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

Abstract 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.