Neumueller, M; Smears, I; (2019) Time-Parallel Iterative Solvers for Parabolic Evolution Equations. SIAM Journal on Scientific Computing , 41 (1) C28-C51. 10.1137/18M1172466.

Preview

Text parallel_parabolic.pdf - Accepted Version Download (507kB) | Preview

Abstract

We present original time-parallel algorithms for the solution of the implicit Euler discretization of general linear parabolic evolution equations with time-dependent self-adjoint spatial operators. Motivated by the inf-sup theory of parabolic problems, we show that the standard nonsymmetric time-global system can be equivalently reformulated as an original symmetric saddlepoint system that remains inf-sup stable with respect to the same natural parabolic norms. We then propose and analyse an efficient and readily implementable parallel-in-time preconditioner to be used with an inexact Uzawa method. The proposed preconditioner is non-intrusive and easy to implement in practice, and also features the key theoretical advantages of robust spectral bounds, leading to convergence rates that are independent of the number of time-steps, final time, or spatial mesh sizes, and also a theoretical parallel complexity that grows only logarithmically with respect to the number of time-steps. Numerical experiments with large-scale parallel computations show the effectiveness of the method, along with its good weak and strong scaling properties.

Download activity - last month

Export as JSONCSVXML

Download activity - last 12 months

Export as JSONXMLCSV

Downloads by country - last 12 months

Export as XMLCSVJSON

Archive Staff Only

View Item