Plot solution of pde toolbox on a line (or submanifold)

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Alessandro 2012-10-31

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https://ww2.mathworks.cn/matlabcentral/answers/52403-plot-solution-of-pde-toolbox-on-a-line-or-submanifold

回答： Lukasz 2025-5-7

I'm using the pde toolbox to solve a certain elliptic equation in 2D.

Solution is fine, although I do need to plot it along a given line, i.e. to cut a planar slice from the 3D mesh representing the solution.

I can't figure out a way that smartly involves the toolbox functions.

Any help appreciated.

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Bill Greene 2012-11-2

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https://ww2.mathworks.cn/matlabcentral/answers/52403-plot-solution-of-pde-toolbox-on-a-line-or-submanifold#answer_64119

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Hi,

Here is one way to create such a plot. Assume you have the point matrix created by the PDE Toolbox mesher, p, and a solution vector, u. The function below will create a plot of that solution along a line defined by the x and y locations of the two end points. My example is for a solution on a unit square and I want a plot along the line (0,.5) to (1,.5). I want to include 25 points in the plot. As you can see, the real work is being done by the TriScatteredInterp function from core MATLAB.

plotAlongLine(p, u, [0,.5], [1,.5], 25);
function plotAlongLine(p, u, xy1, xy2, numpts)
x = linspace(xy1(1),xy2(1),numpts);
y = linspace(xy1(2),xy2(2),numpts);
F = TriScatteredInterp(p(1,:)', p(2,:)', u);
uxy = F(x,y);
figure; plot(x, uxy);
end

Bill

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Torsten 2025-4-19

在 MATLAB Online 中打开

Does this help as an example ?

clear all;

thermalmodel = createpde();

R1= [3,4,0,3,3,0,0,0,10,10]';

R2= [3,4,3,6,6,3,-5,-5,5,5]';

gd= [R1 R2];

sf= 'R1+R2';

ns = char('R1','R2');

ns = ns';

dl = decsg(gd,sf,ns);

geometryFromEdges(thermalmodel,dl);

pdegplot(thermalmodel,"EdgeLabels","on","FaceLabels","on")

xlim([-1 7])

ylim([-6 11])

axis equal

%% Generate and plot mesh

generateMesh(thermalmodel);

figure

pdemesh(thermalmodel)

title("Mesh with Quadratic Triangular Elements")

%% Apply BCs

% Edge 3 is left edge; Edge 5 is right side; edge 8 is middle; Edges 2 & 6 top; Edges 1 & 4 bottom

% Edges 7 & 9 offset vertical edges

applyBoundaryCondition(thermalmodel, "dirichlet",Edge=[3],u=100);

applyBoundaryCondition(thermalmodel, "dirichlet",Edge=[5],u=20);

%% Apply thermal properties in first region

rho1= 1 ; %

cp1= 1 ; %

rhocp1= rho1*cp1 ; %

k1= 1 ; % W/mK

%% Apply thermal properties in second region

rho2= 10 ; %

cp2= 10 ; %

rhocp2= rho2*cp2 ; %

k2= 10 ; % W/mK

%% Define uniform volumetric heat generation rate

Qgen= 0 ; % W/m3 [1e12]

%% Define coefficients for generic Governing Equation to be solved

f= [Qgen];

specifyCoefficients(thermalmodel, m=0, d=rhocp1, c=k1, a=0, f=f, Face=1);

specifyCoefficients(thermalmodel, m=0, d=rhocp2, c=k2, a=0, f=f, Face=2);

coeffs= thermalmodel.EquationCoefficients;

findCoefficients(coeffs, Face=1);

findCoefficients(coeffs, Face=2);

%% Apply initial condition

setInitialConditions(thermalmodel, 20);

%% Define time limits

tlist = 0:1:50;

%% Solve

thermalresults= solvepde(thermalmodel, tlist);

% Plot results

sol = thermalresults.NodalSolution;

subplot(2,2,1)

pdeplot(thermalmodel,"XYData",sol(:,50), ...

"Contour","on",...

"ColorMap","jet")

plotAlongLine(thermalresults.Mesh.Nodes, thermalresults.NodalSolution(:,50), [0,.5], [6,.5], 50);

function plotAlongLine(p, u, xy1, xy2, numpts)

x = linspace(xy1(1),xy2(1),numpts);

y = linspace(xy1(2),xy2(2),numpts);

F = TriScatteredInterp(p(1,:)', p(2,:)', u);

uxy = F(x,y);

figure; plot(x, uxy);

end

Lukasz 2025-4-22

One more question.

How can I export any variables calculated in the function to an external file, especially the data used to create a chart?

Torsten 2025-4-22

编辑：Torsten 2025-4-22

在 MATLAB Online 中打开

timestep = 4;
numpts = 25;
pstart = [0 0];
pend = [1 3];
[x,y,uxy] = plotAlongLine(p, u, pstart, pend, numpts, timestep);
plot(sqrt(x.^2+y.^2),uxy)
writematrix([(sqrt(x.^2+y.^2)).',uxy.'],'Results.xls')
function [x,y,uxy] = plotAlongLine(p, u, xy1, xy2, numpts, timestep)
  x = linspace(xy1(1),xy2(1),numpts);
  y = linspace(xy1(2),xy2(2),numpts);
  F = TriScatteredInterp(p(1,:)', p(2,:)', u(:,timestep));
  uxy = F(x,y);
end

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