hw_relaxation

Homework for Garcia ch 8, relaxation methods

• Problem 1 (in-class)
• Problem 2 (homework)

Problem 1 (in-class)

Modify relaxation2d_exercise.m to solve Laplace's equation with the Jacobi, Gauss-Seidel, and SOR methods. Apply boundary conditions of:

• Φ = 1 at x = ±0.5 (left/right column)
• Φ = 0 at y = ±0.5 (top/bottom row)
• Use an initial guess of 0 in the interior.

Your code is working if you observe this potential:

Problem 2 (homework)

Modify relaxation2d_exercise.m to solve the following Poisson equation with the Jacobi, Gauss-Seidel, and SOR methods. Implement the ID and BC matrices to account for an interior boundary condition.

∇²Φ = 10cos(πx)cos(3πy)

Use the following boundary conditions:

• Φ = 1 for x = -0.5 (left boundary)
• Φ = 0 for all other outside boundaries
• Φ = 2 for an interior square boundary: -0.1 < x < 0.1, -0.1 < y < 0.1

Set your initial guess to 0 for all points not on a boundary and use ω = 1.6 for the SOR method. Animate your solutions using the mesh plots.