Finite element exterior calculus
Finite element exterior calculus (FEEC) is a method of solving mathematical problems that involves using small pieces, called elements, to approximate the behavior of a larger system. Imagine you have a puzzle with many pieces, and you want to understand how it fits together. Instead of trying to solve the puzzle all at once, you break it down into smaller parts and solve each one separately. That’s what FEEC does.
But why is FEEC special? Well, it’s inspired by something called exterior calculus, which is a way of studying calculus (mathematical stuff like derivatives and integrals) that focuses on how things change as you move around in space. Imagine you are walking along a path, and you want to know how something changes as you travel along that path - that’s what exterior calculus is all about.
Now, back to FEEC. When we use FEEC to solve a problem, we break the system down into small pieces (elements). But, we don’t just treat each piece as a simple unit like we might with other methods. Instead, we look at how they are related to each other - kind of like how each piece of a puzzle is related to the ones next to it.
One of the key things we look at is how things change as we move from one element to another. For example, if we’re solving a problem that involves a fluid moving across a boundary, we want to understand how the flow of the fluid changes as it moves from one part of the boundary to another. By using exterior calculus in this way, we can find the best solution to our problem, one element at a time!
But why is FEEC special? Well, it’s inspired by something called exterior calculus, which is a way of studying calculus (mathematical stuff like derivatives and integrals) that focuses on how things change as you move around in space. Imagine you are walking along a path, and you want to know how something changes as you travel along that path - that’s what exterior calculus is all about.
Now, back to FEEC. When we use FEEC to solve a problem, we break the system down into small pieces (elements). But, we don’t just treat each piece as a simple unit like we might with other methods. Instead, we look at how they are related to each other - kind of like how each piece of a puzzle is related to the ones next to it.
One of the key things we look at is how things change as we move from one element to another. For example, if we’re solving a problem that involves a fluid moving across a boundary, we want to understand how the flow of the fluid changes as it moves from one part of the boundary to another. By using exterior calculus in this way, we can find the best solution to our problem, one element at a time!