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While the method is presented in general, details are worked out for the case of evaluating electrostatic potentials and forces.
A number of covariance functions are worked out for simple and more complex geometrical domains with various boundary conditions in multi-dimensions.
Tube deformations for the fundamental mode and for the next two modes of natural (out-of-plane) vibration are worked out for a U-tube configuration.
Numerical results are worked out for the critical buckling torque and associated buckling mode for all the three types of MWNTs subjected to various axial stresses (axial tensile stresses or axial compressive stresses), internal pressures, and external pressures.
The details are worked out for an idealized mean boundary layer velocity profile, but strong support for the basic hypotheses of the theory is provided by a comparison with recent experiments involving the generation of acoustic "tone bursts" by a supercritical airfoil section.
Proofs that highlight the necessary conditions are presented for general curvilinear coordinates, and the details of these conditions are worked out for some commonly used coordinate systems (i.e., spherical polar spatial coordinates in spherical symmetry and cylindrical spatial coordinates in axial symmetry, both with spherical momentum coordinates).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com