Computing interface with quasiperiodicity

Abstract

We propose a method suitable for the computation of quasiperiodic interface, and apply it to simulate the interface between ordered phases in Lifschitz–Petrich model. The function space, initial and boundary conditions are carefully chosen so that it fixes the relative orientation and displacement, and we follow a gradient flow to let the interface find its optimal structure. The gradient flow is discretized by the scalar auxiliary variable (SAV) approach in time, and a spectral method in space using quasiperiodic Fourier series and generalized Jacobi polynomials. We use the method to study interface between striped, hexagonal and dodecagonal phases, especially when the interface is quasiperiodic. The numerical examples show that our method is efficient, accurate, and can successfully capture the interfacial structure.