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HIGH ORDER FINITE DIFFERENCE hermite WENO FAST SWEEPING methods FOR STATIC HAMILTON-JACOBI EQUATIONS

Journal of Computational Mathematics 2023年第6期41卷 1064-1092页

作者： Yupeng Ren Yulong Xing Jianxian Qiu School of Mathematical Sciences Xiamen UniversityXiamenFujian 361005China Department of Mathematics The Ohio State UniversityColumbusOH 43210USA School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing Xiamen UniversityXiamenFujian 361005China

In this paper,we propose a novel hermite weighted essentially non-oscillatory(HWENO)fast sweeping method to solve the static Hamilton-Jacobi equations *** the HWENO reconstruction procedure,the proposed method is built upon a new finite difference fifth order HWENO scheme involving one big stencil and two small ***,one major novelty and difference from the traditional HWENO framework lies in the fact that,we do not need to introduce and solve any additional equations to update the derivatives of the unknown functionϕ.Instead,we use the currentϕand the old spatial derivative ofϕto update *** traditional HWENO fast sweeping method is also introduced in this paper for comparison,where additional equations governing the spatial derivatives ofϕare *** novel HWENO fast sweeping methods are shown to yield great savings in computational time,which improves the computational efficiency of the traditional HWENO *** addition,a hybrid strategy is also introduced to further reduce computational *** numerical experiments are provided to validate the accuracy and efficiency of the proposed approaches.

关键词： Finite difference hermite methods Weighted essentially non-oscillatory method Fast sweeping method Static Hamilton-Jacobi equations Eikonal equation

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hermite-Discontinuous Galerkin Overset Grid methods for the Scalar Wave Equation

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Communications on Applied Mathematics and Computation 2021年第3期3卷 391-418页

作者： Oleksii Beznosov Daniel Appel Department of Mathematics and Statistics The University of New Mexico1 University of New MexicoMSC011115AlbuquerqueNM 87131Mexico Department of Applied Mathematics University of ColoradoUniversity of Colorado 526 UCBBoulderCO 80309USA

We present high order accurate numerical methods for the wave equation that combines efficient hermite methods with geometrically flexible discontinuous Galerkin methods by using overset *** boundaries we use thin boundary fitted curvilinear grids and in the volume we use Cartesian grids so that the computational complexity of the solvers approaches a structured Cartesian hermite *** many other overset methods we do not need to add artificial dissipation but we find that the built-in dissipation of the hermite and discontinuous Galerkin methods is sufficient to maintain the *** numerical experiments we demonstrate the stability,accuracy,efficiency,and the applicability of the methods to forward and inverse problems.

关键词： Wave equation Overset grids High order hermite methods Discontinuous Galerkin methods

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