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DiscontinuousInterpolatingFunction—Wolfram Documentation

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DiscontinuousInterpolatingFunction[]

represents an approximate discontinuous function whose values are found by interpolation.

• DiscontinuousInterpolatingFunction is used to interpolate discontinuous data.
• DiscontinuousInterpolatingFunction works like Function.
• DiscontinuousInterpolatingFunction[…][x] finds the value of an approximate discontinuous function with a particular argument x.
• DiscontinuousInterpolatingFunction objects that take up to three real arguments may be constructed.
• If you supply arguments outside of the domain, a warning is generated, and then an extrapolated value is returned.
• You can take derivatives of DiscontinuousInterpolatingFunction objects using functions such as D, Derivative or Grad.
• EvaluateOnElementMesh can return its results in terms of DiscontinuousInterpolatingFunction objects.
• DiscontinuousInterpolatingFunction can convert InterpolatingFunction objects based on ElementMesh to DiscontinuousInterpolatingFunction objects.
• DiscontinuousInterpolatingFunction[…][prop] gives the property prop of the DiscontinuousInterpolatingFunction object. The following properties may be given:
• "ElementMesh" returns the spatial mesh "InterpolatingFunctions" returns the interpolating functions used for interpolation "MarkerPriority" returns the marker priority "ValuesOnGrid" gives the function values at each mesh coordinate

Load the package:

Generate a multi-material element mesh with element markers 10 and 20:

Visualize the mesh and the material regions in light green and light red.

Evaluate a discontinuous function on the mesh:

Plot the DiscontinuousInterpolatingFunction:

Compute a derivative of the DiscontinuousInterpolatingFunction:

Plot the derivative of the DiscontinuousInterpolatingFunction:

The value at the interface will depend on the priority of the mesh markers:

Inspect the value of the discontinuous function at , :

At the interface, the value associated with marker 10 will have precedence over the values associated with marker 20. The precedence at the interface can be changed by altering the marker priority.

Create a discontinuous interpolating function with an altered marker precedence:

Inspect the marker priority:

Inspect the value of the discontinuous function at , :

Extract the marker priority that is used to determine the order in which values at the material interface are processed:

Extract the values on the grid:

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