A Green–Taylor element method for the solution of Helmholtz problems with variable wavenumber

Boundary element methods are particularly attractive for the analysis of wave propagation problems because of their reduced dimensionality and accurate representation of radiation conditions. However, their application to Helmholtz problems with spatially varying wavenumber is limited by the lack of fundamental solutions in closed form and the complexity associated with the computation of additional domain integrals. In this work, we propose a domain partitioning method combined with a boundary integral formulation applied locally on each element using the Green–Taylor Element Method (GTEM). This approach extends the original one-dimensional formulation of GTEM (Cerrato-Casado and González, 2026) to the two-dimensional Helmholtz equation with variable wavenumber. The method applies Green’s third identity locally on subdomains, accounting for inhomogeneities at the element level, and approximates the interior fields through Taylor series expansions constructed from boundary quantities. This local treatment maintains the boundary character of the formulation by substituting global domain integrations with simpler element integrations. Numerical results demonstrate that the proposed GTEM approach achieves higher accuracy with fewer elements per wavelength compared to finite element and finite difference methods of the same order. Moreover, the method exhibits a low sensitivity to mesh distortion, outperforming classical approaches on irregular meshes commonly used in practical engineering applications.