Matlab pdetoolbox demo

A toolbox for solving 2d & 3d generic pde using Finite Element Method

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Example 1:

Solving Poisson Equation on a Unit Disk Follow along this Matlab Tutorial and try to answer these questions

• What was the domain?
• What was the equation?
• What were the boundary conditions?
• What is it that you just plotted?

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Example 2:

Solve the Poisson equation in the unit square

$$\Dt(u) = 0, \qquad \textrm{for } 0 \le x,y, \le 1,$$

with boundary conditions: $u(y,0) = 0, u(1,y) = 1 \;\forall y$, and $\frac{\p u}{\p y}(x,0) = \frac{\p u}{\p y}(x,1) =0$ for all $0 \le x \le 1$.

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Example 3: Poisson’s Equation with Complex 2-D Geometry

Follow along this Matlab Tutorial and try to answer these questions

• What was the domain?
• What was the equation?
• What were the boundary conditions?
• What is it that you just plotted?

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Exercise 1: A shell with hot inside ring

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Exercise 2: A shell with hot inside ring and Neumann boundary outside

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Project 1: Solve a given PDE with slightly non trivial domain in matlab.

Ajit: coming shortly

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Using pdetoolbox over commandlines

Relevant pages from Matlab documentation

• Matlab PDE workflow
• Geometry of 2 dimensional problems
• Geometry of 3 dimensional problems

Recommended steps:

• Create problems geometry with some GUI based application. Matlab pde app will work fine for 2d problems; I recommend using Gmsh for 3d problems. You can also try some equally good and also free alternatives like Paraview or Salome.

Exercise 1

Solve the problem shown in the figure below using the pdetool app

Then

• Save the app data as exercise1.m
• Modify the script exercise1.m so that innercircle is cold and outer circle hot.
• Study every line in the exercise1.m and find (either guess or look into matlab documentation) what that line does.