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A continuous wavelet-Galerkin method for the linear wave equation

We consider the continuous space-time Galerkin method for the linear second-order wave equation proposed by French and Peterson in 1996. A bottleneck for this approach is how to solve the discrete problems effectively. In this paper, we tackle this bottleneck by essentially employing wavelet bases in space. We show how to decouple the corresponding linear system and we prove that the resulting subsystems can be uniformly preconditioned by simple diagonal preconditioners, leading to efficient iterative solutions.