Discrete Differential Geometry of Thin Materials for Computational Mechanics

Instead of applying numerical methods directly to governing equations, another approach to computation is to discretize the geometric structure specific to the problem first, and then compute with the discrete geometry. This structure-respecting discrete-differential-geometric (DDG) approach often leads to new algorithms that more accurately track the physically behavior of the system with less computational effort. Thin objects, such as pieces of cloth, paper, sheet metal, freeform masonry, and steel-glass structures are particularly rich in geometric structure and so are well-suited for DDG. I show how understanding the geometry of time integration and contact leads to new algorithms, with strong correctness guarantees, for simulating thin elastic objects in contact; how the performance of these algorithms can be dramatically improved without harming the geometric structure, and thus the guarantees, of the original formulation; how the geometry of static equilibrium can be used to efficiently solve design problems related to masonry or glass buildings; and how discrete developable surfaces can be used to model thin sheets undergoing isometric deformation

Advanced Automatic Code Generation for Multiple Relaxation-Time Lattice Boltzmann Methods

The scientific code generation package lbmpy supports the automated design and the efficient implementation of lattice Boltzmann methods (LBMs) through metaprogramming. It is based on a new, concise calculus for describing multiple relaxation-time LBMs, including techniques that enable the numerically advantageous subtraction of the constant background component from the populations. These techniques are generalized to a wide range of collision spaces and equilibrium distributions. The article contains an overview of lbmpy's front-end and its code generation pipeline, which implements the new LBM calculus by means of symbolic formula manipulation tools and object-oriented programming. The generated codes have only a minimal number of arithmetic operations. Their automatic derivation rests on two novel Chimera transforms that have been specifically developed for efficiently computing raw and central moments. Information contained in the symbolic representation of the methods is further exploited in a customized sequence of algebraic simplifications, further reducing computational cost. When combined, these algebraic transformations lead to concise and compact numerical kernels. Specifically, with these optimizations, the advanced central moment- and cumulant-based methods can be realized with only little additional cost as when compared with the simple BGK method. The effectiveness and flexibility of the new lbmpy code generation system is demonstrated in simulating Taylor-Green vortex decay and the automatic derivation of an LBM algorithm to solve the shallow water equations.Comment: 23 pages, 6 figure

Modeling Cardiovascular Hemodynamics Using the Lattice Boltzmann Method on Massively Parallel Supercomputers

Accurate and reliable modeling of cardiovascular hemodynamics has the potential to improve understanding of the localization and progression of heart diseases, which are currently the most common cause of death in Western countries. However, building a detailed, realistic model of human blood flow is a formidable mathematical and computational challenge. The simulation must combine the motion of the fluid, the intricate geometry of the blood vessels, continual changes in flow and pressure driven by the heartbeat, and the behavior of suspended bodies such as red blood cells. Such simulations can provide insight into factors like endothelial shear stress that act as triggers for the complex biomechanical events that can lead to atherosclerotic pathologies. Currently, it is not possible to measure endothelial shear stress in vivo, making these simulations a crucial component to understanding and potentially predicting the progression of cardiovascular disease. In this thesis, an approach for efficiently modeling the fluid movement coupled to the cell dynamics in real-patient geometries while accounting for the additional force from the expansion and contraction of the heart will be presented and examined. First, a novel method to couple a mesoscopic lattice Boltzmann fluid model to the microscopic molecular dynamics model of cell movement is elucidated. A treatment of red blood cells as extended structures, a method to handle highly irregular geometries through topology driven graph partitioning, and an efficient molecular dynamics load balancing scheme are introduced. These result in a large-scale simulation of the cardiovascular system, with a realistic description of the complex human arterial geometry, from centimeters down to the spatial resolution of red-blood cells. The computational methods developed to enable scaling of the application to 294,912 processors are discussed, thus empowering the simulation of a full heartbeat. Second, further extensions to enable the modeling of fluids in vessels with smaller diameters and a method for introducing the deformational forces exerted on the arterial flows from the movement of the heart by borrowing concepts from cosmodynamics are presented. These additional forces have a great impact on the endothelial shear stress. Third, the fluid model is extended to not only recover Navier-Stokes hydrodynamics, but also a wider range of Knudsen numbers, which is especially important in micro- and nano-scale flows. The tradeoffs of many optimizations methods such as the use of deep halo level ghost cells that, alongside hybrid programming models, reduce the impact of such higher-order models and enable efficient modeling of extreme regimes of computational fluid dynamics are discussed. Fourth, the extension of these models to other research questions like clogging in microfluidic devices and determining the severity of co-arctation of the aorta is presented. Through this work, a validation of these methods by taking real patient data and the measured pressure value before the narrowing of the aorta and predicting the pressure drop across the co-arctation is shown. Comparison with the measured pressure drop in vivo highlights the accuracy and potential impact of such patient specific simulations. Finally, a method to enable the simulation of longer trajectories in time by discretizing both spatially and temporally is presented. In this method, a serial coarse iterator is used to initialize data at discrete time steps for a fine model that runs in parallel. This coarse solver is based on a larger time step and typically a coarser discretization in space. Iterative refinement enables the compute-intensive fine iterator to be modeled with temporal parallelization. The algorithm consists of a series of prediction-corrector iterations completing when the results have converged within a certain tolerance. Combined, these developments allow large fluid models to be simulated for longer time durations than previously possible.Engineering and Applied Science

High Performance Computing Techniques to Better Understand Protein Conformational Space

This thesis presents an amalgamation of high performance computing techniques to get better insight into protein molecular dynamics. Key aspects of protein function and dynamics can be learned from their conformational space. Datasets that represent the complex nuances of a protein molecule are high dimensional. Efficient dimensionality reduction becomes indispensable for the analysis of such exorbitant datasets. Dimensionality reduction forms a formidable portion of this work and its application has been explored for other datasets as well. It begins with the parallelization of a known non-liner feature reduction algorithm called Isomap. The code for the algorithm was re-written in C with portions of it parallelized using OpenMP. Next, a novel data instance reduction method was devised which evaluates the information content offered by each data point, which ultimately helps in truncation of the dataset with much fewer data points to evaluate. Once a framework has been established to reduce the number of variables representing a dataset, the work is extended to explore algebraic topology techniques to extract meaningful information from these datasets. This step is the one that helps in sampling the conformations of interest of a protein molecule. The method employs the notion of hierarchical clustering to identify classes within a molecule, thereafter, algebraic topology is used to analyze these classes. Finally, the work is concluded by presenting an approach to solve the open problem of protein folding. A Monte-Carlo based tree search algorithm is put forth to simulate the pathway that a certain protein conformation undertakes to reach another conformation. The dissertation, in its entirety, offers solutions to a few problems that hinder the progress of solution for the vast problem of understanding protein dynamics. The motion of a protein molecule is guided by changes in its energy profile. In this course the molecule gradually slips from one energy class to another. Structurally, this switch is transient spanning over milliseconds or less and hence is difficult to be captured solely by the work in wet laboratories

Swarming Reconnaissance Using Unmanned Aerial Vehicles in a Parallel Discrete Event Simulation

Current military affairs indicate that future military warfare requires safer, more accurate, and more fault-tolerant weapons systems. Unmanned Aerial Vehicles (UAV) are one answer to this military requirement. Technology in the UAV arena is moving toward smaller and more capable systems and is becoming available at a fraction of the cost. Exploiting the advances in these miniaturized flying vehicles is the aim of this research. How are the UAVs employed for the future military? The concept of operations for a micro-UAV system is adopted from nature from the appearance of flocking birds, movement of a school of fish, and swarming bees among others. All of these natural phenomena have a common thread: a global action resulting from many small individual actions. This emergent behavior is the aggregate result of many simple interactions occurring within the flock, school, or swarm. In a similar manner, a more robust weapon system uses emergent behavior resulting in no weakest link because the system itself is made up of simple interactions by hundreds or thousands of homogeneous UAVs. The global system in this research is referred to as a swarm. Losing one or a few individual unmanned vehicles would not dramatically impact the swarms ability to complete the mission or cause harm to any human operator. Swarming reconnaissance is the emergent behavior of swarms to perform a reconnaissance operation. An in-depth look at the design of a reconnaissance swarming mission is studied. A taxonomy of passive reconnaissance applications is developed to address feasibility. Evaluation of algorithms for swarm movement, communication, sensor input/analysis, targeting, and network topology result in priorities of each model\u27s desired features. After a thorough selection process of available implementations, a subset of those models are integrated and built upon resulting in a simulation that explores the innovations of swarming UAVs