Implementing abstract multigrid or multilevel methods

Multigrid methods can be formulated as an algorithm for an abstract problem that is independent of the partial differential equation, domain, and discretization method. In such an abstract setting, problems not arising from partial differential equations can be treated. A general theory exists for linear problems. The general theory was motivated by a series of abstract solvers (Madpack). The latest version was motivated by the theory. Madpack now allows for a wide variety of iterative and direct solvers, preconditioners, and interpolation and projection schemes, including user callback ones. It allows for sparse, dense, and stencil matrices. Mildly nonlinear problems can be handled. Also, there is a fast, multigrid Poisson solver (two and three dimensions). The type of solvers and design decisions (including language, data structures, external library support, and callbacks) are discussed. Based on the author's experiences with two versions of Madpack, a better approach is proposed. This is based on a mixed language formulation (C and FORTRAN + preprocessor). Reasons for not using FORTRAN, C, or C++ (individually) are given. Implementing the proposed strategy is not difficult

An Additive Schwarz Preconditioner for the Spectral Element Ocean Model Formulation of the Shallow Water Equations

We discretize the shallow water equations with an Adams-Bashford scheme combined with the Crank-Nicholson scheme for the time derivatives and spectral elements for the discretization in space. The resulting coupled system of equations will be reduced to a Schur complement system with a special structure of the Schur complement. This system can be solved with a preconditioned conjugate gradients, where the matrix-vector product is only implicitly given. We derive an overlapping block preconditioner based on additive Schwarz methods for preconditioning the reduced system

Towards a Real-Time Data Driven Wildland Fire Model

A wildland fire model based on semi-empirical relations for the spread rate of a surface fire and post-frontal heat release is coupled with the Weather Research and Forecasting atmospheric model (WRF). The propagation of the fire front is implemented by a level set method. Data is assimilated by a morphing ensemble Kalman filter, which provides amplitude as well as position corrections. Thermal images of a fire will provide the observations and will be compared to a synthetic image from the model state.Comment: 5 pages, 4 figure

Parents and School Children Talking about Food and Drink Choices – A Focus Group Study

Peer reviewedPublisher PD

International conference on computational science, ICCS 2010 data-driven pill monitoring

AbstractWe describe a viable dynamic system to guarantee that pills delivered to a patient are what were prescribed, of sucient quality to be eective, and within the correct time frame. A handheld device that identifies pills is also described that is suitable for use by health care providers. Issues of patient privacy, network security, and interacting with multiple databases are inherent to the entire process

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

Mentoring the Mentors: Implementation and Evaluation of Four Fogarty-Sponsored Mentoring Training Workshops in Low-and Middle-Income Countries.

A growing body of evidence highlights the importance of competent mentoring in academic research. We describe the development, implementation, and evaluation of four regional 2-day intensive workshops to train mid- and senior-level investigators conducting public health, clinical, and basic science research across multiple academic institutions in low- and middle-income countries (LMICs) on tools and techniques of effective mentoring. Sponsored by the Fogarty International Center, workshops included didactic presentations, interactive discussions, and small-group problem-based learning and were conducted in Lima, Peru; Mombasa, Kenya; Bangalore, India; and Johannesburg, South Africa, from 2013 to 2016. Mid- or senior-level faculty from multiple academic institutions within each region applied and were selected. Thirty faculty from 12 South America-based institutions, 29 faculty from eight East Africa-based institutions, 37 faculty from 14 South Asia-based institutions, and 36 faculty from 13 Africa-based institutions participated, with diverse representation across disciplines, gender, and academic rank. Discussions and evaluations revealed important comparisons and contrasts in the practice of mentoring, and specific barriers and facilitators to mentoring within each cultural and regional context. Specific regional issues related to hierarchy, the post-colonial legacy, and diversity arose as challenges to mentoring in different parts of the world. Common barriers included a lack of a culture of mentoring, time constraints, lack of formal training, and a lack of recognition for mentoring. These workshops provided valuable training, were among the first of their kind, were well-attended, rated highly, and provided concepts and a structure for the development and strengthening of formal mentoring programs across LMIC institutions

Seventh Copper Mountain Conference on Multigrid Methods

The Seventh Copper Mountain Conference on Multigrid Methods was held on 2-7 Apr. 1995 at Copper Mountain, Colorado. This book is a collection of many of the papers presented at the conference and so represents the conference proceedings. NASA Langley graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The multigrid discipline continues to expand and mature, as is evident from these proceedings. The vibrancy in this field is amply expressed in these important papers, and the collection shows its rapid trend to further diversity and depth