A generalized plane-wave numerical method for smooth nonconstant coefficients

We propose an original method based on generalized plane waves and approximated coefficients for the numerical approximation of the Helmholtz equation with a smooth nonconstant coefficient. This is justified by a high-order convergence estimate rate. Our motivation stems from Maxwell's equations with Hermitian dielectric tensor ε which are used to model reflectometry in fusion plasma. Simplified models split them into two different propagation modes. Some numerical results are presented in dimensions 1 and 2.