Boundary conditions in DGTD - Simulation Object

The Boundary Conditions are listed within a group located under the DGTD solver, in the object tree. It allows the user to define boundary conditions in the simulation region and assign them to an object or surface.

You can add a new boundary condition by selecting one from the Boundary Condition section of the DGTD tab.  Each boundary condition can be edited, renamed, deleted in the same way as any simulation object.

PML

• NAME:  Name of the BC
• GENERAL:
  • SIGMA, ALPHA : The absorption properties of PML regions are controlled by these parameters. Their definition can be found in the second reference. Sigma and alpha must be entered into the PML settings table as normalized unitless values. Sigma and alpha are all graded inside the PML regions using polynomial functions. Parameter alpha is sometimes described as a complex frequency shift (CFS) in the literature2. Its main role is to improve numerical stability. Increasing the ratio alpha / sigma will make a a PML boundary more stable, but it will reduce its absorption effectiveness. To recover the S.I. unit values of alpha and sigma, it is necessary to multiply by twice the permittivity of free space and divide by the time step employed in the simulation.

Perfectly matched layer (PML) boundaries absorb electromagnetic waves incident upon them. They essentially model open (or reflectionless) boundaries.  The user can directly specify all the parameters that control their absorption properties.  PML boundaries perform best when the surrounding structures extend completely through the boundary condition region. Unlike conventional boundary conditions, PML boundaries have a finite thickness. In other words, they occupy a finite volume that surrounds the simulation region. It is within this volume that the absorption of light happens.  The thickness of the PML is defined in the Simulation Region settings as shell thickness.

Absorbing

• NAME: Name of the BC
• GEOMETRY: The geometry option defines where the boundary condition can be applied.

Volume, surface, line and point in 3D and 2D:

Surface Type

• DOMAIN:EXTERIOR : Select the target domain. The reference geometry is the common surface(s) shared by the uttermost surface(s) of the selected domain and the simulation region. The selected domain has to have at least a surface that is shared with one of the simulation region surfaces.
• DOMAIN:DOMAIN :  Select the target domains. The reference geometry is the common surface(s) shared by the two selected domains.
• DOMAIN : Select the target domain. The reference geometry is the surfaces of the selected domain.
• SOLID : Select the target solid. The reference geometry is the surfaces that enclose the selected volume if the solid is a 3D shape, or the surface if the solid is a 2D plane.
• SIMULATION REGION : Select one or more simulation region boundaries. The reference geometry is the selected boundaries.
• SOLID:SIMULATION REGION : Select one or more simulation region boundaries and the target solid. The reference geometry is the common surface(s) shared by the simulation region and the target solid.
• MATERIAL:MATERIAL : Select the target materials. The reference geometry is the surface(s) that is shared by the two selected materials. This is only available in some boundary conditions.
• SURFACE : Type the identifier of the partition surface. If the target partition surface is SURFACE 3, type 3. If the target partition surfaces are SURFACE 3 and SURFACE 5, enter 3,5.

Absorbing BC can be used instead of PML when the incident light come to the BC at a normal (or near normal incidence). At wider angles, PML will be more efficient and should be used.

Periodic

• NAME:  Name of the BC
• GEOMETRY: 
  • SIMULATION REGION PERIODICITY: This option defines which direction(s) the periodic boundary condition applies to (x, y, z).
  • BLOCH VECTOR: Determines the way that the Bloch vector is defined in case a Bloch boundary condition is applied. The "set based on source angle" option enables automatic calculation of the Bloch vector based on the source angle.If you disable this option, you have to input kx, ky, and kz manually based on SI units. Manually setting the bloch vector is important for bandstructure simulations.  

Periodic BC should be used when both the structures and EM fields are periodic. Periodic boundary conditions can be used in one or more directions (i.e. only in the x direction) to simulate a structure which is periodic in one direction but not necessarily other directions. Bloch boundary conditions are used in a variety of situations, but the most common is in simulations of periodic structures that are illuminated with a source propagating at an angle.

PEC

• NAME: Name of the BC
• GEOMETRY: The geometry option defines where the boundary condition can be applied.

Volume, surface, line and point in 3D and 2D:

Surface Type

• DOMAIN:EXTERIOR : Select the target domain. The reference geometry is the common surface(s) shared by the uttermost surface(s) of the selected domain and the simulation region. The selected domain has to have at least a surface that is shared with one of the simulation region surfaces.
• DOMAIN:DOMAIN :  Select the target domains. The reference geometry is the common surface(s) shared by the two selected domains.
• DOMAIN : Select the target domain. The reference geometry is the surfaces of the selected domain.
• SOLID : Select the target solid. The reference geometry is the surfaces that enclose the selected volume if the solid is a 3D shape, or the surface if the solid is a 2D plane.
• SIMULATION REGION : Select one or more simulation region boundaries. The reference geometry is the selected boundaries.
• SOLID:SIMULATION REGION : Select one or more simulation region boundaries and the target solid. The reference geometry is the common surface(s) shared by the simulation region and the target solid.
• MATERIAL:MATERIAL : Select the target materials. The reference geometry is the surface(s) that is shared by the two selected materials. This is only available in some boundary conditions.
• SURFACE : Type the identifier of the partition surface. If the target partition surface is SURFACE 3, type 3. If the target partition surfaces are SURFACE 3 and SURFACE 5, enter 3,5.

The component of the electric field parallel to a Perfect Electric Conductor (PEC) boundary is zero; the component of the magnetic field H perpendicular to a PEC boundary is also zero. PEC boundaries are perfectly reflecting, allowing no energy to escape the simulation volume along that boundary.

PMC

• NAME: Name of the BC
• GEOMETRY: The geometry option defines where the boundary condition can be applied.  

Volume, surface, line and point in 3D and 2D:

Surface Type

• DOMAIN:EXTERIOR : Select the target domain. The reference geometry is the common surface(s) shared by the uttermost surface(s) of the selected domain and the simulation region. The selected domain has to have at least a surface that is shared with one of the simulation region surfaces.
• DOMAIN:DOMAIN :  Select the target domains. The reference geometry is the common surface(s) shared by the two selected domains.
• DOMAIN : Select the target domain. The reference geometry is the surfaces of the selected domain.
• SOLID : Select the target solid. The reference geometry is the surfaces that enclose the selected volume if the solid is a 3D shape, or the surface if the solid is a 2D plane.
• SIMULATION REGION : Select one or more simulation region boundaries. The reference geometry is the selected boundaries.
• SOLID:SIMULATION REGION : Select one or more simulation region boundaries and the target solid. The reference geometry is the common surface(s) shared by the simulation region and the target solid.
• MATERIAL:MATERIAL : Select the target materials. The reference geometry is the surface(s) that is shared by the two selected materials. This is only available in some boundary conditions.
• SURFACE : Type the identifier of the partition surface. If the target partition surface is SURFACE 3, type 3. If the target partition surfaces are SURFACE 3 and SURFACE 5, enter 3,5.

Perfect Magnetic Conductor (PMC) boundary conditions are the magnetic equivalent of the metal (PEC) boundaries. The component of the magnetic field H parallel to a PMC boundary is zero; the component of the electric field perpendicular to a PMC boundary is also zero.

References

1. J. P. Berenger, Perfectly Matched Layer (PML) for Computational Electromagnetics. Morgan & Claypool Publishers, 2007.
2. S. D. Gedney and B. Zhao, An Auxiliary Differential Equation Formulation for the Complex-Frequency Shifted PML, IEEE Trans. on Antennas & Propagat., vol. 58, no. 3, 2010.