Acoustic wave propagation in complicated geometries and heterogeneous media

DOI10.1007/s10915-014-9817-1zbMath1306.65247OpenAlexW2126092018MaRDI QIDQ474976

Ken Mattsson, Kristoffer Virta

Publication date: 25 November 2014

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-014-9817-1

zbMATH Keywords

energy estimatesenergy methodheterogeneous mediahigh-order methodsfinite differencenumerical experimentacoustic wave equationstrong stabilityCurvilinear grids

Mathematics Subject Classification ID

Wave equation (35L05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12)

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Uses Software

• OASES

Cites Work

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• Summation by parts operators for finite difference approximations of second-derivatives with variable coefficients
• Stable boundary treatment for the wave equation on second-order form
• Stable and high order accurate difference methods for the elastic wave equation in discontinuous media
• Stable and accurate wave-propagation in discontinuous media
• A stable and conservative high order multi-block method for the compressible Navier-Stokes equations
• High-order accurate computations for unsteady aerodynamics
• Summation by parts for finite difference approximations for \(d/dx\)
• Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes
• Summation by parts operators for finite difference approximations of second derivatives
• High order stable finite difference methods for the Schrödinger equation
• Boundary Estimates for the Elastic Wave Equation in Almost Incompressible Materials
• Computational Ocean Acoustics
• Stable and Accurate Interpolation Operators for High-Order Multiblock Finite Difference Methods
• A High‐Order Accurate Parallel Solver for Maxwell’s Equations on Overlapping Grids
• On the approximation of singular source terms in differential equations
• Difference Approximations of the Neumann Problem for the Second Order Wave Equation
• A Fourth-Order Accurate Embedded Boundary Method for the Wave Equation
• Stable Grid Refinement and Singular Source Discretization for Seismic Wave Simulations
• An Embedded Boundary Method for the Wave Equation with Discontinuous Coefficients
• A Second Order Accurate Embedded Boundary Method for the Wave Equation with Dirichlet Data
• Mesh Refinement
• High-order finite difference methods, multidimensional linear problems, and curvilinear coordinates