On an improved PDE-based elliptic parameterization method for isogeometric analysis using preconditioned Anderson acceleration

On an improved PDE-based elliptic parameterization method for isogeometric analysis using preconditioned Anderson acceleration

Ji, Y. (TU Delft Numerical Analysis; Dalian University of Technology)
Chen, K. (TU Delft Numerical Analysis; Nanjing University of Information Sciences and Technology)
Möller, M. (TU Delft Numerical Analysis)
Vuik, Cornelis (TU Delft Delft Institute of Applied Mathematics)

2023

Constructing an analysis-suitable parameterization for the computational domain from its boundary representation plays a crucial role in the isogeometric design-through-analysis pipeline. PDE-based elliptic grid generation is an effective method for generating high-quality parameterizations with rapid convergence properties for the planar case. However, it may generate non-uniform grid lines, especially near the concave/convex parts of the boundary. In the present work, we introduce a novel scaled discretization of harmonic mappings in the Sobolev space H¹ to remit it. Analytical Jacobian matrices for the involved nonlinear equations are derived to accelerate the computation. To enhance the numerical stability and the speed of convergence, we propose a simple and yet effective preconditioned Anderson acceleration framework instead of using computationally expensive Newton-type iteration. Three preconditioning strategies are suggested, namely diagonal Jacobian, block-diagonal Jacobian, and full Jacobian. Furthermore, we discuss a delayed update strategy of the preconditioner, i.e., the preconditioner is updated every few steps to reduce the computational cost per iteration. Numerical experiments demonstrate the effectiveness and efficiency of our improved parameterization approach and the computational efficiency of our preconditioned Anderson acceleration scheme.

Analysis-suitable parameterization
Anderson acceleration
Isogeometric analysis
Nonlinear preconditioning

http://resolver.tudelft.nl/uuid:05c81810-0133-403e-8134-2b097de66f56

https://doi.org/10.1016/j.cagd.2023.102191

2023-10-23

0167-8396

Computer-Aided Geometric Design, 102

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Institutional Repository

journal article

© 2023 Y. Ji, K. Chen, M. Möller, Cornelis Vuik