Symmetry Rendering

When solving on a reduced domain with symmetry boundary conditions, the Symmetry class renders the full solution by applying mirror transformations on the GPU.

Mirror Symmetry

Render a quarter-domain solution as a full domain:

from ngsolve import *
from ngsolve_webgpu import MeshData, FunctionData, CFRenderer, Symmetry
from webgpu.jupyter import Draw

# Solve on a quarter of the domain
mesh = Mesh(unit_square.GenerateMesh(maxh=0.1))
cf = sin(3.14159 * x) * sin(3.14159 * y)

md = MeshData(mesh)
fd = FunctionData(md, cf, order=3)

sym = Symmetry()
sym.mirror_x()  # reflect across x=0 -> 2 copies
sym.mirror_y()  # reflect across y=0 -> 4 copies (group closure)

cfr = CFRenderer(fd, symmetry=sym)
Draw(cfr)

Each call to mirror_x/y/z doubles the number of rendered copies by computing the group closure of all generator combinations. The transforms are applied in the vertex shader — no mesh duplication needed.

Antisymmetric Fields (Parity)

For fields that change sign under a mirror operation:

from ngsolve import *
from ngsolve_webgpu import MeshData, FunctionData, CFRenderer, Symmetry, Colorbar
from webgpu.jupyter import Draw

mesh = Mesh(unit_square.GenerateMesh(maxh=0.1))
cf = x * sin(3.14159 * y)  # odd in x

md = MeshData(mesh)
fd = FunctionData(md, cf, order=3)

sym = Symmetry()
sym.mirror_x()
sym_odd = sym.with_parity([-1])  # field is antisymmetric under mirror_x
cfr = CFRenderer(fd, symmetry=sym_odd)
cfr.colormap.set_min(-1)
colorbar = Colorbar(cfr.colormap)
Draw([cfr, colorbar])

with_parity([-1]) tells the renderer to negate function values for copies involving that mirror generator. The parity list has one entry per generator in the order they were added.

Vector Symmetry

Arrow glyphs (SurfaceVectors, ClippingVectors) support the same symmetry system. Positions and directions are expanded on the GPU via a compute shader — no CPU overhead.

from ngsolve import *
from ngsolve_webgpu import MeshData, FunctionData, SurfaceVectors, Symmetry
from webgpu.jupyter import Draw

mesh = Mesh(unit_cube.GenerateMesh(maxh=0.3))
cf = CF((x, y, 0))

md = MeshData(mesh)
fd = FunctionData(md, cf, order=1)

sym = Symmetry()
sym.mirror_x()
sym.mirror_y()

vecs = SurfaceVectors(fd, symmetry=sym)
Draw(vecs)

Warning: failed to init renderer SurfaceVectors: 'directions_imag'

Electromagnetic Symmetry (Polar vs Axial Vectors)

For electromagnetic simulations, vectors transform differently depending on whether they are polar (E-field, displacement) or axial/pseudovectors (B-field, H-field):

vector_symmetry	Transform	Use case
"polar" (default)	d' = M · d	E-field with PMC wall, B-field with PEC wall
"axial"	d' = det(M) · M · d	E-field with PEC wall, B-field with PMC wall

# B-field mirrored at a PMC boundary:
vecs_B = SurfaceVectors(fd_B, symmetry=sym, vector_symmetry="axial")

API Reference

Symmetry()

• .mirror_x(), .mirror_y(), .mirror_z() — add mirror generators (chainable)

• .with_parity(list) — returns new Symmetry with per-generator sign flips for scalar fields

• .n_copies — total number of symmetry copies (read-only)

Scalar renderers (CFRenderer, ClippingCF, MeshElements2d, MeshElements3d, IsoSurfaceRenderer, NegativeSurfaceRenderer, NegativeClippingRenderer, GeometryRenderer):

• Pass symmetry=sym to constructor

Vector renderers (SurfaceVectors, ClippingVectors):

• Pass symmetry=sym to constructor

• Pass vector_symmetry="axial" for pseudovectors (B-field at PMC, E-field at PEC)