Analysis of Two Parareal Algorithms for Time-Periodic Problems
作者： Martin J. Gander , Yao-Lin Jiang , Bo Song , Hui Zhang
DOI: 10.1137/130909172
关键词: Jacobian matrix and determinant 、 Initial value problem 、 Algorithm 、 Context (language use) 、 Boundary value problem 、 Parareal 、 Convergence (routing) 、 Mathematics 、 Shooting method 、 Rate of convergence
摘要: The parareal algorithm, which permits us to solve evolution problems in a time parallel fashion, has created lot of attention over the past decade. algorithm its roots multiple shooting method for boundary value problems, is applied initial with particular coarse approximation Jacobian matrix. It therefore interest formulate parareal-type algorithms time-periodic also couple end interval beginning, and analyze their performance this context. We present two problems: one periodic problem nonperiodic problem. An interesting advantage that no need be solved during iteration, since on subdomains, are not either. prove both linear nonlinear convergence...
sci-hub.se 参考文章(27)
Stefan Vandewalle, Waveform Relaxation Methods Vieweg+Teubner Verlag. pp. 23- 48 ,(1993) , 10.1007/978-3-322-94761-1_2
Paul F. Fischer, Frédéric Hecht, Yvon Maday, A Parareal in Time Semi-implicit Approximation of the Navier-Stokes Equations Springer, Berlin, Heidelberg. pp. 433- 440 ,(2005) , 10.1007/3-540-26825-1_44
Martin J. Gander, Ernst Hairer, Nonlinear Convergence Analysis for the Parareal Algorithm Lecture Notes in Computational Science and Engineering. pp. 45- 56 ,(2008) , 10.1007/978-3-540-75199-1_4
Guillaume Bal, Yvon Maday, A “Parareal” Time Discretization for Non-Linear PDE’s with Application to the Pricing of an American Put Springer, Berlin, Heidelberg. pp. 189- 202 ,(2002) , 10.1007/978-3-642-56118-4_12
Yvon Maday, Gabriel Turinici, The Parareal in Time Iterative Solver: a Further Direction to Parallel Implementation Springer, Berlin, Heidelberg. pp. 441- 448 ,(2005) , 10.1007/3-540-26825-1_45
Guillaume Bal, On the Convergence and the Stability of the Parareal Algorithm to Solve Partial Differential Equations Springer, Berlin, Heidelberg. pp. 425- 432 ,(2005) , 10.1007/3-540-26825-1_43
Charbel Farhat, Marion Chandesris, Time‐decomposed parallel time‐integrators: theory and feasibility studies for fluid, structure, and fluid–structure applications International Journal for Numerical Methods in Engineering. ,vol. 58, pp. 1397- 1434 ,(2003) , 10.1002/NME.860
Yvon Maday, Julien Salomon, Gabriel Turinici, Monotonic Parareal Control for Quantum Systems SIAM Journal on Numerical Analysis. ,vol. 45, pp. 2468- 2482 ,(2007) , 10.1137/050647086
M. Gander, M. Petcu, Analysis of a Krylov subspace enhanced parareal algorithm for linear problems Esaim: Proceedings. ,vol. 25, pp. 114- 129 ,(2008) , 10.1051/PROC:082508
Yvon Maday, Gabriel Turinici, A parareal in time procedure for the control of partial differential equations Comptes Rendus Mathematique. ,vol. 335, pp. 387- 392 ,(2002) , 10.1016/S1631-073X(02)02467-6