Computational complexity and memory usage for multi-frontal direct solvers in structured mesh finite elements

The multi-frontal direct solver is the state-of-the-art algorithm for the direct solution of sparse linear systems. This paper provides computational complexity and memory usage estimates for the application of the multi-frontal direct solver algorithm on linear systems resulting from B-spline-based isogeometric finite elements, where the mesh is a structured grid. Specifically we provide the estimates for systems resulting from $C^{p-1}$ polynomial B-spline spaces and compare them to those obtained using $C^0$ spaces.Comment: 8 pages, 2 figure

A Continuation Multilevel Monte Carlo algorithm

We propose a novel Continuation Multi Level Monte Carlo (CMLMC) algorithm for weak approximation of stochastic models. The CMLMC algorithm solves the given approximation problem for a sequence of decreasing tolerances, ending when the required error tolerance is satisfied. CMLMC assumes discretization hierarchies that are defined a priori for each level and are geometrically refined across levels. The actual choice of computational work across levels is based on parametric models for the average cost per sample and the corresponding weak and strong errors. These parameters are calibrated using Bayesian estimation, taking particular notice of the deepest levels of the discretization hierarchy, where only few realizations are available to produce the estimates. The resulting CMLMC estimator exhibits a non-trivial splitting between bias and statistical contributions. We also show the asymptotic normality of the statistical error in the MLMC estimator and justify in this way our error estimate that allows prescribing both required accuracy and confidence in the final result. Numerical results substantiate the above results and illustrate the corresponding computational savings in examples that are described in terms of differential equations either driven by random measures or with random coefficients

The cost of continuity: performance of iterative solvers on isogeometric finite elements

In this paper we study how the use of a more continuous set of basis functions affects the cost of solving systems of linear equations resulting from a discretized Galerkin weak form. Specifically, we compare performance of linear solvers when discretizing using $C^0$ B-splines, which span traditional finite element spaces, and $C^{p-1}$ B-splines, which represent maximum continuity. We provide theoretical estimates for the increase in cost of the matrix-vector product as well as for the construction and application of black-box preconditioners. We accompany these estimates with numerical results and study their sensitivity to various grid parameters such as element size $h$ and polynomial order of approximation $p$. Finally, we present timing results for a range of preconditioning options for the Laplace problem. We conclude that the matrix-vector product operation is at most \slfrac{33p^2}{8} times more expensive for the more continuous space, although for moderately low $p$, this number is significantly reduced. Moreover, if static condensation is not employed, this number further reduces to at most a value of 8, even for high $p$. Preconditioning options can be up to $p^3$ times more expensive to setup, although this difference significantly decreases for some popular preconditioners such as Incomplete LU factorization

Fully inverted single-digit nanometer domains in ferroelectric films

Achieving stable single-digit nanometer inverted domains in ferroelectric thin films is a fundamental issue that has remained a bottleneck for the development of ultrahigh density (>1 Tbit/in.^2) probe-based memory devices using ferroelectric media. Here, we demonstrate that such domains remain stable only if they are fully inverted through the entire ferroelectric film thickness, which is dependent on a critical ratio of electrode size to the film thickness. This understanding enables the formation of stable domains as small as 4 nm in diameter, corresponding to 10 unit cells in size. Such domain size corresponds to 40 Tbit/in.^2 data storage densitie

Benzolamide improves oxygenation and reduces acute mountain sickness during a high-altitude trek and has fewer side effects than acetazolamide at sea level.

Acetazolamide is the standard carbonic anhydrase (CA) inhibitor used for acute mountain sickness (AMS), however some of its undesirable effects are related to intracellular penetrance into many tissues, including across the blood-brain barrier. Benzolamide is a much more hydrophilic inhibitor, which nonetheless retains a strong renal action to engender a metabolic acidosis and ventilatory stimulus that improves oxygenation at high altitude and reduces AMS. We tested the effectiveness of benzolamide versus placebo in a first field study of the drug as prophylaxis for AMS during an ascent to the Everest Base Camp (5340 m). In two other studies performed at sea level to test side effect differences between acetazolamide and benzolamide, we assessed physiological actions and psychomotor side effects of two doses of acetazolamide (250 and 1000 mg) in one group of healthy subjects and in another group compared acetazolamide (500 mg), benzolamide (200 mg) and lorazepam (2 mg) as an active comparator for central nervous system (CNS) effects. At high altitude, benzolamide-treated subjects maintained better arterial oxygenation at all altitudes (3-6% higher at all altitudes above 4200 m) than placebo-treated subjects and reduced AMS severity by roughly 50%. We found benzolamide had fewer side effects, some of which are symptoms of AMS, than any of the acetazolamide doses in Studies 1 and 2, but equal physiological effects on renal function. The psychomotor side effects of acetazolamide were dose dependent. We conclude that benzolamide is very effective for AMS prophylaxis. With its lesser CNS effects, benzolamide may be superior to acetazolamide, in part, because some of the side effects of acetazolamide may contribute to and be mistaken for AMS

Intelligent fracture creation for shale gas development

Shale gas represents a major fraction of the proven reserves of natural gas in the United States and a collection of other countries. Higher gas prices and the need for cleaner fuels provides motivation for commercializing shale gas deposits even though the cost is substantially higher than traditional gas deposits. Recent advances in horizontal drilling and multistage hydraulic fracturing, which dramatically lower costs of developing shale gas fields, are key to renewed interest in shale gas deposits. Hydraulically induced fractures are quite complex in shale gas reservoirs. Massive, multistage, multiple cluster treatments lead to fractures that interact with existing fractures (whether natural or induced earlier). A dynamic approach to the fracturing process so that the resulting network of reservoirs is known during the drilling and fracturing process is economically enticing. The process needs to be automatic and done in faster than real-time in order to be useful to the drilling crews

Letter From Nathan W. Collier to Eartha M. M. White

Correspondence: From Nathan W. Collier, Principal, Florida Normal and Industrial Institute, St Augustine, Florida, to Eartha White, Jacksonville, Florida, concerning financial status of Alyce Moore. A receipt for payment of bill for room, board, and fees bill. See accompanying letter, Q1-1336. Date: January 19, 1928

RETHINKING THE ROLE OF STORMWATER MANAGEMENT ON CAMPUS IN COLLEGE PARK, MARYLAND

As part of an intense effort to clean up the Anacostia River and the Chesapeake Bay region, the Maryland Department of Environment will soon enforce new policies to increase the treatment of impervious areas. The University of Maryland’s College Park campus needs to identify potential projects in order to meet the pending stormwater regulations as part of the new municipal separate storm sewer systems (MS4) permit for UM-CP. This thesis investigates retrofits a poorly maintained stormwater pond that has maintained itself as a wetland. The 4.89-acre site is located in the north part of campus is a part of the Anacostia watershed and includes the pond, two parking lots, and a wet swale. This thesis proposes a stormwater retrofit that includes various state acceptable BMPs including: a constructed wetland, mirco-bioretentions, pervious concrete, and a bio-swale. The BMPs forms a treatment train that reducing runoff by 7%, capturing and treating 113% of a one-year storm of 2.63 inches. This redesign that would provide a range of environmental, recreational, and educational services. While the proposal is site-specific, the model can be adaptable for retrofitting centralized stormwater facilities and by other college campuses within the Chesapeake Bay watershed