Periodic boundaries IIΒΆ

Learning targets

  • Periodic boundary conditions
  • 2D hexagonal lattice
  • Define unit cell as polygon with specially devoted Unit Cell construction

This example describes a unit cell of a 2D hexagonal lattice (equilateral triangular lattice) of elliptical objects in a background medium. The periodic computational domain is constructed as a polygon where the points are automatically determined from the unit cell geometry. This ease this input of the unit cell point coordinates and also sets the periodic boundary conditions as default.

The resulting geometry and mesh correspond to the following figure:

_images/ex2d_periodic_boundaries_hexagonal.png

.jcm Input File

  • layout.jcm [ASCII]

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    Layout2D { 
  Name = "TutorialExample2D" 
  UnitOfLength = 1e-09 
  
  MeshOptions {
    MinimumMeshAngle = 20 
    MaximumSideLength = 100 
    CurvilinearDegree = 2
  }
  Objects {
    Polygon { 
      Name = "ComputationalDomain/Air" 
      DomainId = 1 
      Priority = -1 
      PeriodicUnitCell {
        LatticeAngle = 60
        LatticeVectorLengths = [500 500] 
        Shape = Hexagonal        
      }
    } 
    
    Ellipse {
      Name = "EllipticalObject"  
      DomainId = 2 
      Priority = 1 
      RefineAll = 2
      RadiusX = 200
      RadiusY = 100
      RotationAngle = 15
      MeshOptions {
        MaximumSideLength = 50 
      }
    }
    
  } 
}