A Fourier continuation (FC) framework for high-order PDE solvers
Ivan MENDEZ CRUZ
The use of Fourier series for high-order trigonometric interpolation can be found in a plethora of applications in science and engineering. Here we present a framework for constructing and testing recently-introduced extension operators that can enable such representations for non-periodic functions (while avoiding the ringing effect). This can ultimately facilitate the construction of high-performance FFT-based solvers for PDEs with general boundary conditions.