ngsPETSc.utils.firedrake_webgui

Firedrake mesh/function visualization via webgui jupyter widgets.

Supports:

2D triangular and 3D tetrahedral meshes.
Scalar and vector function spaces (Lagrange/CG, DG, RT, Nedelec, …).
High polynomial orders (sub-triangulation level controllable via subdivision; defaults to the source element degree, capped at 10).
Live updates via FiredrakeScene.Redraw() for time-dependent simulations and ipywidgets()-driven parameter sliders.

Attributes

`_POINTEVAL_FAMILIES`
`_MAX_SUBDIVISION`
`_MANA_STOPS`
`_NAMED_COLORMAPS`
`_DEFAULT_COLORMAP`
`_COLORMAP_RESOLUTION`
`_intrules`
`_UFC_TET_VERTS`
`_UFC_TET_FACET_VERTS`

Classes

FiredrakeScene

A webgui scene for a Firedrake mesh or function.

Functions

`_make_trig`(N[, x0, y0, dx, dy])
`_make_quad`(N[, x0, y0, dx, dy])
`get_intrules`(dim, order)
`_sample_colormap`(spec[, n])	Resample a ParaView-style stop list into `n` RGB triples.
`_get_mesh_and_func`(obj, order)
`_value_shape`(func_or_space)	Return the function's value shape via UFL on the bound domain.
`_ref_lattice_tri`(n)	Uniform lattice on UFC reference triangle.
`_facet_ref_pts_3d`(local_facet, ref_pts_2d)	Map 2D reference triangle points to a face of the UFC tet.
`_interp_for_vis`(func, mesh, n)	Return a sample-able function and its value rank.
`_tabulate`(func_or_coords, ref_pts)	FIAT-tabulate basis (order 0) of a Function/Coordinate at ref_pts.
`_per_cell_eval`(func, ref_pts)	Evaluate `func` at reference points within every cell.
`_per_cell_coords`(mesh, ref_pts)	Evaluate `mesh.coordinates` at reference points per cell.
`_orient_tris_2d`(verts, tris)	Force CCW winding so normals point +z.
`_flatten_funcvals`(vals)	Flatten per-cell, per-vertex function values to (nverts,) or (nverts, vdim).
`_build_2d_wireframe`(data, mesh, func, n, encoding)
`_build_2d`(data, mesh, func, n, encoding)	Build vertex / triangle / value arrays for a 2D mesh.
`_build_2d_boundary_segments`(mesh, n, npts, encoding)	Sub-segmented boundary of a 2D mesh, indexing into the per-cell lattice.
`_build_3d_boundary`(mesh, func, n, encoding)	Build per-facet sub-triangulated boundary of a 3D tet mesh.
`_build_3d_boundary_edges`(mesh, ef, parent_verts, ...)	Geometry edges between boundary regions with different markers,
`_func_minmax`(func)
`_default_subdivision`(func, mesh)	Pick a sensible sub-triangulation level.
`Draw`(obj[, mesh, subdivision, colormap, order])	Draw a Firedrake Mesh or Function in Jupyter.

Module Contents

ngsPETSc.utils.firedrake_webgui._POINTEVAL_FAMILIES = ('Lagrange', 'Continuous Lagrange', 'CG', 'Discontinuous Lagrange', 'DG', 'DQ', 'Q', 'DPC')

ngsPETSc.utils.firedrake_webgui._MAX_SUBDIVISION = 10

ngsPETSc.utils.firedrake_webgui._MANA_STOPS = [(0.0, (0.098039, 0.137255, 0.352941)), (0.03125, (0.207283, 0.138936, 0.373669)), (0.0625,...

ngsPETSc.utils.firedrake_webgui._NAMED_COLORMAPS

ngsPETSc.utils.firedrake_webgui._DEFAULT_COLORMAP = 'mana'

ngsPETSc.utils.firedrake_webgui._COLORMAP_RESOLUTION = 256

ngsPETSc.utils.firedrake_webgui._make_trig(N, x0=0, y0=0, dx=1, dy=1)

ngsPETSc.utils.firedrake_webgui._make_quad(N, x0=0, y0=0, dx=1, dy=1)

ngsPETSc.utils.firedrake_webgui._intrules

ngsPETSc.utils.firedrake_webgui.get_intrules(dim: int, order: int)

ngsPETSc.utils.firedrake_webgui._sample_colormap(spec, n=_COLORMAP_RESOLUTION)

Resample a ParaView-style stop list into n RGB triples.

spec may be:

None — use webgui’s default colormap (returns None);
a string naming an entry in _NAMED_COLORMAPS;
a list of (t, (r, g, b)) tuples with t in [0, 1];
an (N, 3) array of RGB rows assumed to span [0, 1] evenly.

ngsPETSc.utils.firedrake_webgui._get_mesh_and_func(obj, order)

ngsPETSc.utils.firedrake_webgui._value_shape(func_or_space): Return the function’s value shape via UFL on the bound domain.

ngsPETSc.utils.firedrake_webgui._ref_lattice_tri(n)

Uniform lattice on UFC reference triangle.

Returns (pts, tris) with pts of shape (npts, 2) and tris of shape (ntris, 3). Sub-triangles are CCW so their normals point in +z.

ngsPETSc.utils.firedrake_webgui._UFC_TET_VERTS

ngsPETSc.utils.firedrake_webgui._UFC_TET_FACET_VERTS = ((1, 2, 3), (0, 2, 3), (0, 1, 3), (0, 1, 2))

ngsPETSc.utils.firedrake_webgui._facet_ref_pts_3d(local_facet, ref_pts_2d)

Map 2D reference triangle points to a face of the UFC tet.

ref_pts_2d are (s, t) coordinates with s, t >= 0, s + t <= 1. Returns 3D ref-tet coordinates of shape (npts, 3).

ngsPETSc.utils.firedrake_webgui._interp_for_vis(func, mesh, n)

Return a sample-able function and its value rank.

For Lagrange / DG-style spaces the original func is returned. Non-pointwise families (RT, Nedelec, BDM, …) are interpolated into a discontinuous DG_n / vector-DG_n space so that any genuine cross-cell discontinuity in the field — only the normal/tangential trace of an H(div)/H(curl) field is continuous — is preserved by the renderer.

ngsPETSc.utils.firedrake_webgui._tabulate(func_or_coords, ref_pts)

FIAT-tabulate basis (order 0) of a Function/Coordinate at ref_pts.

Returns the basis array. Scalar element shape is (ndof, npts); vector element shape is (ndof, vdim, npts).

ngsPETSc.utils.firedrake_webgui._per_cell_eval(func, ref_pts)

Evaluate func at reference points within every cell.

Returns array of shape (ncells, npts) for scalar or (ncells, npts, vdim) for vector functions.

ngsPETSc.utils.firedrake_webgui._per_cell_coords(mesh, ref_pts): Evaluate mesh.coordinates at reference points per cell.

ngsPETSc.utils.firedrake_webgui._orient_tris_2d(verts, tris): Force CCW winding so normals point +z.

ngsPETSc.utils.firedrake_webgui._flatten_funcvals(vals): Flatten per-cell, per-vertex function values to (nverts,) or (nverts, vdim).

ngsPETSc.utils.firedrake_webgui._build_2d_wireframe(data, mesh, func, n, encoding)

ngsPETSc.utils.firedrake_webgui._build_2d(data, mesh, func, n, encoding): Build vertex / triangle / value arrays for a 2D mesh.

ngsPETSc.utils.firedrake_webgui._build_2d_boundary_segments(mesh, n, npts, encoding): Sub-segmented boundary of a 2D mesh, indexing into the per-cell lattice.

ngsPETSc.utils.firedrake_webgui._build_3d_boundary(mesh, func, n, encoding): Build per-facet sub-triangulated boundary of a 3D tet mesh.

ngsPETSc.utils.firedrake_webgui._build_3d_boundary_edges(mesh, ef, parent_verts, local_facets, n, npts, encoding): Geometry edges between boundary regions with different markers, sub-divided into the per-facet lattice index space.

ngsPETSc.utils.firedrake_webgui._func_minmax(func)

ngsPETSc.utils.firedrake_webgui._default_subdivision(func, mesh): Pick a sensible sub-triangulation level.

class ngsPETSc.utils.firedrake_webgui.FiredrakeScene(obj, mesh=None, subdivision=None, colormap=_DEFAULT_COLORMAP, order=1, **kwargs)

Bases: webgui_jupyter_widgets.BaseWebGuiScene

A webgui scene for a Firedrake mesh or function.

Parameters

objfiredrake.MeshGeometry or firedrake.Function: Object to visualise.
meshfiredrake.MeshGeometry, optional: Override mesh (when obj is a function but you want to show it on a different mesh).
subdivisionint, optional: Sub-triangles per element edge. Defaults to the source element degree, capped at 10.
colormapstr, list, ndarray, or None, optional: Colour map used by the on-screen colour bar. Strings select a built-in ("mana" (default), "cool_to_warm", "ngs"); a stop list [(t, (r, g, b)), ...] or an (N, 3) RGB array is also accepted. Pass None to fall back to webgui’s default rainbow (equivalent to "ngs").

obj

_mesh_override = None

subdivision = None

colormap = 'mana'

kwargs

encoding = 'b64'

order = 1

GetData(set_minmax=True)

Redraw(obj=None)

Push fresh data to an already-displayed widget.

Pass obj to swap to a different Function/Mesh (useful for slider callbacks) or call without args to re-encode the current object after its dat has been mutated in place (the time-stepping pattern).

ngsPETSc.utils.firedrake_webgui.Draw(obj, mesh=None, subdivision=None, colormap=_DEFAULT_COLORMAP, order=1, **kwargs): Draw a Firedrake Mesh or Function in Jupyter.