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option for PMC boundary in mode solver #2472

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option for PMC boundary in mode solver #2472

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7 changes: 7 additions & 0 deletions tests/test_components/test_mode.py
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Original file line number Diff line number Diff line change
Expand Up @@ -244,3 +244,10 @@ def get_mode_sim_data():
def test_mode_sim_data():
sim_data = get_mode_sim_data()
_ = sim_data.plot_field("Ey", ax=AX, mode_index=0, f=FS[0])


def test_mode_boundary():
_ = td.ModeSpec(boundary="PEC")
_ = td.ModeSpec(boundary="PMC")
with pytest.raises(pydantic.ValidationError):
_ = td.ModeSpec(boundary="PBC")
14 changes: 9 additions & 5 deletions tests/test_plugins/test_mode_solver.py
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Expand Up @@ -167,11 +167,12 @@ def mock_download(resource_id, remote_filename, to_file, *args, **kwargs):
)


def test_compute_modes():
@pytest.mark.parametrize("boundary", ("PEC", "PMC"))
def test_compute_modes(boundary):
"""Test direct call to `compute_modes`."""
eps_cross = np.random.rand(10, 10)
coords = np.arange(11)
mode_spec = td.ModeSpec(num_modes=3, target_neff=2.0)
mode_spec = td.ModeSpec(num_modes=3, target_neff=2.0, boundary=boundary)
_ = compute_modes(
eps_cross=[eps_cross] * 9,
coords=[coords, coords],
Expand Down Expand Up @@ -736,14 +737,16 @@ def test_mode_bend_radius():
assert np.allclose(data1.n_complex, data2.n_complex * 5.5 / 5.0)


def test_mode_solver_2D():
@pytest.mark.parametrize("boundary", ("PEC", "PMC"))
def test_mode_solver_2D(boundary):
"""Run mode solver in 2D simulations."""
mode_spec = td.ModeSpec(
num_modes=3,
filter_pol="te",
filter_pol="te" if boundary == "PEC" else "tm",
precision="double",
num_pml=(0, 10),
track_freq="central",
boundary=boundary,
)
simulation = td.Simulation(
size=(0, SIM_SIZE[1], SIM_SIZE[2]),
Expand All @@ -764,9 +767,10 @@ def test_mode_solver_2D():

mode_spec = td.ModeSpec(
num_modes=3,
filter_pol="te",
filter_pol="te" if boundary == "PEC" else "tm",
precision="double",
num_pml=(10, 0),
boundary=boundary,
)
simulation = td.Simulation(
size=(SIM_SIZE[0], SIM_SIZE[1], 0),
Expand Down
18 changes: 11 additions & 7 deletions tidy3d/components/mode/derivatives.py
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Expand Up @@ -6,13 +6,15 @@
from ...constants import EPSILON_0, ETA_0


def make_dxf(dls, shape, pmc):
def make_dxf(dls, shape, pmc_neg, pmc_pos):
"""Forward derivative in x."""
Nx, Ny = shape
if Nx == 1:
return sp.csr_matrix((Ny, Ny))
dxf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Nx, Nx)))
if not pmc:
if pmc_pos:
dxf[-1, -1] = 0.0
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So I don't think this is right, this will just impose PEC on the next-to-last grid boundary, right?

To impose PMC, this can be placed in the backward derivatives instead. However, it is still tricky: there it will impose it at the last grid center, not at the last grid boundary. I think it's not possible to impose it at the last boundary without expanding by one pixel, and then doing something like seetting a value of 2 for the derivative, like we do for pmc on the negative side (but there we can do without an extra pixel). I think this might have been the reason I only had it working on the negative side in the first place...

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Ah, yeah, this is not quite correct. I believe what I did here is to impose PMC in the middle of the last cell: specifically here by setting this last coefficient to zero we effectively impose the normal derivative of tangential E field to be zero. I did forget to set tangential H to zero there (by setting dxb[-1, -1] = 0.0 and dyb[-1, -1] = 0.0), but somehow it did not matter

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Ah, you are right. I think probably both of those decouple that last dual location from the rest of the simulation, so the only thing is if you don't do both, you might get spurious modes that are purely localized to that location? In fact I see we do both of those for PEC yet we still had to add this to avoid such modes. And we don't do it for the right boundary, because there's no actual field there, but if the PMC right boundary is defined at the last dual location, then will probably be needed at least in the tensorial case where we solve for both E and H?

if not pmc_neg:
dxf[0, 0] = 0.0
dxf = sp.diags(1 / dls).dot(dxf)
dxf = sp.kron(dxf, sp.eye(Ny))
Expand All @@ -34,13 +36,15 @@ def make_dxb(dls, shape, pmc):
return dxb


def make_dyf(dls, shape, pmc):
def make_dyf(dls, shape, pmc_neg, pmc_pos):
"""Forward derivative in y."""
Nx, Ny = shape
if Ny == 1:
return sp.csr_matrix((Nx, Nx))
dyf = sp.csr_matrix(sp.diags([-1, 1], [0, 1], shape=(Ny, Ny)))
if not pmc:
if pmc_pos:
dyf[-1, -1] = 0.0
if not pmc_neg:
dyf[0, 0] = 0.0
dyf = sp.diags(1 / dls).dot(dyf)
dyf = sp.kron(sp.eye(Nx), dyf)
Expand All @@ -62,15 +66,15 @@ def make_dyb(dls, shape, pmc):
return dyb


def create_d_matrices(shape, dls, dmin_pmc=(False, False)):
def create_d_matrices(shape, dls, dmin_pmc=(False, False), dmax_pmc=False):
"""Make the derivative matrices without PML. If dmin_pmc is True, the
'backward' derivative in that dimension will be set to implement PMC
boundary, otherwise it will be set to PEC."""

dlf, dlb = dls
dxf = make_dxf(dlf[0], shape, dmin_pmc[0])
dxf = make_dxf(dlf[0], shape, dmin_pmc[0], dmax_pmc)
dxb = make_dxb(dlb[0], shape, dmin_pmc[0])
dyf = make_dyf(dlf[1], shape, dmin_pmc[1])
dyf = make_dyf(dlf[1], shape, dmin_pmc[1], dmax_pmc)
dyb = make_dyb(dlb[1], shape, dmin_pmc[1])

return (dxf, dxb, dyf, dyb)
Expand Down
5 changes: 3 additions & 2 deletions tidy3d/components/mode/solver.py
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Expand Up @@ -203,7 +203,8 @@ def compute_modes(
always impose PEC boundary at the xmax and ymax interfaces, and on the xmin and ymin
interfaces unless PMC symmetry is present. If so, the PMC boundary is imposed through the
backward derivative matrices."""
dmin_pmc = [sym == 1 for sym in symmetry]
dmax_pmc = mode_spec.boundary == "PMC"
dmin_pmc = [sym == 1 or (sym == 0 and dmax_pmc) for sym in symmetry]

# Primal grid steps for E-field derivatives
dl_f = [new_cs[1:] - new_cs[:-1] for new_cs in new_coords]
Expand All @@ -213,7 +214,7 @@ def compute_modes(
dls = (dl_f, dl_b)

# Derivative matrices with PEC boundaries by default and optional PMC at the near end
der_mats_tmp = d_mats(Nxy, dls, dmin_pmc)
der_mats_tmp = d_mats(Nxy, dls, dmin_pmc, dmax_pmc)

# PML matrices; do not impose PML on the bottom when symmetry present
dmin_pml = np.array(symmetry) == 0
Expand Down
6 changes: 6 additions & 0 deletions tidy3d/components/mode_spec.py
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Expand Up @@ -160,6 +160,12 @@ class ModeSpec(Tidy3dBaseModel):
f"default of {GROUP_INDEX_STEP} is used.",
)

boundary: Literal["PEC", "PMC"] = pd.Field(
"PEC",
title="Boundary Conditions",
description="Boundary conditions to impose at the edges of the mode plane.",
)

@pd.validator("bend_axis", always=True)
@skip_if_fields_missing(["bend_radius"])
def bend_axis_given(cls, val, values):
Expand Down
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