achieves a remarkable resolution and accuracy in a very efficient manner.
Jianshun Shuen - One of the best experts on this subject based on the ideXlab platform.
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upwind differencing and lu factorization for chemical non equilibrium navier stokes equations
Journal of Computational Physics, 1992Co-Authors: Jianshun ShuenAbstract:Abstract An efficient and robust upwind method for solving the chemical non-equilibrium Navier-Stokes equations has been developed. The method uses either the Roe or Van Leer flux-splitting for inviscid terms and central differencing for viscous terms in the Explicit Operator (residual), and the Steger-Warming (SW) splitting and lower-upper (LU) approximate factorization for the implicit Operator. This approach is efficient since the SW-LU combination requires the inversion of only block diagonal matrices, as opposed to the block tridiagonal inversion of the widely used ADI method, and is fully vectorizable. The LU method is particularly advantageous for systems with large number of equations, such as for chemical and thermal nonequilibrium flow. Formulas of the numerical method are presented for the finite-volume discretization of the Navier-Stokes equations in general coordinates. Numerical tests in hypersonic blunt body, ramped-duct, shock wave/boundary layer interaction, and divergent nozzle flows demonstrate the efficiency and robustness of the present method.
Shuying Zhai - One of the best experts on this subject based on the ideXlab platform.
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Stability and Error Estimate of the Operator Splitting Method for the Phase Field Crystal Equation
Journal of Scientific Computing, 2021Co-Authors: Shuying Zhai, Zhifeng Weng, Xinlong FengAbstract:In this paper, we propose a second-order fast Explicit Operator splitting method for the phase field crystal equation. The basic idea lied in our method is to split the original problem into linear and nonlinear parts. The linear subproblem is numerically solved using the Fourier spectral method, which is based on the exact solution and thus has no stability restriction on the time-step size. The nonlinear one is solved via second-order strong stability preserving Runge–Kutta method. The stability and convergence are discussed in $$L^2$$ -norm. Numerical experiments are performed to validate the accuracy and efficiency of the proposed method. Moreover, energy degradation and mass conservation are also verified.
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fast Explicit Operator splitting method and time step adaptivity for fractional non local allen cahn model
Applied Mathematical Modelling, 2016Co-Authors: Shuying Zhai, Zhifeng Weng, Xinlong FengAbstract:The main purpose of this paper is to solve the fractional non-local Allen–Cahn model via a super fast Explicit Operator splitting spectral (FEOSS) method, which is based on the Strang splitting scheme for time discretization and the Fourier spectral method for space discretization. For a problem of size N, this method reduces the amount of storage from O(N2) to O(N) and cuts down the computational cost from O(N3) to O(Nlog2N). Moreover, significant computational gains can be obtained by applying a new adaptive time-stepping algorithm based on the local error method. This allows accessing time-scales that vary by several orders of magnitude. Numerical results demonstrate that the FEOSS method with adaptive time-stepping algorithm achieves a remarkable resolution and accuracy in a very efficient manner.
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Fast Explicit Operator splitting method and time-step adaptivity for fractional non-local Allen–Cahn model ☆
Applied Mathematical Modelling, 2016Co-Authors: Shuying Zhai, Zhifeng Weng, Xinlong FengAbstract:The main purpose of this paper is to solve the fractional non-local Allen–Cahn model via a super fast Explicit Operator splitting spectral (FEOSS) method, which is based on the Strang splitting scheme for time discretization and the Fourier spectral method for space discretization. For a problem of size N, this method reduces the amount of storage from O(N2) to O(N) and cuts down the computational cost from O(N3) to O(Nlog2N). Moreover, significant computational gains can be obtained by applying a new adaptive time-stepping algorithm based on the local error method. This allows accessing time-scales that vary by several orders of magnitude. Numerical results demonstrate that the FEOSS method with adaptive time-stepping algorithm achieves a remarkable resolution and accuracy in a very efficient manner.
Luis P. Castro - One of the best experts on this subject based on the ideXlab platform.
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Mixed boundary value problems of diffraction by a half‐plane with an obstacle perpendicular to the boundary
Mathematical Methods in the Applied Sciences, 2013Co-Authors: Luis P. Castro, David KapanadzeAbstract:The paper is devoted to the analysis of wave diffraction problems modeled by classes of mixed boundary conditions and the Helmholtz equation, within a half-plane with a crack. Potential theory together with Fredholm theory, and Explicit Operator relations, are conveniently implemented to perform the analysis of the problems. In particular, an interplay between Wiener–Hopf plus/minus Hankel Operators and Wiener–Hopf Operators assumes a relevant preponderance in the final results. As main conclusions, this study reveals conditions for the well-posedness of the corresponding boundary value problems in certain Sobolev spaces and equivalent reduction to systems of Wiener–Hopf equations. Copyright © 2013 John Wiley & Sons, Ltd.
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Wave diffraction by a half-plane with an obstacle perpendicular to the boundary
Journal of Differential Equations, 2013Co-Authors: Luis P. Castro, David KapanadzeAbstract:Abstract We prove the unique existence of solutions for different types of boundary value problems of wave diffraction by a half-plane with a screen or a crack perpendicular to the boundary. Representations of the solutions are also obtained upon the consideration of some associated Operators. This is done in a Bessel potential spaces framework and for complex (non-real) wave numbers. The investigation is mostly based on the construction of Explicit Operator relations, the potential method, and a factorization technique for a certain class of oscillating Fourier symbols which naturally arise from the problems.
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Bounds for the Kernel Dimension of Singular Integral Operators with Carleman Shift
2010Co-Authors: Luis P. Castro, E. M. RojasAbstract:Upper bounds for the kernel dimension of singular integral Operators with orientation‐preserving Carleman shift are obtained. This is implemented by using some estimates which are derived with the help of certain Explicit Operator relations. In particular, the interplay between classes of Operators with and without Carleman shifts have a preponderant importance to achieve the mentioned bounds.
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Invertibility of Singular Integral Operators with Flip Through Explicit Operator Relations
Integral Methods in Science and Engineering Volume 1, 2009Co-Authors: Luis P. Castro, E. M. RojasAbstract:The integral equations which are characterized by singular integral Operators with shift appear frequently in a large variety of applied problems (we refer to [KaSa01, KrLi94] for a general background on these Operators and historical references). Thus, it is of fundamental importance to obtain descriptions of the invertibility characteristics of these Operators. Although some invertibility criteria are presently known for several classes of singular integral Operators with shift, the corresponding criteria still remain to be achieved for many others. In addition, among all the classes of singular integral Operators with shifts, the ones with weighted shifts typically reveal extra difficulties.
Zhifeng Weng - One of the best experts on this subject based on the ideXlab platform.
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Stability and Error Estimate of the Operator Splitting Method for the Phase Field Crystal Equation
Journal of Scientific Computing, 2021Co-Authors: Shuying Zhai, Zhifeng Weng, Xinlong FengAbstract:In this paper, we propose a second-order fast Explicit Operator splitting method for the phase field crystal equation. The basic idea lied in our method is to split the original problem into linear and nonlinear parts. The linear subproblem is numerically solved using the Fourier spectral method, which is based on the exact solution and thus has no stability restriction on the time-step size. The nonlinear one is solved via second-order strong stability preserving Runge–Kutta method. The stability and convergence are discussed in $$L^2$$ -norm. Numerical experiments are performed to validate the accuracy and efficiency of the proposed method. Moreover, energy degradation and mass conservation are also verified.
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Numerical approximation of the conservative Allen–Cahn equation by Operator splitting method
Mathematical Methods in the Applied Sciences, 2017Co-Authors: Zhifeng Weng, Qingqu ZhuangAbstract:In this paper, a second-order fast Explicit Operator splitting method is proposed to solve the mass-conserving Allen–Cahn equation with a space–time-dependent Lagrange multiplier. The space–time-dependent Lagrange multiplier can preserve the volume of the system and keep small features. Moreover, we analyze the discrete maximum principle and the convergence rate of the fast Explicit Operator splitting method. The proposed numerical scheme is of spectral accuracy in space and of second-order accuracy in time, which greatly improves the computational efficiency. Numerical experiments are presented to confirm the accuracy, efficiency, mass conservation, and stability of the proposed method. Copyright © 2017 John Wiley & Sons, Ltd.
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fast Explicit Operator splitting method and time step adaptivity for fractional non local allen cahn model
Applied Mathematical Modelling, 2016Co-Authors: Shuying Zhai, Zhifeng Weng, Xinlong FengAbstract:The main purpose of this paper is to solve the fractional non-local Allen–Cahn model via a super fast Explicit Operator splitting spectral (FEOSS) method, which is based on the Strang splitting scheme for time discretization and the Fourier spectral method for space discretization. For a problem of size N, this method reduces the amount of storage from O(N2) to O(N) and cuts down the computational cost from O(N3) to O(Nlog2N). Moreover, significant computational gains can be obtained by applying a new adaptive time-stepping algorithm based on the local error method. This allows accessing time-scales that vary by several orders of magnitude. Numerical results demonstrate that the FEOSS method with adaptive time-stepping algorithm achieves a remarkable resolution and accuracy in a very efficient manner.
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Fast Explicit Operator splitting method and time-step adaptivity for fractional non-local Allen–Cahn model ☆
Applied Mathematical Modelling, 2016Co-Authors: Shuying Zhai, Zhifeng Weng, Xinlong FengAbstract:The main purpose of this paper is to solve the fractional non-local Allen–Cahn model via a super fast Explicit Operator splitting spectral (FEOSS) method, which is based on the Strang splitting scheme for time discretization and the Fourier spectral method for space discretization. For a problem of size N, this method reduces the amount of storage from O(N2) to O(N) and cuts down the computational cost from O(N3) to O(Nlog2N). Moreover, significant computational gains can be obtained by applying a new adaptive time-stepping algorithm based on the local error method. This allows accessing time-scales that vary by several orders of magnitude. Numerical results demonstrate that the FEOSS method with adaptive time-stepping algorithm achieves a remarkable resolution and accuracy in a very efficient manner.
