PARALLEL IMPLEMENTATIONS OF THE FAST SWEEPING METHOD
, 2008 . The fast sweeping method is an efficient iterative method for hyperbolic problems. It combines Gauss-Seidel iteration with alternating sweeping ordering. In this paper several parallel implementations of the fast sweeping method are presented.
Hongkai Zhao
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Necessary Conditions for Uniform Convergence of Finite Difference Schemes for Convection-Diffusion Problems With Exponential and Parabolic Layers [PDF]
, 1995 summary:Singularly perturbed problems of convection-diffusion type cannot be solved numerically in a completely satisfactory manner by standard numerical methods. This indicates the need for robust or $\epsilon $-uniform methods.
Hans-Görg Roos +3 more
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, 2007 . We present a multiple-patch phase space method for computing trajectories on two-dimensional manifolds possibly embedded in a higher-dimensional space. The dynamics of tra-jectories are given by systems of ordinary differential equations (ODEs).
Olof Runborg +3 more
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A GENERAL CLASS OF FINITE-DIFFERENCE METHODS FOR THE LINEAR TRANSPORT EQUATION ∗
, 2008 . A wide family of finite-difference methods for the linear advection equation, based on a six-point stencil, is presented. The family depends on three parameters and includes most of the classical linear schemes.
Daniele Funaro, Giuseppe Pontrelli
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An Accurate and Stable Multigrid Method for Convection-Diffusion Equations
, 1995 : We introduce a high-order compact difference scheme with multigrid algorithm to solve the convection-diffusion equations with constant coefficients. This high-order discretization scheme is shown to be more accurate and stable than the usual five-point
Jun Zhang +2 more
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Finite Element Iterative Methods for the 3D Steady Navier--Stokes Equations. [PDF]
Entropy (Basel), 2021 He Y.
europepmc +1 more source
Residual Scaling Techniques in Multigrid, I: Equivalence Proof
, 1996 This paper addresses the residual scaling techniques (coarse-grid-correction optimization techniques) in multigrid methods. We survey recent developments in this area and prove the equivalence of the over-weighted residual technique and the over ...
Jun Zhang
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Convergence Proof of Jacobi Iterative Method for A Discretized 2D Convection-Diffusion Equation
, 1998 We prove that the Jacobi iterative method converges from any initial values for solving the linear system resulting from a fourth-order compact finite difference discretization of the 2D convection-diffusion equation with constant convection coefficients.
Shiqing Zhang, Deyu Sang
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A Note On Immersed Interface Method For Three Dimensional Elliptic Equations
, 1996 . The Immersed Interface Method proposed by LeVeque and Li [SIAM J. Numer. Anal. 31, No.4 (1994)] is extended to three dimensional elliptic equations of the form: r \Delta (fi(x)ru(x)) + (x)u(x) = f(x): We study the situation in which there is an ...
Zhilin Li
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Scattered Node Compact Finite Difference-Type Formulas Generated from Radial Basis Functions
, 2008 In standard equispaced finite difference (FD) formulas, symmetries can make the order of accuracy relatively high compared to the number of nodes in the FD stencil. With scattered nodes, such symmetries are no longer available.
Grady B. Wright A, Bengt Fornberg B
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