Amplitude-based Generalized Plane Waves: New Quasi-Trefftz Functions for Scalar Equations in two dimensions

Generalized plane waves (GPWs) were introduced to take advantage of Trefftz methods for problems modeled by variable coefficient equations. Despite the fact that GPWs do not satisfy the Trefftz property, i.e., they are not exact solutions to the governing equation, they instead satisfy a quasi-Trefftz property: They are only approximate solutions. They lead to high-order numerical methods, and this quasi-Trefftz property is critical for their...