Multi-Time-Step Domain Decomposition and Coupling Methods for Non-Linear Structural Dynamics

[1]  C. Farhat,et al.  Optimal convergence properties of the FETI domain decomposition method , 1994 .

[2]  Nils-Erik Wiberg,et al.  STRUCTURAL DYNAMIC ANALYSIS BY A TIME‐DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD , 1996 .

[3]  Daniel Rixen,et al.  THEORETICAL COMPARISON OF THE FETI AND ALGEBRAICALLY PARTITIONED FETI METHODS, AND PERFORMANCE COMPARISONS WITH A DIRECT SPARSE SOLVER , 1999 .

[4]  K. C. Park,et al.  Partitioned Transient Analysis Procedures for Coupled-Field Problems. , 1979 .

[5]  M. Gurtin,et al.  An introduction to continuum mechanics , 1981 .

[6]  A. Prakash,et al.  A FETI‐based multi‐time‐step coupling method for Newmark schemes in structural dynamics , 2004 .

[7]  C. Farhat,et al.  Extending substructure based iterative solvers to multiple load and repeated analyses , 1994 .

[8]  J. C. Simo,et al.  Exact energy-momentum conserving algorithms and symplectic schemes for nonlinear dynamics , 1992 .

[9]  Ahmed F. Ghoniem,et al.  K-means clustering for optimal partitioning and dynamic load balancing of parallel hierarchical N-body simulations , 2005 .

[10]  Alain Combescure,et al.  Multi-time-step explicit–implicit method for non-linear structural dynamics , 2001 .

[11]  P. Smolinski.  Subcycling integration with non-integer time steps for structural dynamics problems , 1996 .

[12]  Claes Johnson,et al.  Finite element methods for linear hyperbolic problems , 1984 .

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

[14]  Charbel Farhat,et al.  Time‐decomposed parallel time‐integrators: theory and feasibility studies for fluid, structure, and fluid–structure applications , 2003 .

[15]  Manolis Papadrakakis,et al.  The mosaic of high-performance domain decomposition methods for structural mechanics––Part II: Formulation enhancements, multiple right-hand sides and implicit dynamics , 2004 .

[16]  M. Ortiz,et al.  Unconditionally stable concurrent procedures for transient finite element analysis , 1986 .

[17]  O. C. Zienkiewicz,et al.  An alpha modification of Newmark's method , 1980 .

[18]  F. Armero,et al.  On the formulation of high-frequency dissipative time-stepping algorithms for nonlinear dynamics. Part I: low-order methods for two model problems and nonlinear elastodynamics , 2001 .

[19]  Kumar K. Tamma,et al.  Algorithms by design with illustrations to solid and structural mechanics/dynamics , 2006 .

[20]  Francesco Ubertini,et al.  An efficient time discontinuous Galerkin procedure for non-linear structural dynamics , 2006 .

[21]  J. Marsden,et al.  Variational Integrators and the Newmark Algorithm for Conservative and Dissipative Mechanical Systems , 2000 .

[22]  Jun Zhang,et al.  BILUTM: A Domain-Based Multilevel Block ILUT Preconditioner for General Sparse Matrices , 1999, SIAM J. Matrix Anal. Appl..

[23]  T. Belytschko,et al.  Stability of explicit‐implicit mesh partitions in time integration , 1978 .

[24]  Jintai Chung,et al.  A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method , 1993 .

[25]  A. Veselov.  Integrable discrete-time systems and difference operators , 1988 .

[26]  Mark O. Neal,et al.  Explicit-explicit subcycling with non-integer time step ratios for structural dynamic systems , 1989 .

[27]  Carlos A. Felippa,et al.  An algebraically partitioned FETI method for parallel structural analysis: algorithm description , 1997 .

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

[29]  J. Marsden,et al.  Introduction to mechanics and symmetry , 1994 .

[30]  Thomas J. R. Hughes,et al.  Convergence of implicit-explicit algorithms in nonlinear transient analysis , 1981 .

[31]  Keith Hjelmstad,et al.  SIMPLE NONLINEAR MODEL FOR ELASTIC RESPONSE OF COHESIONLESS GRANULAR MATERIALS , 2002 .

[32]  Yunus Dere,et al.  Modified Iterative Group-Implicit Algorithm for the Dynamic Analysis of Structures , 2004 .

[33]  John Dubinski.  A parallel tree code , 1996 .

[34]  Thomas J. R. Hughes,et al.  Improved numerical dissipation for time integration algorithms in structural dynamics , 1977 .

[35]  E. Hairer,et al.  Geometric Numerical Integration: Structure Preserving Algorithms for Ordinary Differential Equations , 2004 .

[36]  C. Farhat,et al.  The second generation FETI methods and their application to the parallel solution of large-scale linear and geometrically non-linear structural analysis problems , 2000 .

[37]  C. Farhat,et al.  The two-level FETI method for static and dynamic plate problems Part I: An optimal iterative solver for biharmonic systems , 1998 .

[38]  Richard B. Lehoucq,et al.  An Automated Multilevel Substructuring Method for Eigenspace Computation in Linear Elastodynamics , 2004, SIAM J. Sci. Comput..

[39]  Michael A. Puso,et al.  A 3D mortar method for solid mechanics , 2004 .

[40]  D. Rixen,et al.  FETI‐DP: a dual–primal unified FETI method—part I: A faster alternative to the two‐level FETI method , 2001 .

[41]  Thomas J. R. Hughes,et al.  Implicit-explicit finite elements in nonlinear transient analysis , 1979 .

[42]  Patrick Smolinski,et al.  An implicit multi-time step integration method for structural dynamics problems , 1998 .

[43]  T. R. Hughes,et al.  Mathematical foundations of elasticity , 1982 .

[44]  P. Chadwick.  Continuum Mechanics: Concise Theory and Problems , 1976 .

[45]  Elisa D. Sotelino,et al.  A concurrent explicit-implicit algorithm in structural dynamics , 1994 .

[46]  Thomas J. R. Hughes,et al.  Implicit-Explicit Finite Elements in Transient Analysis: Stability Theory , 1978 .

[47]  Patrick Smolinski,et al.  An explicit multi-time step integration method for second order equations , 1992 .

[48]  Ted Belytschko,et al.  Stability analysis of elemental explicit-implicit partitions by Fourier methods , 1992 .

[49]  F. Armero,et al.  On the formulation of high-frequency dissipative time-stepping algorithms for nonlinear dynamics. Part II: second-order methods , 2001 .

[50]  W. Daniel.  Explicit/implicit partitioning and a new explicit form of the generalized alpha method , 2003 .

[51]  Yuan-Sen Yang,et al.  Iterative mesh partitioning optimization for parallel nonlinear dynamic finite element analysis with direct substructuring , 2002 .

[52]  Charbel Farhat,et al.  Implicit time integration of a class of constrained hybrid formulations—Part I: Spectral stability theory , 1995 .

[53]  Sabine Le Borne,et al.  Multilevel Hierarchical Matrices , 2006, SIAM J. Matrix Anal. Appl..

[54]  M. Ortiz,et al.  Accuracy of a class of concurrent algorithms for transient finite element analysis , 1988 .

[55]  Y. S. Wu,et al.  A multi-time step integration algorithm for structural dynamics based on the modified trapezoidal rule , 2000 .

[56]  J. C. Simo,et al.  Unconditionally stable algorithms for rigid body dynamics that exactly preserve energy and momentum , 1991 .

[57]  Thomas J. R. Hughes,et al.  IMPLICIT-EXPLICIT FINITE ELEMENTS IN TRANSIENT ANALYSIS: IMPLEMENTATION AND NUMERICAL EXAMPLES. , 1978 .

[58]  Wolfgang Hackbusch,et al.  On the Computation of Approximate Eigenvalues and Eigenfunctions of Elliptic Operators by Means of a Multi-Grid Method , 1979 .

[59]  Charbel Farhat,et al.  Implicit parallel processing in structural mechanics , 1994 .

[60]  Charbel Farhat,et al.  A transient FETI methodology for large‐scale parallel implicit computations in structural mechanics , 1994 .

[61]  Masha Sosonkina,et al.  pARMS: a parallel version of the algebraic recursive multilevel solver , 2003, Numer. Linear Algebra Appl..

[62]  Peter Hansbo,et al.  A Lagrange multiplier method for the finite element solution of elliptic interface problems using non-matching meshes , 2005, Numerische Mathematik.

[63]  Elisa D. Sotelino,et al.  The iterative group implicit algorithm for parallel transient finite element analysis , 2000 .

[64]  J. Marsden,et al.  Discrete mechanics and variational integrators , 2001, Acta Numerica.

[65]  Peter Betsch,et al.  Conservation properties of a time FE method—part II: Time‐stepping schemes for non‐linear elastodynamics , 2001 .

[66]  J. Mandel.  Balancing domain decomposition , 1993 .

[67]  U. Hetmaniuk,et al.  A comparison of eigensolvers for large‐scale 3D modal analysis using AMG‐preconditioned iterative methods , 2005 .

[68]  W. Daniel.  A study of the stability of subcycling algorithms in structural dynamics , 1998 .

[69]  Charbel Farhat,et al.  Partitioned analysis of coupled mechanical systems , 2001 .

[70]  P. Smolinski.  Stability analysis of a multi-time step explicit integration method , 1992 .

[71]  T. Hughes,et al.  Space-time finite element methods for elastodynamics: formulations and error estimates , 1988 .

[72]  Ted Belytschko,et al.  Mixed-time implicit-explicit finite elements for transient analysis , 1982 .

[73]  K. Hjelmstad.  Fundamentals of Structural Mechanics , 1996 .

[74]  C. Farhat,et al.  A method of finite element tearing and interconnecting and its parallel solution algorithm , 1991 .

[75]  Ted Belytschko,et al.  Multi-Stepping Implicit-Explicit Procedures in Transient Analysis , 1984 .

[76]  Alain Combescure,et al.  A numerical scheme to couple subdomains with different time-steps for predominantly linear transient analysis , 2002 .

[77]  S. Natsiavas,et al.  Dynamics of large scale mechanical models using multilevel substructuring , 2007 .

[78]  Robert B. Haber,et al.  A space-time discontinuous Galerkin method for linearized elastodynamics with element-wise momentum balance , 2006 .

[79]  T. Belytschko,et al.  Stability of an explicit multi-time step integration algorithm for linear structural dynamics equations , 1996 .

[80]  Peter Haupt,et al.  Continuum Mechanics and Theory of Materials , 1999 .

[81]  Elisa D. Sotelino,et al.  Efficiency of group implicit concurrent algorithms for transient finite element analysis , 1989 .

[82]  William J.T. Daniel,et al.  The subcycled Newmark algorithm , 1997 .

[83]  T. Belytschko,et al.  Explicit multi-time step integration for first and second order finite element semidiscretizations , 1993 .

[84]  Carlos A. Felippa,et al.  A variational principle for the formulation of partitioned structural systems , 2000 .

[85]  T. Hughes,et al.  An improved implicit-explicit time integration method for structural dynamics , 1989 .

[86]  R. D. Wood,et al.  Nonlinear Continuum Mechanics for Finite Element Analysis , 1997 .

[87]  Manolis Papadrakakis,et al.  The mosaic of high performance domain Decomposition Methods for Structural Mechanics: Formulation, interrelation and numerical efficiency of primal and dual methods , 2003 .

[88]  Barbara Wohlmuth,et al.  A new dual mortar method for curved interfaces: 2D elasticity , 2005 .

[89]  Andrea Toselli,et al.  Domain decomposition methods : algorithms and theory , 2005 .

[90]  Robert H. Dodds,et al.  Substructuring in linear and nonlinear analysis , 1980 .

[91]  J. Marsden,et al.  Asynchronous Variational Integrators , 2003 .

[92]  L. R. Scott,et al.  The Mathematical Theory of Finite Element Methods , 1994 .

[93]  Charbel Farhat,et al.  Time‐parallel implicit integrators for the near‐real‐time prediction of linear structural dynamic responses , 2006 .

[94]  Michael Griebel,et al.  Parallel adaptive subspace correction schemes with applications to elasticity , 2000 .

[95]  C. Truesdell,et al.  The Non-Linear Field Theories Of Mechanics , 1992 .

[96]  J. Marsden,et al.  Variational time integrators , 2004 .

[97]  Thomas J. R. Hughes,et al.  Space-time finite element methods for second-order hyperbolic equations , 1990 .

[98]  Nathan M. Newmark,et al.  A Method of Computation for Structural Dynamics , 1959 .

[99]  Ted Belytschko,et al.  Mixed methods for time integration , 1979 .

[100]  Michael T. Heath,et al.  Scientific Computing: An Introductory Survey , 1996 .