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

• 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 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.