Domain Reduction Method (DRM) Implementation¶

Hercules is capable of implementing the Domain Reduction Method (DRM). You can implement it by setting

implement_drm = yes

And set parameter drm_directory to the directory you want to store the DRM information. If you do not set drm_directory, the default setting is drm_directory = outputfiles/DRM. Folders named part0, part1, and part2 will be created automatically in this directory when you run the corresponding part of DRM simulation.

There are three steps should be executed sequentially for implementing DRM in Hercules, which are part 0, part 1, and part 2. You can choose within these three parts by setting the value of which_drm_part in the input file. For example, setting the following line in the input file for running part 0 in Hercules:

which_drm_part = part0

Other parameters that are needed to be assigned for DRM will be explained in this documentation. Note that if implement_drm = no or it is not set (it is an optional parameter), then all the parameters related to DRM in the input file will be neglected, including

drm_directory
which_drm_part
drm_edgesize
part1_delta_t
part1_simulation_time
drm_print_rate
drm_offset_x
drm_offset_y
drm_boundary
DRMBox_Noelem_Halfwidth_EW
DRMBox_Noelem_Halfwidth_NS
DRMBox_Noelem_depth
DRMBox_element_size
DRM_xo
DRM_yo

If implement_drm = yes, all the DRM parameters, except which_drm_part, should be the same for all three parts.

Part 0, Part 1, and Part 2¶

Part 0¶

In part 0, the information of the coordinates of the DRM box would be generated.

To execute part 0 analysis, simply setting the following line in the input file.

which_drm_part = part0

Since the information of the coordinates of the DRM box is the only data that are generated, the end time of the simulation can be set as a small value (e.g., 1 sec). You can do so by setting the following line in the input file.

simulation_end_time_sec = 1

Part 1¶

In part 1, the displacements of DRM nodes would be saved.

To execute part 1 analysis, setting the following line in the input file.

which_drm_part = part1

Part 2¶

If you are not going to run nonlinear analysis, you don’t need to run part 2 unless you want to store effective forces information for local use (e.g., for Abaqus).

In part 2, Hercules no longer get the information from the source. Instead, it gets the information from the results that are calculated in part 0 and part 1.

To execute part 2 analysis, setting the following line in the input file.

which_drm_part = part2

Other Parameters¶

Defining the Element Size¶

drm_edgesize

Optional: Conditional
Type: Float
Description: The element edge size (in meter) you want to define for elements in the DRM box.

Note that all the dimensions in Hercules have to be “octree dimension.” For more information, please refer to Octree Dimension

\(\Delta t\) and Simulation Time for Part 1¶

These parameters only used for part 2 analysis.

You should set the same values for these two parameters, part1_delta_t and part1_simulation_time, to simulation_delta_time_sec and simulation_end_time_sec, respectively. You can do so by setting the following lines in the input file.

part1_delta_t = delta_t_used_in_part1_in_second
part1_simulation_time = simulation_time_used_in_part1_in_second

delta_t_used_in_part1_in_second and simulation_time_used_in_part1_in_second mentioned above should be replaced with the \(\Delta t\) and the simulation end time that are used in part 1.

Print Rate¶

drm_print_rate

Optional: Conditional
Type: Integer
Description: The rate Hercules saves output data for DRM. For example, if you set drm_print_rate = 2, it means Hercules would store output data every 2 time step (\(\Delta t\)).

DRM Offsets¶

DRM offsets are the distances (in meter) from the origin that is defined by parameters region_origin_latitude_deg and region_origin_longitude_deg. You can define these parameters by setting the following parameters.

drm_offset_x

Optional: Conditional
Type: Float
Description: The DRM offset (in meter) from the origin in x direction.

drm_offset_y

Optional: Conditional
Type: Float
Description: The DRM offset (in meter) from the origin in y direction.

Note that x direction is north-south direction (north is positive), while y direction is east-west direction (east is positive). And both offsets are still Octree Dimension.

DRM offsets create a box bigger than the DRM boundary. The space between these two boundaries is used for the absorbing boundary conditions (ABCs).

DRM Boundary¶

drm_boundary

Optional: Conditional
Type: Multiple numbers
Format: min_x min_y max_x max_y depth
Description: Dimensions in DRM boundary section are distances (in meter) from the box that is created with DRM offsets. There are five dimensions needed to be defined., which are min_x, min_y, max_x, max_y, and depth.