MATLAB PROGRAMMING (SAMPLE ASSIGNMENT)
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Wave Equation on a Square Domain
This sample assignment shows how to solve the wave equation using
the hyperbolic function in the Partial Differential Equation Toolbox™.
We solve the standard second-order wave equation
on a square domain with zero Dirichlet boundary conditions on left and right and zero
Neumann boundary conditions on the top and bottom.
The following variables will define our problem:
g: A specification function that is used by initmesh. For more information, please see the
documentation page for squarereg andpdegeom.
b: A boundary file used by assempde. For more information, please see the
documentation pages for squareb3 and pdebound.
c, a, f, d: The coefficients of the PDE.
pdemesh(p,e,t); axis equal
Generate Initial Conditions
The initial conditions:
This choice avoids putting energy into the higher vibration modes and permits a
reasonable time step size.
We want the solution at 31 points in time between 0 and 5.
Find FEM Solution
428 successful steps
62 failed attempts
982 function evaluations
1 partial derivatives
142 LU decompositions
981 solutions of linear systems
Animate FEM Solution
To speed up the plotting, we interpolate to a rectangular grid.
axis([-1 1 -1 1 umin umax]); caxis([umin umax]);
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