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Frontiers in Applied and Computational Mathematics: Special Collection in Honor of Bjorn Engquist in the Occasion of His 70th Birthday

  1. Content type: Research

    In this paper we study the stochastic Galerkin approximation for the linear transport equation with random inputs and diffusive scaling. We first establish uniform (in the Knudsen number) stability results in ...

    Authors: Shi Jin, Jian-Guo Liu and Zheng Ma

    Citation: Research in the Mathematical Sciences 2017 4:15

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  2. Content type: Research

    The hierarchical interpolative factorization (HIF) offers an efficient way for solving or preconditioning elliptic partial differential equations. By exploiting locality and low-rank properties of the operator...

    Authors: Yingzhou Li and Lexing Ying

    Citation: Research in the Mathematical Sciences 2017 4:12

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  3. Content type: Research

    We present a ray-based finite element method for the high-frequency Helmholtz equation in smooth media, whose basis is learned adaptively from the medium and source. The method requires a fixed number of grid ...

    Authors: Jun Fang, Jianliang Qian, Leonardo Zepeda-Núñez and Hongkai Zhao

    Citation: Research in the Mathematical Sciences 2017 4:9

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  4. Content type: Research

    We present a spectrally accurate method for the rapid evaluation of free-space Stokes potentials, i.e., sums involving a large number of free space Green’s functions. We consider sums involving stokeslets, str...

    Authors: Ludvig af Klinteberg, Davoud Saffar Shamshirgar and Anna-Karin Tornberg

    Citation: Research in the Mathematical Sciences 2017 4:1

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  5. Content type: Research

    We study the qualitative homogenization of second-order Hamilton–Jacobi equations in space-time stationary ergodic random environments. Assuming that the Hamiltonian is convex and superquadratic in the momentu...

    Authors: Wenjia Jing, Panagiotis E. Souganidis and Hung V. Tran

    Citation: Research in the Mathematical Sciences 2017 4:6

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