Geometric Rectangular Grid

The Geometric Rectangular Grid mesh part type (implemented as GeometricStructuredRectangular3D in the code) creates a three-dimensional rectangular grid mesh with geometric spacing in each direction. This mesh type allows you to create a grid with progressively increasing or decreasing cell sizes based on geometric ratios, which is useful for creating refined meshes in areas of interest.

Parameters

Parameter Name	Description
x_min	Minimum X coordinate (float)
x_max	Maximum X coordinate (float)
y_min	Minimum Y coordinate (float)
y_max	Maximum Y coordinate (float)
z_min	Minimum Z coordinate (float)
z_max	Maximum Z coordinate (float)
nx	Number of cells in X direction (integer)
ny	Number of cells in Y direction (integer)
nz	Number of cells in Z direction (integer)
x_ratio	Ratio of cell increment in X direction (float, optional, default=1)
y_ratio	Ratio of cell increment in Y direction (float, optional, default=1)
z_ratio	Ratio of cell increment in Z direction (float, optional, default=1)

Required parameters are: x_min, x_max, y_min, y_max, z_min, z_max, nx, ny, and nz. Optional parameters are: x_ratio, y_ratio, and z_ratio, which default to 1.0 if not specified.

Compatible Elements

This mesh part type is compatible with the following elements:

• stdBrick

• bbarBrick

• SSPbrick

• PML3D

Usage Example

The following example demonstrates how to create a 3D rectangular domain with geometric spacing using the Geometric Rectangular Grid mesh part type:

import femora as fm

# Create a Femora instance


# Create a material
material = fm.material.create_material(
    material_category="nDMaterial",
    material_type="ElasticIsotropic",
    user_name="Soil",
    E=30e3,
    nu=0.3,
    rho=1.8e-9
)

# Create an element using this material
element = fm.element.create_element(
    element_type="stdBrick",
    ndof=3,
    material=material,
    b1=0,
    b2=0,
    b3=-9.81*1.8e-9
)

# Create a region with damping
damping = fm.damping.create_damping("frequency rayleigh", dampingFactor=0.05, f1=1, f2=10)
region = fm.region.create_region("elementRegion", damping=damping)

# Create the geometric rectangular grid mesh part
# Cells will progressively get larger in the z-direction (from surface down)
fm.meshPart.create_mesh_part(
    "Volume mesh",
    "Geometric Rectangular Grid",
    user_name="SoilLayer",
    element=element,
    region=region,
    **{
        'x_min': -50, 'x_max': 50,
        'y_min': -50, 'y_max': 50,
        'z_min': -20, 'z_max': 0,
        'nx': 10, 'ny': 10, 'nz': 8,
        'x_ratio': 1.0,   # Uniform spacing in x-direction
        'y_ratio': 1.0,   # Uniform spacing in y-direction
        'z_ratio': 1.25   # Each cell is 1.25x larger than the previous one in z-direction
    }
)

Geometric Ratio Effect

The geometric ratio parameters control how cell sizes vary across the mesh:

• Ratio = 1.0: Uniform spacing (cells have equal size)

• Ratio > 1.0: Cell size increases in the positive direction (cells get larger)

• Ratio < 1.0: Cell size decreases in the positive direction (cells get smaller)

For example, with a ratio of 1.25 in the z-direction, each cell will be 1.25 times larger than the previous cell when moving from z_min to z_max.

Notes

• Used for creating 3D meshes with variable spacing in each direction based on geometric progression

• Suitable for problems requiring refined mesh in specific regions

• Useful for boundary layer meshing or capturing gradients near interfaces

• More efficient than uniform grids when different resolution is needed in different regions

• Consider the appropriate ratio values for your specific application needs