add computational of integral values

[dodu94]

Add functions to compute the integral values of the interpolation

[coderabbitai]

Caution

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Pull request was closed or merged during review

Walkthrough

This PR adds post-processing and validation analysis capabilities to the interpolation framework. It introduces two new Interpolator methods to compute weighted scalar field integrals and EM force/moment resultants with error metrics, supported by exception handling, parser updates to carry mesh volume/area data, comprehensive tests, APDL export enhancements, and working documentation examples.

Changes

Post-Processing and Analysis Capabilities

Layer / File(s)	Summary
Exception and Parser Foundations src/interpcore/errors.py, src/interpcore/parsers.py	New IncompatibleResultsError exception and updated parse_mech_mesh signature to optionally accept volume and area column indices, returning a dictionary with conditionally included numpy arrays alongside coordinates and ID numbers.
Interpolator Analysis Methods src/interpcore/interpolator.py	Imports updated to include the new exception; __init__ modified to parse and store destination mesh volumes and areas; two public methods added: compute_scalar_integrals() for weighted integration by volume/area, and compute_EM_resultants() for source vs. interpolated force/moment resultant comparison with per-component relative error metrics.
Test Coverage for Analysis Methods tests/test_interpolator.py	New test cases for compute_scalar_integrals() and compute_EM_resultants(), validating required interpolation state, return value structure and dimensionality, optional pole behavior, and error handling when invoked before interpolation.
Data and Export Tool Updates apdl-scripts/export_centroids.apdl, doc/heat_flux/destination_mesh.txt, doc/heat_gen/destination_mesh.txt	APDL script updated to retrieve and export per-element area and volume via *GET queries; destination mesh text files extended with Area column (heat flux domain) and Volume column (heat generation domain) to support weighted integral computations.
Documentation and Working Examples README.md, doc/em_force/em_force.ipynb, doc/heat_flux/heat_flux.ipynb, doc/heat_gen/heat_gen.ipynb	README updated with "Analysis tools" feature description and "Analysis Methods" section documenting scalar integrals and EM force/moment resultants; three example notebooks extended with new cells demonstrating the analysis method calls, showing returned force/moment resultants, integral values, and error metrics.

Sequence Diagram(s)

sequenceDiagram
  participant User
  participant Interpolator
  participant Parser
  participant Analysis
  User->>Interpolator: initialize with destination mesh file
  Interpolator->>Parser: parse_mech_mesh with vol/area column indices
  Parser-->>Interpolator: return dict with coordinates, volumes, areas
  Interpolator->>Interpolator: store volumes/areas on instance
  User->>Interpolator: interpolate_all()
  User->>Interpolator: compute_scalar_integrals()
  Interpolator->>Analysis: validate interpolation, sum weighted integrals
  Analysis-->>Interpolator: dict of integral results by load
  User->>Interpolator: compute_EM_resultants(pole)
  Interpolator->>Analysis: compute source/destination force/moment resultants
  Analysis-->>Interpolator: dict with resultants, errors, unmapped norm

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Estimated code review effort

🎯 3 (Moderate) | ⏱️ ~25 minutes

Poem

🐰 With volumes measured and forces aligned,
Integrals flow through the fields we've designed,
Conservation checked from pole to pole,
The interpolator now plays a complete role!
📊✨

🚥 Pre-merge checks | ✅ 5

✅ Passed checks (5 passed)

Check name	Status	Explanation
Description Check	✅ Passed	Check skipped - CodeRabbit’s high-level summary is enabled.
Title check	✅ Passed	The title 'add computational of integral values' is partially related to the changeset. While the PR does add integral computation capabilities (compute_scalar_integrals), it also substantially adds EM force/moment resultant computation (compute_EM_resultants), updates mesh parsing to support volume/area data, and includes comprehensive documentation and tests. The title focuses on only one aspect of the changes.
Docstring Coverage	✅ Passed	Docstring coverage is 85.71% which is sufficient. The required threshold is 80.00%.
Linked Issues check	✅ Passed	Check skipped because no linked issues were found for this pull request.
Out of Scope Changes check	✅ Passed	Check skipped because no linked issues were found for this pull request.

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✨ Finishing Touches

📝 Generate docstrings

• Create stacked PR
• Commit on current branch

🧪 Generate unit tests (beta)

• Create PR with unit tests
• Commit unit tests in branch extract-volumes-and-areas

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