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Outline

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

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Outline

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  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: >> pdetool

  5. Boundary Value Problem (BVP) • Find PDEin • Under the BC (Boundary Condition) BC on

  6. Example of BVP • Find in • with the BC (Boundary Condition) on (1,1)

  7. 3 Steps I- Define PDE problem II- Solve the PDE problem III- Visualize the results

  8. Example • Solve

  9. 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)

  10. 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)

  11. III- Visualize the results 1 –Plot mode: wide range of visualization possibilities ( color, vector field plots, surface, mesh, contour) ( time-dependent: animated movie)

  12. Solve A PDE problem

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