pdeintrp

(Not recommended) Interpolate mesh nodal data to triangle midpoints

pdeintrp is not recommended. Use interpolateSolution and evaluateGradient instead.

Syntax

ut = pdeintrp(p,t,un)

Description

ut = pdeintrp(p,t,un) uses the data un at mesh nodes to linearly interpolate data at mesh triangle midpoints.

pdeintrp and pdeprtni are not inverse functions because the interpolation introduces some averaging.

Examples

Data at Mesh Nodes and Triangle Midpoints

Solve the equation $$-\Delta u=1$$ on the L-shaped membrane and interpolate the solution from nodes to triangle midpoints.

First, create a [p,e,t] mesh on the L-shaped membrane.

[p,e,t] = initmesh('lshapeg'); 

Solve the equation using the Dirichlet boundary condition $$u=0$$ on $$\partial \Omega$$. The result is the solution at the mesh nodes.

un = assempde('lshapeb',p,e,t,1,0,1);

Interpolate the solution from the mesh nodes to the triangle midpoints.

ut = pdeintrp(p,t,un);

Interpolate the solution back to nodes by using the pdeprtni function. Compare the result and the original solution at the mesh nodes. The pdeprtni and pdeintrp functions are not inverse.

un2 = pdeprtni(p,t,ut);
isequal(un,un2)

ans = logical
   0

Input Arguments

p — Mesh nodes

matrix

Mesh nodes, specified as a 2-by-Np matrix of nodes (points), where Np is the number of nodes in the mesh. For details on the mesh data representation, see initmesh.

Data Types: double

t — Mesh elements

matrix

Mesh elements, specified as a 4-by-Nt matrix of triangles, where Nt is the number of triangles in the mesh. For details on the mesh data representation, see initmesh.

Data Types: double

un — Data at nodes

column vector

Data at nodes, specified as a column vector.

For a PDE system of N equations and a mesh with Np node points, the first Np values of un describe the first component, the following Np values of un describe the second component, and so on.

Data Types: double

Output Arguments

ut — Data at triangle midpoints

row vector

Data at triangle midpoints, returned as a row vector.

For a PDE system of N equations and a mesh with Nt elements, the first Nt values of ut describe the first component, the following Nt values of ut describe the second component, and so on.

Version History

Introduced before R2006a

R2016a: Not recommended

pdeintrp is not recommended. Use interpolateSolution and evaluateGradient instead. There are no plans to remove pdeintrp.