Improvement of system quality in a generalized finite element method using discrete curvelet transform

The generalized finite element method (GFEM) enriched by Plane Waves has been proved suitable to solve the two-dimensional Helmholtz equation. However, when the numbers of unknowns increase, some difficulties arise, such as bad condition number. To reduce the total number of degrees of freedom, this paper presents a method to identify the most significant plane waves in different locations in the problem. It is based on the analysis of the traditional Finite Element Method solution with a poor mesh resolution using the Fast Discrete Curvelet Transform (FDCT) through wedge wrapping.