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Boundary Element

Fields

cfsem.flux_density_triangle_mesh 

flux_density_triangle_mesh(
    obs: NDArray[float64],
    nodes: NDArray[float64],
    triangles: NDArray[int64],
    s: NDArray[float64],
    par: bool = True,
    quad: str = "dunavant3",
) -> Array3xN

Biot-Savart law calculation for B-field contribution from a triangle mesh with one stream-function value per node.

Parameters:

Name Type Description Default
obs NDArray[float64]

[m] observation points with shape (nobs, 3)

 required
nodes NDArray[float64]

[m] mesh node coordinates with shape (nnode, 3)

 required
triangles NDArray[int64]

node indices with shape (ntri, 3)

 required
s NDArray[float64]

[A] nodal stream-function values with shape (nnode,)

 required
par bool

Whether to use CPU parallelism

 True
quad str

Triangle quadrature rule, one of "dunavant1", "dunavant2", "dunavant3", "dunavant4", or "dunavant5"

 'dunavant3'

Returns:

Type Description
Array3xN

[T] (Bx, By, Bz) magnetic flux density at observation points
Source code in cfsem/bindings.py 
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def flux_density_triangle_mesh(
    obs: NDArray[float64],
    nodes: NDArray[float64],
    triangles: NDArray[int64],
    s: NDArray[float64],
    par: bool = True,
    quad: str = "dunavant3",
) -> Array3xN:
    """
    Biot-Savart law calculation for B-field contribution from a triangle mesh
    with one stream-function value per node.

    Args:
        obs: [m] observation points with shape `(nobs, 3)`
        nodes: [m] mesh node coordinates with shape `(nnode, 3)`
        triangles: node indices with shape `(ntri, 3)`
        s: [A] nodal stream-function values with shape `(nnode,)`
        par: Whether to use CPU parallelism
        quad: Triangle quadrature rule, one of `"dunavant1"`, `"dunavant2"`,
            `"dunavant3"`, `"dunavant4"`, or `"dunavant5"`

    Returns:
        [T] (Bx, By, Bz) magnetic flux density at observation points
    """
    obs = ascontiguousarray(obs, dtype=float64)
    nodes = ascontiguousarray(nodes, dtype=float64)
    triangles = ascontiguousarray(triangles, dtype=int64)
    s = ascontiguousarray(s, dtype=float64).ravel()
    return em_flux_density_triangle_mesh(obs, nodes, triangles, s, par, quad)

cfsem.vector_potential_triangle_mesh 

vector_potential_triangle_mesh(
    obs: NDArray[float64],
    nodes: NDArray[float64],
    triangles: NDArray[int64],
    s: NDArray[float64],
    par: bool = True,
    quad: str = "dunavant3",
) -> Array3xN

Vector potential calculation for A-field contribution from a triangle mesh with one stream-function value per node.

Parameters:

Name Type Description Default
obs NDArray[float64]

[m] observation points with shape (nobs, 3)

 required
nodes NDArray[float64]

[m] mesh node coordinates with shape (nnode, 3)

 required
triangles NDArray[int64]

node indices with shape (ntri, 3)

 required
s NDArray[float64]

[A] nodal stream-function values with shape (nnode,)

 required
par bool

Whether to use CPU parallelism

 True
quad str

Triangle quadrature rule, one of "dunavant1", "dunavant2", "dunavant3", "dunavant4", or "dunavant5"

 'dunavant3'

Returns:

Type Description
Array3xN

[Wb/m] or [V-s/m] (Ax, Ay, Az) magnetic vector potential at observation points
Source code in cfsem/bindings.py 
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def vector_potential_triangle_mesh(
    obs: NDArray[float64],
    nodes: NDArray[float64],
    triangles: NDArray[int64],
    s: NDArray[float64],
    par: bool = True,
    quad: str = "dunavant3",
) -> Array3xN:
    """
    Vector potential calculation for A-field contribution from a triangle mesh
    with one stream-function value per node.

    Args:
        obs: [m] observation points with shape `(nobs, 3)`
        nodes: [m] mesh node coordinates with shape `(nnode, 3)`
        triangles: node indices with shape `(ntri, 3)`
        s: [A] nodal stream-function values with shape `(nnode,)`
        par: Whether to use CPU parallelism
        quad: Triangle quadrature rule, one of `"dunavant1"`, `"dunavant2"`,
            `"dunavant3"`, `"dunavant4"`, or `"dunavant5"`

    Returns:
        [Wb/m] or [V-s/m] (Ax, Ay, Az) magnetic vector potential at observation points
    """
    obs = ascontiguousarray(obs, dtype=float64)
    nodes = ascontiguousarray(nodes, dtype=float64)
    triangles = ascontiguousarray(triangles, dtype=int64)
    s = ascontiguousarray(s, dtype=float64).ravel()
    return em_vector_potential_triangle_mesh(obs, nodes, triangles, s, par, quad)

Field Mappings

cfsem.flux_density_triangle_mesh_mapping 

flux_density_triangle_mesh_mapping(
    obs: NDArray[float64],
    nodes: NDArray[float64],
    triangles: NDArray[int64],
    par: bool = True,
    quad: str = "dunavant3",
) -> tuple[
    NDArray[float64], NDArray[float64], NDArray[float64]
]

Assemble the dense source-node to target-point B-field mapping for a triangle mesh.

Parameters:

Name Type Description Default
obs NDArray[float64]

[m] observation points with shape (nobs, 3)

 required
nodes NDArray[float64]

[m] mesh node coordinates with shape (nnode, 3)

 required
triangles NDArray[int64]

node indices with shape (ntri, 3)

 required
par bool

Whether to use CPU parallelism

 True
quad str

Triangle quadrature rule, one of "dunavant1", "dunavant2", "dunavant3", "dunavant4", or "dunavant5"

 'dunavant3'

Returns:

Type Description
tuple[NDArray[float64], NDArray[float64], NDArray[float64]]

[T/A] (bx_map, by_map, bz_map) with shape (nobs, nnode)
Source code in cfsem/bindings.py 
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def flux_density_triangle_mesh_mapping(
    obs: NDArray[float64],
    nodes: NDArray[float64],
    triangles: NDArray[int64],
    par: bool = True,
    quad: str = "dunavant3",
) -> tuple[NDArray[float64], NDArray[float64], NDArray[float64]]:
    """
    Assemble the dense source-node to target-point B-field mapping for a triangle mesh.

    Args:
        obs: [m] observation points with shape `(nobs, 3)`
        nodes: [m] mesh node coordinates with shape `(nnode, 3)`
        triangles: node indices with shape `(ntri, 3)`
        par: Whether to use CPU parallelism
        quad: Triangle quadrature rule, one of `"dunavant1"`, `"dunavant2"`,
            `"dunavant3"`, `"dunavant4"`, or `"dunavant5"`

    Returns:
        [T/A] `(bx_map, by_map, bz_map)` with shape `(nobs, nnode)`
    """
    obs = ascontiguousarray(obs, dtype=float64)
    nodes = ascontiguousarray(nodes, dtype=float64)
    triangles = ascontiguousarray(triangles, dtype=int64)
    bx, by, bz = em_flux_density_triangle_mesh_mapping(obs, nodes, triangles, par, quad)
    nobs = obs.shape[0]
    nnode = nodes.shape[0]
    return (
        ascontiguousarray(bx).reshape(nobs, nnode),
        ascontiguousarray(by).reshape(nobs, nnode),
        ascontiguousarray(bz).reshape(nobs, nnode),
    )

cfsem.vector_potential_triangle_mesh_mapping 

vector_potential_triangle_mesh_mapping(
    obs: NDArray[float64],
    nodes: NDArray[float64],
    triangles: NDArray[int64],
    par: bool = True,
    quad: str = "dunavant3",
) -> tuple[
    NDArray[float64], NDArray[float64], NDArray[float64]
]

Assemble the dense source-node to target-point A-field mapping for a triangle mesh.

Parameters:

Name Type Description Default
obs NDArray[float64]

[m] observation points with shape (nobs, 3)

 required
nodes NDArray[float64]

[m] mesh node coordinates with shape (nnode, 3)

 required
triangles NDArray[int64]

node indices with shape (ntri, 3)

 required
par bool

Whether to use CPU parallelism

 True
quad str

Triangle quadrature rule, one of "dunavant1", "dunavant2", "dunavant3", "dunavant4", or "dunavant5"

 'dunavant3'

Returns:

Type Description
tuple[NDArray[float64], NDArray[float64], NDArray[float64]]

[Vs/(mA)] (ax_map, ay_map, az_map) with shape (nobs, nnode)
Source code in cfsem/bindings.py 
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def vector_potential_triangle_mesh_mapping(
    obs: NDArray[float64],
    nodes: NDArray[float64],
    triangles: NDArray[int64],
    par: bool = True,
    quad: str = "dunavant3",
) -> tuple[NDArray[float64], NDArray[float64], NDArray[float64]]:
    """
    Assemble the dense source-node to target-point A-field mapping for a triangle mesh.

    Args:
        obs: [m] observation points with shape `(nobs, 3)`
        nodes: [m] mesh node coordinates with shape `(nnode, 3)`
        triangles: node indices with shape `(ntri, 3)`
        par: Whether to use CPU parallelism
        quad: Triangle quadrature rule, one of `"dunavant1"`, `"dunavant2"`,
            `"dunavant3"`, `"dunavant4"`, or `"dunavant5"`

    Returns:
        [V*s/(m*A)] `(ax_map, ay_map, az_map)` with shape `(nobs, nnode)`
    """
    obs = ascontiguousarray(obs, dtype=float64)
    nodes = ascontiguousarray(nodes, dtype=float64)
    triangles = ascontiguousarray(triangles, dtype=int64)
    ax, ay, az = em_vector_potential_triangle_mesh_mapping(obs, nodes, triangles, par, quad)
    nobs = obs.shape[0]
    nnode = nodes.shape[0]
    return (
        ascontiguousarray(ax).reshape(nobs, nnode),
        ascontiguousarray(ay).reshape(nobs, nnode),
        ascontiguousarray(az).reshape(nobs, nnode),
    )

Mesh Utilities

cfsem.triangle_mesh_current_density 

triangle_mesh_current_density(
    nodes: NDArray[float64],
    triangles: NDArray[int64],
    s: NDArray[float64],
) -> NDArray[float64]

Extract the constant physical surface current density on each triangle of a mesh.

Parameters:

Name Type Description Default
nodes NDArray[float64]

[m] mesh node coordinates with shape (nnode, 3)

 required
triangles NDArray[int64]

node indices with shape (ntri, 3)

 required
s NDArray[float64]

[A] nodal stream-function values with shape (nnode,)

 required

Returns:

Type Description
NDArray[float64]

[A/m] triangle-wise surface current density with shape (ntri, 3)
Source code in cfsem/bindings.py 
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def triangle_mesh_current_density(
    nodes: NDArray[float64],
    triangles: NDArray[int64],
    s: NDArray[float64],
) -> NDArray[float64]:
    """
    Extract the constant physical surface current density on each triangle of a mesh.

    Args:
        nodes: [m] mesh node coordinates with shape `(nnode, 3)`
        triangles: node indices with shape `(ntri, 3)`
        s: [A] nodal stream-function values with shape `(nnode,)`

    Returns:
        [A/m] triangle-wise surface current density with shape `(ntri, 3)`
    """
    nodes = ascontiguousarray(nodes, dtype=float64)
    triangles = ascontiguousarray(triangles, dtype=int64)
    s = ascontiguousarray(s, dtype=float64).ravel()
    jx, jy, jz = em_triangle_mesh_current_density(nodes, triangles, s)
    return column_stack((jx, jy, jz))

cfsem.triangle_mesh_quadrature_points 

triangle_mesh_quadrature_points(
    nodes: NDArray[float64],
    triangles: NDArray[int64],
    quad: str = "dunavant3",
) -> tuple[NDArray[float64], NDArray[float64]]

Extract physical quadrature-point coordinates and area weights for each triangle.

Parameters:

Name Type Description Default
nodes NDArray[float64]

[m] mesh node coordinates with shape (nnode, 3)

 required
triangles NDArray[int64]

node indices with shape (ntri, 3)

 required
quad str

Triangle quadrature rule, one of "dunavant1", "dunavant2", "dunavant3", "dunavant4", or "dunavant5"

 'dunavant3'

Returns:

Name Type Description
points NDArray[float64]

[m] quadrature-point coordinates with shape (ntri, nqp, 3)
weights NDArray[float64]

[m^2] physical quadrature weights with shape (ntri, nqp)
Source code in cfsem/bindings.py 
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def triangle_mesh_quadrature_points(
    nodes: NDArray[float64],
    triangles: NDArray[int64],
    quad: str = "dunavant3",
) -> tuple[NDArray[float64], NDArray[float64]]:
    """
    Extract physical quadrature-point coordinates and area weights for each triangle.

    Args:
        nodes: [m] mesh node coordinates with shape `(nnode, 3)`
        triangles: node indices with shape `(ntri, 3)`
        quad: Triangle quadrature rule, one of `"dunavant1"`, `"dunavant2"`,
            `"dunavant3"`, `"dunavant4"`, or `"dunavant5"`

    Returns:
        points: [m] quadrature-point coordinates with shape `(ntri, nqp, 3)`
        weights: [m^2] physical quadrature weights with shape `(ntri, nqp)`
    """
    nodes = ascontiguousarray(nodes, dtype=float64)
    triangles = ascontiguousarray(triangles, dtype=int64)
    xq, yq, zq, wq, nqp = em_triangle_mesh_quadrature_points(nodes, triangles, quad)
    ntri = triangles.shape[0]
    points = column_stack((xq, yq, zq)).reshape(ntri, nqp, 3)
    weights = ascontiguousarray(wq).reshape(ntri, nqp)
    return points, weights

Inductance

cfsem.triangle_mesh_inductance_matrix 

triangle_mesh_inductance_matrix(
    nodes: NDArray[float64],
    triangles: NDArray[int64],
    par: bool = True,
    quad: str = "dunavant3",
) -> NDArray[float64]

Assemble the dense nodal inductance matrix for a triangle stream-function mesh.

If par=True and the per-worker scratch matrices cannot be allocated, the implementation falls back to the serial path instead of failing outright.

Parameters:

Name Type Description Default
nodes NDArray[float64]

[m] mesh node coordinates with shape (nnode, 3)

 required
triangles NDArray[int64]

node indices with shape (ntri, 3)

 required
par bool

Whether to use CPU parallelism

 True
quad str

Triangle quadrature rule, one of "dunavant1", "dunavant2", "dunavant3", "dunavant4", or "dunavant5"

 'dunavant3'

Returns:

Type Description
NDArray[float64]

[H] dense nodal inductance matrix with shape (nnode, nnode)
Source code in cfsem/bindings.py 
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def triangle_mesh_inductance_matrix(
    nodes: NDArray[float64],
    triangles: NDArray[int64],
    par: bool = True,
    quad: str = "dunavant3",
) -> NDArray[float64]:
    """
    Assemble the dense nodal inductance matrix for a triangle stream-function mesh.

    If `par=True` and the per-worker scratch matrices cannot be allocated, the
    implementation falls back to the serial path instead of failing outright.

    Args:
        nodes: [m] mesh node coordinates with shape `(nnode, 3)`
        triangles: node indices with shape `(ntri, 3)`
        par: Whether to use CPU parallelism
        quad: Triangle quadrature rule, one of `"dunavant1"`, `"dunavant2"`,
            `"dunavant3"`, `"dunavant4"`, or `"dunavant5"`

    Returns:
        [H] dense nodal inductance matrix with shape `(nnode, nnode)`
    """
    nodes = ascontiguousarray(nodes, dtype=float64)
    triangles = ascontiguousarray(triangles, dtype=int64)
    lmat = em_triangle_mesh_inductance_matrix(nodes, triangles, par, quad)
    nnode = nodes.shape[0]
    return ascontiguousarray(lmat).reshape(nnode, nnode)

cfsem.triangle_mesh_inductance_mapping_from_linear_filaments 

triangle_mesh_inductance_mapping_from_linear_filaments(
    xyzfil: Array3xN,
    dlxyzfil: Array3xN,
    nodes_tgt: NDArray[float64],
    triangles_tgt: NDArray[int64],
    wire_radius: float | NDArray[float64] = 0.0,
    par: bool = True,
    quad: str = "dunavant3",
) -> NDArray[float64]

Assemble the source-current to target-node inductance mapping from linear filaments.

Parameters:

Name Type Description Default
xyzfil Array3xN

[m] x,y,z filament start coordinates

 required
dlxyzfil Array3xN

[m] x,y,z filament segment deltas

 required
nodes_tgt NDArray[float64]

[m] target mesh node coordinates with shape (nnode_tgt, 3)

 required
triangles_tgt NDArray[int64]

target node indices with shape (ntri_tgt, 3)

 required
wire_radius float | NDArray[float64]

[m] filament radius, scalar or array of length nfil

 0.0
par bool

Whether to use CPU parallelism

 True
quad str

Triangle quadrature rule, one of "dunavant1", "dunavant2", "dunavant3", "dunavant4", or "dunavant5"

 'dunavant3'

Returns:

Type Description
NDArray[float64]

[H] mapping matrix with shape (nnode_tgt, nfil)
Source code in cfsem/bindings.py 
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def triangle_mesh_inductance_mapping_from_linear_filaments(
    xyzfil: Array3xN,
    dlxyzfil: Array3xN,
    nodes_tgt: NDArray[float64],
    triangles_tgt: NDArray[int64],
    wire_radius: float | NDArray[float64] = 0.0,
    par: bool = True,
    quad: str = "dunavant3",
) -> NDArray[float64]:
    """
    Assemble the source-current to target-node inductance mapping from linear filaments.

    Args:
        xyzfil: [m] x,y,z filament start coordinates
        dlxyzfil: [m] x,y,z filament segment deltas
        nodes_tgt: [m] target mesh node coordinates with shape `(nnode_tgt, 3)`
        triangles_tgt: target node indices with shape `(ntri_tgt, 3)`
        wire_radius: [m] filament radius, scalar or array of length `nfil`
        par: Whether to use CPU parallelism
        quad: Triangle quadrature rule, one of `"dunavant1"`, `"dunavant2"`,
            `"dunavant3"`, `"dunavant4"`, or `"dunavant5"`

    Returns:
        [H] mapping matrix with shape `(nnode_tgt, nfil)`
    """
    xyzfil = _3tup_contig(xyzfil)
    dlxyzfil = _3tup_contig(dlxyzfil)
    nodes_tgt = ascontiguousarray(nodes_tgt, dtype=float64)
    triangles_tgt = ascontiguousarray(triangles_tgt, dtype=int64)
    if asarray(wire_radius).ndim == 0:
        wire_radius = full(xyzfil[0].size, float(wire_radius))
    wire_radius = ascontiguousarray(wire_radius).ravel()
    out = em_triangle_mesh_inductance_mapping_from_linear_filaments(
        xyzfil, dlxyzfil, wire_radius, nodes_tgt, triangles_tgt, par, quad
    )
    return ascontiguousarray(out).reshape(nodes_tgt.shape[0], xyzfil[0].size)

cfsem.triangle_mesh_inductance_mapping_from_circular_filaments 

triangle_mesh_inductance_mapping_from_circular_filaments(
    rfil: NDArray[float64],
    zfil: NDArray[float64],
    nodes_tgt: NDArray[float64],
    triangles_tgt: NDArray[int64],
    par: bool = True,
    quad: str = "dunavant3",
) -> NDArray[float64]

Assemble the source-current to target-node inductance mapping from circular filaments.

Parameters:

Name Type Description Default
rfil NDArray[float64]

[m] circular filament radii

 required
zfil NDArray[float64]

[m] circular filament axial coordinates

 required
nodes_tgt NDArray[float64]

[m] target mesh node coordinates with shape (nnode_tgt, 3)

 required
triangles_tgt NDArray[int64]

target node indices with shape (ntri_tgt, 3)

 required
par bool

Whether to use CPU parallelism

 True
quad str

Triangle quadrature rule, one of "dunavant1", "dunavant2", "dunavant3", "dunavant4", or "dunavant5"

 'dunavant3'

Returns:

Type Description
NDArray[float64]

[H] mapping matrix with shape (nnode_tgt, nfil)
Source code in cfsem/bindings.py 
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def triangle_mesh_inductance_mapping_from_circular_filaments(
    rfil: NDArray[float64],
    zfil: NDArray[float64],
    nodes_tgt: NDArray[float64],
    triangles_tgt: NDArray[int64],
    par: bool = True,
    quad: str = "dunavant3",
) -> NDArray[float64]:
    """
    Assemble the source-current to target-node inductance mapping from circular filaments.

    Args:
        rfil: [m] circular filament radii
        zfil: [m] circular filament axial coordinates
        nodes_tgt: [m] target mesh node coordinates with shape `(nnode_tgt, 3)`
        triangles_tgt: target node indices with shape `(ntri_tgt, 3)`
        par: Whether to use CPU parallelism
        quad: Triangle quadrature rule, one of `"dunavant1"`, `"dunavant2"`,
            `"dunavant3"`, `"dunavant4"`, or `"dunavant5"`

    Returns:
        [H] mapping matrix with shape `(nnode_tgt, nfil)`
    """
    rfil = ascontiguousarray(rfil, dtype=float64).ravel()
    zfil = ascontiguousarray(zfil, dtype=float64).ravel()
    nodes_tgt = ascontiguousarray(nodes_tgt, dtype=float64)
    triangles_tgt = ascontiguousarray(triangles_tgt, dtype=int64)
    out = em_triangle_mesh_inductance_mapping_from_circular_filaments(
        rfil, zfil, nodes_tgt, triangles_tgt, par, quad
    )
    return ascontiguousarray(out).reshape(nodes_tgt.shape[0], rfil.size)

cfsem.triangle_mesh_flux_linkage_mapping_from_dipoles 

triangle_mesh_flux_linkage_mapping_from_dipoles(
    loc: Array3xN,
    moment_dir: Array3xN,
    nodes_tgt: NDArray[float64],
    triangles_tgt: NDArray[int64],
    outer_radius: float | NDArray[float64] = 0.0,
    par: bool = True,
    quad: str = "dunavant3",
) -> NDArray[float64]

Assemble the source-amplitude to target-node flux-linkage mapping from dipoles.

Parameters:

Name Type Description Default
loc Array3xN

[m] dipole locations

 required
moment_dir Array3xN

dipole moment direction vectors

 required
nodes_tgt NDArray[float64]

[m] target mesh node coordinates with shape (nnode_tgt, 3)

 required
triangles_tgt NDArray[int64]

target node indices with shape (ntri_tgt, 3)

 required
outer_radius float | NDArray[float64]

[m] dipole finite-core radius, scalar or array of length ndip

 0.0
par bool

Whether to use CPU parallelism

 True
quad str

Triangle quadrature rule, one of "dunavant1", "dunavant2", "dunavant3", "dunavant4", or "dunavant5"

 'dunavant3'

Returns:

Type Description
NDArray[float64]

mapping matrix with shape (nnode_tgt, ndip)
Source code in cfsem/bindings.py 
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def triangle_mesh_flux_linkage_mapping_from_dipoles(
    loc: Array3xN,
    moment_dir: Array3xN,
    nodes_tgt: NDArray[float64],
    triangles_tgt: NDArray[int64],
    outer_radius: float | NDArray[float64] = 0.0,
    par: bool = True,
    quad: str = "dunavant3",
) -> NDArray[float64]:
    """
    Assemble the source-amplitude to target-node flux-linkage mapping from dipoles.

    Args:
        loc: [m] dipole locations
        moment_dir: dipole moment direction vectors
        nodes_tgt: [m] target mesh node coordinates with shape `(nnode_tgt, 3)`
        triangles_tgt: target node indices with shape `(ntri_tgt, 3)`
        outer_radius: [m] dipole finite-core radius, scalar or array of length `ndip`
        par: Whether to use CPU parallelism
        quad: Triangle quadrature rule, one of `"dunavant1"`, `"dunavant2"`,
            `"dunavant3"`, `"dunavant4"`, or `"dunavant5"`

    Returns:
        mapping matrix with shape `(nnode_tgt, ndip)`
    """
    loc = _3tup_contig(loc)
    moment_dir = _3tup_contig(moment_dir)
    nodes_tgt = ascontiguousarray(nodes_tgt, dtype=float64)
    triangles_tgt = ascontiguousarray(triangles_tgt, dtype=int64)
    if asarray(outer_radius).ndim == 0:
        outer_radius = full(loc[0].size, float(outer_radius))
    outer_radius = ascontiguousarray(outer_radius).ravel()
    out = em_triangle_mesh_flux_linkage_mapping_from_dipoles(
        loc, moment_dir, outer_radius, nodes_tgt, triangles_tgt, par, quad
    )
    return ascontiguousarray(out).reshape(nodes_tgt.shape[0], loc[0].size)

Force

cfsem.triangle_mesh_force_mapping 

triangle_mesh_force_mapping(
    nodes_src: NDArray[float64],
    triangles_src: NDArray[int64],
    nodes_tgt: NDArray[float64],
    triangles_tgt: NDArray[int64],
    s_tgt: NDArray[float64],
    par: bool = True,
    quad: str = "dunavant3",
) -> tuple[
    NDArray[float64], NDArray[float64], NDArray[float64]
]

Assemble the frozen-target source-node to target-triangle force mapping between two meshes.

Parameters:

Name Type Description Default
nodes_src NDArray[float64]

[m] source mesh node coordinates with shape (nnode_src, 3)

 required
triangles_src NDArray[int64]

source node indices with shape (ntri_src, 3)

 required
nodes_tgt NDArray[float64]

[m] target mesh node coordinates with shape (nnode_tgt, 3)

 required
triangles_tgt NDArray[int64]

target node indices with shape (ntri_tgt, 3)

 required
s_tgt NDArray[float64]

[A] fixed target nodal current-potential values with shape (nnode_tgt,)

 required
par bool

Whether to use CPU parallelism

 True
quad str

Triangle quadrature rule, one of "dunavant1", "dunavant2", "dunavant3", "dunavant4", or "dunavant5"

 'dunavant3'

Returns:

Type Description
tuple[NDArray[float64], NDArray[float64], NDArray[float64]]

[N/A] (fx, fy, fz) force mappings, each with shape (ntri_tgt, nnode_src)
Source code in cfsem/bindings.py 
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def triangle_mesh_force_mapping(
    nodes_src: NDArray[float64],
    triangles_src: NDArray[int64],
    nodes_tgt: NDArray[float64],
    triangles_tgt: NDArray[int64],
    s_tgt: NDArray[float64],
    par: bool = True,
    quad: str = "dunavant3",
) -> tuple[NDArray[float64], NDArray[float64], NDArray[float64]]:
    """
    Assemble the frozen-target source-node to target-triangle force mapping between two meshes.

    Args:
        nodes_src: [m] source mesh node coordinates with shape `(nnode_src, 3)`
        triangles_src: source node indices with shape `(ntri_src, 3)`
        nodes_tgt: [m] target mesh node coordinates with shape `(nnode_tgt, 3)`
        triangles_tgt: target node indices with shape `(ntri_tgt, 3)`
        s_tgt: [A] fixed target nodal current-potential values with shape `(nnode_tgt,)`
        par: Whether to use CPU parallelism
        quad: Triangle quadrature rule, one of `"dunavant1"`, `"dunavant2"`,
            `"dunavant3"`, `"dunavant4"`, or `"dunavant5"`

    Returns:
        [N/A] `(fx, fy, fz)` force mappings, each with shape `(ntri_tgt, nnode_src)`
    """
    nodes_src = ascontiguousarray(nodes_src, dtype=float64)
    triangles_src = ascontiguousarray(triangles_src, dtype=int64)
    nodes_tgt = ascontiguousarray(nodes_tgt, dtype=float64)
    triangles_tgt = ascontiguousarray(triangles_tgt, dtype=int64)
    s_tgt = ascontiguousarray(s_tgt, dtype=float64).ravel()
    fx, fy, fz = em_triangle_mesh_force_mapping(
        nodes_src, triangles_src, nodes_tgt, triangles_tgt, s_tgt, par, quad
    )
    ntri_tgt = triangles_tgt.shape[0]
    nnode_src = nodes_src.shape[0]
    return (
        ascontiguousarray(fx).reshape(ntri_tgt, nnode_src),
        ascontiguousarray(fy).reshape(ntri_tgt, nnode_src),
        ascontiguousarray(fz).reshape(ntri_tgt, nnode_src),
    )

cfsem.triangle_mesh_self_force_mapping 

triangle_mesh_self_force_mapping(
    nodes: NDArray[float64],
    triangles: NDArray[int64],
    s: NDArray[float64],
    par: bool = True,
    quad: str = "dunavant3",
) -> tuple[
    NDArray[float64], NDArray[float64], NDArray[float64]
]

Assemble the self-excluded frozen-target source-node to target-triangle force mapping.

Parameters:

Name Type Description Default
nodes NDArray[float64]

[m] mesh node coordinates with shape (nnode, 3)

 required
triangles NDArray[int64]

node indices with shape (ntri, 3)

 required
s NDArray[float64]

[A] fixed nodal current-potential values with shape (nnode,)

 required
par bool

Whether to use CPU parallelism

 True
quad str

Triangle quadrature rule, one of "dunavant1", "dunavant2", "dunavant3", "dunavant4", or "dunavant5"

 'dunavant3'

Returns:

Type Description
tuple[NDArray[float64], NDArray[float64], NDArray[float64]]

[N/A] (fx, fy, fz) force mappings, each with shape (ntri, nnode)
Source code in cfsem/bindings.py 
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def triangle_mesh_self_force_mapping(
    nodes: NDArray[float64],
    triangles: NDArray[int64],
    s: NDArray[float64],
    par: bool = True,
    quad: str = "dunavant3",
) -> tuple[NDArray[float64], NDArray[float64], NDArray[float64]]:
    """
    Assemble the self-excluded frozen-target source-node to target-triangle force mapping.

    Args:
        nodes: [m] mesh node coordinates with shape `(nnode, 3)`
        triangles: node indices with shape `(ntri, 3)`
        s: [A] fixed nodal current-potential values with shape `(nnode,)`
        par: Whether to use CPU parallelism
        quad: Triangle quadrature rule, one of `"dunavant1"`, `"dunavant2"`,
            `"dunavant3"`, `"dunavant4"`, or `"dunavant5"`

    Returns:
        [N/A] `(fx, fy, fz)` force mappings, each with shape `(ntri, nnode)`
    """
    nodes = ascontiguousarray(nodes, dtype=float64)
    triangles = ascontiguousarray(triangles, dtype=int64)
    s = ascontiguousarray(s, dtype=float64).ravel()
    fx, fy, fz = em_triangle_mesh_self_force_mapping(nodes, triangles, s, par, quad)
    ntri = triangles.shape[0]
    nnode = nodes.shape[0]
    return (
        ascontiguousarray(fx).reshape(ntri, nnode),
        ascontiguousarray(fy).reshape(ntri, nnode),
        ascontiguousarray(fz).reshape(ntri, nnode),
    )

cfsem.triangle_mesh_force_mapping_from_linear_filaments 

triangle_mesh_force_mapping_from_linear_filaments(
    xyzfil: Array3xN,
    dlxyzfil: Array3xN,
    nodes_tgt: NDArray[float64],
    triangles_tgt: NDArray[int64],
    s_tgt: NDArray[float64],
    wire_radius: float | NDArray[float64] = 0.0,
    par: bool = True,
    quad: str = "dunavant3",
) -> tuple[
    NDArray[float64], NDArray[float64], NDArray[float64]
]

Assemble the frozen-target source-current to target-triangle force mapping from linear filaments.

Parameters:

Name Type Description Default
xyzfil Array3xN

[m] x,y,z filament start coordinates

 required
dlxyzfil Array3xN

[m] x,y,z filament segment deltas

 required
nodes_tgt NDArray[float64]

[m] target mesh node coordinates with shape (nnode_tgt, 3)

 required
triangles_tgt NDArray[int64]

target node indices with shape (ntri_tgt, 3)

 required
s_tgt NDArray[float64]

[A] fixed target nodal current-potential values with shape (nnode_tgt,)

 required
wire_radius float | NDArray[float64]

[m] filament radius, scalar or array of length nfil

 0.0
par bool

Whether to use CPU parallelism

 True
quad str

Triangle quadrature rule, one of "dunavant1", "dunavant2", "dunavant3", "dunavant4", or "dunavant5"

 'dunavant3'

Returns:

Type Description
tuple[NDArray[float64], NDArray[float64], NDArray[float64]]

[N/A] (fx, fy, fz) force mappings, each with shape (ntri_tgt, nfil)
Source code in cfsem/bindings.py 
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def triangle_mesh_force_mapping_from_linear_filaments(
    xyzfil: Array3xN,
    dlxyzfil: Array3xN,
    nodes_tgt: NDArray[float64],
    triangles_tgt: NDArray[int64],
    s_tgt: NDArray[float64],
    wire_radius: float | NDArray[float64] = 0.0,
    par: bool = True,
    quad: str = "dunavant3",
) -> tuple[NDArray[float64], NDArray[float64], NDArray[float64]]:
    """
    Assemble the frozen-target source-current to target-triangle force mapping from linear filaments.

    Args:
        xyzfil: [m] x,y,z filament start coordinates
        dlxyzfil: [m] x,y,z filament segment deltas
        nodes_tgt: [m] target mesh node coordinates with shape `(nnode_tgt, 3)`
        triangles_tgt: target node indices with shape `(ntri_tgt, 3)`
        s_tgt: [A] fixed target nodal current-potential values with shape `(nnode_tgt,)`
        wire_radius: [m] filament radius, scalar or array of length `nfil`
        par: Whether to use CPU parallelism
        quad: Triangle quadrature rule, one of `"dunavant1"`, `"dunavant2"`,
            `"dunavant3"`, `"dunavant4"`, or `"dunavant5"`

    Returns:
        [N/A] `(fx, fy, fz)` force mappings, each with shape `(ntri_tgt, nfil)`
    """
    xyzfil = _3tup_contig(xyzfil)
    dlxyzfil = _3tup_contig(dlxyzfil)
    nodes_tgt = ascontiguousarray(nodes_tgt, dtype=float64)
    triangles_tgt = ascontiguousarray(triangles_tgt, dtype=int64)
    s_tgt = ascontiguousarray(s_tgt, dtype=float64).ravel()
    if asarray(wire_radius).ndim == 0:
        wire_radius = full(xyzfil[0].size, float(wire_radius))
    wire_radius = ascontiguousarray(wire_radius).ravel()
    fx, fy, fz = em_triangle_mesh_force_mapping_from_linear_filaments(
        xyzfil, dlxyzfil, wire_radius, nodes_tgt, triangles_tgt, s_tgt, par, quad
    )
    ntri_tgt = triangles_tgt.shape[0]
    nfil = xyzfil[0].size
    return (
        ascontiguousarray(fx).reshape(ntri_tgt, nfil),
        ascontiguousarray(fy).reshape(ntri_tgt, nfil),
        ascontiguousarray(fz).reshape(ntri_tgt, nfil),
    )

cfsem.triangle_mesh_force_mapping_from_circular_filaments 

triangle_mesh_force_mapping_from_circular_filaments(
    rfil: NDArray[float64],
    zfil: NDArray[float64],
    nodes_tgt: NDArray[float64],
    triangles_tgt: NDArray[int64],
    s_tgt: NDArray[float64],
    par: bool = True,
    quad: str = "dunavant3",
) -> tuple[
    NDArray[float64], NDArray[float64], NDArray[float64]
]

Assemble the frozen-target source-current to target-triangle force mapping from circular filaments.

Parameters:

Name Type Description Default
rfil NDArray[float64]

[m] circular filament radii

 required
zfil NDArray[float64]

[m] circular filament axial coordinates

 required
nodes_tgt NDArray[float64]

[m] target mesh node coordinates with shape (nnode_tgt, 3)

 required
triangles_tgt NDArray[int64]

target node indices with shape (ntri_tgt, 3)

 required
s_tgt NDArray[float64]

[A] fixed target nodal current-potential values with shape (nnode_tgt,)

 required
par bool

Whether to use CPU parallelism

 True
quad str

Triangle quadrature rule, one of "dunavant1", "dunavant2", "dunavant3", "dunavant4", or "dunavant5"

 'dunavant3'

Returns:

Type Description
tuple[NDArray[float64], NDArray[float64], NDArray[float64]]

[N/A] (fx, fy, fz) force mappings, each with shape (ntri_tgt, nfil)
Source code in cfsem/bindings.py 
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def triangle_mesh_force_mapping_from_circular_filaments(
    rfil: NDArray[float64],
    zfil: NDArray[float64],
    nodes_tgt: NDArray[float64],
    triangles_tgt: NDArray[int64],
    s_tgt: NDArray[float64],
    par: bool = True,
    quad: str = "dunavant3",
) -> tuple[NDArray[float64], NDArray[float64], NDArray[float64]]:
    """
    Assemble the frozen-target source-current to target-triangle force mapping from circular filaments.

    Args:
        rfil: [m] circular filament radii
        zfil: [m] circular filament axial coordinates
        nodes_tgt: [m] target mesh node coordinates with shape `(nnode_tgt, 3)`
        triangles_tgt: target node indices with shape `(ntri_tgt, 3)`
        s_tgt: [A] fixed target nodal current-potential values with shape `(nnode_tgt,)`
        par: Whether to use CPU parallelism
        quad: Triangle quadrature rule, one of `"dunavant1"`, `"dunavant2"`,
            `"dunavant3"`, `"dunavant4"`, or `"dunavant5"`

    Returns:
        [N/A] `(fx, fy, fz)` force mappings, each with shape `(ntri_tgt, nfil)`
    """
    rfil = ascontiguousarray(rfil, dtype=float64).ravel()
    zfil = ascontiguousarray(zfil, dtype=float64).ravel()
    nodes_tgt = ascontiguousarray(nodes_tgt, dtype=float64)
    triangles_tgt = ascontiguousarray(triangles_tgt, dtype=int64)
    s_tgt = ascontiguousarray(s_tgt, dtype=float64).ravel()
    fx, fy, fz = em_triangle_mesh_force_mapping_from_circular_filaments(
        rfil, zfil, nodes_tgt, triangles_tgt, s_tgt, par, quad
    )
    ntri_tgt = triangles_tgt.shape[0]
    nfil = rfil.size
    return (
        ascontiguousarray(fx).reshape(ntri_tgt, nfil),
        ascontiguousarray(fy).reshape(ntri_tgt, nfil),
        ascontiguousarray(fz).reshape(ntri_tgt, nfil),
    )

cfsem.triangle_mesh_force_mapping_from_dipoles 

triangle_mesh_force_mapping_from_dipoles(
    loc: Array3xN,
    moment_dir: Array3xN,
    nodes_tgt: NDArray[float64],
    triangles_tgt: NDArray[int64],
    s_tgt: NDArray[float64],
    par: bool = True,
    outer_radius: NDArray[float64] | None = None,
    quad: str = "dunavant3",
) -> tuple[
    NDArray[float64], NDArray[float64], NDArray[float64]
]

Assemble the frozen-target source-amplitude to target-triangle force mapping from dipoles.

Parameters:

Name Type Description Default
loc Array3xN

[m] x,y,z dipole locations

 required
moment_dir Array3xN

dipole moment direction vectors, linear in scalar source amplitudes

 required
nodes_tgt NDArray[float64]

[m] target mesh node coordinates with shape (nnode_tgt, 3)

 required
triangles_tgt NDArray[int64]

target node indices with shape (ntri_tgt, 3)

 required
s_tgt NDArray[float64]

[A] fixed target nodal current-potential values with shape (nnode_tgt,)

 required
par bool

Whether to use CPU parallelism

 True
outer_radius NDArray[float64] | None

[m] radius inside which to defer to magnetized sphere calc. Defaults to zeroes.

 None
quad str

Triangle quadrature rule, one of "dunavant1", "dunavant2", "dunavant3", "dunavant4", or "dunavant5"

 'dunavant3'

Returns:

Type Description
tuple[NDArray[float64], NDArray[float64], NDArray[float64]]

[N/source_amplitude] (fx, fy, fz) force mappings, each with shape (ntri_tgt, ndip)
Source code in cfsem/bindings.py 
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def triangle_mesh_force_mapping_from_dipoles(
    loc: Array3xN,
    moment_dir: Array3xN,
    nodes_tgt: NDArray[float64],
    triangles_tgt: NDArray[int64],
    s_tgt: NDArray[float64],
    par: bool = True,
    outer_radius: NDArray[float64] | None = None,
    quad: str = "dunavant3",
) -> tuple[NDArray[float64], NDArray[float64], NDArray[float64]]:
    """
    Assemble the frozen-target source-amplitude to target-triangle force mapping from dipoles.

    Args:
        loc: [m] x,y,z dipole locations
        moment_dir: dipole moment direction vectors, linear in scalar source amplitudes
        nodes_tgt: [m] target mesh node coordinates with shape `(nnode_tgt, 3)`
        triangles_tgt: target node indices with shape `(ntri_tgt, 3)`
        s_tgt: [A] fixed target nodal current-potential values with shape `(nnode_tgt,)`
        par: Whether to use CPU parallelism
        outer_radius: [m] radius inside which to defer to magnetized sphere calc. Defaults to zeroes.
        quad: Triangle quadrature rule, one of `"dunavant1"`, `"dunavant2"`,
            `"dunavant3"`, `"dunavant4"`, or `"dunavant5"`

    Returns:
        [N/source_amplitude] `(fx, fy, fz)` force mappings, each with shape `(ntri_tgt, ndip)`
    """
    loc = _3tup_contig(loc)
    moment_dir = _3tup_contig(moment_dir)
    nodes_tgt = ascontiguousarray(nodes_tgt, dtype=float64)
    triangles_tgt = ascontiguousarray(triangles_tgt, dtype=int64)
    s_tgt = ascontiguousarray(s_tgt, dtype=float64).ravel()
    outer_radius = outer_radius if outer_radius is not None else zeros_like(loc[0])
    outer_radius = ascontiguousarray(outer_radius).ravel()
    fx, fy, fz = em_triangle_mesh_force_mapping_from_dipoles(
        loc, moment_dir, outer_radius, nodes_tgt, triangles_tgt, s_tgt, par, quad
    )
    ntri_tgt = triangles_tgt.shape[0]
    ndip = loc[0].size
    return (
        ascontiguousarray(fx).reshape(ntri_tgt, ndip),
        ascontiguousarray(fy).reshape(ntri_tgt, ndip),
        ascontiguousarray(fz).reshape(ntri_tgt, ndip),
    )