Matlab programming project
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This document provides a sample MATLAB assignment to solve the wave equation on a square domain with zero boundary conditions. It defines the problem variables, generates a mesh, sets the initial conditions, defines the time discretization, finds the finite element solution, and animates the solution over time. The wave equation is solved using the hyperbolic function in MATLAB's Partial Differential Equation Toolbox.
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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.
Problem Definition
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.
g='squareg';
b='squareb3';
c=1;
a=0;
f=0;
d=1;
Generate Mesh
[p,e,t]=initmesh('squareg');
figure;
pdemesh(p,e,t); axis equal
info@assignmentpedia.com](https://image.slidesharecdn.com/matlabprogrammingproject-130919065804-phpapp01/85/Matlab-programming-project-1-320.jpg)
![uu=hyperbolic(u0,ut0,tlist,b,p,e,t,c,a,f,d);
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.
figure; set(gcf,'renderer','zbuffer');
delta=-1:0.1:1;
[uxy,tn,a2,a3]=tri2grid(p,t,uu(:,1),delta,delta);
gp=[tn;a2;a3];
newplot;
umax=max(max(uu));
umin=min(min(uu));
for i=1:n
pdeplot(p,e,t,'xydata',uu(:,i),'zdata',uu(:,i),'zstyle','continuous',...
'mesh','off','xygrid','on','gridparam',gp,'colorbar','off');
axis([-1 1 -1 1 umin umax]); caxis([umin umax]);
M(i)=getframe;
end
movie(M,1);](https://image.slidesharecdn.com/matlabprogrammingproject-130919065804-phpapp01/85/Matlab-programming-project-3-320.jpg)
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YSPH VMOC Special Report - Measles Outbreak Southwest US 6-14-2025.pptx
YSPH VMOC Special Report - Measles Outbreak Southwest US 6-14-2025.pptxYale School of Public Health - The Virtual Medical Operations Center (VMOC)
Matlab programming project
- 1. MATLAB PROGRAMMING (SAMPLE ASSIGNMENT) Our online Tutors are available 24*7 to provide Help with Help with Matlab Programming Homework/Assignment or a long term Graduate/Undergraduate Help with Matlab Programming Project. Our Tutors being experienced and proficient in Help with Matlab Programming ensure to provide high quality Help with Matlab Programming Homework Help. Upload your Help with Matlab Programming Assignment at ‘Submit Your Assignment’ button or email it to . You can use our ‘Live Chat’ option to schedule an Online Tutoring session with our Help with Matlab Programming Tutors. 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. Problem Definition 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. g='squareg'; b='squareb3'; c=1; a=0; f=0; d=1; Generate Mesh [p,e,t]=initmesh('squareg'); figure; pdemesh(p,e,t); axis equal [email protected]
- 2. Generate Initial Conditions The initial conditions: . . This choice avoids putting energy into the higher vibration modes and permits a reasonable time step size. x=p(1,:)'; y=p(2,:)'; u0=atan(cos(pi/2*x)); ut0=3*sin(pi*x).*exp(sin(pi/2*y)); Define Time-Discretization We want the solution at 31 points in time between 0 and 5. n=31; tlist=linspace(0,5,n); Find FEM Solution
- 3. uu=hyperbolic(u0,ut0,tlist,b,p,e,t,c,a,f,d); 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. figure; set(gcf,'renderer','zbuffer'); delta=-1:0.1:1; [uxy,tn,a2,a3]=tri2grid(p,t,uu(:,1),delta,delta); gp=[tn;a2;a3]; newplot; umax=max(max(uu)); umin=min(min(uu)); for i=1:n pdeplot(p,e,t,'xydata',uu(:,i),'zdata',uu(:,i),'zstyle','continuous',... 'mesh','off','xygrid','on','gridparam',gp,'colorbar','off'); axis([-1 1 -1 1 umin umax]); caxis([umin umax]); M(i)=getframe; end movie(M,1);
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