Periodic solutions to the wave equation that governs an acoustic field (for example) allow us to reduce it to a sequence of Helmholtz problems, one for each sample frequency. The Helmholtz equation governs the field in a domain. The field may be defined as interior or exterior to a closed boundary. The equation can be solved by a domain method such as the finite element method FEM or finite difference method FDM , which require a mesh of the full domain.
An alternative method, and the subject of this work, is the boundary element method (BEM) .
The boundary element method requires a mesh of the boundary of the field only. Hence the method is generally easier to apply and often more efficient than the other methods.
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The BEM for Helmholtz Problems