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How can I locally refine the mesh?

How can I locally refine the mesh?#

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2023-12-11 18:55:58

Grid Specification

In some problems, the user may want to refine the grid mesh locally around specific geometry features, such as the gap between two very close waveguides where we expect the fields to be strongest. This can be achieved by adding override_structures to the simulation grid_spec. The override structures is a list of Tidy3D structures, each with an arbitrary geometry, used exclusively for the meshing. It is added on top of any physical simulation structures. There are two types of Tidy3D structures that can be added to override_structures list. The first type defines a fictitious medium inside the override structure so that the grid size is decided by the minimum steps per wavelength in the medium. The second type is more straightforward: one can directly define the grid size along each axis inside the override structures.

Fictitious Medium#

The first type is identical to the Structure object that consists of a Geometry and a Medium. The grid step in the override_structure region is decided by the minimum steps per wavelength in this medium.


# Define a "dummy" box with a refractive index 5 around the central location of a slot waveguide.
refine_box = tidy3d.Structure(
    geometry=tidy3d.Box(center=(0, 0, 0), size=(td.inf, 0.4, 0.4)),
    medium=tidy3d.Medium(permittivity=5**2),
)

# Use the box as a grid refinement structure.
sim_refined = tidy3d.Simulation(
    size=[5, 3, 3],
    grid_spec=tidy3d.GridSpec.auto(
        wavelength=1.55,
        min_steps_per_wvl=20,
        override_structures=[refine_box],
    ),
    medium=tidy3d.Medium(permittivity=1.44**2),
    structures=[wave_guide_1, wave_guide_2],
    boundary_spec=tidy3d.BoundarySpec.all_sides(boundary=tidy3d.PML()),
    run_time=1e-12,
)

Override Structure#

The second type is the tidy3d.MeshOverrideStructure object that consists of a Geometry, and a tuple dl specifying the grid sizes along x, y, and z-directions. We can override the grid sizes just along a few selected directions by setting the value to be None in the dl tuple along the other directions. E.g., if we only plan to refine the grid size along x-direction with grid size 0.01 \(\mu\)m, we can apply dl=(0.01, None, None). In the following, we override the grid size along y and z to be 15.5nm.


# Define a MeshOverrideStructure.
refine_box = tidy3d.MeshOverrideStructure(
    geometry=tidy3d.Box(center=(0, 0, 0), size=(td.inf, 0.4, 0.4)),
    dl=[None, 0.015, 0.015],
)

# Use the box as a grid refinement structure.
sim_refined = tidy3d.Simulation(
    size=[5, 3, 3],
    grid_spec=tidy3d.GridSpec.auto(
        wavelength=1.55,
        min_steps_per_wvl=20,
        override_structures=[refine_box],
    ),
    medium=tidy3d.Medium(permittivity=1.44**2),
    structures=[wave_guide_1, wave_guide_2],
    boundary_spec=tidy3d.BoundarySpec.all_sides(boundary=tidy3d.PML()),
    run_time=1e-12,
)
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