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TimeDependentResults

Time-dependent PDE solution and derived quantities

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Description

A TimeDependentResults object contains the solution of a PDE and its gradients in a form convenient for plotting and postprocessing.

  • A TimeDependentResults object contains the solution and its gradient calculated at the nodes of the triangular or tetrahedral mesh, generated by generateMesh.

  • Solution values at the nodes appear in the NodalSolution property.

  • The solution times appear in the SolutionTimes property.

  • The three components of the gradient of the solution values at the nodes appear in the XGradients, YGradients, and ZGradients properties.

  • The array dimensions of NodalSolution, XGradients, YGradients, and ZGradients enable you to extract solution and gradient values for specified time indices, and for the equation indices in a PDE system.

To interpolate the solution or its gradient to a custom grid (for example, specified by meshgrid), use interpolateSolution or evaluateGradient.

Creation

There are several ways to create a TimeDependentResults object:

  • Solve a time-dependent problem using the solvepde function. This function returns a PDE solution as a TimeDependentResults object. This is the recommended approach.

  • Solve a time-dependent problem using the parabolic or hyperbolic function. Then use the createPDEResults function to obtain a TimeDependentResults object from a PDE solution returned by parabolic or hyperbolic. Note that parabolic and hyperbolic are legacy functions. They are not recommended for solving PDE problems.

Properties

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This property is read-only.

Finite element mesh, returned as a FEMesh object.

This property is read-only.

Solution values at the nodes, returned as a vector or array. For details about the dimensions of NodalSolution, see Dimensions of Solutions, Gradients, and Fluxes.

Data Types: double
Complex Number Support: Yes

This property is read-only.

Solution times, returned as a real vector. SolutionTimes is the same as the tlist input to solvepde, or the tlist input to the legacy parabolic or hyperbolic solvers.

Data Types: double

This property is read-only.

x-component of the gradient at the nodes, returned as a vector or array. For details about the dimensions of XGradients, see Dimensions of Solutions, Gradients, and Fluxes.

Data Types: double
Complex Number Support: Yes

This property is read-only.

y-component of the gradient at the nodes, returned as a vector or array. For details about the dimensions of YGradients, see Dimensions of Solutions, Gradients, and Fluxes.

Data Types: double
Complex Number Support: Yes

This property is read-only.

z-component of the gradient at the nodes, returned as a vector or array. For details about the dimensions of ZGradients, see Dimensions of Solutions, Gradients, and Fluxes.

Data Types: double

Object Functions

evaluateCGradientEvaluate flux of PDE solution
evaluateGradientEvaluate gradients of PDE solutions at arbitrary points
interpolateSolutionInterpolate PDE solution to arbitrary points

Examples

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Open Live Script

Solve a parabolic problem with 2-D geometry.

Create and view the geometry: a square with a circular subdomain.

% Square centered at (1,1)
rect1 = [3;4;0;2;2;0;0;0;2;2];
% Circle centered at (1.5,0.5)
circ1 = [1;1.5;.75;0.25];
% Append extra zeros to the circle
circ1 = [circ1;zeros(length(rect1)-length(circ1),1)];
gd = [rect1,circ1];
ns = char('rect1','circ1');
ns = ns';
sf = 'rect1+circ1';
[dl,bt] = decsg(gd,sf,ns);
pdegplot(dl,"EdgeLabels","on","FaceLabels","on")
axis equal
ylim([-0.1,2.1])

Figure contains an axes object. The axes object contains 11 objects of type line, text.

Include the geometry in a PDE model.

model = createpde();
geometryFromEdges(model,dl);

Set boundary conditions that the upper and left edges are at temperature 10.

applyBoundaryCondition(model,"dirichlet","Edge",[2,3],"u",10);

Set initial conditions that the square region is at temperature 0, and the circle is at temperature 100.

setInitialConditions(model,0);
setInitialConditions(model,100,"Face",2);

Define the model coefficients.

specifyCoefficients(model,"m",0,"d",1,"c",1,"a",0,"f",0);

Solve the problem for times 0 through 1/2 in steps of 0.01.

generateMesh(model,"Hmax",0.05);
tlist = 0:0.01:0.5;
results = solvepde(model,tlist);

Plot the solution for times 0.02, 0.04, 0.1, and 0.5.

sol = results.NodalSolution;
subplot(2,2,1)
pdeplot(model,"XYData",sol(:,3))
title("Time 0.02")
subplot(2,2,2)
pdeplot(model,"XYData",sol(:,5))
title("Time 0.04")
subplot(2,2,3)
pdeplot(model,"XYData",sol(:,11))
title("Time 0.1")
subplot(2,2,4)
pdeplot(model,"XYData",sol(:,51))
title("Time 0.5")

Figure contains 4 axes objects. Axes object 1 with title Time 0.02 contains an object of type patch. Axes object 2 with title Time 0.04 contains an object of type patch. Axes object 3 with title Time 0.1 contains an object of type patch. Axes object 4 with title Time 0.5 contains an object of type patch.

Version History

Introduced in R2016a

See Also

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