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A hybrid Hermite WENO scheme for hyperbolic conservation laws 1

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arXiv 2019年

作者： Zhao, Zhuang Chen, Yibing Qiu, Jianxian School of Mathematical Sciences Xiamen University Xiamen Fujian361005 China Institute of Applied Physics and Computational Mathematics Beijing100094 China School of Mathematical Sciences Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing Xiamen University Xiamen Fujian361005 China

In this paper, we propose a hybrid finite volume Hermite weighted essentially nonoscillatory (HWENO) scheme for solving one and two dimensional hyperbolic conservation laws. The zeroth-order and the first-order moments are used in the spatial reconstruction, with total variation diminishing Runge-Kutta time discretization. The main idea of the hybrid HWENO scheme is that we first use a shock-detection technique to identify the troubled cell, then, if the cell is identified as a troubled cell, we would modify the first order moment in the troubled cell and employ HWENO reconstruction in spatial discretization;otherwise, we directly use high order linear reconstruction. Unlike other HWENO schemes, we borrow the thought of limiter for discontinuous Galerkin (DG) method to control the spurious oscillations, after this procedure, the scheme would avoid the oscillations by using HWENO reconstruction nearby discontinuities and have higher efficiency for using linear approximation straightforwardly in the smooth regions. In addition, the hybrid HWENO scheme still keeps the compactness. A collection of benchmark numerical tests for one and two dimensional cases are performed to demonstrate the numerical accuracy, high resolution and robustness of the proposed *** Codes 65M60, 35L65 Copyright © 2019, The Authors. All rights reserved.

关键词： Galerkin methods

A NEW PHYSICS-PRESERVING IMPES SCHEME FOR INCOMPRESSIBLE AND IMMISCIBLE TWO-PHASE FLOW IN HETEROGENEOUS POROUS MEDIA

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arXiv 2019年

作者： Chen, Huangxin Shuyu, S.U.N. School of Mathematical Sciences Fujian Provincial Key Laboratory on Mathematical Modeling High Performance Scientific Computing Xiamen University Fujian361005 China Computational Transport Phenomena Laboratory Division of Physical Science Engineering King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

In this work we consider a new efficient IMplicit Pressure Explicit Saturation (IMPES) scheme for the simulation of incompressible and immiscible two-phase flow in heterogeneous porous media with capillary pressure. Compared with the conventional IMPES schemes, the new IMPES scheme is inherently physics-preserving, namely, the new algorithm is locally mass conservative for both phases and it also enjoys another appealing feature that the total velocity is continuous in the normal direction. Moreover, the new scheme is unbiased with regard to the two phases and the saturations of both phases are bounds-preserving if the time step size is smaller than a certain value. The key ideas in the new scheme include that the Darcy flows for both phases are rewritten in the formulation based on the total velocity and an auxiliary velocity referring to as the capillary potential gradient, and the total discretized conservation equation is obtained by the summation of the discretized conservation equation for each phase. The upwind strategy is applied to update the saturations explicitly, and the upwind mixed finite element methods are used to solve the pressure-velocity systems which can be decoupled. We also present some interesting examples to demonstrate the efficiency and robustness of the new algorithm. Copyright © 2019, The Authors. All rights reserved.

关键词： Capillarity

High-order conservative positivity-preserving DG-interpolation for deforming meshes and application to moving mesh DG simulation of radiative transfer

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arXiv 2019年

作者： Zhang, Min Huang, Weizhang Qiu, Jianxian School of Mathematical Sciences Xiamen University Xiamen Fujian361005 China Department of Mathematics University of Kansas LawrenceKS66045 United States School of Mathematical Sciences Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing Xiamen University Xiamen Fujian361005 China

Solution interpolation between deforming meshes is an important component for several applications in scientific computing, including indirect arbitrary-Lagrangian-Eulerian and rezoning moving mesh methods in numerical solution of partial differential equations. In this paper, a high-order, conservative, and positivity-preserving interpolation scheme is developed based on the discontinuous Galerkin solution of a linear time-dependent equation on deforming meshes. The scheme works for bounded but otherwise arbitrary mesh deformation from the old mesh to the new one. The cost and positivity preservation (with a linear scaling limiter) of the DG-interpolation are investigated. Numerical examples are presented to demonstrate the properties of the interpolation scheme. The DG-interpolation is applied to the rezoning moving mesh DG solution of the radiative transfer equation, an integro-differential equation modeling the conservation of photons and involving time, space, and angular variables. Numerical results obtained for examples in one and two spatial dimensions with various settings show that the resulting rezoning moving mesh DG method maintains the same convergence order as the standard DG method, is more efficient than the method with a fixed uniform mesh, and is able to preserve the positivity of the radiative *** Codes 65M50, 65M60, 65M70, 65R05, 65.75 Copyright © 2019, The Authors. All rights reserved.

关键词： Interpolation

Anisotropic spectral manifold wavelet descriptor for deformable shape analysis and matching 26

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Anisotropic spectral manifold wavelet descriptor for deforma...

26th Pacific Conference on Computer Graphics and Applications, Pacific Graphics 2018

作者： Li, Qinsong Liu, Shengjun Hu, Ling Liu, Xinru Institute of Engineering Modeling and Scientific Computing Central South University Hunan Changsha410083 China School of Mathematics and Computational Science Hunan First Normal University Hunan Changsha410205 China State Key Laboratory of High Performance Manufacturing Complex Central South University Hunan Changsha410083 China

ISBN: (纸本)9783038680734

In this paper, we present a novel framework termed Anisotropic Spectral Manifold Wavelet Transform (ASMWT) for shape analysis. ASMWT comprehensively analyzes the signals from multiple directions on local manifold regions of the shape with a series of low-pass and band-pass frequency filters in each direction. Using the ASMWT coefficients of a very simple function, we efficiently construct a localizable and discriminative multiscale point descriptor, named as the Anisotropic Spectral Manifold Wavelet Descriptor (ASMWD). Since the filters used in our descriptor are direction-sensitive and able to robustly reconstruct the signals with a finite number of scales, it makes our descriptor be intrinsic-symmetry unambiguous, compact as well as efficient. The extensive experimental results demonstrate that our method achieves significant performance than several state-of-the-art methods when applied in vertex-wise shape matching. © 2018 The Author(s).

关键词： Wavelet transforms

A Hybrid Spectral Element Method for Fractional Two-Point Boundary Value Problems

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高等学校计算数学学报（英文版） 2017年第2期10卷 437-464页

作者： Changtao Sheng Jie Shen Fujian Provincial Key Laboratory on Mathematical Modeling & High Performance Scientific Computing and School of Mathematical Sciences Xiamen University Xiamen Fujian 361005 China Fujian Provincial Key Laboratory on Mathematical Modeling & High Performance Scientific Computing and School of Mathematical Sciences Xiamen University Xiamen Fujian 361005 China Department of Mathematics Purdue University West LafayetteIN 47907-1957 USA

We propose a hybrid spectral element method for fractional two-point boundary value problem (FBVPs) involving both Caputo and Riemann-Liouville (RL)fractional *** first formulate these FBVPs as a second kind Volterra integral equation (VIEs) with weakly singular kernel,following a similar procedure in [16].We then design a hybrid spectral element method with generalized Jacobi functions and Legendre polynomials as basis *** use of generalized Jacobi functions allow us to deal with the usual singularity of solutions at t =*** establish the existence and uniqueness of the numerical solution,and derive a hptype error estimates under L2 (I)-norm for the transformed *** results are provided to show the effectiveness of the proposed methods.

关键词： Boundary value problems generalized Jacobi functions spectral element method fractional differential equations error bounds

A Müntz-Collocation spectral method for weakly singular volterra integral equations

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arXiv 2019年

作者： Hou, Dianming Lin, Yumin Azaiez, Mejdi Xu, Chuanju School of Mathematics and Statistics Jiangsu Normal University Xuzhou221116 China School of Mathematical Sciences Fujian Provincial Key Laboratory of Mathematical Modeling High Performance Scientific Computing Xiamen University Xiamen361005 China Laboratoire I2M Umr 5295 Bordeaux Inp Pessac33607 France

In this paper we propose and analyze a fractional Jacobi-collocation spectral method for the second kind Volterra integral equations (VIEs) with weakly singular kernel $(x-s)^{-\mu},0 Copyright © 2019, The Author... 详细信息

关键词： Integral equations

Highly efficient schemes for time fractional allen-cahn equation using extended sav approach

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arXiv 2019年

作者： Hou, Dianming Zhu, Hongyi Xu, Chuanju School of Mathematics and Statistics Jiangsu Normal University Xuzhou221116 China School of Mathematical Sciences Fujian Provincial Key Laboratory of Mathematical Modeling and High Performance Scientific Computing Xiamen University Xiamen361005 China Bordeaux INP Laboratoire I2M UMR 5295 Pessac33607 France

In this paper, we propose and analyze high order efficient schemes for the time fractional Allen-Cahn equation. The proposed schemes are based on the L1 discretization for the time fractional derivative and the extended scalar auxiliary variable (SAV) approach developed very recently to deal with the nonlinear terms in the equation. The main contributions of the paper consist in: 1) constructing first and higher order unconditionally stable schemes for different mesh types, and proving the unconditional stability of the constructed schemes for the uniform mesh;2) carrying out numerical experiments to verify the efficiency of the schemes and to investigate the coarsening dynamics governed by the time fractional Allen-Cahn equation. Particularly, the influence of the fractional order on the coarsening behavior is carefully examined. Our numerical evidence shows that the proposed schemes are more robust than the existing methods, and their efficiency is less restricted to particular forms of the nonlinear potentials. Copyright © 2019, The Authors. All rights reserved.

关键词： Mesh generation

Ergodic optimization theory for a class of typical maps

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arXiv 2019年

作者： Huang, Wen Lian, Zeng Ma, Xiao Xu, Leiye Zhang, Yiwei Wu Wen-Tsun Key Laboratory of Mathematics USTC Chinese Academy of Sciences Department of Mathematics University of Science and Technology of China Hefei Anhui China College of Mathematical Sciences Sichuan University Chengdu Sichuan610016 China School of Mathematics and Statistics Center for Mathematical Sciences Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Sciences and Technology Wuhan430074 China

In this article, we consider the weighted ergodic optimization problem of a class of dynamical systems T: X → X where X is a compact metric space and T is Lipschitz continuous. We show that once T: X → X satisfies both the Anosov shadowing property (ASP) and the Mañé-Conze-Guivarc'h-Bousch property (MCGBP), the minimizing measures of generic Hölder observables are unique and supported on a periodic orbit. Moreover, if T: X → X is a subsystem of a dynamical system f: M → M (i.e. X ⊂ M and f|X= T ) where M is a compact smooth manifold, the above conclusion holds for C1observables. Note that a broad class of classical dynamical systems satisfies both ASP and MCGBP, which includes Axiom A attractors, Anosov diffeomorphisms and uniformly expanding maps. Therefore, the open problem proposed by Yuan and Hunt in [YH] for C1-observables is solved consequentially. Copyright © 2019, The Authors. All rights reserved.

关键词： Dynamical systems

Ergodic optimization theory for axiom a flows

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arXiv 2019年

作者： Huang, Wen Lian, Zeng Ma, Xiao Xu, Leiye Zhang, Yiwei Wu Wen-Tsun Key Laboratory of Mathematics USTC Chinese Academy of Sciences Department of Mathematics University of Science and Technology of China Hefei Anhui China College of Mathematical Sciences Sichuan University Chengdu Sichuan610016 China School of Mathematics and Statistics Center for Mathematical Sciences Hubei Key Laboratory of Engineering Modeling and Scientific Computing Hua-Zhong University of Sciences and Technology Wuhan430074 China

In this article, we consider the weighted ergodic optimization problem Axiom A attractors of a C2flow on a compact smooth manifold. The main result obtained in this paper is that for a generic observable from function space C0,α(α∈ (0, 1]) or C1the minimizing measure is unique and is supported on a periodic orbit. Copyright © 2019, The Authors. All rights reserved.

关键词： Site selection