Hi I am very new to Fortran, I am trying to find if there is a simple way to do partial derivative, like in MATLAB or python for instance-. Is there a package that I can use ? Thank you !

Welcome to the forum. Some threads on automatic differentiation are [image] Backward Mode Auto-Diff in Modern Fortran Announcements Hello, I don’t know if you are interested, I’m also not sure if we are doing the right thing? @St_Maxwell wrote a Fortran code for backwar…

Welcome @dka ! Could you be more specific what type of partial derivatives do you need? Is it related to finite differences, finite elements, or a perhaps just a Jacobian calculation?

Hi @ivanpribec Yes it is related to finite elements. I need to calculate the Jacobian and B-matrix for a specific element.

For analytical jacobian or partial derivatives, I think you would require symbolic computing. But for the numerical ones - simple forward, backward or central difference would do. For which element are you doing ? Are you working on solid/structural elements - beam, plate, shell …?

Hi @Ashok it is for a 4 nodes isoparametric element

For FEM, the Jacobian and other derivatives depend on the shape functions you are using. The Jacobian to map derivatives between iso-parametric and physical coordinates can be computed analytically (they are just polynomials or rational functions such as NURBS). The resulting equations are the same …

[image] rwmsu: For FEM, the Jacobian and other derivatives depend on the shape functions you are using. The Jacobian to map derivatives between iso-parametric and physical coordinates can be computed analytically (they are just polynomials or rational functions such as NURBS). The resulting equa…

For a 4 node isoparametric element, the shape functions are: N1 = (1-s)(1-t)/4 N2 = (1-s)(1+t)/4 N3 = (1+s)(1+t)/4 N4 = (1+s)(1-t)/4 The B matrix would be as shown in the attached image. Replace x and y in the figure with s and t (isoparametric coordinates) [b_matrix] The partial derivatives can…

@Ashok @Beliavsky @rwmsu Thank you very much! I am actually aware of the mathematical part, I was wondering if there is a tool that does this automatically like diff() in matlab.

MATLAB has two diff routines: diff(X) to calculate differences and approximate derivatives diff(f,var) to differentiate a symbolic expression or function. I guess the second one is what you had in mind. Here’s a MATLAB script, which generates the Jacobian for the shape functions given by @Ashok :…

Partial derivative

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Beliavsky January 21, 2022, 3:29pm 2

Welcome to the forum. Some threads on automatic differentiation are

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Partial derivative

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