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arXiv · 2311.18603

Energy conservative isogeometric techniques for the wave equation

Andrea Bressan·Annalisa Buffa·Alen Kushova·Rafael Vázquez
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Abstract

We analyze the wave equation in mixed form, with periodic and/or Dirichlet homogeneous boundary conditions, and nonconstant coefficients that depend on the spatial variable. For the discretization, the weak form of the second equation is replaced by a strong form, written in terms of a projection operator. The system of equations is discretized with B-splines forming a De Rham complex along with suitable commutative projectors for the approximation of the second equation. The discrete scheme is energy conservative when discretized in time with a conservative method such as Crank-Nicolson. We propose a convergence analysis of the method to study the dependence with respect to the mesh size $h$, with focus on the consistency error. Numerical results show optimal convergence of the error in energy norm, and a relative error in energy conservation for long-time simulations of the order of machine precision.

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Andrea Bressan, Annalisa Buffa, Alen Kushova, Rafael Vázquez. 2023-11-30. Energy conservative isogeometric techniques for the wave equation. https://arxiv.org/abs/2311.18603

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