Modeling Ice Streams

Modeling glacier and ice sheet flow is a computationally challenging problem. The most challenging part in simulating ice sheet flow is modeling the fastest moving part of ice sheets, ice streams. In the first part of the thesis, we have constructed two numerical models of isothermal ice stream flow, a three-dimensional full-Stokes ice-sheet/ice-stream/ice-shelf model and a modified MacAyeal-Morland ice-stream/ice-shelf model. In the second part of the thesis, we studied the possibility of using SuperLU-DIST multiprocessor software package for solving the systems of linear equations generated by the model. The uniqueness of the modified MacAyeal-Morland model is in its inclusion of the basal shear friction in the derivation of the equations. In the original MacAyeal-Morland equations, the shear friction is not included in the fundamental formulation but instead is added as a small correction to the final equations. Inclusion of the basal friction in the derivation generates equations that contain a term that depends on the bed gradients; that is, it generates equations that show how the ice stream flowmay depend on the bed topography. To validate the model, the European Ice Sheet Modeling Initiative 1 intercomparison test is conducted and the results are compared with the results generated by MacAyeal (1994). The three-dimensional full-Stokes model includes all higher-order stress gradients in the force-balance equation. To validate the full-Stokes model, experiments demonstrating the importance of the inclusion of all higher order stresses in the model, such as simulation of the evolution of an ice stream within the ice sheet and simulation of iceberg profiles, are conducted. The computational demands of the full-Stokes model do not allow us using it in large problem domains. To solve this problem, application of SuperLU-DIST multiprocessor software package has been examined. The software’s performance characteristics have been explored and benchmarked on the matrices generated by the three-dimensional full- Stokes model. The performed tests indicate that for the big-size matrices computations may not be stable. However, we have shown that it is possible to improve stability of the algorithm by using a priori knowledge of the matrix and permuting rows prior to applying the algorithm

Modeling Ice Streams

Modeling glacier and ice sheet flow is a computationally challenging problem. The most challenging part in simulating ice sheet flow is modeling the fastest moving part of ice sheets, ice streams. In the first part of the thesis, we have constructed two numerical models of isothermal ice stream flow, a three-dimensional full-Stokes ice-sheet/ice-stream/ice-shelf model and a modified MacAyeal-Morland ice-stream/ice-shelf model. In the second part of the thesis, we studied the possibility of using SuperLU-DIST multiprocessor software package for solving the systems of linear equations generated by the model. The uniqueness of the modified MacAyeal-Morland model is in its inclusion of the basal shear friction in the derivation of the equations. In the original MacAyeal-Morland equations, the shear friction is not included in the fundamental formulation but instead is added as a small correction to the final equations. Inclusion of the basal friction in the derivation generates equations that contain a term that depends on the bed gradients; that is, it generates equations that show how the ice stream flowmay depend on the bed topography. To validate the model, the European Ice Sheet Modeling Initiative 1 intercomparison test is conducted and the results are compared with the results generated by MacAyeal (1994). The three-dimensional full-Stokes model includes all higher-order stress gradients in the force-balance equation. To validate the full-Stokes model, experiments demonstrating the importance of the inclusion of all higher order stresses in the model, such as simulation of the evolution of an ice stream within the ice sheet and simulation of iceberg profiles, are conducted. The computational demands of the full-Stokes model do not allow us using it in large problem domains. To solve this problem, application of SuperLU-DIST multiprocessor software package has been examined. The software’s performance characteristics have been explored and benchmarked on the matrices generated by the three-dimensional full- Stokes model. The performed tests indicate that for the big-size matrices computations may not be stable. However, we have shown that it is possible to improve stability of the algorithm by using a priori knowledge of the matrix and permuting rows prior to applying the algorithm

Solar Wind Helium, Neon, And Argon In Genesis Aluminum Collectors

The Genesis mission collected samples of solar wind: SW) for 853 days and returned them to Earth for analysis. There are several processes that have the potential to significantly alter the composition between the time when SW ions are accelerated away from the sun, to the time the laboratory measurements are made. This work attempts to constrain these sources of fractionation and present the best estimate of the isotopic composition of SW helium, neon, and argon implanted into two different aluminum SW collectors on board the Genesis Mission. We have conducted a diffusion experiment on a similar time scale as the Genesis mission to determine the diffusion parameters of the two different aluminum collector materials and to quantify the changes in the measured ratios due to diffusive losses for the light noble gases. The results of this experiment show that the polished Al collector is not sufficiently retentive of the light noble gases to be a reliable collector for the light gases, but that the composition of the light gases implanted in the Al on sapphire collector does not show a measurable effect due to thermal diffusion. The Genesis mission collected separate samples of different types: `regimes\u27) of SW: low-speed, high-speed, and coronal mass ejections. Compositional differences between the different SW regimes: especially the low-speed and high-speed SW) are thought to provide a measure of possible fractionation during the acceleration of the SW. By making high-precision isotopic measurements on collectors of the three SW regimes, we have put strict upper limits on the difference between the low-speed and high-speed SW regimes: 20Ne/22Ne \u3c 0.24 ± 0.37% and 36Ar/38Ar \u3c 0.11 ± 0.26%. And we have made isotopic measurements of the light noble gases of the bulk SW: without selective collection of different SW regimes) from the aluminum collectors. Accounting for the sources of fractionation discussed above, I propose the following as the best current bulk SW isotopic values: 20Ne/22Ne = 13.75 ± 0.02, 21Ne/22Ne = 0.0329 ± 0.0002, and 36Ar/38Ar = 5.501 ± 0.005: all errors are 1σ)

Self Assembly Problems of Anisotropic Particles in Soft Matter.

Anisotropic building blocks assembled from colloidal particles are attractive building blocks for self-assembled materials because their complex interactions can be exploited to drive self-assembly. In this dissertation we address the self-assembly of anisotropic particles from multiple novel computational and mathematical angles. First, we accelerate algorithms for modeling systems of anisotropic particles via massively parallel GPUs. We provide a scheme for generating statistically robust pseudo-random numbers that enables GPU acceleration of Brownian and dissipative particle dynamics. We also show how rigid body integration can be accelerated on a GPU. Integrating these two algorithms into a GPU-accelerated molecular dynamics code (HOOMD-blue), make a single GPU the ideal computing environment for modeling the self-assembly of anisotropic nanoparticles. Second, we introduce a new mathematical optimization problem, filling, a hybrid of the familiar shape packing and covering problem, which can be used to model shaped particles. We study the rich mathematical structures of the solution space and provide computational methods for finding optimal solutions for polygons and convex polyhedra. We present a sequence of isosymmetric optimal filling solutions for the Platonic solids. We then consider the filling of a hyper-cone in dimensions two to eight and show the solution remains scale-invariant but dependent on dimension. Third, we study the impact of size variation, polydispersity, on the self-assembly of an anisotropic particle, the polymer-tethered nanosphere, into ordered phases. We show that the local nanoparticle packing motif, icosahedral or crystalline, determines the impact of polydispersity on energy of the system and phase transitions. We show how extensions of the Voronoi tessellation can be calculated and applied to characterize such micro-segregated phases. By applying a Voronoi tessellation, we show that properties of the individual domains can be studied as a function of system properties such as temperature and concentration. Last, we consider the thermodynamically driven self-assembly of terminal clusters of particles. We predict that clusters related to spherical codes, a mathematical sequence of points, can be synthesized via self-assembly. These anisotropic clusters can be tuned to different anisotropies via the ratio of sphere diameters and temperature. The method suggests a rich new way for assembling anisotropic building blocks.Ph.D.Applied Physics and Scientific ComputingUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/91576/1/phillicl_1.pd

Large-scale tree-based unfitted finite elements for metal additive manufacturing

This thesis addresses large-scale numerical simulations of partial differential equations posed on evolving geometries. Our target application is the simulation of metal additive manufacturing (or 3D printing) with powder-bed fusion methods, such as Selective Laser Melting (SLM), Direct Metal Laser Sintering (DMLS) or Electron-Beam Melting (EBM). The simulation of metal additive manufacturing processes is a remarkable computational challenge, because processes are characterised by multiple scales in space and time and multiple complex physics that occur in intricate three-dimensional growing-in-time geometries. Only the synergy of advanced numerical algorithms and high-performance scientific computing tools can fully resolve, in the short run, the simulation needs in the area. The main goal of this Thesis is to design a a novel highly-scalable numerical framework with multi-resolution capability in arbitrarily complex evolving geometries. To this end, the framework is built by combining three computational tools: (1) parallel mesh generation and adaptation with forest-of-trees meshes, (2) robust unfitted finite element methods and (3) parallel finite element modelling of the geometry evolution in time. Our numerical research is driven by several limitations and open questions in the state-of-the-art of the three aforementioned areas, which are vital to achieve our main objective. All our developments are deployed with high-end distributed-memory implementations in the large-scale open-source software project FEMPAR. In considering our target application, (4) temporal and spatial model reduction strategies for thermal finite element models are investigated. They are coupled to our new large-scale computational framework to simplify optimisation of the manufacturing process. The contributions of this Thesis span the four ingredients above. Current understanding of (1) is substantially improved with rigorous proofs of the computational benefits of the 2:1 k-balance (ease of parallel implementation and high-scalability) and the minimum requirements a parallel tree-based mesh must fulfil to yield correct parallel finite element solvers atop them. Concerning (2), a robust, optimal and scalable formulation of the aggregated unfitted finite element method is proposed on parallel tree-based meshes for elliptic problems with unfitted external contour or unfitted interfaces. To the author’s best knowledge, this marks the first time techniques (1) and (2) are brought together. After enhancing (1)+(2) with a novel parallel approach for (3), the resulting framework is able to mitigate a major performance bottleneck in large-scale simulations of metal additive manufacturing processes by powder-bed fusion: scalable adaptive (re)meshing in arbitrarily complex geometries that grow in time. Along the development of this Thesis, our application problem (4) is investigated in two joint collaborations with the Monash Centre for Additive Manufacturing and Monash University in Melbourne, Australia. The first contribution is an experimentally-supported thorough numerical assessment of time-lumping methods, the second one is a novel experimentally-validated formulation of a new physics-based thermal contact model, accounting for thermal inertia and suitable for model localisation, the so-called virtual domain approximation. By efficiently exploiting high-performance computing resources, our new computational framework enables large-scale finite element analysis of metal additive manufacturing processes, with increased fidelity of predictions and dramatical reductions of computing times. It can also be combined with the proposed model reductions for fast thermal optimisation of the manufacturing process. These tools open the path to accelerate the understanding of the process-to-performance link and digital product design and certification in metal additive manufacturing, two milestones that are vital to exploit the technology for mass-production.Aquesta tesi tracta la simulació a gran escala d'equacions en derivades parcials sobre geometries variables. L'aplicació principal és la simulació de procesos de fabricació additiva (o impressió 3D) amb metalls i per mètodes de fusió de llit de pols, com ara Selective Laser Melting (SLM), Direct Metal Laser Sintering (DMLS) o Electron-Beam Melting (EBM). La simulació d'aquests processos és un repte computacional excepcional, perquè els processos estan caracteritzats per múltiples escales espaitemporals i múltiples físiques que tenen lloc sobre geometries tridimensionals complicades que creixen en el temps. La sinèrgia entre algorismes numèrics avançats i eines de computació científica d'alt rendiment és la única via per resoldre completament i a curt termini les necessitats en simulació d'aquesta àrea. El principal objectiu d'aquesta tesi és dissenyar un nou marc numèric escalable de simulació amb capacitat de multiresolució en geometries complexes i variables. El nou marc es construeix unint tres eines computacionals: (1) mallat paral·lel i adaptatiu amb malles de boscs d'arbre, (2) mètodes d'elements finits immersos robustos i (3) modelització en paral·lel amb elements finits de geometries que creixen en el temps. Algunes limitacions i problemes oberts en l'estat de l'art, que són claus per aconseguir el nostre objectiu, guien la nostra recerca. Tots els desenvolupaments s'implementen en arquitectures de memòria distribuïda amb el programari d'accés obert FEMPAR. Quant al problema d'aplicació, (4) s'investiguen models reduïts en espai i temps per models tèrmics del procés. Aquests models reduïts s'acoplen al nostre marc computacional per simplificar l'optimització del procés. Les contribucions d'aquesta tesi abasten els quatre punts de dalt. L'estat de l'art de (1) es millora substancialment amb proves riguroses dels beneficis computacionals del 2:1 balancejat (fàcil paral·lelització i alta escalabilitat), així com dels requisits mínims que aquest tipus de mallat han de complir per garantir que els espais d'elements finits que s'hi defineixin estiguin ben posats. Quant a (2), s'ha formulat un mètode robust, òptim i escalable per agregació per problemes el·líptics amb contorn o interface immerses. Després d'augmentar (1)+(2) amb un nova estratègia paral·lela per (3), el marc de simulació resultant mitiga de manera efectiva el principal coll d'ampolla en la simulació de processos de fabricació additiva en llits de pols de metall: adaptivitat i remallat escalable en geometries complexes que creixen en el temps. Durant el desenvolupament de la tesi, es col·labora amb el Monash Centre for Additive Manufacturing i la Universitat de Monash de Melbourne, Austràlia, per investigar el problema d'aplicació. En primer lloc, es fa una anàlisi experimental i numèrica exhaustiva dels mètodes d'aggregació temporal. En segon lloc, es proposa i valida experimental una nova formulació de contacte tèrmic que té en compte la inèrcia tèrmica i és adequat per a localitzar el model, l'anomenada aproximació per dominis virtuals. Mitjançant l'ús eficient de recursos computacionals d'alt rendiment, el nostre nou marc computacional fa possible l'anàlisi d'elements finits a gran escala dels processos de fabricació additiva amb metalls, amb augment de la fidelitat de les prediccions i reduccions significatives de temps de computació. Així mateix, es pot combinar amb els models reduïts que es proposen per l'optimització tèrmica del procés de fabricació. Aquestes eines contribueixen a accelerar la comprensió del lligam procés-rendiment i la digitalització del disseny i certificació de productes en fabricació additiva per metalls, dues fites crucials per explotar la tecnologia en producció en massa.Postprint (published version