Herein, the solution of partial differential equations (PDEs) using spectral methods is developed for irregular domains, which preserves their accuracy. Previously, to solve these problems, the finite differences method or the embedded domains method was typically applied. The approach presented in this article can be used for any boundary described by a Jordan curve, and the solution behavior outside the domain need not to considered. The computational process has low cost and generality because the map constructions and changing variables are unnecessary. In addition, by using the presented parametrization process, boundary conditions (boundary bordering) can be implemented conveniently, where the rectangular domains can be considered as an asymptotical case. The structure is numerically oriented, which facilitates the application of any algorithm related to spectral methods.

在此，针对不规则域开发了使用频谱方法的偏微分方程（PDE）的解决方案，从而保留了它们的准确性。以前，为了解决这些问题，通常采用有限差分法或嵌入式域方法。本文介绍的方法可用于约旦曲线描述的任何边界，并且无需考虑域外的求解行为。由于不需要地图构造和变化的变量，因此计算过程具有低成本和通用性。另外，通过使用提出的参数化过程，可以方便地实现边界条件（边界边界），其中矩形域可以被视为渐近情况。结构是数字导向的