Quasiperiodic structures, related to irrational numbers, are a class of important and widely existing systems. Typical examples include quasicrystals, incommensurate systems, defects, interfacial problems. Due to the irrational numbers, the quasiperiodic system is a space-filling structure without decay, which results in difficulty in numerical computation. A traditional method is using a periodic system to approximate the quasiperiodic system. It produces a Diophantine approximation error. In this talk, we will propose an efficient method to avoid the Diophantine approximation and obtain high accurate quasiperiodic solutions. We also apply the novel method to material computation, including soft quasicrystals, quasiperiodic quantum systems, and interfacial problems.