Analysis and checks¶

After interpolate_all(), the Interpolator offers methods to check the quality of the interpolation.

Scalar integrals¶

For scalar loads (HEAT_FLUX, HEAT_GEN), compute_scalar_integrals() integrates the interpolated field over the destination mesh:

\[ Q = \sum_{e} q_e\, V_e \]

where \(V_e\) is the volume (or area) of element \(e\). For heat generation in W/m³ and volumes in m³, the result is the total power in W. Compare it with the same quantity computed in the source model to check the interpolation.

The volume_area column must be set in the ColumnsConfig:

columns = ColumnsConfig(id=0, dest_xyz=1, source_xyz=1, value=4, volume_area=4)

interpolator = Interpolator(
    path_to_src_folder="source_data",
    path_to_dest_mesh="destination_mesh.txt",
    config=config,
    columns=columns,
)
interpolator.interpolate_all()

integrals = interpolator.compute_scalar_integrals()
# {"data_001": array([total_value])}

An IncompatibleResultsError is raised for multi-component loads or when no volume or area is available.

Tip

Element centroids with areas and volumes can be exported with the export_centroids.apdl script.

EM force resultants¶

For EM_FORCE, compute_EM_resultants(pole) compares the total force and moment of the source data with those of the interpolated nodal forces:

\[ \mathbf{R}_F = \sum_i \mathbf{F}_i, \qquad \mathbf{R}_M = \sum_i (\mathbf{x}_i - \mathbf{p}) \times \mathbf{F}_i \]

where \(\mathbf{p}\) is the pole (origin by default).

import numpy as np

resultants = interpolator.compute_EM_resultants(pole=np.array([0.0, 0.0, 0.0]))

For each source file, the returned dictionary contains:

Key	Description
`R_F_EM`	Total force of the source data \([F_x, F_y, F_z]\)
`R_F_Mech`	Total force of the interpolated data
`R_M_EM`	Total moment of the source data about the pole \([M_x, M_y, M_z]\)
`R_M_Mech`	Total moment of the interpolated data about the pole
`f_err_comp`	Relative force error per component, \((R_{F,EM} - R_{F,Mech}) / R_{F,EM}\)
`m_err_comp`	Relative moment error per component
`Unmapped_EM_Force`	Norm of the sum of the source forces that found no destination neighbour

Both source-to-target kernels conserve the total force by construction, so a force error usually means that part of the force was unmapped. The moment is not conserved exactly, since forces are moved from the source points to the nodes: its error depends on the distance between the two point sets and is a good indicator of the interpolation quality.

Visualisation¶

build_vtk_output(outdir) builds PyVista PolyData point clouds of both the source and the interpolated data, stored in the src_vtk and dest_vtk dictionaries. If outdir is given, they are also saved as <name>_src.vtk and <name>_interpolated.vtk for ParaView.

import pyvista as pv

interpolator.build_vtk_output()
name = "data_001"

pl = pv.Plotter(shape=(1, 2))
pl.subplot(0, 0)
pl.add_mesh(interpolator.src_vtk[name], scalars="Value")
pl.subplot(0, 1)
pl.add_mesh(interpolator.dest_vtk[name], scalars="Value")
pl.link_views()
pl.show()

For multi-component loads, each component is also stored as a separate Component_<i> array.