Additive Schwarz method

The additive Schwarz method is a fancy way of solving big math problems using teamwork. Imagine you and your friends all have different parts of a big puzzle to solve, but you can only talk to one another a little bit at a time. You can't just solve your own piece of the puzzle; you have to talk to your friends and coordinate in order to put the puzzle together.

In math, the pieces of the puzzle are called domains. Each domain is a little piece of a big math problem that needs to be solved. The additive Schwarz method splits up the problem into these smaller domains and tries to solve each one separately. When it's time to put the pieces back together, the method uses what it learned from solving the separate domains to solve the bigger problem as a whole.

Just like you and your friends, the domains in the additive Schwarz method have to communicate with each other to solve the problem. Each domain tells the other domains what it has learned, and they work together to make sure everything fits together in the end. This teamwork makes solving the big math problem much easier and more efficient!