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For time-dependent partial differential equations, parallel-in-time integration using the "parallel full approximation scheme in space and time" (PFASST) is a promising way to accelerate existing space-parallel approaches beyond their…

Numerical Analysis · Mathematics 2018-06-07 Matthias Bolten , Dieter Moser , Robert Speck

For the numerical solution of time-dependent partial differential equations, time-parallel methods have recently shown to provide a promising way to extend prevailing strong-scaling limits of numerical codes. One of the most complex methods…

Numerical Analysis · Mathematics 2016-03-14 Matthias Bolten , Dieter Moser , Robert Speck

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 a…

Mathematical Software · Computer Science 2019-12-03 Ruth Schöbel , Robert Speck

The parallel full approximation scheme in space and time (PFASST) introduced by Emmett and Minion in 2012 is an iterative strategy for the temporal parallelization of ODEs and discretized PDEs. As the name suggests, PFASST is similar in…

Numerical Analysis · Mathematics 2015-11-17 Michael Minion , Robert Speck , Matthias Bolten , Matthew Emmett , Daniel Ruprecht

Speeding up computationally expensive problems, such as numerical simulations of large micromagnetic systems, requires efficient use of parallel computing infrastructures. While parallelism across space is commonly exploited in…

Computational Physics · Physics 2023-10-19 Robert Kraft , Sabri Koraltan , Markus Gattringer , Florian Bruckner , Dieter Suess , Claas Abert

The modeling of atmospheric processes in the context of weather and climate simulations is an important and computationally expensive challenge. The temporal integration of the underlying PDEs requires a very large number of time steps,…

Numerical Analysis · Mathematics 2020-01-03 Francois P. Hamon , Martin Schreiber , Michael L. Minion

To solve optimization problems with parabolic PDE constraints, often methods working on the reduced objective functional are used. They are computationally expensive due to the necessity of solving both the state equation and a…

Optimization and Control · Mathematics 2019-12-17 Sebastian Götschel , Michael L. Minion

While many ideas and proofs of concept for parallel-in-time integration methods exists, the number of large-scale, accessible time-parallel codes is rather small. This is often due to the apparent or subtle complexity of the algorithms and…

Performance · Computer Science 2020-08-31 Robert Speck , Michael Knobloch , Sebastian Lührs , Andreas Gocht

We introduce and analyze different strategies for the parallel-in-time integration method PFASST to recover from hard faults and subsequent data loss. Since PFASST stores solutions at multiple time steps on different processors, information…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-03-21 Robert Speck , Daniel Ruprecht

We propose a parareal based time parallelization scheme in the phase-space for the particle-in-Fourier (PIF) discretization of the Vlasov-Poisson system used in kinetic plasma simulations. We use PIF with a coarse tolerance for the…

Numerical Analysis · Mathematics 2025-06-17 Sriramkrishnan Muralikrishnan , Robert Speck

The paper investigates a non-intrusive parallel time integration with multigrid for space-fractional diffusion equations in two spatial dimensions. We firstly obtain a fully discrete scheme via using the linear finite element method to…

Numerical Analysis · Mathematics 2018-05-18 Xiaoqiang Yue , Shi Shu , Xiaowen Xu , Weiping Bu , Kejia Pan

Solving multiscale diffusion problems is often computationally expensive due to the spatial and temporal discretization challenges arising from high-contrast coefficients. To address this issue, a partially explicit temporal splitting…

Numerical Analysis · Mathematics 2026-02-26 Yating Wang , Zhengya Yang , Wing Tat Leung

The paper presents a combination of the time-parallel "parallel full approximation scheme in space and time" (PFASST) with a parallel multigrid method (PMG) in space, resulting in a mesh-based solver for the three-dimensional heat equation…

Numerical Analysis · Computer Science 2015-07-28 Robert Speck , Daniel Ruprecht , Matthew Emmett , Matthias Bolten , Rolf Krause

We construct a space-time parallel method for solving parabolic partial differential equations by coupling the Parareal algorithm in time with overlapping domain decomposition in space. The goal is to obtain a discretization consisting of…

Numerical Analysis · Mathematics 2022-01-17 Jehanzeb Chaudhry , Donald Estep , Simon Tavener

In view of the existing limitations of sequential computing, parallelization has emerged as an alternative in order to improve the speedup of numerical simulations. In the framework of evolutionary problems, space-time parallel methods…

Numerical Analysis · Mathematics 2025-02-13 Andrés Arrarás , Francisco J. Gaspar , Iñigo Jimenez-Ciga , Laura Portero

The full approximation storage (FAS) scheme is a widely used multigrid method for nonlinear problems. In this paper, a new framework to design and analyze FAS-like schemes for convex optimization problems is developed. The new method, the…

Numerical Analysis · Mathematics 2019-10-22 Long Chen , Xiaozhe Hu , Steven M. Wise

We present an adaptive methodology for the solution of (linear and) non-linear time dependent problems that is especially tailored for massively parallel computations. The basic concept is to solve for large blocks of space-time unknowns…

Computational Physics · Physics 2016-08-30 Robert Dyja , Baskar Ganapathysubramanian , Kristoffer G. van der Zee

Simulation of the monodomain equation, crucial for modeling the heart's electrical activity, faces scalability limits when traditional numerical methods only parallelize in space. To optimize the use of large multi-processor computers by…

Numerical Analysis · Mathematics 2024-05-31 Giacomo Rosilho de Souza , Simone Pezzuto , Rolf Krause

In this paper we present the Python framework pySDC for solving collocation problems with spectral deferred correction methods (SDC) and their time-parallel variant PFASST, the parallel full approximation scheme in space and time. pySDC…

Mathematical Software · Computer Science 2018-08-09 Robert Speck

The FEAST algorithm is a subspace iteration method that uses a spectral projector as a rational filter in order to efficiently solve interior eigenvalue problems in parallel. Although the solutions from the FEAST algorithm converge rapidly…

Numerical Analysis · Mathematics 2016-05-30 Brendan Gavin , Eric Polizzi
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