# Tag Info

## New answers tagged finite-element

0

I finally did it! You can check the code on my GitLab repo. The function is to do this is the domain_extract which identifies the meshed boundaries to separate. To check a working example, you can check the sphere_meshing.py file, under the Scripts/Meshing directory.

2

Yes. That's all there is to the stability condition. Taking the material properties - shear modulus ($\mu$), bulk modulus ($\kappa$) and density ($\rho$) - into account, the global critical time step is evaluated as the minimum of the critical time step for each element ($\Delta t^e$) $\Delta t^e = CFL * h^e / c_{\kappa}$ where CFL is the Courant-Friedrichs-...

6

Domain decomposition was developed in the late 1990s and early 2000s because it allowed the re-use of sequential PDE solvers: You only have to write a wrapper around it that sends the computed solution to other processors, receives other processors' solutions, and uses these as boundary values for the next iteration. This works reasonably well for the small ...

1

Although I have never used these modules you mentioned, I do believe Comsol is an appropriate choice. My experience with the software was very positive a couple of years ago, mainly because of its support team. Unfortunately I cannot compare it to other alternatives because I have never used another commercial multiphysics FE software. You can parametrize ...

2

This can be solved as follows. If $L_0$ is the initial distance between the two nodes you want to displace, $L$ is the distance between the two nodes in the displaced body, and $d$ is the amount of length change you want to define, the following constraint relation can be defined $$G=L-L_0-d=0$$ Note that $L$ is a nonlinear function of the nodal ...

3

Suppose that we have a piecewise-linear one-dimensional basis. Technically the gradient has no point value defined at the finite element nodes because the derivative is discontinuous at the nodes as you've noticed. However, there are several techniques to approximate the gradient. One example is based on projecting the weak derivative onto a piecewise-linear ...

4

So so many places you have to rewrite. The whole mesh handling (accessing faces and edges from cells, neighbors from cells, ...). Shape functions. Dealing with the question of how the normal vector of a face when seen from one cell matches that on a neighboring cell. You will also likely encounter that 3d problems are always much larger and that solvers, ...

4

Ok, here comes the answer promised in the comment section. Let's start the other way round. In grid methods, one basically selects a number of $N+1$ gridpoints $\{x_k\}_{k=0}^{N}$. As basis functions, one can use Lagrange polynomials constructed over these nodes, each one having polynomial order $N$. For this setup, using Newton-Cotes-like quadrature weights ...

1

I would suggest Introduction to Numerical Methods for Variational Problems by Langtangen and Mardal. Besides that, you could check: scikit-fem. SfePy. I would also suggest our own course Introductory Finite Elements. It has Notebooks with the material and lecture notes; and our own package SolidsPy.

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