Doctor of Philosophy

dissertationOne of the fundamental building blocks of many computational sciences is the construction and use of a discretized, geometric representation of a problem domain, often referred to as a mesh. Such a discretization enables an otherwise complex domain to be represented simply, and computation to be performed over that domain with a finite number of basis elements. As mesh generation techniques have become more sophisticated over the years, focus has largely shifted to quality mesh generation techniques that guarantee or empirically generate numerically well-behaved elements. In this dissertation, the two complementary meshing subproblems of vertex placement and element creation are analyzed, both separately and together. First, a dynamic particle system achieves adaptivity over domains by inferring feature size through a new information passing algorithm. Second, a new tetrahedral algorithm is constructed that carefully combines lattice-based stenciling and mesh warping to produce guaranteed quality meshes on multimaterial volumetric domains. Finally, the ideas of lattice cleaving and dynamic particle systems are merged into a unified framework for producing guaranteed quality, unstructured and adaptive meshing of multimaterial volumetric domains

Higher-order Finite Difference Time Domain Algorithms for Room Acoustic Modelling

The acoustic qualities of indoor spaces are fundamental to the intelligibility of speech, the quality of musical performances, and perceived noise levels. Computationally heavy wave-based acoustic modelling algorithms have gained momentum in the field of room acoustic modelling, as ever-increasing computational power makes their use more feasible. Most notably the Finite Difference Time Domain (FDTD) method is often employed for rendering the low- and mid-frequency part of room impulse responses (RIRs). However, this algorithm has known disadvantages, most prominently dispersion error, which renders a large part of the simulated RIR invalid. This thesis is concerned with the implementation and analysis of higher-order FDTD stencils as a means to improve the current state-of-art FDTD methods that solve the room acoustic wave equation. A detailed analysis of dispersive properties, stability, and required grid spacing of current and higher-order stencils is presented, and has been verified using a GPU implementation of the different algorithms. It is argued that the 4th-order stencil gives the best result in terms of output quality versus computational effort. In addition, this thesis focusses on the derivation of absorbing boundaries for the 4th-order scheme, its stability analysis, and detailed analysis of absorptive properties compared to established boundary models for 2nd-order schemes. The newly proposed 4th-order scheme and its boundaries are tested in two case studies: a large shoebox model, in order to test the validity against a common benchmark and a complex acoustic space. For the latter study, impulse responses were measured in the National Centre for Early Music in York, UK, and computationally generated using the current state-of-the-art as well as the proposed 4th-order FDTD algorithm and boundaries. It is shown that the 4th-order stencil gives at least as good as, or better results than those achieved using the 2nd-order stencil, at lower computational costs

External Memory Algorithms for Factoring Sparse Matrices

We consider the factorization of sparse symmetric matrices in the context of a two-layer storage system: disk/core. When the core is sufficiently large the factorization can be performed in-core. In this case we must read the input, compute, and write the output, in this sequence. On the other hand, when the core is not large enough, the factorization becomes out-of-core, which means that data movement and computation must be interleaved. We identify two major out-of-core factorization scenarios: read-once/write-once (R1/W1) and read-many/write-many (RM/WM). The former requires minimum traffic, exactly as much as the in-core factorization: reading the input and writing the output. More traffic is required for the latter. We investigate three issues: the size of the core that determines the boundary between the two out-of-core scenarios, the in-core data structure reorganizations required by the R1/W1 factorization and the traffic required by the RM/WM factorization. We use three common factorization algorithms: left-looking, right-looking and multifrontal. In the R1/W1 scenario, our results indicate that for problems with good separators, such as those coming from the discretization of partial differential equations, ordered with nested dissection, right-looking and multifrontal factorization perform slightly better than left-looking factorization. There are, however, applications for which multifrontal is a bad choice, requiring too much temporary storage. On the other hand, right-looking factorization should be avoided in the RM/WM scenario. Left-looking is a good choice, but only if data is blocked along one dimension. Multifrontal performs well for both one and two dimensional blocks as long as not too much storage is required. We also explore a framework for a software implementation. We have implemented an in-core solver that relies on some object-oriented constructs. Most of the code is written in C++, except for some kernels written in Fortran 77. We intend to add out-of-core functionality to the code and data movement is a major concern. Implicit data movement represents the easy way, but, as some of our experiments show, good performance can be achieved only with explicit data movement. This complicates the code and we expect a substantial effort in order to implement an efficient out-of-core solver

A Computational Fluid-Structure Interaction Method for Simulating Supersonic Parachute Inflation

Following the successful landing of the Curiosity rover on the Martian surface in 2012, NASA/JPL conducted the low-density supersonic decelerator (LDSD) missions to develop large diameter parachutes to land the increasingly heavier payloads being sent to the Martian surface. Unexpectedly, both of the tested parachutes failed far below their design loads. It became clear that there was an inability to model and predict loads that occur during supersonic parachute inflation. In this dissertation, a new computational method that was developed to provide NASA with the capability to simulate supersonic parachute inflation is presented and validated. The method considers the loose coupling of two different immersed boundary methods with a nonlinear finite element solver. Following validation on canonical FSI problems, methods to simulate the permeability of parachute broadcloth and to identify and enforce contact in parallel are presented and validated. The coupled solvers are first applied to the supersonic parachute problem on a sub-scale MSL parachute and capsule geometry, and subsequently, a full-scale test flight from the Advanced Supersonic Parachute Inflation Research Experiments (ASPIRE) is simulated. To the best of the author’s knowledge, these are the first FSI simulations to match the ASPIRE flight test data

The Sixth Copper Mountain Conference on Multigrid Methods, part 2

The Sixth Copper Mountain Conference on Multigrid Methods was held on April 4-9, 1993, at Copper Mountain, Colorado. This book is a collection of many of the papers presented at the conference and so represents the conference proceedings. NASA Langley graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The multigrid discipline continues to expand and mature, as is evident from these proceedings. The vibrancy in this field is amply expressed in these important papers, and the collection clearly shows its rapid trend to further diversity and depth

Software for Exascale Computing - SPPEXA 2016-2019

This open access book summarizes the research done and results obtained in the second funding phase of the Priority Program 1648 "Software for Exascale Computing" (SPPEXA) of the German Research Foundation (DFG) presented at the SPPEXA Symposium in Dresden during October 21-23, 2019. In that respect, it both represents a continuation of Vol. 113 in Springer’s series Lecture Notes in Computational Science and Engineering, the corresponding report of SPPEXA’s first funding phase, and provides an overview of SPPEXA’s contributions towards exascale computing in today's sumpercomputer technology. The individual chapters address one or more of the research directions (1) computational algorithms, (2) system software, (3) application software, (4) data management and exploration, (5) programming, and (6) software tools. The book has an interdisciplinary appeal: scholars from computational sub-fields in computer science, mathematics, physics, or engineering will find it of particular interest

Research and technology highlights, 1993

This report contains highlights of the major accomplishments and applications that have been made by Langley researchers and by our university and industry colleagues during the past year. The highlights illustrate both the broad range of the research and technology activities supported by NASA Langley Research Center and the contributions of this work toward maintaining United States leadership in aeronautics and space research. This report also describes some of the Center's most important research and testing facilities

Lattice Boltzmann Methods for Partial Differential Equations

Lattice Boltzmann methods provide a robust and highly scalable numerical technique in modern computational fluid dynamics. Besides the discretization procedure, the relaxation principles form the basis of any lattice Boltzmann scheme and render the method a bottom-up approach, which obstructs its development for approximating broad classes of partial differential equations. This work introduces a novel coherent mathematical path to jointly approach the topics of constructability, stability, and limit consistency for lattice Boltzmann methods. A new constructive ansatz for lattice Boltzmann equations is introduced, which highlights the concept of relaxation in a top-down procedure starting at the targeted partial differential equation. Modular convergence proofs are used at each step to identify the key ingredients of relaxation frequencies, equilibria, and moment bases in the ansatz, which determine linear and nonlinear stability as well as consistency orders of relaxation and space-time discretization. For the latter, conventional techniques are employed and extended to determine the impact of the kinetic limit at the very foundation of lattice Boltzmann methods. To computationally analyze nonlinear stability, extensive numerical tests are enabled by combining the intrinsic parallelizability of lattice Boltzmann methods with the platform-agnostic and scalable open-source framework OpenLB. Through upscaling the number and quality of computations, large variations in the parameter spaces of classical benchmark problems are considered for the exploratory indication of methodological insights. Finally, the introduced mathematical and computational techniques are applied for the proposal and analysis of new lattice Boltzmann methods. Based on stabilized relaxation, limit consistent discretizations, and consistent temporal filters, novel numerical schemes are developed for approximating initial value problems and initial boundary value problems as well as coupled systems thereof. In particular, lattice Boltzmann methods are proposed and analyzed for temporal large eddy simulation, for simulating homogenized nonstationary fluid flow through porous media, for binary fluid flow simulations with higher order free energy models, and for the combination with Monte Carlo sampling to approximate statistical solutions of the incompressible Euler equations in three dimensions