Parallel Extrapolation Methods for Differential Equations | Utkarsh | SciMLCon 2022

Parallel Extrapolation Methods for Differential Equations | Utkarsh | SciMLCon 2022

Abstract: Is there a way to parallelize serial ODE solvers where the Jacobian Matrix is too small to effectively parallelize in the LU-factorization stage? The answer is yes!

The implicit versions are of practical importance in solving stiff ODEs and higher-order precision problems. There's a potential to parallelize these methods and gain the advantage of multi-core machines. While sufficiently large sets of ODEs will be parallelized inside the LU-factorization stage, on systems of stiff ODEs of approximately 100 ODEs or less, this does not overcome the threading overhead in the factorization stage, and thus the solves are effectively serial. Parallel extrapolation methods require multiple factorizations per stage to achieve larger time steps performed in parallel.

For ease of use for the Julia community, these algorithms are purely implemented in Julia and part of the OrdinaryDiffEq solver suite.

Contents:
- What are extrapolation methods?
- Parallelizing them
- Comparison against Hairer's ODEX and SEULEX
- Demonstration of methods on problems and benchmarking
- Integration with SciML ecosystem

00:00 Welcome!
00:10 Help us add time stamps or captions to this video! See the description for details.