A spectral hybridizable discontinuous Galerkin method for elastic-acoustic wave propagation

[1]  Jean-Pierre Vilotte,et al.  Solving elastodynamics in a fluid-solid heterogeneous sphere: a parallel spectral element approximation on non-conforming grids , 2003 .

[2]  Wim A. Mulder,et al.  Local time stepping with the discontinuous Galerkin method for wave propagation in 3D heterogeneous media , 2013 .

[3]  Omar Ghattas,et al.  Analysis of an hp-Nonconforming Discontinuous Galerkin Spectral Element Method for Wave Propagation , 2012, SIAM J. Numer. Anal..

[4]  Emmanuel Chaljub,et al.  Spectral element modelling of three-dimensional wave propagation in a self-gravitating Earth with an arbitrarily stratified outer core , 2003, physics/0308102.

[5]  F. S. Lamb,et al.  On the Propagation of Tremors over the Surface of an Elastic Solid , 1904 .

[6]  Michel Fortin,et al.  Mixed and Hybrid Finite Element Methods , 2011, Springer Series in Computational Mathematics.

[7]  Bernardo Cockburn,et al.  Analysis of an HDG method for linear elasticity , 2015 .

[8]  F. D. Martin,et al.  Verification of a Spectral-Element Method Code for the Southern California Earthquake Center LOH.3 Viscoelastic Case , 2011 .

[9]  Nathalie Glinsky,et al.  Analysis of a high-order space and time discontinuous Galerkin method for elastodynamic equations. Application to 3D wave propagation , 2015 .

[10]  P. Fischer,et al.  High-Order Methods for Incompressible Fluid Flow , 2002 .

[11]  Romain Brossier,et al.  Modelling Seismic Wave Propagation for Geophysical Imaging , 2012 .

[12]  E. Diego Mercerat,et al.  A nodal high-order discontinuous Galerkin method for elastic wave propagation in arbitrary heterogeneous media , 2013 .

[13]  David A. Kopriva,et al.  Metric Identities and the Discontinuous Spectral Element Method on Curvilinear Meshes , 2006, J. Sci. Comput..

[14]  Ruichao Ye,et al.  A discontinuous Galerkin method with a modified penalty flux for the propagation and scattering of acousto-elastic waves , 2015, 1511.00675.

[15]  Francesca Rapetti,et al.  Dispersion analysis of triangle-based spectral element methods for elastic wave propagation , 2012, Numerical Algorithms.

[16]  Julien Diaz,et al.  ROBUST HIGH ORDER NON-CONFORMING FINITE ELEMENT FORMULATION FOR TIME DOMAIN FLUID-STRUCTURE INTERACTION , 2005 .

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

[18]  Marcus J. Grote,et al.  Discontinuous Galerkin Finite Element Method for the Wave Equation , 2006, SIAM J. Numer. Anal..

[19]  J. Virieux,et al.  An hp-adaptive discontinuous Galerkin finite-element method for 3-D elastic wave modelling , 2010 .

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

[21]  Kenji Shimada,et al.  Fully-automated hex-dominant mesh generation with directionality control via packing rectangular solid cells , 2003 .

[22]  Emanuele Casarotti,et al.  Forward and adjoint simulations of seismic wave propagation on fully unstructured hexahedral meshes , 2011 .

[23]  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.

[24]  Barbara Romanowicz,et al.  Fundamentals of Seismic Wave Propagation , 2005 .

[25]  A. T. Hoop,et al.  A modification of cagniard’s method for solving seismic pulse problems , 1960 .

[26]  C. Groot‐Hedlin,et al.  An analysis of ground shaking and transmission loss from infrasound generated by the 2011 Tohoku earthquake , 2013 .

[27]  D Komatitsch,et al.  CASTILLO-COVARRUBIAS JM, SANCHEZ-SESMA FJ. THE SPECTRAL ELEMENT METHOD FOR ELASTIC WAVE EQUATIONS-APPLICATION TO 2-D AND 3-D SEISMIC PROBLEMS , 1999 .

[28]  J. Vilotte,et al.  The Newmark scheme as velocity–stress time-staggering: an efficient PML implementation for spectral element simulations of elastodynamics , 2005 .

[29]  Géza Seriani,et al.  Spectral element method for acoustic wave simulation in heterogeneous media , 1994 .

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

[31]  P. Raviart,et al.  A mixed finite element method for 2-nd order elliptic problems , 1977 .

[32]  Francisco-Javier Sayas,et al.  HDG methods for elastodynamics , 2016, Comput. Math. Appl..

[33]  Jean-Pierre Vilotte,et al.  Triangular Spectral Element simulation of two-dimensional elastic wave propagation using unstructured triangular grids , 2006 .

[34]  Tan Bui-Thanh,et al.  From Godunov to a unified hybridized discontinuous Galerkin framework for partial differential equations , 2015, J. Comput. Phys..

[35]  Ilaria Perugia,et al.  On the Coupling of Local Discontinuous Galerkin and Conforming Finite Element Methods , 2001, J. Sci. Comput..

[36]  Bernardo Cockburn,et al.  High-order implicit hybridizable discontinuous Galerkin methods for acoustics and elastodynamics , 2011, J. Comput. Phys..

[37]  E. Hairer,et al.  Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems , 2010 .

[38]  J. Peraire,et al.  An explicit hybridizable discontinuous Galerkin method for the acoustic wave equation , 2016 .

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

[40]  Jeroen Tromp,et al.  A 1.8 trillion degrees-of-freedom, 1.24 petaflops global seismic wave simulation on the K computer , 2016, Int. J. High Perform. Comput. Appl..

[41]  Francisco-Javier Sayas,et al.  Analysis of HDG methods for Stokes flow , 2010, Math. Comput..

[42]  Bernardo Cockburn,et al.  Uniform-in-time superconvergence of HDG methods for the heat equation , 2012, Math. Comput..

[43]  L. Fezoui,et al.  A high-order Discontinuous Galerkin method for the seismic wave propagation , 2009 .

[44]  Bernardo Cockburn,et al.  A hybridizable discontinuous Galerkin method for linear elasticity , 2009 .

[45]  Diego Mercerat,et al.  Triangular Spectral Element simulation of 2D elastic wave propagation using unstructured triangular grids , 2005 .

[46]  Martin Galis,et al.  The Finite-Difference Modelling of Earthquake Motions: Waves and Ruptures , 2014 .

[47]  Bernardo Cockburn,et al.  Uniform-in-time superconvergence of the HDG methods for the acoustic wave equation , 2013, Math. Comput..

[48]  S. Gedney,et al.  An Auxiliary Differential Equation Formulation for the Complex-Frequency Shifted PML , 2010, IEEE Transactions on Antennas and Propagation.

[49]  D. Arnold,et al.  Mixed and nonconforming finite element methods : implementation, postprocessing and error estimates , 1985 .

[50]  Bernardo Cockburn,et al.  Hybridizable discontinuous Galerkin methods for the time-harmonic Maxwell's equations , 2011, J. Comput. Phys..

[51]  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 .

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

[53]  G. Cohen,et al.  Higher-Order Numerical Methods for Transient Wave Equations , 2001 .

[54]  C. Chapman.  Fundamentals of Seismic Wave Propagation: Frontmatter , 2004 .

[55]  Bernardo Cockburn,et al.  A Hybridizable Discontinuous Galerkin Method for the Compressible Euler and Navier-Stokes Equations , 2010, 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition.

[56]  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 .

[57]  A. Pichon,et al.  Modelling Ground-to-Air Coupling for the Shallow ML 4.3 Folkestone, United Kingdom, Earthquake of 28 April 2007 , 2009 .

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

[59]  David A. Kopriva,et al.  Implementing Spectral Methods for Partial Differential Equations: Algorithms for Scientists and Engineers , 2009 .

[60]  Jean-Pierre Vilotte,et al.  RegSEM: a versatile code based on the spectral element method to compute seismic wave propagation at the regional scale , 2012 .

[61]  C. Pelties,et al.  Regional wave propagation using the discontinuous Galerkin method , 2012 .

[62]  Raytcho D. Lazarov,et al.  Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems , 2009, SIAM J. Numer. Anal..

[63]  L. D. Marini,et al.  Two families of mixed finite elements for second order elliptic problems , 1985 .

[64]  Bernardo Cockburn,et al.  A Characterization of Hybridized Mixed Methods for Second Order Elliptic Problems , 2004, SIAM J. Numer. Anal..

[65]  Bernardo Cockburn,et al.  Superconvergent HDG methods for linear elasticity with weakly symmetric stresses , 2013 .

[66]  Mark Ainsworth,et al.  Dispersive and Dissipative Properties of Discontinuous Galerkin Finite Element Methods for the Second-Order Wave Equation , 2006, J. Sci. Comput..

[67]  David A. Kopriva,et al.  Implementing Spectral Methods for Partial Differential Equations , 2009 .

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

[69]  Georg Stadler,et al.  A high-order discontinuous Galerkin method for wave propagation through coupled elastic-acoustic media , 2010, J. Comput. Phys..

[70]  Douglas N. Arnold,et al.  Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems , 2001, SIAM J. Numer. Anal..

[71]  Roland Martin,et al.  A High-Order Time and Space Formulation of the Unsplit Perfectly Matched Layer for the Seismic Wave Equation Using Auxiliary Differential Equations (ADE-PML) , 2010 .

[72]  Timothy J. Tautges,et al.  The "Hex-Tet" Hex-Dominant Meshing Algorithm as Implemented in CUBIT , 1998, IMR.

[73]  C. H. Dix,et al.  Reflection and Refraction of Progressive Seismic Waves , 1963 .

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

[75]  Bernardo Cockburn,et al.  A Comparison of HDG Methods for Stokes Flow , 2010, J. Sci. Comput..

[76]  T. A. Zang,et al.  Spectral methods for fluid dynamics , 1987 .

[77]  Haiying Wang,et al.  Locally Conservative Fluxes for the Continuous Galerkin Method , 2007, SIAM J. Numer. Anal..

[78]  Mrinal K. Sen,et al.  Dispersion analysis of the spectral element method using a triangular mesh , 2012 .

[79]  D. Komatitsch,et al.  Wave propagation near a fluid-solid interface : A spectral-element approach , 2000 .

[80]  Martin Käser,et al.  Non-conforming hybrid meshes for efficient 2-D wave propagation using the Discontinuous Galerkin Method , 2011 .

[81]  Ezio Faccioli,et al.  2d and 3D elastic wave propagation by a pseudo-spectral domain decomposition method , 1997 .

[82]  Dimitri Komatitsch,et al.  An axisymmetric time-domain spectral-element method for full-wave simulations: Application to ocean acoustics. , 2016, The Journal of the Acoustical Society of America.

[83]  Antonio Huerta,et al.  Hybridizable discontinuous Galerkin p‐adaptivity for wave propagation problems , 2013 .