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<p>We review space–time isogeometric analysis and in particular present and extend the unconditionally stable space–time isogeometric method introduced in Fraschini et al. (Comput Math Appl 169:205–222, 2024) for the linear acoustic wave equation to multi-patch spatial domains. This formulation incorporates a stabilization strategy that enhances numerical robustness by penalizing high-order derivatives within the variational framework. Additionally, we present a solver that exploits the Kronecker structure of the problem, eliminating the need to assemble global space–time matrices, and reduces computational overhead and memory usage. A numerical experiment is proposed, that confirms the method’s stability, accuracy, and computational efficiency, highlighting its effectiveness for large-scale wave propagation problems on complex geometries.</p>

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Space–time isogeometric analysis: a review with application to wave propagation

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月5日

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  • G. Loli,
  • G. Sangalli

摘要

We review space–time isogeometric analysis and in particular present and extend the unconditionally stable space–time isogeometric method introduced in Fraschini et al. (Comput Math Appl 169:205–222, 2024) for the linear acoustic wave equation to multi-patch spatial domains. This formulation incorporates a stabilization strategy that enhances numerical robustness by penalizing high-order derivatives within the variational framework. Additionally, we present a solver that exploits the Kronecker structure of the problem, eliminating the need to assemble global space–time matrices, and reduces computational overhead and memory usage. A numerical experiment is proposed, that confirms the method’s stability, accuracy, and computational efficiency, highlighting its effectiveness for large-scale wave propagation problems on complex geometries.