Choosing a solver

Start with the least costly method that supports both your physics and your desired output. The table lists supported combinations. All seven solver families return solution objects. Hover a column header for what that solver is. Hover the ℹ️ icon next to a geometry for its caveats, or follow a linked geometry name to the page covering it.

Choosing by question

Generated shapes extend the surface methods beyond the canonical entries above. RevolvedBody and Torus support axisymmetric and full BEM. LoftedBody, Ellipsoid and Superellipsoid support full BEM. The cone, bicone and frustum constructors return revolution bodies or elliptical lofts. These full meshes also support MFS and Kirchhoff, and may form interfaces in coupled fluid BEM. Material restrictions still apply. See Geometries for profile sampling, section frames and mesh refinement.

• Use sphere or spheroid modal methods as analytical references, while checking series convergence and special-function conditioning.
• Use Kirchhoff to explore physical-optics behavior. A numerically converged surface integral does not establish validity of physical optics at low frequency.
• Use FEM or BEM when checking analytical reductions, geometry discretization, or interface coupling. Compare against a canonical case first. Full 3D volume FEM is the general-purpose reference for elastic and shelled spheres and spheroids.
• Use volume FEM with SpatialFluid for smooth density and sound-speed variation inside sphere/spheroid regions. The exterior remains homogeneous. See Full 3D volume FEM for coordinates and mesh controls.
• Use MFS when source placement is well controlled and its supported geometry suits the problem.
• Use BEM surface results for repeated observation-angle queries. Radial FEM spheres and cylinders provide complex backscatter; meridian FEM cylinders and spheroids also provide complex amplitudes at arbitrary bistatic angles.
• Use Fourier matching for a smooth irregular body of revolution between the canonical (sphere/spheroid) and general numerical (BEM/MFS/FEM) solvers. See Fourier matching.

See BEM and MFS for the underlying boundary integral and source-fitting theory.