Parallel solution of reaction-diffusion equations with a stabilization method

Task:

• solve systems of partial differential equations with nonlinear coupling
• background: chemical process engineering
• problem with parameter studies: a few modes become unstable
• fast standard solvers don't work
• other solvers work slowly

Basic Idea:

• split the solution space into a (small) hard part and a (huge) easy part
• use different (parallel) solvers in each subspace
• synchronize both solvers when necessary

Difficult load balancing:

• solvers have different convergence speed
• synchronization using traditional messages difficult (e.g. via polling)

Solution:

• solvers write results directly into control task
• use onesided communication