Time Parallel Algorithms

[zhyxue0]

Hello, everyone, I want to implement a time parallel algorithm.

The algorithm is as follows

Step 1.1
Known u_{n}, solve the PDE to get u11
Step 1.2
Known u_{n}, solve the PDE to get u21

Step 2
Known u_{n}, u11, u12，solve the PDE to get u_{n+1}

Step 1.1 and step 1.2 can be solved independently at the same time in parallel. Is it possible to realize it in the framework of firedrake? Or has anyone implemented a similar algorithm? Please give me some ideas.