Feasibility study of the parareal algorithm

[1]  Rolf Krause,et al.  A massively space-time parallel N-body solver , 2012, 2012 International Conference for High Performance Computing, Networking, Storage and Analysis.

[2]  Einar M. Rønquist,et al.  Stability of the Parareal Algorithm , 2005 .

[3]  Yvon Maday,et al.  The parareal in time algorithm , 2008 .

[4]  Kenneth R. Jackson,et al.  A survey of parallel numerical methods for initial value problems for ordinary differential equations , 1991 .

[5]  Yvon Maday,et al.  Monotonic Parareal Control for Quantum Systems , 2007, SIAM J. Numer. Anal..

[6]  W. Miranker,et al.  Parallel methods for the numerical integration of ordinary differential equations , 1967 .

[7]  Eric Aubanel.  Scheduling of tasks in the parareal algorithm , 2011, Parallel Comput..

[8]  Y Maday,et al.  Parallel-in-time molecular-dynamics simulations. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Guillaume Bal,et al.  PARALLELIZATION IN TIME OF ( STOCHASTIC ) ORDINARY DIFFERENTIAL EQUATIONS , 2006 .

[10]  Izaskun Garrido Hernandez,et al.  Convergent iterative schemes for time parallelization , 2006, Math. Comput..

[11]  Yvon Maday,et al.  A Parareal in Time Semi-implicit Approximation of the Navier-Stokes Equations , 2005 .

[12]  J. Lions,et al.  Résolution d'EDP par un schéma en temps « pararéel » , 2001 .

[13]  Stefan Vandewalle,et al.  Waveform Relaxation with Fast Direct Methods as Preconditioner , 2000, SIAM J. Sci. Comput..

[14]  M. Kiehl,et al.  Parallel Multiple Shooting for the Solution of Initial Value Problems , 1994, Parallel Comput..

[15]  Harry B. Bingham,et al.  On the accuracy of finite-difference solutions for nonlinear water waves , 2007 .

[16]  Raúl Sánchez,et al.  Parallelization in time of numerical simulations of fully-developed plasma turbulence using the parareal algorithm , 2010, J. Comput. Phys..

[17]  Yvon Maday.  Parareal in time algorithm for kinetic systems based on model reduction , 2007 .

[18]  Xiaoying Dai,et al.  Stable Parareal in Time Method for First- and Second-Order Hyperbolic Systems , 2012, SIAM J. Sci. Comput..

[19]  Rolf Krause,et al.  Parallel-in-Space-and-Time Simulation of the Three-Dimensional, Unsteady Navier-Stokes Equations for Incompressible Flow , 2014, HPSC.

[20]  Kenneth R. Jackson,et al.  The potential for parallelism in Runge-Kutta methods. Part 1: RK formulas in standard form , 1995 .

[21]  Y. Maday,et al.  A parareal in time procedure for the control of partial differential equations , 2002 .

[22]  Christopher Dyken,et al.  State-of-the-art in heterogeneous computing , 2010, Sci. Program..

[23]  C. A. Fleming,et al.  A three dimensional multigrid model for fully nonlinear water waves , 1997 .

[24]  Li-Ping He,et al.  Parareal in Time Simulation Of Morphological Transformation in Cubic Alloys with Spatially Dependent Composition , 2012 .

[25]  Allan Peter Engsig-Karup,et al.  Parallel Programming using OpenCL on Modern Architectures , 2012 .

[26]  Christopher Harden.  Real Time Computing with the Parareal Algorithm , 2009 .

[27]  Adrian Sandu,et al.  An efficient error control mechanism for the adaptive 'parareal' time discretization algorithm , 2010, SpringSim.

[28]  Franz Chouly,et al.  An Enhanced Parareal Algorithm for Partitioned Parabolic‐Hyperbolic Coupling , 2009 .

[29]  Y. Maday,et al.  A “Parareal” Time Discretization for Non-Linear PDE’s with Application to the Pricing of an American Put , 2002 .

[30]  John Shalf,et al.  Exascale Computing Technology Challenges , 2010, VECPAR.

[31]  Martin J. Gander,et al.  Analysis of the Parareal Time-Parallel Time-Integration Method , 2007, SIAM J. Sci. Comput..

[32]  Alfredo Bellen,et al.  Parallel algorithms for initial-value problems for difference and differential equations , 1989 .

[33]  Michael L. Minion,et al.  A HYBRID PARAREAL SPECTRAL DEFERRED CORRECTIONS METHOD , 2010 .

[34]  Charbel Farhat,et al.  A time‐parallel implicit method for accelerating the solution of non‐linear structural dynamics problems , 2009 .

[35]  Y. Maday,et al.  Symmetric parareal algorithms for Hamiltonian systems , 2010, 1011.6222.

[36]  Samuel Williams,et al.  The Landscape of Parallel Computing Research: A View from Berkeley , 2006 .

[37]  Guillaume Bal,et al.  On the Convergence and the Stability of the Parareal Algorithm to Solve Partial Differential Equations , 2005 .

[38]  Jose C. F. Pereira,et al.  Parallel-in-Time Simulation of Two-Dimensional, Unsteady, Incompressible Laminar Flows , 2006 .

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

[40]  Samantha S. Foley,et al.  A dependency-driven formulation of parareal: parallel-in-time solution of PDEs as a many-task application , 2011, MTAGS '11.

[41]  Yvon Maday,et al.  The Parareal in Time Iterative Solver: a Further Direction to Parallel Implementation , 2005 .

[42]  A. Savitzky,et al.  Smoothing and Differentiation of Data by Simplified Least Squares Procedures. , 1964 .

[43]  Allan Peter Engsig-Karup,et al.  A massively parallel GPU‐accelerated model for analysis of fully nonlinear free surface waves , 2012 .

[44]  Raúl Sánchez,et al.  Event-based parareal: A data-flow based implementation of parareal , 2012, J. Comput. Phys..

[45]  S. Güttel,et al.  Coupling methods for heat transfer and heat flow: Operator splitting and the parareal algorithm , 2012 .

[46]  Jürg Nievergelt,et al.  Parallel methods for integrating ordinary differential equations , 1964, CACM.

[47]  Harry B. Bingham,et al.  An efficient flexible-order model for 3D nonlinear water waves , 2009, J. Comput. Phys..

[48]  Marc Massot,et al.  Symplectic multi-time step parareal algorithms applied to molecular dynamics , 2009 .

[49]  Bernard Philippe,et al.  A parallel shooting technique for solving dissipative ODE's , 1993, Computing.

[50]  H. H. Rachford,et al.  On the numerical solution of heat conduction problems in two and three space variables , 1956 .

[51]  H. Samuel,et al.  Time domain parallelization for computational geodynamics , 2012 .

[52]  Kevin Burrage,et al.  Parallel and sequential methods for ordinary differential equations , 1995, Numerical analysis and scientific computation.

[53]  Martin J. Gander,et al.  On the Superlinear and Linear Convergence of the Parareal Algorithm , 2007, CSE 2007.

[54]  Ashok Srinivasan,et al.  Latency tolerance through parallelization of time in scientific applications , 2004, 18th International Parallel and Distributed Processing Symposium, 2004. Proceedings..

[55]  Alberto L. Sangiovanni-Vincentelli,et al.  The Waveform Relaxation Method for Time-Domain Analysis of Large Scale Integrated Circuits , 1982, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

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

[57]  D. Hutchinson,et al.  Parallel algorithms for initial value problems: parallel shooting , 1992, Parallel Comput..

[58]  G. Sta,et al.  Convergence and Stability of the Parareal algorithm: A numerical and theoretical investigation , 2003 .

[59]  Jean-Pierre Vilotte,et al.  Application of the Parareal Algorithm for Acoustic Wave Propagation , 2009 .