Efficient sparse-grid implementation of a fifth-order multi-resolution WENO scheme for hyperbolic equations

DOI10.1007/s42967-022-00202-4OpenAlexW4296123402WikidataQ114216628 ScholiaQ114216628MaRDI QIDQ6063541

Xiaozhi Zhu, Yong-Tao Zhang, Ernie Tsybulnik

Publication date: 12 December 2023

Published in: Communications on Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s42967-022-00202-4

zbMATH Keywords

sparse gridsweighted essentially non-oscillatory (WENO) schemeshigh spatial dimensionsmulti-resolution WENO schemeshyperbolic partial differential equations (PDEs)

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06)

Cites Work

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• Accuracy of the weighted essentially non-oscillatory conservative finite difference schemes
• High order weighted essentially non-oscillatory WENO-Z schemes for hyperbolic conservation laws
• A new fifth order finite difference WENO scheme for solving hyperbolic conservation laws
• A conservative high order semi-Lagrangian WENO method for the Vlasov equation
• A systematic methodology for constructing high-order energy stable WENO schemes
• Weighted essentially non-oscillatory schemes
• A simple bound-preserving sweeping technique for conservative numerical approximations
• A third order hierarchical basis WENO interpolation for sparse grids with application to conservation laws with uncertain data
• Mapped weighted essentially non-oscillatory schemes: Achieving optimal order near critical points
• Adaptive multiresolution approach for solution of hyperbolic PDEs
• A WENO-solver for the transients of Boltzmann-Poisson system for semiconductor devices: Performance and comparisons with Monte Carlo methods.
• Efficient implementation of weighted ENO schemes
• A robust reconstruction for unstructured WENO schemes
• A new type of multi-resolution WENO schemes with increasingly higher order of accuracy
• Krylov integration factor method on sparse grids for high spatial dimension convection-diffusion equations
• Fast sparse grid simulations of fifth order WENO scheme for high dimensional hyperbolic PDEs
• Absolutely convergent fixed-point fast sweeping WENO methods for steady state of hyperbolic conservation laws
• A new type of third-order finite volume multi-resolution WENO schemes on tetrahedral meshes
• Third order WENO scheme on sparse grids for hyperbolic equations
• Quadrature-free non-oscillatory finite volume schemes on unstructured meshes for nonlinear hyperbolic systems
• A central WENO scheme for solving hyperbolic conservation laws on non-uniform meshes
• Convergence to steady-state solutions of the new type of high-order multi-resolution WENO schemes: a numerical study
• Strong Stability-Preserving High-Order Time Discretization Methods
• Solution of Time-dependent Advection-Diffusion Problems with the Sparse-grid Combination Technique and a Rosenbrock Solver
• A Sparse Grid Discontinuous Galerkin Method for High-Dimensional Transport Equations and Its Application to Kinetic Simulations
• Central WENO schemes for hyperbolic systems of conservation laws
• High-Order WENO Schemes for Hamilton--Jacobi Equations on Triangular Meshes
• An Adaptive Multiresolution Discontinuous Galerkin Method for Time-Dependent Transport Equations in Multidimensions
• Sparse grids
• The mechanism of sound generation in the interaction between a shock wave and two counter-rotating vortices
• The sparse-grid combination technique applied to time-dependent advection problems

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