ElementMeshInterpolation
ElementMeshInterpolation[{emesh},{f1,f2,…}]
constructs an InterpolatingFunction object of the function values fj, corresponding to coordinate j of an ElementMesh object.
ElementMeshInterpolation[{{t1,t2,…},emesh},
{{{f11,f12,…}},{{f21,f22,…}},…}]
constructs an interpolation of the function values fij, corresponding to discrete ti and coordinate j of an ElementMesh object.
更多信息和选项
- ElementMeshInterpolation returns an InterpolatingFunction object, which can be used like any other pure function.
- The function values f can be real or complex numbers.
- The ElementMesh object may contain curved elements.
- ElementMeshInterpolation works by fitting polynomial curves between data points belonging to the same element.
- The degree of the polynomial curves is specified by the option InterpolationOrder.
- The default InterpolationOrder is the order of the ElementMesh.
- You can do linear interpolation by using the setting InterpolationOrder1.
- ElementMeshInterpolation[data] generates an InterpolatingFunction object that returns values with MachinePrecision.
- ElementMeshInterpolation has the same options as Interpolation, with the following additions:
-
"ExtrapolationHandler" Automatic specify how extrapolation is handled - Setting the option from NDSolve and related functions is explained in NDSolve Finite Element Options.
范例
打开所有单元关闭所有单元基本范例 (2)
Set up an ElementMesh:
Set up function values at the mesh coordinates:
Create an InterpolatingFunction:
Apply the function to find interpolated values:
Plot the interpolating function:
Generate function values for a time-dependent interpolation:
Options (5)
"ExtrapolationHandler" (5)
Construct an InterpolatingFunction:
Query the InterpolatingFunction outside of its domain:
Construct an InterpolatingFunction with an extrapolation handler that returns Indeterminate for queries outside the domain:
Query the InterpolatingFunction outside of its domain:
Construct an InterpolatingFunction with an extrapolation handler that returns 0 outside its domain:
Query the InterpolatingFunction outside of its domain:
Construct an InterpolatingFunction with an extrapolation handler that returns Indeterminate outside its domain and does not give a warning message:
Query the InterpolatingFunction outside of its domain:
The default for NDSolve and the finite element method is to return InterpolatingFunction objects that do not extrapolate outside of the given domain:
Allow InterpolatingFunction objects generated by NDSolve to extrapolate when evaluated outside of the simulation domain and not warn about it:
While it is not generally possible to construct periodic interpolating functions for arbitrary meshes, one can mimic periodic interpolating functions based on rectangular regions by specifying an "ExtrapolatiopnHandler".
Generate a temporary interpolating function from this mesh and data:
Use the extrapolation handler to map the coordinates outside of the meshed domain back into the domain and evaluate over the temporary interpolating function:
To verify that the interpolation is now periodic, visualize the function f both inside and outside the original domain:
Properties & Relations (1)
For time-independent interpolation, ListInterpolation can also be used:
文本
Wolfram Research (2020)，ElementMeshInterpolation，Wolfram 语言函数，https://reference.wolfram.com/language/FEMDocumentation/ref/ElementMeshInterpolation.html （更新于 2021 年）.
CMS
Wolfram 语言. 2020. "ElementMeshInterpolation." Wolfram 语言与系统参考资料中心. Wolfram Research. 最新版本 2021. https://reference.wolfram.com/language/FEMDocumentation/ref/ElementMeshInterpolation.html.
APA
Wolfram 语言. (2020). ElementMeshInterpolation. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/FEMDocumentation/ref/ElementMeshInterpolation.html 年