Method of fundamental solutions

Imagine you have a very big puzzle with lots of pieces, and you want to know what shape it makes when it's all put together. The method of fundamental solutions is like having a bunch of helpers who each know what one piece of the puzzle looks like.

First, you take the puzzle and draw a big circle around it. This is the place where you want to find out what shape the puzzle makes. Then you ask each of your helpers to stand on the edge of the circle and tell you what their puzzle piece looks like.

Each helper tells you about their piece by giving you a number. This number tells you how strong or big the puzzle piece is at a certain point. You write all of these numbers down.

Next, you take all of these numbers and put them into a special equation. This equation helps you figure out what the puzzle looks like inside the circle. When you solve the equation, you get a picture that shows you what the puzzle should look like.

The method of fundamental solutions is a way to solve big problems by breaking them down into smaller pieces. It's like having lots of little helpers who each know a little bit about the problem, and they all work together to figure out the solution.