The surrogate matrix methodology: Accelerating isogeometric analysis of waves

Abstract

The surrogate matrix methodology delivers low-cost approximations of matrices (i.e., surrogate matrices) which are normally computed in Galerkin methods via element-scale quadrature formulas. In this paper, the methodology is applied to a number of model problems in wave mechanics treated in the Galerkin isogeometic setting. Herein, the resulting surrogate methods are shown to significantly reduce the assembly time in high frequency wave propagation problems. In particular, the assembly time is reduced with negligible loss in solution accuracy. This paper also extends the scope of previous articles in its series by considering multi-patch discretizations of time-harmonic, transient, and nonlinear PDEs as particular use cases of the methodology. Our a priori error analysis for the Helmholtz equation demonstrates that the additional consistency error introduced by the presence of surrogate matrices is independent of the wave number. In addition, our floating point analysis establishes that the computational complexity of the methodology compares favorably to other contemporary fast assembly techniques for isogeometric methods. Our numerical experiments demonstrate clear performance gains for time-harmonic problems, both with and without the presence of perfectly matched layers. Notable speed-ups are also presented for a transient problem with a compressible neo-Hookean material.

References in corpus (8)

• Fast formation of isogeometric Galerkin matrices by weighted quadrature
• Nonlinear static isogeometric analysis of arbitrarily curved Kirchhoff-Love shells
• Matrix-free weighted quadrature for a computationally efficient isogeometric $k$-method
• Sum-factorization techniques in Isogeometric Analysis
• On perfectly matched layers for discontinuous Petrov-Galerkin methods
• The surrogate matrix methodology: Low-cost assembly for isogeometric analysis
• The surrogate matrix methodology: a priori error estimation
• The surrogate matrix methodology: A reference implementation for low-cost assembly in isogeometric analysis

Cited by in corpus (4)

• Isogeometric Analysis of Acoustic Scattering with Perfectly Matched Layers (IGAPML)
• Weighted quadrature for hierarchical B-splines
• Towards Accuracy and Scalability: Combining Isogeometric Analysis with Deflation to Obtain Scalable Convergence for the Helmholtz Equation
• Automatic stabilization of finite-element simulations using neural networks and hierarchical matrices