Outline 1 Quick Introduction to MATLAB 2 PDE

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 q. MATLAB Help (Help/MATLAB Help/Getting Startted/Manipulating Matrices) q. Read getstart. pdf file q. 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.

PDE Toolbox • The Partial Differential Equation Toolbox is a Matlab based collection of tools for solving Partial Differential Equations (PDEs) on a twodimensional 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:

Start PDE toolbox • Start MATLAB • Start PDE Toolbox type: >> pdetool

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

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

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

Example • Solve

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)

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)

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

Solve A PDE problem