Hi FEniCS family, I am using lagrange linear element mesh for my analysis of periodic homogenization. I wanted to compute shape function derivatives for each cell. The mesh data is taken from this source. Periodic homogenization of linear elastic materials — Numerical tours of continuum mechanics…

I would suggest having a look at Automated shape differentiation in the Unified Form Language | SpringerLink Note that shape derivatives are not computer per cell, but for each mesh node (usually in fenics a vector function space of first order Lagrange elements). See for instance: Shape Derivativ…

Thanks @dokken for your response and sharing the reference. I have doubts regarding your statement for above case. “Note that shape derivatives are not computer per cell, but for each mesh node (usually in fenics a vector function space of first order Lagrange elements).” Does this mean that, at …

I would suggest you look at the references I have provided. The first one: [image] dokken: I would suggest having a look at Automated shape differentiation in the Unified Form Language | SpringerLink goes into detail about the mathematics, and the expected input/output, while the second refe…

Hi @dokken , thanks for your response. The resources you suggested shows Automatic differentiation algorithm to find change in functional w.r.t. some variable and looks more of time dependent application. I wanted to compute the derivatives of shape functions w.r.t x, y (for an element, evaluated t…

[image] bagla0: I wanted to use the shape function derivatives w.r.t spatial coordinates for each element like dN1/dx_element= (Summation dN1/dx_i * weight_i) , i=1… no. of guass points. I dont understand what you mean by this. A shape derivative for me is the change of an integral when you…

Based on the requirement, shape derivative means derivative of lagrangian basis functions used in general finite element formulation. \:u=\:\sum _{i=1}^Nu_i\:\phi i\: , N is the number of nodes. \phi -lagrangian shape/basis function. This u is used as Function (Coefficient) u=Function(W) and \…

Dear dokken In legacy FEniCS, evaluate shape function value can be done by the code evaluate_basis , but there are not those function in FEniCSx, are there similar function in FEniCSx? Best regards Chen

Computing shape function derivatives for each cell

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dokken March 14, 2023, 3:33pm 8

I think you just want: Bitbucket

Handling the Finite Element Functions

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Computing shape function derivatives for each cell

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