Hi, I am writing my Finite Element Solver for CFD simulations. I encounter a what should be like an easy problem but I cant figure out how to do it. In my code, I want to account for periodic boundary conditions. For that I have to manipulate my matrices and vectors. I use a technique shown below. …

Not sure. Would it help here to start considering a one-dimensional problem with a coarse mesh? What kind of problem are you trying to solve? I am happy to look along.

Ferrite.jl supports periodic boundary conditions (see for example this tutorial on computational homogenization ). The implementation is very efficient and all required modifications to the system matrix, for all periodic constraints, are perfomred in a single sweep of the sparse data structure. The…

[image] priyanshuFSI: In my code, I want to account for periodic boundary conditions. For that I have to manipulate my matrices and vectors. I use a technique shown below. I am only showing for matrices. Gridap.jl supports periodic boundary conditions as well. See below — in FEM, it should b…

Hi, Do you mean that Gridap does not do any additional modification to the matrices if we define the mesh correctly ?

Can you share a MWE (minimal working example) for us to have a look at?

I second this. It is all a mater of connectivity. The local nodes on the periodic BC should refer to the same global node.

[image] stevengj: It surprises me that you have to make a special sweep. In Gridap, you just have to generate a mesh that lives on a torus (i.e. one side is connected to the other side — Gmsh can do this, for example) and the ordinary matrix assembly works as-is. Sure, that’s a possibility, b…

[image] fredrikekre: What happens in Gridap/Gmsh if you complicate things slighly and use a linear mesh with quadratic function approximation, for example? High order element basis functions just work. (Last I checked, curved periodic elements, e.g. curved triangles, were not supported, howe…

A possible way to implemented periodic BCs in FEM (e.g. in Gridap) is by modifying the generation of the map cell to dofs ids (not cell to node ids!). In this way, the matrix automatically contains the periodic couplings without an additional sweep. This works also for high-order FEM, Hdiv, HCurl, e…

Implementation of Periodic Boundary Conditions

General Usage Performance

PeterSimon November 6, 2024, 9:05am 3

See this post for a discussion of “ghost cells” commonly used to implement periodic boundary conditions.

Topic		Replies	Views
Ferrite.jl periodic boundary conditions Modelling & Simulations question	2	1441	October 6, 2022
Periodic Boundary conditions in ParallelStencil / ImplicitGlobalGrid Modelling & Simulations question , diffeq	2	469	October 14, 2021
Arrays with periodic boundaries New to Julia	5	6854	June 30, 2022
Implementing Laplacian operator acting on a 2D array Modelling & Simulations finite-element , finitediff , operator	6	1002	March 18, 2024
Implementing parallel computing in finite element problems Numerics	6	2091	August 15, 2018

Implementation of Periodic Boundary Conditions

Related topics