A Unified Framework for Parallel Anisotropic Mesh Adaptation

Finite-element methods are a critical component of the design and analysis procedures of many (bio-)engineering applications. Mesh adaptation is one of the most crucial components since it discretizes the physics of the application at a relatively low cost to the solver. Highly scalable parallel mesh adaptation methods for High-Performance Computing (HPC) are essential to meet the ever-growing demand for higher fidelity simulations. Moreover, the continuous growth of the complexity of the HPC systems requires a systematic approach to exploit their full potential. Anisotropic mesh adaptation captures features of the solution at multiple scales while, minimizing the required number of elements. However, it also introduces new challenges on top of mesh generation. Also, the increased complexity of the targeted cases requires departing from traditional surface-constrained approaches to utilizing CAD (Computer-Aided Design) kernels. Alongside the functionality requirements, is the need of taking advantage of the ubiquitous multi-core machines. More importantly, the parallel implementation needs to handle the ever-increasing complexity of the mesh adaptation code. In this work, we develop a parallel mesh adaptation method that utilizes a metric-based approach for generating anisotropic meshes. Moreover, we enhance our method by interfacing with a CAD kernel, thus enabling its use on complex geometries. We evaluate our method both with fixed-resolution benchmarks and within a simulation pipeline, where the resolution of the discretization increases incrementally. With the Telescopic Approach for scalable mesh generation as a guide, we propose a parallel method at the node (multi-core) for mesh adaptation that is expected to scale up efficiently to the upcoming exascale machines. To facilitate an effective implementation, we introduce an abstract layer between the application and the runtime system that enables the use of task-based parallelism for concurrent mesh operations. Our evaluation indicates results comparable to state-of-the-art methods for fixed-resolution meshes both in terms of performance and quality. The integration with an adaptive pipeline offers promising results for the capability of the proposed method to function as part of an adaptive simulation. Moreover, our abstract tasking layer allows the separation of different aspects of the implementation without any impact on the functionality of the method

The Fully Nonlocal, Finite-Temperature, Adaptive 3D Quasicontinuum Method for Bridging Across Scales

Computational modeling of metallic materials across various length and time scales has been on the rise since the advent of efficient, fast computing machines. From atomistic methods like molecular statics and dynamics at the nanoscale to continuum mechanics modeled by finite element methods at the macroscale, various techniques have been established that describe and predict the mechanics of materials. Many recent technologies, however, fall into a gap between length scales (referred to as mesoscales), with microstructural features on the order of nanometers (thereby requiring full atomistic resolution) but large representative volumes on the order of micrometers (beyond the scope of molecular dynamics). There is an urgent need to predict material behavior using scale-bridging techniques that build up from the atomic level and reach larger length and time scales. To this end, there is extensive ongoing research in building hierarchical and concurrent scale-bridging techniques to master the gap between atomistics and the continuum, but robust, adaptive schemes with finite-temperature modeling at realistic length and time scales are still missing. In this thesis, we use the quasicontinuum (QC) method, a concurrent scale-bridging technique that extends atomistic accuracy to significantly larger length scales by reducing the full atomic ensemble to a small set of representative atoms, and using interpolation to recover the motion of all lattice sites where full atomistic resolution is not necessary. We develop automatic model adaptivity by adding mesh refinement and adaptive neighborhood updates to the new fully nonlocal energy-based 3D QC framework, which allows for automatic resolution to full atomistics around regions of interest such as nanovoids and moving lattice defects. By comparison to molecular dynamics (MD), we show that these additions allow for a successful and computationally efficient coarse graining of atomistic ensembles while maintaining the same atomistic accuracy. We further extend the fully nonlocal QC formulation to finite temperature (termed hotQC) using the principle of maximum entropy in statistical mechanics and averaging the thermal motion of atoms to obtain a temperature-dependent free energy using numerical quadrature. This hotQC formulation implements recently developed optimal summation rules and successfully captures temperature-dependent elastic constants and thermal expansion. We report for the first time the influence of temperature on force artifacts and conclude that our novel finite-temperature adaptive nonlocal QC shows minimal force artifacts and outperforms existing formulations. We also highlight the influence of quadrature in phase space on simulation outcomes. We study 3D grain boundaries in the nonlocal hotQC framework (previously limited to single-crystals) by modeling coarse-grained symmetric-tilt grain boundaries in coincidence site lattice (CSL) based bicrystals. We predict relaxed energy states of various Σ-boundaries with reasonable accuracy by comparing grain boundary energies to MD simulations and outline a framework to model polycrystalline materials that surpasses both spatial and temporal limitations of traditional MD.</p