PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method

• Published in: Computing and visualization in science Vol. 23; no. 1-4
• Main Authors: Schöbel, Ruth, Speck, Robert
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2020; Springer Nature B.V
• Subjects: Algorithms; Approximation; Calculus of Variations and Optimal Control; Optimization; Computational Mathematics and Numerical Analysis; Computer Applications in Chemistry; Concurrency; Mathematical analysis; Mathematics; Mathematics and Statistics; Numerical Analysis; Parallel processing; Partial differential equations; PinT 2019; Time dependence; Visualization; Parallel full approximation scheme in space and time; Quasi-Newton; Parallel-in-time integration; Spectral deferred corrections; Parallelization across the step; Parallelization across the method
• ISSN: 1432-9360; 1433-0369
• DOI: 10.1007/s00791-020-00330-5

To extend prevailing scaling limits when solving time-dependent partial differential equations, the parallel full approximation scheme in space and time (PFASST) has been shown to be a promising parallel-in-time integrator. Similar to space–time multigrid, PFASST is able to compute multiple time-steps simultaneously and is therefore in particular suitable for large-scale applications on high performance computing systems. In this work we couple PFASST with a parallel spectral deferred correction (SDC) method, forming an unprecedented doubly time-parallel integrator. While PFASST provides global, large-scale “parallelization across the step”, the inner parallel SDC method allows integrating each individual time-step “parallel across the method” using a diagonalized local Quasi-Newton solver. This new method, which we call “PFASST with Enhanced concuRrency” (PFASST-ER), therefore exposes even more temporal concurrency. For two challenging nonlinear reaction-diffusion problems, we show that PFASST-ER works more efficiently than the classical variants of PFASST and can use more processors than time-steps.