A finite element method enriched for wave propagation problems

[1]  I. Babuska,et al.  Finite element solution of the Helmholtz equation with high wave number Part I: The h-version of the FEM☆ , 1995 .

[2]  K. Bathe,et al.  The CIP method embedded in finite element discretizations of incompressible fluid flows , 2007 .

[3]  Omar Laghrouche,et al.  Improvement of PUFEM for the numerical solution of high‐frequency elastic wave scattering on unstructured triangular mesh grids , 2010 .

[4]  K. Bathe,et al.  Review: A posteriori error estimation techniques in practical finite element analysis , 2005 .

[5]  D. Chapelle,et al.  The Finite Element Analysis of Shells - Fundamentals , 2003 .

[6]  K. Bathe,et al.  The Mechanics of Solids and Structures - Hierarchical Modeling and the Finite Element Solution , 2011 .

[7]  G. Karniadakis,et al.  Spectral/hp Element Methods for Computational Fluid Dynamics , 2005 .

[8]  K. Bathe.  Conserving energy and momentum in nonlinear dynamics: A simple implicit time integration scheme , 2007 .

[9]  K. Bathe,et al.  The MITC7 and MITC9 Plate bending elements , 1989 .

[10]  M. Christon.  The influence of the mass matrix on the dispersive nature of the semi-discrete, second-order wave equation , 1999 .

[11]  Usik Lee,et al.  An FFT-based spectral analysis method for linear discrete dynamic systems with non-proportional damping , 2006 .

[12]  R. Lee,et al.  A study of discretization error in the finite element approximation of wave solutions , 1992 .

[13]  Jason R. Foley,et al.  Accurate finite element modeling of linear elastodynamics problems with the reduced dispersion error , 2011 .

[14]  R. J. Astley,et al.  Modelling of short wave diffraction problems using approximating systems of plane waves , 2002 .

[15]  Klaus-Jürgen Bathe,et al.  A Simple and Effective Pipe Elbow Element—Linear Analysis , 1980 .

[16]  Theodoros D. Tsiboukis,et al.  Reduction of numerical dispersion in FDTD method through artificial anisotropy , 2000 .

[17]  L. D. Marini,et al.  Stabilization mechanisms in discontinuous Galerkin finite element methods , 2006 .

[18]  R. C. Y. Chin,et al.  Dispersion and Gibbs phenomenon associated with difference approximations to initial boundary-value problems for hyperbolic equations☆ , 1975 .

[19]  Srinivasan Gopalakrishnan,et al.  A Spectral Finite Element Model for Wave Propagation Analysis in Laminated Composite Plate , 2006 .

[20]  K. Marfurt.  Accuracy of finite-difference and finite-element modeling of the scalar and elastic wave equations , 1984 .

[21]  U. Lee.  Spectral Element Method in Structural Dynamics , 2009 .

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

[23]  David W. Zingg,et al.  High-Accuracy Finite-Difference Schemes for Linear Wave Propagation , 1996, SIAM J. Sci. Comput..

[24]  Joannes J. Westerink,et al.  Two‐dimensional dispersion analyses of finite element approximations to the shallow water equations , 2004 .

[25]  K. Bathe,et al.  Effects of element distortions on the performance of isoparametric elements , 1993 .

[26]  I. Babuska,et al.  Dispersion and pollution of the FEM solution for the Helmholtz equation in one, two and three dimensions , 1999 .

[27]  I. Babuska,et al.  Finite Element Solution of the Helmholtz Equation with High Wave Number Part II: The h - p Version of the FEM , 1997 .

[28]  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 .

[29]  Klaus-Jürgen Bathe,et al.  The solution of Maxwell's equations in multiphysics , 2014 .

[30]  Klaus-Jürgen Bathe,et al.  A flow-condition-based interpolation finite element procedure for incompressible fluid flows , 2002 .

[31]  W. Zhong,et al.  Precise Solutions for Surface Wave Propagation in Stratified Material , 2001 .

[32]  K. Bathe,et al.  Stability and accuracy analysis of direct integration methods , 1972 .

[33]  Somasundaram Valliappan,et al.  Assessment of the accuracy of the Newmark method in transient analysis of wave propagation problems , 1992 .

[34]  J. Z. Zhu,et al.  The finite element method , 1977 .

[35]  Phill-Seung Lee,et al.  Measuring the convergence behavior of shell analysis schemes , 2011 .

[36]  Klaus-Jürgen Bathe,et al.  A SIMPLE AND EFFECTIVE PIPE ELBOW ELEMENT-SOME NONLINEAR CAPABILITIES , 1983 .

[37]  Carlo G. Lai,et al.  Surface waves in geomechanics : direct and inverse modelling for soils and rocks , 2005 .

[38]  D. Komatitsch,et al.  Simulation of anisotropic wave propagation based upon a spectral element method , 2000 .

[39]  S. Krenk.  Dispersion-corrected explicit integration of the wave equation , 2001 .

[40]  Klaus-Jürgen Bathe,et al.  A finite element procedure for multiscale wave equations with application to plasma waves , 2010 .

[41]  L. Massidda,et al.  The spectral element method as an effective tool for solving large scale dynamic soil-structure interaction problems , 2006 .

[42]  Isaac Harari,et al.  A survey of finite element methods for time-harmonic acoustics , 2006 .

[43]  C. Farhat,et al.  A discontinuous enrichment method for three‐dimensional multiscale harmonic wave propagation problems in multi‐fluid and fluid–solid media , 2008 .

[44]  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.

[45]  Thomas Grätsch,et al.  Review: A posteriori error estimation techniques in practical finite element analysis , 2005 .

[46]  I. Babuska,et al.  The partition of unity finite element method: Basic theory and applications , 1996 .

[47]  Marek Krawczuk,et al.  Spectral Finite Element Method , 2012 .

[48]  T. Strouboulis,et al.  The generalized finite element method: an example of its implementation and illustration of its performance , 2000 .

[49]  Klaus-Jürgen Bathe,et al.  The inf–sup condition and its evaluation for mixed finite element methods , 2001 .

[50]  Chi-Wang Shu,et al.  Discontinuous Galerkin Methods: Theory, Computation and Applications , 2011 .

[51]  Alfredo Bermúdez,et al.  An optimal perfectly matched layer with unbounded absorbing function for time-harmonic acoustic scattering problems , 2007, J. Comput. Phys..

[52]  Radek Kolman,et al.  Dispersion of elastic waves in the contact-impact problem of a long cylinder , 2010, J. Comput. Appl. Math..

[53]  Omar Laghrouche,et al.  Numerical modelling of elastic wave scattering in frequency domain by the partition of unity finite element method , 2009 .

[54]  Stefan A. Sauter,et al.  Is the Pollution Effect of the FEM Avoidable for the Helmholtz Equation Considering High Wave Numbers? , 1997, SIAM Rev..

[55]  Long Chen.  FINITE ELEMENT METHOD , 2013 .

[56]  H. Cherukuri.  Dispersion analysis of numerical approximations to plane wave motions in an isotropic elastic solid , 2000 .

[57]  B. James,et al.  Wave propagation in elastic solids , 1975 .

[58]  Anil Chaudhary,et al.  On the displacement formulation of torsion of shafts with rectangular cross‐sections , 1982 .

[59]  Jin-Fa Lee,et al.  Time-domain finite-element methods , 1997 .

[60]  Charbel Farhat,et al.  A space–time discontinuous Galerkin method for the solution of the wave equation in the time domain , 2009 .

[61]  M. Guddati,et al.  Modified integration rules for reducing dispersion error in finite element methods , 2004 .

[62]  D. Gottlieb,et al.  Numerical analysis of spectral methods : theory and applications , 1977 .

[63]  Klaus-Jürgen Bathe,et al.  Crushing and crashing of tubes with implicit time integration , 2012 .

[64]  T. Belytschko,et al.  The extended/generalized finite element method: An overview of the method and its applications , 2010 .

[65]  K. Bathe.  Finite Element Procedures , 1995 .

[66]  M. Guddati,et al.  Dispersion-reducing finite elements for transient acoustics , 2005 .

[67]  S. P. Oliveira,et al.  Dispersion analysis of spectral element methods for elastic wave propagation , 2008 .

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