Quick Start in MATLAB

1
Outline
1- Quick Introduction to MATLAB 2- PDE
Toolbox 3- BVP 4- 3 Steps to use PDE
Toolbox 5- Worked Example
2
Quick Start in MATLAB

• MATLAB Help (Help/MATLAB Help/Getting
  Startted/Manipulating Matrices)
• Read getstart.pdf file
• A Matlab tutorial from the University of New
  Hampshire

• Matlab Primer (for an earlier version of Matlab)
• A Matlab tutorial from the University of New
  Hampshire
• MATLAB Online Reference Documentation provides
  direct hypertext links to specific MATLAB
  function descriptions (from the Math Dept,
  University of Florida).
• Matlab Help Desk (including manuals).
• Mathworks, Inc., producers of Matlab.
• Mathtools.net a technical computing portal for
  scientific and engineering needs.

3
PDE Toolbox

• The Partial Differential Equation Toolbox is a
  Matlab based collection of tools for solving
  Partial Differential Equations (PDEs) on a
  two-dimensional surface using the Finite Element
  Method (FEM).
• The 2-D surface can be drawn using four different
  types of solid objects rectangles, ellipses,
  circles, and polygons.
• A brief overview of the major steps of a PDE
  Toolbox GUI (pdetool) session

4
Start PDE toolbox

• Start MATLAB
• Start PDE Toolbox
• type gtgt pdetool

5
Boundary Value Problem (BVP)

• Find
• PDE in
• Under the BC (Boundary Condition)
• BC on

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Example of BVP
(1,1)

• Find
• in
• with the BC (Boundary Condition)
• on

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3 Steps

• I- Define PDE problem
• II- Solve the PDE problem
• III- Visualize the results

8
Example

• Solve

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I- Define a PDE problem

• 1 Draw mode you create the geometry
• ( set of rectangle, circle, ellipse,
  and polygon)
• 2- Boundary mode specify the boundary
  conditions
• (different types of BC on different
  boundary segments)
• 3- PDE mode specify the type of PDE and the
  coeff
• (Elliptic, Parabolic, Hyperbolic)

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II- Solve a PDE problem

• 1 Mesh mode generate and plot meshes
• ( generate, refine, control
  parameters, show labels)
• 2- Solve mode solve the discrete problem
• (Elliptic, Parabolic, Hyperbolic)

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III- Visualize the results

• 1 Plot mode wide range of visualization
  possibilities
• ( color, vector field plots,
  surface, mesh, contour)
• ( time-dependent animated movie)

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Solve A PDE problem