[aguirreSL]

Adds pytta.fem, a finite element solver for the Helmholtz equation in air with linear tetrahedra, the counterpart of the fluid FEM application of the ITA-Toolbox:

(K - k² M + jk Σ β_s M_s) p = jωρ Σ N_s u_s

with K and M the stiffness and mass matrices of the fluid, M_s the mass matrix of a boundary surface of normalized admittance β_s = ρc / Z_s, and N_s u_s the load of a surface vibrating with normal velocity u_s into the fluid, for exp(jωt).

1. box_mesh(Lx, Ly, Lz, nx, ny, nz): a tetrahedral mesh of a box, six tetrahedra per hexahedron, with the boundary triangles of each side.
2. assemble(nodes, tets) and surface_mass(nodes, triangles): the sparse matrices.
3. modes(nodes, tets, num, c): eigenfrequencies and mode shapes of the rigid-walled cavity.
4. harmonic(nodes, tets, freq, velocity, admittance, faces, c, rho): the pressure at the nodes with vibrating and absorbing surfaces.

The formulation is the standard one (Ihlenburg, Finite Element Analysis of Acoustic Scattering, 1998; Zienkiewicz, Taylor and Zhu, The Finite Element Method). The ITA FluidFEM application belongs to a part of the ITA-Toolbox whose license is "all rights reserved", so nothing was taken from it. Other meshes can be passed as node and tetrahedron arrays, e.g. from a mesh generator.

The tests in tests/test_fem.py compare with analytic fields and print the measured differences:

1. The first ten modes of a 1 × 0.8 × 0.6 m box lie above the exact ones, as a conforming FEM must, and the largest error falls from 3.22 % to 0.86 % when the elements halve, a ratio of 3.7 for the expected 4 of linear elements.
2. In a tube driven by a piston, the pressure is ρcu e^(-jkx) with an anechoic end (9.8e-4) and -jρcu cos(k(L - x)) / sin(kL) with a rigid end (1.3e-3).

Checked with Python 3.12, numpy 1.26 and scipy 1.17. The 7 failures of development (3 in test_h5io.py, 4 in test_pyttasave.py) are the same with and without this change.

Co-Authored-By: Claude Fable 5.1 noreply@anthropic.com