Krylov-based algebraic multigrid for edge elements

International audienceThis work tackles the evaluation of a multigrid cycling strategy using inner flexible Krylov subspace iterations. It provides a valuable improvement to the Reitzinger and Sch¨oberl algebraic multigrid method for systems coming from edge element discretization

Models for Metal Hydride Particle Shape, Packing, and Heat Transfer

A multiphysics modeling approach for heat conduction in metal hydride powders is presented, including particle shape distribution, size distribution, granular packing structure, and effective thermal conductivity. A statistical geometric model is presented that replicates features of particle size and shape distributions observed experimentally that result from cyclic hydride decreptitation. The quasi-static dense packing of a sample set of these particles is simulated via energy-based structural optimization methods. These particles jam (i.e., solidify) at a density (solid volume fraction) of 0.665+/-0.015 - higher than prior experimental estimates. Effective thermal conductivity of the jammed system is simulated and found to follow the behavior predicted by granular effective medium theory. Finally, a theory is presented that links the properties of bi-porous cohesive powders to the present systems based on recent experimental observations of jammed packings of fine powder. This theory produces quantitative experimental agreement with metal hydride powders of various compositions.Comment: 12 pages, 12 figures, 2 table

Fast interior point solution of quadratic programming problems arising from PDE-constrained optimization

Interior point methods provide an attractive class of approaches for solving linear, quadratic and nonlinear programming problems, due to their excellent efficiency and wide applicability. In this paper, we consider PDE-constrained optimization problems with bound constraints on the state and control variables, and their representation on the discrete level as quadratic programming problems. To tackle complex problems and achieve high accuracy in the solution, one is required to solve matrix systems of huge scale resulting from Newton iteration, and hence fast and robust methods for these systems are required. We present preconditioned iterative techniques for solving a number of these problems using Krylov subspace methods, considering in what circumstances one may predict rapid convergence of the solvers in theory, as well as the solutions observed from practical computations

Kotter\u27s Model for Change and Distributed Leadership: A Multifaceted Approach for Canadian Colleges to Become Less Reliant on Operating Grant Funding

The emergence of performance-based frameworks for funding and declining government operating grant funding are contemporary challenges for Canadian public higher education institutions. Operating grants are a sizable portion of the funding institutions receive from the provincial government, and continued conditions on and declines in these grants pose significant risks to the sustainability and viability of these public institutions. Higher education institutions today need to become less reliant on government funds while remaining aligned with mandates to provide the programs and services necessary to meet the needs of the regions and communities they serve. Frontier College (a pseudonym) has revenue diversification strategies in place, but these strategies were developed with individual departmental needs in mind rather than an institutional focus. This Organizational Improvement Plan demonstrates how a distributed leadership approach with an iterative implementation of Kotter’s eight-step model for change can be used to institutionalize the college’s revenue diversification strategies. Because revenue diversification strategies may involve entrepreneurial activity that is outside typical college operations, the change initiative will be led through the lens of equity, diversity, inclusivity, and decolonization to ensure that all initiatives align with Frontier College’s strategic plan without compromising the institution’s mandates, vision, or mission. This plan also demonstrates how a balanced scorecard can be used as an effective monitoring, evaluation, and communication tool throughout the change process, allowing leaders to collaborate with employees to adjust, amend, and alter plans as they revisit Kotter’s steps together to successfully embed the change within the college’s culture

Multigrid methods for two-player zero-sum stochastic games

We present a fast numerical algorithm for large scale zero-sum stochastic games with perfect information, which combines policy iteration and algebraic multigrid methods. This algorithm can be applied either to a true finite state space zero-sum two player game or to the discretization of an Isaacs equation. We present numerical tests on discretizations of Isaacs equations or variational inequalities. We also present a full multi-level policy iteration, similar to FMG, which allows to improve substantially the computation time for solving some variational inequalities.Comment: 31 page

Enhancing structure relaxations for first-principles codes: an approximate Hessian approach

We present a method for improving the speed of geometry relaxation by using a harmonic approximation for the interaction potential between nearest neighbor atoms to construct an initial Hessian estimate. The model is quite robust, and yields approximately a 30% or better reduction in the number of calculations compared to an optimized diagonal initialization. Convergence with this initializer approaches the speed of a converged BFGS Hessian, therefore it is close to the best that can be achieved. Hessian preconditioning is discussed, and it is found that a compromise between an average condition number and a narrow distribution in eigenvalues produces the best optimization.Comment: 9 pages, 3 figures, added references, expanded optimization sectio

Hierarchical Schur complement preconditioner for the stochastic Galerkin finite element methods

Use of the stochastic Galerkin finite element methods leads to large systems of linear equations obtained by the discretization of tensor product solution spaces along their spatial and stochastic dimensions. These systems are typically solved iteratively by a Krylov subspace method. We propose a preconditioner which takes an advantage of the recursive hierarchy in the structure of the global matrices. In particular, the matrices posses a recursive hierarchical two-by-two structure, with one of the submatrices block diagonal. Each one of the diagonal blocks in this submatrix is closely related to the deterministic mean-value problem, and the action of its inverse is in the implementation approximated by inner loops of Krylov iterations. Thus our hierarchical Schur complement preconditioner combines, on each level in the approximation of the hierarchical structure of the global matrix, the idea of Schur complement with loops for a number of mutually independent inner Krylov iterations, and several matrix-vector multiplications for the off-diagonal blocks. Neither the global matrix, nor the matrix of the preconditioner need to be formed explicitly. The ingredients include only the number of stiffness matrices from the truncated Karhunen-Lo\`{e}ve expansion and a good preconditioned for the mean-value deterministic problem. We provide a condition number bound for a model elliptic problem and the performance of the method is illustrated by numerical experiments.Comment: 15 pages, 2 figures, 9 tables, (updated numerical experiments

Evolution of lubricant degradation and lubricant behaviour in a piston assembly of a reciprocating gasoline engine

The most difficult and challenging area for the tribology of reciprocating internal combustion engines to improve efficiency and life is the lubricant health within the piston ring pack. It is here where extreme temperatures, pressures and noxious gases interact with the small volume of lubricant designed to protect the components. There is a lack of knowledge of the correlation between the lubricant condition and its performance. This research is an original contribution to this field and addressed the influence of lubricant degradation on lubricant film thicknesses and residence times in the piston ring pack. A laser induced fluorescence (LIF) system was first implemented on an operating motored gasoline engine to examine the piston ring to cylinder wall lubricant film thickness. A bespoke optical setup was designed and developed with excellent spatial resolution incorporating an argon ion laser, operating at 488 nm, combined with photomultiplier tubes to measure reference laser and incoming fluorescent light via a sapphire window in the cylinder liner. Lubricants were doped with Pyrromethene 567A fluorescent dye and the fluorescence signals were calibrated through a strict method, which allowed the fluorescence of degraded samples, and hence the lubricant film thickness, to be quantified. A range of degraded engine lubricant samples were acquired from Mercedes Benz, Leeds, UK and Southwest Research Institute, Texas, USA. The LIF system was then adapted and transferred to a high speed, fired Ricardo Hydra single cylinder gasoline engine. The capability of the LIF system was finally extended to examine lubricant flow in the piston ring pack through a novel tracer technique, which enabled direct measurement of piston ring pack lubricant residence time. A LIF system was developed that could clearly distinguish between lubricants of different viscosities and degradation state. It was found that degraded lubricants, with increased viscosity compared to fresh lubricant, produce thicker lubricant films in the piston ring to cylinder wall interface, which would directly impact on engine efficiency. Additionally, it was found that engine speed, load and lubricant viscosity influence the piston ring pack lubricant residence time and the replenishment of the lubricant within the piston ring pack

On Convergence of the Inexact Rayleigh Quotient Iteration with the Lanczos Method Used for Solving Linear Systems

For the Hermitian inexact Rayleigh quotient iteration (RQI), the author has established new local general convergence results, independent of iterative solvers for inner linear systems. The theory shows that the method locally converges quadratically under a new condition, called the uniform positiveness condition. In this paper we first consider the local convergence of the inexact RQI with the unpreconditioned Lanczos method for the linear systems. Some attractive properties are derived for the residuals, whose norms are $\xi_{k+1}$'s, of the linear systems obtained by the Lanczos method. Based on them and the new general convergence results, we make a refined analysis and establish new local convergence results. It is proved that the inexact RQI with Lanczos converges quadratically provided that $\xi_{k+1}\leq\xi$ with a constant $\xi\geq 1$. The method is guaranteed to converge linearly provided that $\xi_{k+1}$ is bounded by a small multiple of the reciprocal of the residual norm $\|r_k\|$ of the current approximate eigenpair. The results are fundamentally different from the existing convergence results that always require $\xi_{k+1}<1$, and they have a strong impact on effective implementations of the method. We extend the new theory to the inexact RQI with a tuned preconditioned Lanczos for the linear systems. Based on the new theory, we can design practical criteria to control $\xi_{k+1}$ to achieve quadratic convergence and implement the method more effectively than ever before. Numerical experiments confirm our theory.Comment: 20 pages, 8 figures. arXiv admin note: text overlap with arXiv:0906.223

Effect of Isotretinoin on Adolescent Growth: a retrospective chart review

• Isotretinoin (13-cis-retinoic acid) is a retinoid or vitamin A derivative widely used to treat severe acne vulgaris.• Decreases sebum production and prevents comedo formation.• Isotretinoin use is associated with a variety of toxicities: developmental, cutaneous, musculoskeletal, etc.• including hyperosteosis and premature epiphyseal closure at high doses.&nbsp;• No studies examining pediatric growth in patients treated with isotretinoin at doses appropriate for severe, recalcitrant acne vulgaris treatment