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PDE ToolboxThe 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.
Start PDE toolbox
Start MATLAB
• Start PDE Toolbox type: >> pdetool
Boundary Value Problem (BVP)Find
PDE in
Under the BC (Boundary Condition)
BC on
u
Ωn u
Ωu
o0
in 1
)1,1()1,1(
Example:
)1,1(
)1,1(
Example of BVP
Find
in
with the BC (Boundary Condition)
on
u u f
0u
(1,1)
3 Steps
I- Define PDE problem
u f
II- Solve the PDE
problem
III- Visualize the results
Setup and Setting
ExampleSolve
u f 0u
I- Define a PDE problem1 – 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)
MATLAB Help (Help/MATLAB Help/Getting Startted/Manipulating Matrices)Read getstart.pdf fileA 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.