2026-08-13 –, Room 4
For specific classes of time-dependent PDEs it can become handy to split the full problem up into simpler to handle subproblems, such that we can exploit the specific structure of each subproblem during time integration. To achieve this goal we introduce https://github.com/SciML/OrdinaryDiffEqOperatorSplitting.jl a library that allows user to split ODEs and DAEs into sub-problems, where we allow problems to be recursively split. The library coordinates in which order the sub-problems need to be integrated, while each of the sub-problems can be solved which a suitable solver from OrdinaryDiffEq.jl .
One aspect of partial differential equations that makes efficient solving difficult is that different parts of the equations may have different timescales which traditionally has led to scientists writing their own custom timestepping algorithms. A better solution to this problem is to have ODE solver libraries define an API by which the user can communicate the desired splitting of the problem to the solver, and then the solver can use appropriate algorithms to solve the individual pieces. This package uses a splitting technique where each component takes a timestep independent of the other components, and then the communicating the state updates between the components.
This splitting of equations can lead to significant performance increases because the sub-problems can be chosen to have additional structure when compared to the full problem. Splitting can separate non-stiff components of the equations, linear or affine pieces, or simply separating loosely related components to reduce the size of the nonlinear problems that need to be solved. As such, splitting can significantly accelerate simulation.
I work for JuliaHub at making ODEs go fast.
Researcher in Computational Cardiology at the chair of continuum mechanics of Professor Dr.-Ing. Daniel Balzani at the Ruhr University Bochum.
Leading developer of Thunderbolt.jl and developer of Ferrite.jl. More detailed information on my contributions to the open source ecosystem can be found at my GitHub profile.