6,791 research outputs found
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 Order Modeling based Inexact FETI-DP solver for lattice structures
This paper addresses the overwhelming computational resources needed with
standard numerical approaches to simulate architected materials. Those
multiscale heterogeneous lattice structures gain intensive interest in
conjunction with the improvement of additive manufacturing as they offer, among
many others, excellent stiffness-to-weight ratios. We develop here a dedicated
HPC solver that benefits from the specific nature of the underlying problem in
order to drastically reduce the computational costs (memory and time) for the
full fine-scale analysis of lattice structures. Our purpose is to take
advantage of the natural domain decomposition into cells and, even more
importantly, of the geometrical and mechanical similarities among cells. Our
solver consists in a so-called inexact FETI-DP method where the local,
cell-wise operators and solutions are approximated with reduced order modeling
techniques. Instead of considering independently every cell, we end up with
only few principal local problems to solve and make use of the corresponding
principal cell-wise operators to approximate all the others. It results in a
scalable algorithm that saves numerous local factorizations. Our solver is
applied for the isogeometric analysis of lattices built by spline composition,
which offers the opportunity to compute the reduced basis with macro-scale
data, thereby making our method also multiscale and matrix-free. The solver is
tested against various 2D and 3D analyses. It shows major gains with respect to
black-box solvers; in particular, problems of several millions of degrees of
freedom can be solved with a simple computer within few minutes.Comment: 30 pages, 12 figures, 2 table
Laplacian Mixture Modeling for Network Analysis and Unsupervised Learning on Graphs
Laplacian mixture models identify overlapping regions of influence in
unlabeled graph and network data in a scalable and computationally efficient
way, yielding useful low-dimensional representations. By combining Laplacian
eigenspace and finite mixture modeling methods, they provide probabilistic or
fuzzy dimensionality reductions or domain decompositions for a variety of input
data types, including mixture distributions, feature vectors, and graphs or
networks. Provable optimal recovery using the algorithm is analytically shown
for a nontrivial class of cluster graphs. Heuristic approximations for scalable
high-performance implementations are described and empirically tested.
Connections to PageRank and community detection in network analysis demonstrate
the wide applicability of this approach. The origins of fuzzy spectral methods,
beginning with generalized heat or diffusion equations in physics, are reviewed
and summarized. Comparisons to other dimensionality reduction and clustering
methods for challenging unsupervised machine learning problems are also
discussed.Comment: 13 figures, 35 reference
Aerated blast furnace slag filters for enhanced nitrogen and phosphorus removal from small wastewater treatment plants
Rock filters (RF) are a promising alternative technology for natural
wastewater treatment for upgrading WSP effluent. However, the application
of RF in the removal of eutrophic nutrients, nitrogen and phosphorus, is very
limited. Accordingly, the overall objective of this study was to develop a lowcost
RF system for the purpose of enhanced nutrient removal from WSP
effluents, which would be able to produce effluents which comply with the
requirements of the EU Urban Waste Water Treatment Directive (UWWTD)
(911271lEEC) and suitable for small communities. Therefore, a combination
system comprising a primary facultative pond and an aerated rock filter
(ARF) system-either vertically or horizontally loaded-was investigated at
the University of Leeds' experimental station at Esholt Wastewater
Treatment Works, Bradford, UK.
Blast furnace slag (BFS) and limestone were selected for use in the ARF
system owing to their high potential for P removal and their low cost. This
study involved three major qperiments: (1) a comparison of aerated
vertical-flow and horizontal-flow limestone filters for nitrogen removal; (2) a
comparison of aerated limestone + blast furnace slag (BFS) filter and
aerated BFS filters for nitrogen and phosphorus removal; and (3) a
comparison of vertical-flow and horizontal-flow BFS filters for nitrogen and
phosphorus removal.
The vertical upward-flow ARF system was found to be superior to the
horizontal-flow ARF system in terms of nitrogen removal, mostly thiough
bacterial nitrification processes in both the aerated limestone and BFS filter
studies. The BFS filter medium (whieh is low-cost) showed a much higher
potential in removing phosphortls from pond effluent than the limestone
medium. As a result, the combination of a vertical upward-flow ARF system
and an economical and effective P-removal filter medium, such as BFS,
was found to be an ideal optionfor the total nutrient removal of both nitrogen
and phosphorus from wastewater.
In parallel with these experiments, studies on the aerated BFS filter effective
life and major in-filter phosphorus removal pathways were carried out. From
the standard batch experiments of Pmax adsorption capacity of BFS, as well
as six-month data collection of daily average P-removal, it was found that
the effective life of the aerated BFS filter was 6.5 years. Scanning electron
microscopy and X-ray diffraction spectrometric analyses on the surface of
BFS, particulates and sediment samples revealed that the apparent
mechanisms of P-removal in the filter are adsorption on the amorphous
oxide phase of the BFS surface and precipitation within the filter
Scalable domain decomposition methods for finite element approximations of transient and electromagnetic problems
The main object of study of this thesis is the development of scalable and robust solvers based on domain decomposition (DD) methods for the linear systems arising from the finite element (FE) discretization of transient and electromagnetic problems.
The thesis commences with a theoretical review of the curl-conforming edge (or Nédélec) FEs of the first kind and a comprehensive description of a general implementation strategy for h- and p- adaptive elements of arbitrary order on tetrahedral and hexahedral non-conforming meshes. Then, a novel balancing domain decomposition by constraints (BDDC) preconditioner that is robust for multi-material and/or heterogeneous problems posed in curl-conforming spaces is presented. The new method, in contrast to existent approaches, is based on the definition of the ingredients of the preconditioner according to the physical coefficients of the problem and does not require spectral information. The result is a robust and highly scalable preconditioner that preserves the simplicity of the original BDDC method.
When dealing with transient problems, the time direction offers itself an opportunity for further parallelization. Aiming to design scalable space-time solvers, first, parallel-in-time parallel methods for linear and non-linear ordinary differential equations (ODEs) are proposed, based on (non-linear) Schur complement efficient solvers of a multilevel partition of the time interval. Then, these ideas are combined with DD concepts in order to design a two-level preconditioner as an extension to space-time of the BDDC method. The key ingredients for these new methods are defined such that they preserve the time causality, i.e., information only travels from the past to the future. The proposed schemes are weakly scalable in time and space-time, i.e., one can efficiently exploit increasing computational resources to solve more time steps in (approximately) the same time-to-solution.
All the developments presented herein are motivated by the driving application of the thesis, the 3D simulation of the low-frequency electromagnetic response of High Temperature Superconductors (HTS). Throughout the document, an exhaustive set of numerical experiments, which includes the simulation of a realistic 3D HTS problem, is performed in order to validate the suitability and assess the parallel performance of the High Performance Computing (HPC) implementation of the proposed algorithms.L’objecte principal d’estudi d’aquesta tesi és el desenvolupament de solucionadors escalables i robustos basats en mètodes de descomposició de dominis (DD) per a sistemes lineals que sorgeixen en la discretització mitjançant elements finits (FE) de problemes transitoris i electromagnètics.
La tesi comença amb una revisió teòrica dels FE d’eix (o de Nédélec) de la primera família i una descripció exhaustiva d’una estratègia d’implementació general per a elements h- i p-adaptatius d’ordre arbitrari en malles de tetraedres i hexaedres noconformes.
Llavors, es presenta un nou precondicionador de descomposició de dominis balancejats per restricció (BDDC) que és robust per a problemes amb múltiples materials i/o heterogenis definits en espais curl-conformes. El nou mètode, en contrast amb els enfocaments existents, està basat en la definició dels ingredients del precondicionador segons els coeficients físics del problema i no requereix informació espectral. El resultat és un precondicionador robust i escalable que preserva la simplicitat del mètode original BDDC.
Quan tractem amb problemes transitoris, la direcció temporal ofereix ella mateixa l’oportunitat de seguir explotant paral·lelisme. Amb l’objectiu de dissenyar precondicionadors en espai-temps, primer, proposem solucionadors paral·lels en temps per equacions diferencials lineals i no-lineals, basats en un solucionador eficient del complement de Schur d’una partició multinivell de l’interval de temps. Seguidament, aquestes idees es combinen amb conceptes de DD amb l’objectiu de dissenyar precondicionadors com a extensió a espai-temps dels mètodes de BDDC. Els ingredients clau d’aquests nous mètodes es defineixen de tal manera que preserven la causalitat del temps, on la informació només viatja de temps passats a temps futurs. Els esquemes proposats són dèbilment escalables en temps i en espai-temps, és a dir, es poden explotar eficientment recursos computacionals creixents per resoldre més passos de temps en (aproximadament) el mateix temps transcorregut de càlcul.
Tots els desenvolupaments presentats aquí són motivats pel problema d’aplicació de la tesi, la simulació de la resposta electromagnètica de baixa freqüència dels superconductors d’alta temperatura (HTS) en 3D. Al llarg del document, es realitza un conjunt exhaustiu d’experiments numèrics, els quals inclouen la simulació d’un problema de HTS realista en 3D, per validar la idoneïtat i el rendiment paral·lel de la implementació per a computació d’alt rendiment dels algorismes proposatsPostprint (published version
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