Developments in the Extended Finite Element Method and Algebraic Multigrid for Solid Mechanics Problems Involving Discontinuities

In this dissertation, some contributions related to computational modeling and solution of solid mechanics problems involving discontinuities are discussed. The main tool employed for discrete modeling of discontinuities is the extended finite element method and the primary solution method discussed is the algebraic multigrid. The extended finite element method has been shown to be effective for both weak and strong discontinuities. With respect to weak discontinuities, a new approach that couples the extended finite element method with Monte Carlo simulations with the goal of quantifying uncertainty in homogenization of material properties of random microstructures is presented. For accelerated solution of linear systems arising from problems involving cracks, several new methods involving the algebraic multigrid are presented. In the first approach, the Schur complement of the linear system arising from XFEM is used to develop a Hybrid-AMG method such that crack-conforming aggregates are formed. Another alternative approach involves transforming the original linear system into a modified system that is amenable for a direct application of algebraic multigrid. It is shown that if only Heaviside-enrichments are present, a simple transformation based on the phantom-node approach is available, which decouples the linear system along the discontinuities such that crack conforming aggregates are automatically generated via smoother aggregation algebraic multigrid. Various numerical examples are presented to verify the accuracy of the resulting solutions and the convergence properties of the proposed algorithms. The parallel scalability performance of the implementation are also discussed

High-fidelity real-time simulation on deployed platforms

We present a certified reduced basis method for high-fidelity real-time solution of parametrized partial differential equations on deployed platforms. Applications include in situ parameter estimation, adaptive design and control, interactive synthesis and visualization, and individuated product specification. We emphasize a new hierarchical architecture particularly well suited to the reduced basis computational paradigm: the expensive Offline stage is conducted pre-deployment on a parallel supercomputer (in our examples, the TeraGrid machine Ranger); the inexpensive Online stage is conducted “in the field” on ubiquitous thin/inexpensive platforms such as laptops, tablets, smartphones (in our examples, the Nexus One Android-based phone), or embedded chips. We illustrate our approach with three examples: a two-dimensional Helmholtz acoustics “horn” problem; a three-dimensional transient heat conduction “Swiss Cheese” problem; and a three-dimensional unsteady incompressible Navier–Stokes low-Reynolds-number “eddy-promoter” problem.United States. Air Force Office of Scientific Research (Grant FA9550-07-1-0425)United States. Air Force Office of Scientific Research (OSD Grant FA9550-09-1-0613)National Science Foundation (U.S.) (University of Texas at Austin. Texas Advanced Computing Center Grant TG-ASC100016

A scalable parallel finite element framework for growing geometries. Application to metal additive manufacturing

This work introduces an innovative parallel, fully-distributed finite element framework for growing geometries and its application to metal additive manufacturing. It is well-known that virtual part design and qualification in additive manufacturing requires highly-accurate multiscale and multiphysics analyses. Only high performance computing tools are able to handle such complexity in time frames compatible with time-to-market. However, efficiency, without loss of accuracy, has rarely held the centre stage in the numerical community. Here, in contrast, the framework is designed to adequately exploit the resources of high-end distributed-memory machines. It is grounded on three building blocks: (1) Hierarchical adaptive mesh refinement with octree-based meshes; (2) a parallel strategy to model the growth of the geometry; (3) state-of-the-art parallel iterative linear solvers. Computational experiments consider the heat transfer analysis at the part scale of the printing process by powder-bed technologies. After verification against a 3D benchmark, a strong-scaling analysis assesses performance and identifies major sources of parallel overhead. A third numerical example examines the efficiency and robustness of (2) in a curved 3D shape. Unprecedented parallelism and scalability were achieved in this work. Hence, this framework contributes to take on higher complexity and/or accuracy, not only of part-scale simulations of metal or polymer additive manufacturing, but also in welding, sedimentation, atherosclerosis, or any other physical problem where the physical domain of interest grows in time

Reduced basis method for the shape optimization of racing car components

In this work we apply reduced basis methods to parametrized airfoils configurations to study inviscid potential, thermal and viscous flows. Parametrization includes geometry, ground effect and airfoils interaction

Image-based Modeling of Flow through Porous Media: Development of Multiscale Techniques for the Pore Level

Increasingly, imaging technology allows porous media problems to be modeled at microscopic and sub-microscopic levels with finer resolution. However, the physical domain size required to be representative of the media prohibits comprehensive micro-scale simulation. A hybrid or multiscale approach is necessary to overcome this challenge. In this work, a technique was developed for determining the characteristic scales of porous materials, and a multiscale modeling methodology was developed to better understand the interaction/dependence of phenomena occurring at different microscopic scales. The multiscale method couples microscopic simulations at the pore and sub-pore scales. Network modeling is a common pore-scale technique which employs severe assumptions, making it more computationally efficient than direct numerical simulation, enabling simulation over larger length scales. However, microscopic features of the medium are lost in the discretization of a material into a network of interconnected pores and throats. In contrast, detailed microstructure and flow patterns can be captured by modern meshing and direct numerical simulation techniques, but these models are computationally expensive. In this study, a data-driven multiscale technique has been developed that couples the two types of models, taking advantage of the benefits of each. Specifically, an image-based physically-representative pore network model is coupled to an FEM (finite element method) solver that operates on unstructured meshes capable of resolving details orders of magnitude smaller than the pore size. In addition to allowing simulation at multiple scales, the current implementation couples the models using a machine learning approach, where results from the FEM model are used to learn network model parameters. Examples of the model operating on real materials are given that demonstrate improvements in network modeling enabled by the multiscale framework. The framework enables more advanced multiscale and multiphysics modeling – an application to particle straining problems is shown. More realistic network filtration simulations are possible by incorporating information from the sub-pore-scale. New insights into the size exclusion mechanism of particulate filtration were gained in the process of generating data for machine learning of conductivity reduction due to particle trapping. Additional tests are required to validate the multiscale network filtration model, and compare with experimental findings in literature

HPCCP/CAS Workshop Proceedings 1998

This publication is a collection of extended abstracts of presentations given at the HPCCP/CAS (High Performance Computing and Communications Program/Computational Aerosciences Project) Workshop held on August 24-26, 1998, at NASA Ames Research Center, Moffett Field, California. The objective of the Workshop was to bring together the aerospace high performance computing community, consisting of airframe and propulsion companies, independent software vendors, university researchers, and government scientists and engineers. The Workshop was sponsored by the HPCCP Office at NASA Ames Research Center. The Workshop consisted of over 40 presentations, including an overview of NASA's High Performance Computing and Communications Program and the Computational Aerosciences Project; ten sessions of papers representative of the high performance computing research conducted within the Program by the aerospace industry, academia, NASA, and other government laboratories; two panel sessions; and a special presentation by Mr. James Bailey

3D parallel computations of turbofan noise propagation using a spectral element method

A three-dimensional code has been developed for the simulation of tone noise generated by turbofan engine inlets using computational aeroacoustics. The governing equations are the linearized Euler equations, which are further simplified to a set of equations in terms of acoustic potential, using the irrotational flow assumption, and subsequently solved in the frequency domain.Due to the special nature of acoustic wave propagation, the spatial discretization is performed using a spectral element method, where a tensor product of the nth-degree polynomials based on Chebyshev orthogonal functions is used to approximate variations within hexahedral elements. Non-reflecting boundary conditions are imposed at the far-field using a damping layer concept. This is done by augmenting the continuity equation with an additional term without modifying the governing equations as in PML methods.Solution of the linear system of equations for the acoustic problem is based on the Schur complement method, which is a nonoverlapping domain decomposition technique. The Schur matrix is first solved using a matrix-free iterative method, whose convergence is accelerated with a novel local preconditioner. The solution in the entire domain is then obtained by finding solutions in smaller subdomains.The 3D code also contains a mean flow solver based on the full potential equation in order to take into account the effects of flow variations around the nacelle on the scattering of the radiated sound field.All aspects of numerical simulations, including building and assembling the coefficient matrices, implementation of the Schur complement method, and solution of the system of equations for both the acoustic and mean flow problems are performed on multiprocessors in parallel using the resources of the CLUMEQ Supercomputer Center. A large number of test cases are presented, ranging in size from 100 000-2 000 000 unknowns for which, depending on the size of the problem, between 8-48 CPU's are used.The developed code is demonstrated to be robust and efficient in simulating acoustic propagation for a large number of problems, with an excellent parallel performance

Modeling of Complex Large-Scale Flow Phenomena

Flows at large scales are capable of unmatched complexity. At large spatial scales, they can exhibit phenomena like waves, tornadoes, and a screaming concert audience; at high densities, they can create shockwaves, and can cause stampedes. Though strides have been made in simulating flows like fluids and crowds, extending these algorithms with scale poses challenges in ensuring accuracy while maintaining computational efficiency. In this dissertation, I present novel techniques to simulate large-scale flows using coupled Eulerian-Lagrangian models that employ a combination of discretized grids and dynamic particle-based representations. I demonstrate how such models can efficiently simulate flows at large-scales, while maintaining fine-scale features. In fluid simulation, a long-standing problem has been the simulation of large-scale scenes without compromising fine-scale features. Though approximate multi-scale models exist, accurate simulation of large-scale fluid flow has remained constrained by memory and computational limits of current generation PCs. I propose a hybrid domain-decomposition model that, by coupling Lagrangian vortex-based methods with Eulerian velocity-based methods, reduces memory requirements and improves performance on parallel architectures. The resulting technique can efficiently simulate scenes significantly larger than those possible with either model alone. The motion of crowds is another class of flows that exhibits novel complexities with increasing scale. Navigation of crowds in virtual worlds is traditionally guided by a static global planner, combined with dynamic local collision avoidance. However, such models cannot capture long-range crowd interactions commonly observed in pedestrians. This discrepancy can cause sharp changes in agent trajectories, and sub-optimal navigation. I present a technique to add long-range vision to virtual crowds by performing collision avoidance at multiple spatial and temporal scales for both Eulerian and Lagrangian crowd navigation models, and a novel technique to blend both approaches in order to obtain collision-free velocities efficiently. The resulting simulated crowds show better correspondence with real-world pedestrians in both qualitative and quantitative metrics, while adding a minimal computational overhead. Another aspect of real-world crowds missing from virtual agents is their behavior at high densities. Crowds at such scales can often exhibit chaotic behavior commonly known as emph{crowd turbulence}; this phenomenon has the potential to cause mishaps leading to loss of life. I propose modeling inter-personal stress in dense crowds using an Eulerian model, coupled with a physically-based Lagrangian agent-based model to simulate crowd turbulence. I demonstrate how such a hybrid model can create virtual crowds whose trajectories show visual and quantifiable similarities to turbulent crowds in the real world. The techniques proposed in this thesis demonstrate that hybrid Eulerian-Lagrangian modeling presents a versatile approach for modeling large-scale flows, such as fluids and crowds, efficiently on current generation PCs.Doctor of Philosoph