The Dirichlet problem is extremely important in mathematical physics.
mathematics
Description
The Dirichlet problem is extremely important in mathematical physics. It has been studied initially for determining the equilibrium temperature distribution on a disk from measurements taken along the boundary. Over regular domains such as a disk or a rectangle, a classical (and textbook) approach is to employ the so called Green’s function. Over irregular domains, this analytic approach becomes infeasible, if not entirely impossible. However, the idea of computing a numerical solution still prevails. To practice this idea, this project asks you to imagine the following domain Ω as a zoom-in corner of a much larger and more irregular domain. The main point is that you have to convert the differential equation into an algebraic equation. The challenge is at the setup. Once you figure out how this can be done by hand over the coarse grids shown below, write a generic code that can automatically generating grids to any prescribed precision so long as your computer can handle it.
Instruction Files
Project1.pdf
47.5 KB
