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arXiv · 2606.09688

A space-time sparse-grid method for the wave equation

Matteo Ferrari·Andrea Moiola·Chiara Perinati·Ilaria Perugia
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Abstract

We develop a fast space-time numerical scheme for approximating solutions to the linear wave equation. The approach is based on the sparse-grid combination technique applied to a coercive space-time discretization. Designed for tensor-product space-time discretizations, the method enables efficient parallelization of the resulting solver. We provide a rigorous theoretical analysis establishing convergence rates and computational complexity estimates. Numerical experiments validate the theoretical estimates and demonstrate the efficiency of the proposed method.

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Matteo Ferrari, Andrea Moiola, Chiara Perinati, Ilaria Perugia. 2026-06-08. A space-time sparse-grid method for the wave equation. https://arxiv.org/abs/2606.09688

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