A new spectral finite volume method for elastic wave modelling on unstructured meshes

[1]  Dinghui Yang,et al.  A Nearly Analytic Discrete Method for Acoustic and Elastic Wave Equations in Anisotropic Media , 2003 .

[2]  Ernst Hairer,et al.  Solving Ordinary Differential Equations I: Nonstiff Problems , 2009 .

[3]  J. Hesthaven,et al.  Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications , 2007 .

[4]  Wensheng Zhang,et al.  Stability Conditions for Wave Simulation in 3-D Anisotropic Media with the Pseudospectral Method , 2012 .

[5]  Harold L. Atkins,et al.  Eigensolution analysis of the discontinuous Galerkin method with non-uniform grids , 2001 .

[6]  Zhi J. Wang,et al.  Evaluation of discontinuous Galerkin and spectral volume methods for scalar and system conservation laws on unstructured grids , 2004 .

[7]  Mengping Zhang,et al.  An analysis of and a comparison between the discontinuous Galerkin and the spectral finite volume methods , 2005 .

[8]  Li Tong,et al.  A hybrid finite difference/control volume method for the three dimensional poroelastic wave equations in the spherical coordinate system , 2014, J. Comput. Appl. Math..

[9]  Géza Seriani,et al.  3-D large-scale wave propagation modeling by spectral element method on Cray T3E multiprocessor , 1998 .

[10]  D. Komatitsch,et al.  Spectral-element simulations of global seismic wave propagation—I. Validation , 2002 .

[11]  Jianfeng Zhang,et al.  Elastic wave modelling in heterogeneous media with high velocity contrasts , 2004 .

[12]  Eric T. Chung,et al.  Multiscale modeling of acoustic wave propagation in 2D media , 2014 .

[13]  A. Patera A spectral element method for fluid dynamics: Laminar flow in a channel expansion , 1984 .

[14]  Jean-Pierre Berenger,et al.  A perfectly matched layer for the absorption of electromagnetic waves , 1994 .

[15]  Jean Virieux,et al.  SH-wave propagation in heterogeneous media: velocity-stress finite-difference method , 1984 .

[16]  Michael Dumbser,et al.  Arbitrary high order finite volume schemes for linear wave propagation , 2006 .

[17]  Zhiliang Xu,et al.  Hierarchical reconstruction for spectral volume method on unstructured grids , 2009, J. Comput. Phys..

[18]  Hongwei Gao,et al.  Implementation of perfectly matched layers in an arbitrary geometrical boundary for elastic wave modelling , 2008 .

[19]  Wim A. Mulder,et al.  HIGHER-ORDER MASS-LUMPED FINITE ELEMENTS FOR THE WAVE EQUATION , 2001 .

[20]  R. LeVeque Finite Volume Methods for Hyperbolic Problems: Characteristics and Riemann Problems for Linear Hyperbolic Equations , 2002 .

[21]  Gary Cohen,et al.  Mixed Spectral Finite Elements for the Linear Elasticity System in Unbounded Domains , 2005, SIAM J. Sci. Comput..

[22]  Paul G. Richards,et al.  Quantitative Seismology: Theory and Methods , 1980 .

[23]  Dinghui Yang,et al.  Optimal Nearly Analytic Discrete Approximation to the Scalar Wave Equation , 2006 .

[24]  S. Osher,et al.  Efficient implementation of essentially non-oscillatory shock-capturing schemes,II , 1989 .

[25]  Dinghui Yang,et al.  An Optimal Nearly Analytic Discrete Method for 2D Acoustic and Elastic Wave Equations , 2004 .

[26]  Gary Cohen,et al.  MIXED FINITE ELEMENTS WITH MASS-LUMPING FOR THE TRANSIENT WAVE EQUATION , 2000 .

[27]  Yuzhi Sun,et al.  Spectral (finite) volume method for conservation laws on unstructured grids VI: Extension to viscous flow , 2006, J. Comput. Phys..

[28]  Marcel Vinokur,et al.  Spectral (finite) volume method for conservation laws on unstructured grids V: Extension to three-dimensional systems , 2006, J. Comput. Phys..

[29]  M. Y. Hussaini,et al.  An Analysis of the Discontinuous Galerkin Method for Wave Propagation Problems , 1999 .

[30]  Zhang Jianfeng,et al.  Quadrangle-grid velocity-stress finite-difference method for elastic-wave-propagation simulation , 1997 .

[31]  M. Dumbser,et al.  An arbitrary high-order discontinuous Galerkin method for elastic waves on unstructured meshes - I. The two-dimensional isotropic case with external source terms , 2006 .

[32]  Michael Dumbser,et al.  Arbitrary high-order finite volume schemes for seismic wave propagation on unstructured meshes in 2D and 3D , 2007 .

[33]  M. Dumbser,et al.  An arbitrary high-order discontinuous Galerkin method for elastic waves on unstructured meshes — II. The three-dimensional isotropic case , 2006 .

[34]  Mrinal K. Sen,et al.  Grid dispersion and stability criteria of some common finite-element methods for acoustic and elastic wave equations , 2007 .

[35]  J. Virieux P-SV wave propagation in heterogeneous media: Velocity‐stress finite‐difference method , 1986 .

[36]  Jeroen Tromp,et al.  A perfectly matched layer absorbing boundary condition for the second-order seismic wave equation , 2003 .

[37]  E. Toro,et al.  An arbitrary high-order Discontinuous Galerkin method for elastic waves on unstructured meshes - V. Local time stepping and p-adaptivity , 2007 .

[38]  Zhi J. Wang,et al.  Extension of the spectral volume method to high-order boundary representation , 2006 .

[39]  Edip Baysal,et al.  Forward modeling by a Fourier method , 1982 .

[40]  B. Fornberg High-order finite differences and the pseudospectral method on staggered grids , 1990 .

[41]  D. Komatitsch,et al.  Introduction to the spectral element method for three-dimensional seismic wave propagation , 1999 .

[42]  Li Tong,et al.  A new high accuracy locally one-dimensional scheme for the wave equation , 2011, J. Comput. Appl. Math..

[43]  Michael Dumbser,et al.  A highly accurate discontinuous Galerkin method for complex interfaces between solids and moving fluids , 2008 .

[44]  Zhang Jianfeng,et al.  P–SV-wave propagation in heterogeneous media: grid method , 1999 .

[45]  Chi-Wang Shu Total-variation-diminishing time discretizations , 1988 .

[46]  Roland Martin,et al.  WAVE PROPAGATION IN 2-D ELASTIC MEDIA USING A SPECTRAL ELEMENT METHOD WITH TRIANGLES AND QUADRANGLES , 2001 .

[47]  Qiang Du,et al.  Convergence Analysis of a Finite Volume Method for Maxwell's Equations in Nonhomogeneous Media , 2003, SIAM J. Numer. Anal..

[48]  Patrick Joly,et al.  A New Family of Mixed Finite Elements for the Linear Elastodynamic Problem , 2001, SIAM J. Numer. Anal..

[49]  Eric T. Chung,et al.  Optimal Discontinuous Galerkin Methods for Wave Propagation , 2006, SIAM J. Numer. Anal..

[50]  Zhi J. Wang,et al.  Spectral (Finite) Volume Method for Conservation Laws on Unstructured Grids. Basic Formulation , 2002 .

[51]  Michael Dumbser,et al.  An arbitrary high-order discontinuous Galerkin method for elastic waves on unstructured meshes - IV. Anisotropy , 2007 .

[52]  Eric T. Chung,et al.  Optimal Discontinuous Galerkin Methods for the Acoustic Wave Equation in Higher Dimensions , 2009, SIAM J. Numer. Anal..

[53]  Heinz-Otto Kreiss,et al.  Difference Approximations for the Second Order Wave Equation , 2002, SIAM J. Numer. Anal..

[54]  Zhi J. Wang,et al.  Spectral (finite) volume method for conservation laws on unstructured grids IV: extension to two-dimensional systems , 2004 .

[55]  Chris Lacor,et al.  An accuracy and stability study of the 2D spectral volume method , 2007, J. Comput. Phys..

[56]  Zhi Jian Wang,et al.  Spectral (Finite) Volume Method for Conservation Laws on Unstructured Grids III: One Dimensional Systems and Partition Optimization , 2004, J. Sci. Comput..

[57]  Armin Iske,et al.  ADER schemes on adaptive triangular meshes for scalar conservation laws , 2005 .

[58]  J. Sochacki Absorbing boundary conditions for the elastic wave equations , 1988 .

[59]  Michael Dumbser,et al.  Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systems , 2007, J. Comput. Phys..

[60]  Eric T. Chung,et al.  Exact nonreflecting boundary conditions for three dimensional poroelastic wave equations , 2014 .

[61]  Eric T. Chung,et al.  Convergence and superconvergence of staggered discontinuous Galerkin methods for the three-dimensional Maxwell's equations on Cartesian grids , 2013, J. Comput. Phys..

[62]  Mrinal K. Sen,et al.  The interior penalty discontinuous Galerkin method for elastic wave propagation: grid dispersion , 2008 .

[63]  Eleuterio F. Toro,et al.  Towards Very High Order Godunov Schemes , 2001 .

[64]  Rémi Abgrall,et al.  On essentially non-oscillatory schemes on unstructured meshes: analysis and implementation , 1994 .

[65]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[66]  Zhang Jianfeng,et al.  Elastic wave modelling in 3D heterogeneous media: 3D grid method , 2002 .

[67]  Michael Dumbser,et al.  Discontinuous Galerkin methods for wave propagation in poroelastic media , 2008 .

[68]  Géza Seriani,et al.  Numerical simulation of interface waves by high‐order spectral modeling techniques , 1992 .

[69]  M. Dumbser,et al.  An arbitrary high-order Discontinuous Galerkin method for elastic waves on unstructured meshes — III. Viscoelastic attenuation , 2007 .

[70]  Z. Wang,et al.  Spectral (Finite) Volume Method for Conservation Laws on Unstructured Grids , 2002 .

[71]  Hongwei Gao,et al.  Irregular perfectly matched layers for 3D elastic wave modeling , 2011 .

[72]  Jean E. Roberts,et al.  Higher Order Triangular Finite Elements with Mass Lumping for the Wave Equation , 2000, SIAM J. Numer. Anal..

[73]  J. Butcher The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods , 1987 .

[74]  D. Komatitsch,et al.  The spectral element method: An efficient tool to simulate the seismic response of 2D and 3D geological structures , 1998, Bulletin of the Seismological Society of America.

[75]  Alain Sei A Family of Numerical Schemes for the Computation of Elastic Waves , 1995, SIAM J. Sci. Comput..

[76]  Géza Seriani,et al.  Numerical simulation of seismic wave propagation in realistic 3‐D geo‐models with a Fourier pseudo‐spectral method , 2010 .

[77]  Dinghui Yang,et al.  An Explicit Method Based on the Implicit Runge-Kutta Algorithm for Solving Wave Equations , 2009 .

[78]  Eric T. Chung,et al.  Convergence Analysis of Fully Discrete Finite Volume Methods for Maxwell's Equations in Nonhomogeneous Media , 2005, SIAM J. Numer. Anal..

[79]  Bengt Fornberg,et al.  A practical guide to pseudospectral methods: Introduction , 1996 .

[80]  Dinghui Yang,et al.  A weighted Runge–Kutta discontinuous Galerkin method for wavefield modelling , 2015 .

[81]  Wei Zhang,et al.  Three-dimensional elastic wave numerical modelling in the presence of surface topography by a collocated-grid finite-difference method on curvilinear grids , 2012 .

[82]  Moshe Reshef,et al.  Elastic wave calculations by the Fourier method , 1984 .

[83]  Susan E. Minkoff,et al.  Spatial Parallelism of a 3D Finite Difference Velocity-Stress Elastic Wave Propagation Code , 1999, SIAM J. Sci. Comput..