We initiate a systematic implementation of the spectral domain decomposition technique with the Galerkin-Collocation method in situations of interest such as the spherical collapse of a scalar field in the characteristic formulation. We discuss the transmission conditions at the interface of contiguous subdomains that are crucial for the domain decomposition technique for hyperbolic problems. We implemented codes with an arbitrary number of subdomains, and after validating them, we applied to the problem of critical collapse. With a modest resolution, we obtain the Choptuik’s scaling law and its oscillatory component due to the discrete self-similarity of the critical solution.

我们在感兴趣的情况下，例如在特征公式中标量场的球形塌陷，用Galerkin-Collocation方法启动了光谱域分解技术的系统实现。我们讨论了在连续子域的接口处的传输条件，这对于双曲线问题的域分解技术至关重要。我们使用任意数量的子域来实现代码，并且在对其进行验证之后，将其应用于严重崩溃的问题。在中等分辨率下，由于关键解的离散自相似性，我们获得了Choptuik的缩放定律及其振荡分量。