The Experts below are selected from a list of 320967 Experts worldwide ranked by ideXlab platform
Yanli Wang - One of the best experts on this subject based on the ideXlab platform.
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burnett Spectral Method for the spatially homogeneous boltzmann equation
Computers & Fluids, 2020Co-Authors: Yanli WangAbstract:Abstract We develop a Spectral Method for the spatially homogeneous Boltzmann equation using Burnett polynomials in the basis functions. Using the sparsity of the coefficients in the expansion of the collision term, we reduce the computational cost by one order of magnitude for general collision kernels and by two orders of magnitude for Maxwell molecules. The proposed Method can couple seamlessly with the BGK-type modelling techniques to make future applications affordable. The implementation of the algorithm is discussed in detail, including a numerical scheme to compute all the coefficients accurately, and the design of the data structure to achieve a high cache hit ratio. Numerical examples are provided to demonstrate the accuracy and efficiency of our Method.
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approximation of the boltzmann collision operator based on hermite Spectral Method
Journal of Computational Physics, 2019Co-Authors: Yanli Wang, Zhenning CaiAbstract:Abstract Based on the Hermite expansion of the distribution function, we introduce a Galerkin Spectral Method for the spatially homogeneous Boltzmann equation with the realistic inverse-power-law models. A practical algorithm is proposed to evaluate the coefficients in the Spectral Method with high accuracy, and these coefficients are also used to construct new computationally affordable collision models. Numerical experiments show that our Method captures the low-order moments very efficiently.
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burnett Spectral Method for the spatially homogeneous boltzmann equation
arXiv: Computational Physics, 2018Co-Authors: Yanli WangAbstract:We develop a Spectral Method for the spatially homogeneous Boltzmann equation using Burnett polynomials in the basis functions. Using the sparsity of the coefficients in the expansion of the collision term, the computational cost is reduced by one order of magnitude for general collision kernels and by two orders of magnitude for Maxwell molecules. The proposed Method can couple seamlessly with the BGK-type modelling techniques to make future applications affordable. The implementation of the algorithm is discussed in detail, including a numerical scheme to compute all the coefficients accurately, and the design of the data structure to achieve high cache hit ratio. Numerical examples are provided to demonstrate the accuracy and efficiency of our Method
Soheila Mirzaei - One of the best experts on this subject based on the ideXlab platform.
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numerical study of the two term time fractional differential equation using the lagrange polynomial pseudo Spectral Method
alexandria engineering journal, 2020Co-Authors: Ali Shokri, Soheila MirzaeiAbstract:Abstract This paper is about the implementation of the pseudo-Spectral Method based on the Lagrange polynomials to the numerical study of the multi-term time-fractional differential equations. Also, a semi-discrete approximation scheme used to the conversion of this equation to a system of ordinary fractional differential equations. To maintain the high accuracy of the Spectral Method, we applied the Mittag-Leffler function for time integration. A comparison of numerical results highlights the accuracy and efficiency of the provided scheme.
Jie Shen - One of the best experts on this subject based on the ideXlab platform.
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A GPU parallelized Spectral Method for elliptic equations in rectangular domains
Journal of Computational Physics, 2013Co-Authors: Feng Chen, Jie ShenAbstract:We design and implement a polynomial-based Spectral Method on graphic processing units (GPUs). The key to success lies in the seamless integration of the matrix diagonalization technique and the new generation CUDA tools. The Method is applicable to elliptic equations in rectangular domains with general boundary condition. We show remarkable speedups of up to 15 times in the 2-D case and more than 35 times in the 3-D case.
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A Triangular Spectral Method for the Stokes Equations
Numerical Mathematics-theory Methods and Applications, 2011Co-Authors: Lizhen Chen, Jie Shen, Chuanju XuAbstract:A triangular Spectral Method for the Stokes equations is developed in this paper. The main contributions are two-fold: First of all, a Spectral Method using the rational approximation is constructed and analyzed for the Stokes equations in a tri- angular domain. The existence and uniqueness of the solution, together with an error estimate for the velocity, are proved. Secondly, a nodal basis is constructed for the effi- cient implementation of the Method. These new basis functions enjoy the fully tensorial product property as in a tensor-produce domain. The new triangular Spectral Method makes it easy to treat more complex geometries in the classical Spectral-element frame- work, allowing us to use arbitrary triangular and tetrahedral elements. AMS subject classifications: 65N35, 65N22, 65F05, 35J05
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applications of semi implicit fourier Spectral Method to phase field equations
Computer Physics Communications, 1998Co-Authors: Longqing Chen, Jie ShenAbstract:Abstract An efficient and accurate numerical Method is implemented for solving the time-dependent Ginzburg—Landau equation and the Cahn—Hilliard equation. The time variable is discretized by using semi-implicit schemes which allow much larger time step sizes than explicit schemes; the space variables are discretized by using a Fourier-Spectral Method whose convergence rate is exponential in contrast to second order by a usual finite-difference Method. We have applied our Method to predict the equilibrium profiles of an order parameter across a stationary planar interface and the velocity of a moving interface by solving the time-dependent Ginzburg—Landau equation, and compared the accuracy and efficiency of our results with those obtained by others. We demonstrate that, for a specified accuracy of 0.5%, the speedup of using semi-implicit Fourier-Spectral Method, when compared with the explicit finite-difference schemes, is at least two orders of magnitude in two dimensions, and close to three orders of magnitude in three dimensions. The Method is shown to be particularly powerful for systems in which the morphologies and microstructures are dominated by long-range elastic interactions.
Ali Shokri - One of the best experts on this subject based on the ideXlab platform.
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numerical study of the two term time fractional differential equation using the lagrange polynomial pseudo Spectral Method
alexandria engineering journal, 2020Co-Authors: Ali Shokri, Soheila MirzaeiAbstract:Abstract This paper is about the implementation of the pseudo-Spectral Method based on the Lagrange polynomials to the numerical study of the multi-term time-fractional differential equations. Also, a semi-discrete approximation scheme used to the conversion of this equation to a system of ordinary fractional differential equations. To maintain the high accuracy of the Spectral Method, we applied the Mittag-Leffler function for time integration. A comparison of numerical results highlights the accuracy and efficiency of the provided scheme.
Yonghao Zhang - One of the best experts on this subject based on the ideXlab platform.
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A fast Spectral Method for the Boltzmann equation for monatomic gas mixtures
Journal of Computational Physics, 2015Co-Authors: Jun Zhang, Jason M. Reese, Yonghao ZhangAbstract:Although the fast Spectral Method has been established for solving the Boltzmann equation for single-species monatomic gases, its extension to gas mixtures is not easy because of the non-unitary mass ratio between the different molecular species. The conventional Spectral Method can solve the Boltzmann collision operator for binary gas mixtures but with a computational cost of the order m r 3 N 6 , where m r is the mass ratio of the heavier to the lighter species, and N is the number of frequency nodes in each frequency direction. In this paper, we propose a fast Spectral Method for binary mixtures of monatomic gases that has a computational cost O ( m r M 2 N 4 log ? N ) , where M 2 is the number of discrete solid angles. The algorithm is validated by comparing numerical results with analytical Bobylev-Krook-Wu solutions for the spatially-homogeneous relaxation problem, for m r up to 36. In spatially-inhomogeneous problems, such as normal shock waves and planar Fourier/Couette flows, our results compare well with those of both the numerical kernel and the direct simulation Monte Carlo Methods. As an application, a two-dimensional temperature-driven flow is investigated, for which other numerical Methods find it difficult to resolve the flow field at large Knudsen numbers. The fast Spectral Method is accurate and effective in simulating highly rarefied gas flows, i.e. it captures the discontinuities and fine structures in the velocity distribution functions.
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deterministic numerical solutions of the boltzmann equation using the fast Spectral Method
Journal of Computational Physics, 2013Co-Authors: Craig White, Jason M. Reese, T J Scanlon, Yonghao ZhangAbstract:The Boltzmann equation describes the dynamics of rarefied gas flows, but the multidimensional nature of its collision operator poses a real challenge for its numerical solution. In this paper, the fast Spectral Method 36], originally developed by Mouhot and Pareschi for the numerical approximation of the collision operator, is extended to deal with other collision kernels, such as those corresponding to the soft, Lennard-Jones, and rigid attracting potentials. The accuracy of the fast Spectral Method is checked by comparing our numerical solutions of the space-homogeneous Boltzmann equation with the exact Bobylev-Krook-Wu solutions for a gas of Maxwell molecules. It is found that the accuracy is improved by replacing the trapezoidal rule with Gauss-Legendre quadrature in the calculation of the kernel mode, and the conservation of momentum and energy are ensured by the Lagrangian multiplier Method without loss of Spectral accuracy. The relax-to-equilibrium processes of different collision kernels with the same value of shear viscosity are then compared; the numerical results indicate that different forms of the collision kernels can be used as long as the shear viscosity (not only the value, but also its temperature dependence) is recovered. An iteration scheme is employed to obtain stationary solutions of the space-inhomogeneous Boltzmann equation, where the numerical errors decay exponentially. Four classical benchmarking problems are investigated: the normal shock wave, and the planar Fourier/Couette/force-driven Poiseuille flows. For normal shock waves, our numerical results are compared with a finite difference solution of the Boltzmann equation for hard sphere molecules, experimental data, and molecular dynamics simulation of argon using the realistic Lennard-Jones potential. For planar Fourier/Couette/force-driven Poiseuille flows, our results are compared with the direct simulation Monte Carlo Method. Excellent agreements are observed in all test cases, demonstrating the merit of the fast Spectral Method as a computationally efficient Method for rarefied gas dynamics.
