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user21
user21
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AsukaMinato
AsukaMinato
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I am solving non-linear PDE using iterations. Correspondingly, the coefficients are functions on the (same) mesh that I have created and fixed. Between iterations I need to update these function by doing some arithmetic operations on them. Just doing all in a straightforward way leads to Mathematica being very slow. So, I have to prepare my PDE coefficients in advance by creating new interpolating functions for them. I do this via, for example

ElementMeshInterpolation[oldfunction["ElementMesh"], oldfunction["ValuesOnGrid"]^2]

ElementMeshInterpolation[oldfunction["ElementMesh"], oldfunction["ValuesOnGrid"]^2]

Is there a smart way to tell Mathematica to create a single interpolating function from arithmetic operations (and derivatives) of several functions on the same grid?

I am solving non-linear PDE using iterations. Correspondingly, the coefficients are functions on the (same) mesh that I have created and fixed. Between iterations I need to update these function by doing some arithmetic operations on them. Just doing all in a straightforward way leads to Mathematica being very slow. So, I have to prepare my PDE coefficients in advance by creating new interpolating functions for them. I do this via, for example

ElementMeshInterpolation[oldfunction["ElementMesh"], oldfunction["ValuesOnGrid"]^2]

Is there a smart way to tell Mathematica to create a single interpolating function from arithmetic operations (and derivatives) of several functions on the same grid?

I am solving non-linear PDE using iterations. Correspondingly, the coefficients are functions on the (same) mesh that I have created and fixed. Between iterations I need to update these function by doing some arithmetic operations on them. Just doing all in a straightforward way leads to Mathematica being very slow. So, I have to prepare my PDE coefficients in advance by creating new interpolating functions for them. I do this via, for example

ElementMeshInterpolation[oldfunction["ElementMesh"], oldfunction["ValuesOnGrid"]^2]

Is there a smart way to tell Mathematica to create a single interpolating function from arithmetic operations (and derivatives) of several functions on the same grid?

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Sergey Slizovskiy
Sergey Slizovskiy
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New interpolating function on the mesh from operations on other ones

I am solving non-linear PDE using iterations. Correspondingly, the coefficients are functions on the (same) mesh that I have created and fixed. Between iterations I need to update these function by doing some arithmetic operations on them. Just doing all in a straightforward way leads to Mathematica being very slow. So, I have to prepare my PDE coefficients in advance by creating new interpolating functions for them. I do this via, for example

ElementMeshInterpolation[oldfunction["ElementMesh"], oldfunction["ValuesOnGrid"]^2]

Is there a smart way to tell Mathematica to create a single interpolating function from arithmetic operations (and derivatives) of several functions on the same grid?