On the Scalability of Anisotropic Mesh Adaptation on Distributed and Shared Memory Architectures for Numerical Approximations

Mesh generation is a critical component in numerical approximations of Partial Differential Equations (PDEs). One such example includes Computational Fluid Dynamics (CFD), as CFD simulations in turn are crucial for applications in many industries, such as personalized healthcare and the design of aerospace vehicles. Generating high quality meshes for large-scale CFD problems presents a significant bottleneck in the CFD workflow. This dissertation proposes “fast,” parallel 3D mesh generation methodologies that are designed to leverage the concurrency offered by emerging High-Performance Computing (HPC) architectures. First, a distributed memory method is presented that integrates a sequential state-of-the-art isotropic, advancing front local reconnection-based mesh generation software. While outperforming its serial counterpart, lessons are presented regarding the challenges and feasibility of parallelizing such a software as a black box (i.e., a constrained functionality-first approach), motivating this dissertation’s second contribution of a scalability-first approach. It entails a distributed memory method for adaptive anisotropic mesh generation. This method resolves data dependencies and maintains mesh conformity while avoiding the use of collective communication techniques seen in some state-of-the-art HPC methods that are known to hinder potential performance. It also leverages a multicore cc-NUMA-based (shared memory) method. In order to efficiently utilize its speculative execution model, the shared memory method was re-designed (presenting several design abstractions based on additional lessons learned). The proposed method is shown to generate meshes of good quality with up to approximately 1 billion elements in about 3.5 hours when utilizing 512 CPU cores, compared to a state-of-the-art method that takes about 6 hours for the same case with the same resources. Finally, two techniques are proposed to help streamline the discretization of complex vascular geometries within the CFD modeling process. Given a 3D medical image, the first method approximates a user-defined sizing function, generating adaptive isotropic meshes of good quality and fidelity. The second integrates multiple software tools into a single pipeline to generate adaptive anisotropic meshes from segmented medical images. The shared memory method is again utilized within this pipeline, where it is shown to satisfy near real-time requirements given its newly optimized local reconnection algorithm and hierarchical load balancing model.