Solving the wave equation on an infinite domain has been an ongoing challenge in scientific computing. Conventional approaches to this problem only generate numerical solutions on a small subset of the infinite domain. In this paper, we present a method for solving the wave equation on the entire infinite domain using only finite computation time and memory. Our method is based on the conformal invariance of the scalar wave equation under the Kelvin transformation in Minkowski spacetime. As a result of the conformal invariance, any wave problem with compact initial data contained in a causality cone is equivalent to a wave problem on a bounded set in Minkowski spacetime. We use this fact to perform wave simulations in infinite spacetime using a finite discretization of the bounded spacetime with no additional loss of accuracy introduced by the Kelvin transformation.

翻译：在无限域上求解波动方程一直是科学计算中的一个持续挑战。传统方法仅能在无限域的一小部分子集上生成数值解。本文提出一种方法，仅使用有限的计算时间和内存即可在整个无限域上求解波动方程。该方法基于闵可夫斯基时空下Kelvin变换中标量波动方程的共形不变性。由于共形不变性，任何因果锥内具有紧致初始数据的波动问题都等价于闵可夫斯基时空中有界集上的波动问题。我们利用这一事实，通过对有界时空进行有限离散化来执行无限时空中的波动模拟，且Kelvin变换不会引入额外的精度损失。