Outline

1- Quick Introduction to MATLAB

2- PDE Toolbox

3- BVP

4- 3 Steps to use PDE Toolbox

5- Worked Example

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

Matlab Primer (for an earlier version of Matlab)A M tl b t t i l f th U i it f N H hiA Matlab tutorial from the University of New HampshireMATLAB Online Reference Documentation provides direct hypertext links to specific MATLAB

function descriptions (from the Math Dept, University of Florida). Matlab Help Desk (including manuals). M th k I d f M tl bMathworks, Inc., producers of Matlab. Mathtools.net: a technical computing portal for scientific and engineering needs.

PDE ToolboxThe Partial Differential Equation Toolbox is a Matlab based collection of tools for solving Partial Matlab based collection of tools for solving Partial Differential Equations (PDEs) on a two‐dimensional surface using the Finite Element gMethod (FEM).The 2‐D surface can be drawn using four different gtypes 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 Toolboxtype: >> pdetooltype: >> pdetool

Boundary Value Problem (BVP)y ( )Find u

PDE in ΩUnder the BC (Boundary Condition)

BC on ∂Ω∂Ω

Example of BVPExample of BVP

(1,1)Find

in

u Ωf∆ in

with the BC (Boundary Condition)u f∆ =

on0u = ∂Ω

3 Steps Ω3 Steps Ω Setup and Setting

I‐ Define PDE problem ∂Ωu f∆ =

II Solve the PDE problemII‐ Solve the PDE problem

III‐ Visualize the results

ExampleSolve

u f∆ = Ωu f∆0u = 0u =

I‐ Define a PDE problem1 – Draw mode: you create the geometryΩ

( set of rectangle, circle, ellipse, and polygon)

B d d if h b d 2‐ Boundary mode: specify the boundary conditions

(different types of BC on different boundary segments)

PDE d if th t f PDE d th ff3‐ 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( fi l h l b l )( generate, refine, control parameters, show labels)

2‐ Solve mode: solve the discrete problem2 Solve mode: solve the discrete problem(Elliptic, Parabolic, Hyperbolic)

III‐ Visualize the results

1 – Plot mode: wide range of visualization ibilitipossibilities( color, vector field plots, surface, mesh, contour)( time dependent: animated movie)( time‐dependent: animated movie)

Solve A PDE problemp