DeepAI AI Chat
Log In Sign Up

pySDC - Prototyping spectral deferred corrections

08/08/2018
by   Robert Speck, et al.
Forschungszentrum Jülich
0

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 features many implementations of SDC and PFASST, from simple implicit time-stepping to high-order implicit-explicit or multi-implicit splitting and multi-level spectral deferred corrections. It comes with many different, pre-implemented examples and has seven tutorials to help new users with their first steps. Time-parallelism is implemented either in an emulated way for debugging and prototyping as well as using MPI for benchmarking. The code is fully documented and tested using continuous integration, including most results of previous publications. Here, we describe the structure of the code by taking two different perspectives: the user's and the developer's perspective. While the first sheds light on the front-end, the examples and the tutorials, the second is used to describe the underlying implementation and the data structures. We show three different examples to highlight various aspects of the implementation, the capabilities and the usage of pySDC. Also, couplings to the FEniCS framework and PETSc, the latter including spatial parallelism with MPI, are described.

READ FULL TEXT

page 15

page 17

08/12/2020

PyMGRIT: A Python Package for the parallel-in-time method MGRIT

In this paper, we introduce the Python framework PyMGRIT, which implemen...
07/01/2016

Massively parallel implementation in Python of a pseudo-spectral DNS code for turbulent flows

Direct Numerical Simulations (DNS) of the Navier Stokes equations is a v...
06/18/2018

Implementation of Peridynamics utilizing HPX -- the C++ standard library for parallelism and concurrency

Peridynamics is a non-local generalization of continuum mechanics tailor...
04/30/2019

Pushing the Limit: A Hybrid Parallel Implementation of the Multi-resolution Approximation for Massive Data

The multi-resolution approximation (MRA) of Gaussian processes was recen...
07/17/2022

Parallelizing Explicit and Implicit Extrapolation Methods for Ordinary Differential Equations

Numerically solving ordinary differential equations (ODEs) is a naturall...
09/11/2020

Kvik: A task based middleware with composable scheduling policies

In this paper we present Kvik: an implementation of a task-based "middle...