An unconditionally stable space-time isogeometric method for the acoustic wave equation

TL;DR

This paper introduces a novel space--time isogeometric method for the acoustic wave equation that is unconditionally stable and exhibits excellent numerical properties, independent of mesh size constraints.

Contribution

It develops a new stabilized space--time isogeometric discretization with a non-consistent penalty term, ensuring unconditional stability in solving the acoustic wave equation.

Findings

Unconditionally stable for arbitrary mesh sizes in space and time.

Demonstrates superior stability, dissipation, and dispersion properties.

Performs well for constant and variable wave speeds.

Abstract

We study space--time isogeometric discretizations of the linear acoustic wave equation that use splines of arbitrary degree p, both in space and time. We propose a space--time variational formulation that is obtained by adding a non-consistent penalty term of order 2p+2 to the bilinear form coming from integration by parts. This formulation, when discretized with tensor-product spline spaces with maximal regularity in time, is unconditionally stable: the mesh size in time is not constrained by the mesh size in space. We give extensive numerical evidence for the good stability, approximation, dissipation and dispersion properties of the stabilized isogeometric formulation, comparing against stabilized finite element schemes, for a range of wave propagation problems with constant and variable wave speed.