Automatic Penalty and Degree Continuation for Parallel Pre-Conditioned Mesh Curving on Virtual Geometry. (May 2022)

• Record Type: Journal Article
• Authors: Ruiz-Gironés, Eloi; Roca, Xevi
• Is Part Of: Computer aided design. Volume 146(2022)
• Publication Date: 2022-05
• Subjects: High-order mesh curving -- Distributed parallel -- Pre-conditioner -- p-continuation; Computer-aided design -- Periodicals; Engineering design -- Data processing -- Periodicals; Computer graphics -- Periodicals; Conception technique -- Informatique -- Périodiques; Infographie -- Périodiques; Computer graphics; Engineering design -- Data processing; Periodicals; Electronic journals; 620.00420285
• DOI: 10.1016/j.cad.2022.103208
• Languages: English
• ISSNs: 0010-4485

Abstract

Abstract: We present a distributed parallel mesh curving method for virtual geometry. The main application is to generate large-scale curved meshes on complex geometry suitable for analysis with unstructured high-order methods. Accordingly, we devise the technique to generate geometrically accurate meshes composed of high-quality elements. To this end, we advocate for degree continuation on a penalty-based second-order optimizer that uses global tight tolerances to converge the distortion residuals. To reduce the method memory footprint, waiting time, and energy consumption, we combine three main ingredients. First, we propose a matrix-free GMRES solver pre-conditioned with successive over-relaxation by blocks to reduce the memory footprint three times. We also propose an adaptive penalty technique, to reduce the number of non-linear iterations. Third, we propose an indicator of the required linear solver tolerance to reduce the number of linear iterations. On thousands of cores, the method curves meshes composed of millions of quartic elements featuring highly stretched elements while matching a virtual topology. Graphical abstract: Highlights: Curving with tight residual tolerance large-scale meshes on a virtual geometry. Reducing the memory, time, energy consumption, and iterations on thousands of cores. Adapting the penalty parameter to reduce the number of non-linear problems. Reducing three times the memory footprint with a block-SOR pre-conditioner. Indicating the forcing term to reduce the number of linear solver iterations.