This block contains information about the boundary conditions for this run. See EPOCH input deck for more information on the input deck.

Basics

The boundaries block sets the boundary conditions of each boundary of the domain. Some types of boundaries allow EM wave sources (lasers) to be attached to a boundary. Lasers are attached at the initial conditions stage.

An example boundary block for EPOCH2D is as follows:

begin:boundaries
   bc_x_min = simple_laser
   bc_x_max_field = simple_outflow
   bc_x_max_particle = simple_outflow
   bc_y_min = periodic
   bc_y_max = periodic
end:boundaries

The boundaries block accepts the following parameters:

• bc_{x,y,z}_min - The condition for the lower boundary for both fields and particles. “xbc_left”, “ybc_down” and “zbc_back” are accepted as a synonyms.
• bc_{x,y,z}_min_{field,particle} - The condition for the lower boundary for {fields,particles}. “xbc_left_{field,particle}”, “ybc_down_{field,particle}” and “zbc_back_{field,particle}” are accepted as a synonyms.
• bc_{x,y,z}_max - The condition for the upper boundary for both fields and particles. “xbc_right”, “ybc_up” and “zbc_front” are accepted as a synonyms.
• bc_{x,y,z}_max_{field,particle} - The condition for the upper boundary for {fields,particles}. “xbc_right_{field,particle}”, “ybc_up_{field,particle}” and “zbc_front_{field,particle}” are accepted as a synonyms.
• cpml_thickness - The thickness of the CPML boundary in terms of the number of grid cells. The default value is 6.
• cpml_kappa_max - A tunable CPML parameter.
• cpml_a_max - A tunable CPML parameter.
• cpml_sigma_max - A tunable CPML parameter. There are ten boundary types in EPOCH and each boundary of the domain can have one and only one of these boundaries attached to it. These boundary types are:
• periodic - A simple periodic boundary condition. Fields and/or particles reaching one edge of the domain are wrapped round to the opposite boundary. If either boundary condition is set to periodic then the boundary condition on the matching boundary at the other side of the box is also assumed periodic.
• simple_laser - A characteristic based boundary condition to which one or more EM wave sources can be attached. EM waves impinging on a simple_laser boundary are transmitted with as little reflection as possible. Particles are fully transmitted. The field boundary condition works by allowing outflowing characteristics to propagate through the boundary while using the attached lasers to specify the inflowing characteristics. The particles are simply removed from the simulation when they reach the boundary. See laser blocks for details.
• simple_outflow - A simplified version of simple_laser which has the same properties of transmitting incident waves and particles, but which cannot have EM wave sources attached to it. These boundaries are about 5% more computationally efficient than simple_laser boundaries with no attached sources. This boundary condition again allows outflowing characteristics to flow unchanged, but this time the inflowing characteristics are set to zero. The particles are again simply removed from the simulation when they reach the boundary.
• reflect - This applies reflecting boundary conditions to particles. When specified for fields, all field components are clamped to zero.
• conduct - This applies perfectly conducting boundary conditions to the field. When specified for particles, the particles are reflected.
• open - When applied to fields, EM waves outflowing characteristics propagate through the boundary. Particles are transmitted through the boundary and removed from the system.
• cpml_laser - See #CPML boundary conditions.
• cpml_outflow - See #CPML boundary conditions.
• thermal - See #Thermal boundaries.

NOTE: If simple_laser, simple_outflow, cpml_laser, cpml_outflow or open are specified on one or more boundaries then the code will no longer necessarily conserve mass. Note also that it is possible for the user to specify contradictory, unphysical boundary conditions. It is the users responsibility that these flags are set correctly.

CPML boundary conditions

There are now Convolutional Perfectly Matched Layer boundary conditions in EPOCH. The implementation closely follows that outlined in the book “Computational Electrodynamics: The Finite-Difference Time-Domain Method” by Taflove and Hagness¹. See also Roden and Gedney².

CPML boundaries are specified in the input deck by specifying either “cpml_outflow” or “cpml_laser” in the boundaries block. “cpml_outflow” specifies an absorbing boundary condition whereas “cpml_laser” is used to attach a laser to an otherwise absorbing boundary condition.

There are also four configurable parameters:

• cpml_thickness - The thickness of the CPML boundary in terms of the number of grid cells. The default value is 6.
• cpml_kappa_max, cpml_a_max, cpml_sigma_max - These are tunable parameters which affect the behaviour of the absorbing media. The notation follows that used in the two references quoted above. Note that the “cpml_sigma_max” parameter is normalised by $\sigma_{\rm opt}$ which is taken to be 3.2/dx (see Taflove and Hagness¹ for details). These are real valued parameters which take the following default values: cpml_kappa_max=20, cpml_a_max=0.15, cpml_sigma_max=0.7 An example usage is as follows:

    begin:boundaries
       cpml_thickness = 16
       cpml_kappa_max = 20
       cpml_a_max = 0.2
       cpml_sigma_max = 0.7
       bc_x_min = cpml_laser
       bc_x_max = cpml_outflow
       bc_y_min = cpml_outflow
       bc_y_max = cpml_outflow
    end:boundaries

Thermal boundaries

Thermal boundary conditions have been added to the “boundaries” block. These simulate the existence of a “thermal bath” of particles in the domain adjacent to the boundary. When a particle leaves the simulation it is replace with an incoming particle sampled from a Maxwellian of a temperature corresponding to that of the initial conditions. It is requested using the keyword “thermal”. For example:

    begin:boundaries
       bc_x_min = laser
       bc_x_max = thermal
    end:boundaries

References