The Human Mind As General Problem Solver
NASA Astrophysics Data System (ADS)
Gurr, Henry
2011-10-01
Since leaving U Cal Irvine Neutrino Research, I have been a University Physics Teacher, and an Informal Researcher Of Human Functionality. My talk will share what I discovered about the best ways to learn, many of which are regularities that are to be expected from the Neuronal Network Properties announced in the publications of physicist John Joseph Hopfield. Hopfield's Model of mammalian brain-body, provides solid instructive understanding of how best Learn, Solve Problems, Live! With it we understand many otherwise puzzling features of our intellect! Examples Why 1) Analogies and metaphors powerful in class instruction, ditto poems. 2) Best learning done in physical (Hands-On) situations with tight immediate dynamical feedback such as seen in learning to ride bike, drive car, speak language, etc. 3) Some of the best learning happens in seeming random exploration, bump around, trial and error. 4) Scientific discoveries happen, with no apparent effort, at odd moments. 5) Important discoveries DEPEND on considerable frustrating effort, then Flash of Insight AHA EURIKA.
Navier-Stokes Solvers and Generalizations for Reacting Flow Problems
Elman, Howard C
2013-01-27
This is an overview of our accomplishments during the final term of this grant (1 September 2008 -- 30 June 2012). These fall mainly into three categories: fast algorithms for linear eigenvalue problems; solution algorithms and modeling methods for partial differential equations with uncertain coefficients; and preconditioning methods and solvers for models of computational fluid dynamics (CFD).
Schmidhuber, Jürgen
2013-01-01
Most of computer science focuses on automatically solving given computational problems. I focus on automatically inventing or discovering problems in a way inspired by the playful behavior of animals and humans, to train a more and more general problem solver from scratch in an unsupervised fashion. Consider the infinite set of all computable descriptions of tasks with possibly computable solutions. Given a general problem-solving architecture, at any given time, the novel algorithmic framework PowerPlay (Schmidhuber, 2011) searches the space of possible pairs of new tasks and modifications of the current problem solver, until it finds a more powerful problem solver that provably solves all previously learned tasks plus the new one, while the unmodified predecessor does not. Newly invented tasks may require to achieve a wow-effect by making previously learned skills more efficient such that they require less time and space. New skills may (partially) re-use previously learned skills. The greedy search of typical PowerPlay variants uses time-optimal program search to order candidate pairs of tasks and solver modifications by their conditional computational (time and space) complexity, given the stored experience so far. The new task and its corresponding task-solving skill are those first found and validated. This biases the search toward pairs that can be described compactly and validated quickly. The computational costs of validating new tasks need not grow with task repertoire size. Standard problem solver architectures of personal computers or neural networks tend to generalize by solving numerous tasks outside the self-invented training set; PowerPlay’s ongoing search for novelty keeps breaking the generalization abilities of its present solver. This is related to Gödel’s sequence of increasingly powerful formal theories based on adding formerly unprovable statements to the axioms without affecting previously provable theorems. The continually increasing
Sherlock Holmes, Master Problem Solver.
ERIC Educational Resources Information Center
Ballew, Hunter
1994-01-01
Shows the connections between Sherlock Holmes's investigative methods and mathematical problem solving, including observations, characteristics of the problem solver, importance of data, questioning the obvious, learning from experience, learning from errors, and indirect proof. (MKR)
NASA Astrophysics Data System (ADS)
Contarino, Christian; Toro, Eleuterio F.; Montecinos, Gino I.; Borsche, Raul; Kall, Jochen
2016-06-01
In this paper we design a new implicit solver for the Junction-Generalized Riemann Problem (J-GRP), which is based on a recently proposed implicit method for solving the Generalized Riemann Problem (GRP) for systems of hyperbolic balance laws. We use the new J-GRP solver to construct an ADER scheme that is globally explicit, locally implicit and with no theoretical accuracy barrier, in both space and time. The resulting ADER scheme is able to deal with stiff source terms and can be applied to non-linear systems of hyperbolic balance laws in domains consisting on networks of one-dimensional sub-domains. In this paper we specifically apply the numerical techniques to networks of blood vessels. We report on a test problem with exact solution for a simplified network of three vessels meeting at a single junction, which is then used to carry out a systematic convergence rate study of the proposed high-order numerical methods. Schemes up to fifth order of accuracy in space and time are implemented and tested. We then show the ability of the ADER scheme to deal with stiff sources through a numerical simulation in a network of vessels. An application to a physical test problem consisting of a network of 37 compliant silicon tubes (arteries) and 21 junctions, reveals that it is imperative to use high-order methods at junctions, in order to preserve the desired high order of accuracy in the full computational domain. For example, it is demonstrated that a second-order method throughout, gives comparable results to a method that is fourth order in the interior of the domain and first order at junctions.
Edmondson, Amy C
2016-06-01
Companies today increasingly rely on teams that span many industries for radical innovation, especially to solve "wicked problems." So leaders have to understand how to promote collaboration when roles are uncertain, goals are shifting, expertise and organizational cultures are varied, and participants have clashing or even antagonistic perspectives. HBS professor Amy Edmondson has studied more than a dozen cross-industry innovation projects, among them the creation of a new city, a mango supply-chain transformation, and the design and construction of leading-edge buildings. She has identified the leadership practices that make successful cross-industry teams work: fostering an adaptable vision, promoting psychological safety, enabling knowledge sharing, and encouraging collaborative innovation. Though these practices are broadly familiar, their application within cross-industry teams calls for unique leadership approaches that combine flexibility, open-mindedness, humility, and fierce resolve.
An FC-based spectral solver for elastodynamic problems in general three-dimensional domains
NASA Astrophysics Data System (ADS)
Amlani, Faisal; Bruno, Oscar P.
2016-02-01
This paper presents a spectral numerical algorithm for the solution of elastodynamics problems in general three-dimensional domains. Based on a recently introduced "Fourier continuation" (FC) methodology for accurate Fourier expansion of non-periodic functions, the proposed approach possesses a number of appealing properties: it yields results that are essentially free of dispersion errors, it entails mild CFL constraints, it runs at a cost that scales linearly with the discretization sizes, and it lends itself easily to efficient parallelization in distributed-memory computing clusters. The proposed algorithm is demonstrated in this paper by means of a number of applications to problems of isotropic elastodynamics that arise in the fields of materials science and seismology. These examples suggest that the new approach can yield solutions within a prescribed error tolerance by means of significantly smaller discretizations and shorter computing times than those required by other methods.
The Scientist as Problem Solver.
1989-01-01
history. or imagined history. no magic and no mystery Each step appears to proceed. if not inexorably at least plausibly from the preceding one If the...discovery process appears quite unremarkable. The problem was found in the literatue (Goodwin S paper). and it can be represented in a quite standard way by
Problem Solvers' Conceptions about Osmosis.
ERIC Educational Resources Information Center
Zuckerman, June T.
1994-01-01
Discusses the scheme and findings of a study designed to identify the conceptual knowledge used by high school students to solve a significant problem related to osmosis. Useful tips are provided to teachers to aid students in developing constructs that maximize understanding. (ZWH)
Aleph Field Solver Challenge Problem Results Summary
Hooper, Russell; Moore, Stan Gerald
2015-01-01
Aleph models continuum electrostatic and steady and transient thermal fields using a finite-element method. Much work has gone into expanding the core solver capability to support enriched modeling consisting of multiple interacting fields, special boundary conditions and two-way interfacial coupling with particles modeled using Aleph's complementary particle-in-cell capability. This report provides quantitative evidence for correct implementation of Aleph's field solver via order- of-convergence assessments on a collection of problems of increasing complexity. It is intended to provide Aleph with a pedigree and to establish a basis for confidence in results for more challenging problems important to Sandia's mission that Aleph was specifically designed to address.
Parallel Solver for H(div) Problems Using Hybridization and AMG
Lee, Chak S.; Vassilevski, Panayot S.
2016-01-15
In this paper, a scalable parallel solver is proposed for H(div) problems discretized by arbitrary order finite elements on general unstructured meshes. The solver is based on hybridization and algebraic multigrid (AMG). Unlike some previously studied H(div) solvers, the hybridization solver does not require discrete curl and gradient operators as additional input from the user. Instead, only some element information is needed in the construction of the solver. The hybridization results in a H1-equivalent symmetric positive definite system, which is then rescaled and solved by AMG solvers designed for H1 problems. Weak and strong scaling of the method are examined through several numerical tests. Our numerical results show that the proposed solver provides a promising alternative to ADS, a state-of-the-art solver [12], for H(div) problems. In fact, it outperforms ADS for higher order elements.
Thinking Process of Naive Problem Solvers to Solve Mathematical Problems
ERIC Educational Resources Information Center
Mairing, Jackson Pasini
2017-01-01
Solving problems is not only a goal of mathematical learning. Students acquire ways of thinking, habits of persistence and curiosity, and confidence in unfamiliar situations by learning to solve problems. In fact, there were students who had difficulty in solving problems. The students were naive problem solvers. This research aimed to describe…
Experiences with linear solvers for oil reservoir simulation problems
Joubert, W.; Janardhan, R.; Biswas, D.; Carey, G.
1996-12-31
This talk will focus on practical experiences with iterative linear solver algorithms used in conjunction with Amoco Production Company`s Falcon oil reservoir simulation code. The goal of this study is to determine the best linear solver algorithms for these types of problems. The results of numerical experiments will be presented.
Intellectual Abilities That Discriminate Good and Poor Problem Solvers.
ERIC Educational Resources Information Center
Meyer, Ruth Ann
1981-01-01
This study compared good and poor fourth-grade problem solvers on a battery of 19 "reference" tests for verbal, induction, numerical, word fluency, memory, perceptual speed, and simple visualization abilities. Results suggest verbal, numerical, and especially induction abilities are important to successful mathematical problem solving.…
General purpose nonlinear system solver based on Newton-Krylov method.
2013-12-01
KINSOL is part of a software family called SUNDIALS: SUite of Nonlinear and Differential/Algebraic equation Solvers [1]. KINSOL is a general-purpose nonlinear system solver based on Newton-Krylov and fixed-point solver technologies [2].
Benchmarking transport solvers for fracture flow problems
NASA Astrophysics Data System (ADS)
Olkiewicz, Piotr; Dabrowski, Marcin
2015-04-01
Fracture flow may dominate in rocks with low porosity and it can accompany both industrial and natural processes. Typical examples of such processes are natural flows in crystalline rocks and industrial flows in geothermal systems or hydraulic fracturing. Fracture flow provides an important mechanism for transporting mass and energy. For example, geothermal energy is primarily transported by the flow of the heated water or steam rather than by the thermal diffusion. The geometry of the fracture network and the distribution of the mean apertures of individual fractures are the key parameters with regard to the fracture network transmissivity. Transport in fractures can occur through the combination of advection and diffusion processes like in the case of dissolved chemical components. The local distribution of the fracture aperture may play an important role for both flow and transport processes. In this work, we benchmark various numerical solvers for flow and transport processes in a single fracture in 2D and 3D. Fracture aperture distributions are generated by a number of synthetic methods. We examine a single-phase flow of an incompressible viscous Newtonian fluid in the low Reynolds number limit. Periodic boundary conditions are used and a pressure difference is imposed in the background. The velocity field is primarly found using the Stokes equations. We systematically compare the obtained velocity field to the results obtained by solving the Reynolds equation. This allows us to examine the impact of the aperture distribution on the permeability of the medium and the local velocity distribution for two different mathematical descriptions of the fracture flow. Furthermore, we analyse the impact of aperture distribution on the front characteristics such as the standard deviation and the fractal dimension for systems in 2D and 3D.
A Comparison of Stiff ODE Solvers for Astrochemical Kinetics Problems
NASA Astrophysics Data System (ADS)
Nejad, Lida A. M.
2005-09-01
The time dependent chemical rate equations arising from astrochemical kinetics problems are described by a system of stiff ordinary differential equations (ODEs). In this paper, using three astrochemical models of varying physical and computational complexity, and hence different degrees of stiffness, we present a comprehensive performance survey of a set of well-established ODE solver packages from the ODEPACK collection, namely LSODE, LSODES, VODE and VODPK. For completeness, we include results from the GEAR package in one of the test models. The results demonstrate that significant performance improvements can be obtained over GEAR which is still being used by many astrochemists by default. We show that a simple appropriate ordering of the species set results in a substantial improvement in the performance of the tested ODE solvers. The sparsity of the associated Jacobian matrix can be exploited and results using the sparse direct solver routine LSODES show an extensive reduction in CPU time without any loss in accuracy. We compare the performance and the computed abundances of one model with a 175 species set and a reduced set of 88 species, keeping all physical and chemical parameters identical with both sets.We found that the calculated abundances using two different size models agree quite well. However, with no extra computational effort and more reliable results, it is possible for the computation to be many times faster with the larger species set than the reduced set, depending on the use of solvers, the ordering and the chosen options. It is also shown that though a particular solver with certain chosen parameters may have severe difficulty or even fail to complete a run over the required integration time, another solver can easily complete the run with a wider range of control parameters and options. As a result of the superior performance of LSODES for the solution of astrochemical kinetics systems, we have tailor-made a sparse version of the VODE
Menu-Driven Solver Of Linear-Programming Problems
NASA Technical Reports Server (NTRS)
Viterna, L. A.; Ferencz, D.
1992-01-01
Program assists inexperienced user in formulating linear-programming problems. A Linear Program Solver (ALPS) computer program is full-featured LP analysis program. Solves plain linear-programming problems as well as more-complicated mixed-integer and pure-integer programs. Also contains efficient technique for solution of purely binary linear-programming problems. Written entirely in IBM's APL2/PC software, Version 1.01. Packed program contains licensed material, property of IBM (copyright 1988, all rights reserved).
An optimal iterative solver for the Stokes problem
Wathen, A.; Silvester, D.
1994-12-31
Discretisations of the classical Stokes Problem for slow viscous incompressible flow gives rise to systems of equations in matrix form for the velocity u and the pressure p, where the coefficient matrix is symmetric but necessarily indefinite. The square submatrix A is symmetric and positive definite and represents a discrete (vector) Laplacian and the submatrix C may be the zero matrix or more generally will be symmetric positive semi-definite. For `stabilised` discretisations (C {ne} 0) and descretisations which are inherently `stable` (C = 0) and so do not admit spurious pressure components even as the mesh size, h approaches zero, the Schur compliment of the matrix has spectral condition number independent of h (given also that B is bounded). Here the authors will show how this property together with a multigrid preconditioner only for the Laplacian block A yields an optimal solver for the Stokes problem through use of the Minimum Residual iteration. That is, combining Minimum Residual iteration for the matrix equation with a block preconditioner which comprises a small number of multigrid V-cycles for the Laplacian block A together with a simple diagonal scaling block provides an iterative solution procedure for which the computational work grows only linearly with the problem size.
Optical solver of combinatorial problems: nanotechnological approach.
Cohen, Eyal; Dolev, Shlomi; Frenkel, Sergey; Kryzhanovsky, Boris; Palagushkin, Alexandr; Rosenblit, Michael; Zakharov, Victor
2013-09-01
We present an optical computing system to solve NP-hard problems. As nano-optical computing is a promising venue for the next generation of computers performing parallel computations, we investigate the application of submicron, or even subwavelength, computing device designs. The system utilizes a setup of exponential sized masks with exponential space complexity produced in polynomial time preprocessing. The masks are later used to solve the problem in polynomial time. The size of the masks is reduced to nanoscaled density. Simulations were done to choose a proper design, and actual implementations show the feasibility of such a system.
Problem Solvers: Solutions--Playing Basketball
ERIC Educational Resources Information Center
Smith, Jeffrey
2014-01-01
In this article, fourth grade Upper Allen Elementary School (Mechanicsburg, Pennsylvania) teacher Jeffrey Smith describes his exploration of the Playing Basketball activity. Herein he describes how he found the problem to be an effective way to review concepts associated with the measurement of elapsed time with his students. Additionally, it…
Problem Solvers: Solutions--The Inaugural Address
ERIC Educational Resources Information Center
Dause, Emily
2014-01-01
Fourth graders in Miss Dause's and Mrs. Hicks's mathematics classes at South Mountain Elementary School in Dillsburg, Pennsylvania, worked with the data from the Inauagural Address problem that was previously published published in the February 2013 issue of "Teaching Children Mathematics". This activity allowed students to showcase…
Scalable Adaptive Multilevel Solvers for Multiphysics Problems
Xu, Jinchao
2014-11-26
In this project, we carried out many studies on adaptive and parallel multilevel methods for numerical modeling for various applications, including Magnetohydrodynamics (MHD) and complex fluids. We have made significant efforts and advances in adaptive multilevel methods of the multiphysics problems: multigrid methods, adaptive finite element methods, and applications.
A generalized Poisson solver for first-principles device simulations
Bani-Hashemian, Mohammad Hossein; VandeVondele, Joost; Brück, Sascha; Luisier, Mathieu
2016-01-28
Electronic structure calculations of atomistic systems based on density functional theory involve solving the Poisson equation. In this paper, we present a plane-wave based algorithm for solving the generalized Poisson equation subject to periodic or homogeneous Neumann conditions on the boundaries of the simulation cell and Dirichlet type conditions imposed at arbitrary subdomains. In this way, source, drain, and gate voltages can be imposed across atomistic models of electronic devices. Dirichlet conditions are enforced as constraints in a variational framework giving rise to a saddle point problem. The resulting system of equations is then solved using a stationary iterative method in which the generalized Poisson operator is preconditioned with the standard Laplace operator. The solver can make use of any sufficiently smooth function modelling the dielectric constant, including density dependent dielectric continuum models. For all the boundary conditions, consistent derivatives are available and molecular dynamics simulations can be performed. The convergence behaviour of the scheme is investigated and its capabilities are demonstrated.
Parallel Auxiliary Space AMG Solver for $H(div)$ Problems
Kolev, Tzanio V.; Vassilevski, Panayot S.
2012-12-18
We present a family of scalable preconditioners for matrices arising in the discretization of $H(div)$ problems using the lowest order Raviart--Thomas finite elements. Our approach belongs to the class of “auxiliary space''--based methods and requires only the finite element stiffness matrix plus some minimal additional discretization information about the topology and orientation of mesh entities. Also, we provide a detailed algebraic description of the theory, parallel implementation, and different variants of this parallel auxiliary space divergence solver (ADS) and discuss its relations to the Hiptmair--Xu (HX) auxiliary space decomposition of $H(div)$ [SIAM J. Numer. Anal., 45 (2007), pp. 2483--2509] and to the auxiliary space Maxwell solver AMS [J. Comput. Math., 27 (2009), pp. 604--623]. Finally, an extensive set of numerical experiments demonstrates the robustness and scalability of our implementation on large-scale $H(div)$ problems with large jumps in the material coefficients.
The Prisoner Problem--A Generalization.
ERIC Educational Resources Information Center
Gannon, Gerald E.; Martelli, Mario U.
2000-01-01
Presents a generalization to the classic prisoner problem, which is inherently interesting and has a solution within the reach of most high school mathematics students. Suggests the problem as a way to emphasize to students the final step in a problem-solver's tool kit, considering possible generalizations when a particular problem has been…
Application of NASA General-Purpose Solver to Large-Scale Computations in Aeroacoustics
NASA Technical Reports Server (NTRS)
Watson, Willie R.; Storaasli, Olaf O.
2004-01-01
Of several iterative and direct equation solvers evaluated previously for computations in aeroacoustics, the most promising was the NASA-developed General-Purpose Solver (winner of NASA's 1999 software of the year award). This paper presents detailed, single-processor statistics of the performance of this solver, which has been tailored and optimized for large-scale aeroacoustic computations. The statistics, compiled using an SGI ORIGIN 2000 computer with 12 Gb available memory (RAM) and eight available processors, are the central processing unit time, RAM requirements, and solution error. The equation solver is capable of solving 10 thousand complex unknowns in as little as 0.01 sec using 0.02 Gb RAM, and 8.4 million complex unknowns in slightly less than 3 hours using all 12 Gb. This latter solution is the largest aeroacoustics problem solved to date with this technique. The study was unable to detect any noticeable error in the solution, since noise levels predicted from these solution vectors are in excellent agreement with the noise levels computed from the exact solution. The equation solver provides a means for obtaining numerical solutions to aeroacoustics problems in three dimensions.
A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments.
Fisicaro, G; Genovese, L; Andreussi, O; Marzari, N; Goedecker, S
2016-01-07
The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes.
A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments
Fisicaro, G. Goedecker, S.; Genovese, L.; Andreussi, O.; Marzari, N.
2016-01-07
The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes.
Mathematical Tasks without Words and Word Problems: Perceptions of Reluctant Problem Solvers
ERIC Educational Resources Information Center
Holbert, Sydney Margaret
2013-01-01
This qualitative research study used a multiple, holistic case study approach (Yin, 2009) to explore the perceptions of reluctant problem solvers related to mathematical tasks without words and word problems. Participants were given a choice of working a mathematical task without words or a word problem during four problem-solving sessions. Data…
Problem Solvers: Problem--How Long Can You Stand?
ERIC Educational Resources Information Center
Teaching Children Mathematics, 2010
2010-01-01
Healthy lifestyles are increasingly emphasized these days. This month the authors begin a series of mathematical problems that also address physical activity. They hope that these problems offer opportunities to investigate mathematics and also reinforce the desire to lead a healthy life. In their first problem of the academic year, students…
Teaching problem solving: Don't forget the problem solver(s)
NASA Astrophysics Data System (ADS)
Ranade, Saidas M.; Corrales, Angela
2013-05-01
The importance of intrapersonal and interpersonal intelligences has long been known but educators have debated whether to and how to incorporate those topics in an already crowded engineering curriculum. In 2010, the authors used the classroom as a laboratory to observe the usefulness of including selected case studies and exercises from the fields of neurology, artificial intelligence, cognitive sciences and social psychology in a new problem-solving course. To further validate their initial findings, in 2012, the authors conducted an online survey of engineering students and engineers. The main conclusion is that engineering students will benefit from learning more about the impact of emotions, culture, diversity and cognitive biases when solving problems. Specifically, the work shows that an augmented problem-solving curriculum needs to include lessons on labelling emotions and cognitive biases, 'evidence-based' data on the importance of culture and diversity and additional practice on estimating conditional probability.
Incremental planning to control a blackboard-based problem solver
NASA Technical Reports Server (NTRS)
Durfee, E. H.; Lesser, V. R.
1987-01-01
To control problem solving activity, a planner must resolve uncertainty about which specific long-term goals (solutions) to pursue and about which sequences of actions will best achieve those goals. A planner is described that abstracts the problem solving state to recognize possible competing and compatible solutions and to roughly predict the importance and expense of developing these solutions. With this information, the planner plans sequences of problem solving activities that most efficiently resolve its uncertainty about which of the possible solutions to work toward. The planner only details actions for the near future because the results of these actions will influence how (and whether) a plan should be pursued. As problem solving proceeds, the planner adds new details to the plan incrementally, and monitors and repairs the plan to insure it achieves its goals whenever possible. Through experiments, researchers illustrate how these new mechanisms significantly improve problem solving decisions and reduce overall computation. They briefly discuss current research directions, including how these mechanisms can improve a problem solver's real-time response and can enhance cooperation in a distributed problem solving network.
Problem Solvers: Problem--Jesse's Train
ERIC Educational Resources Information Center
James, Julie; Steimle, Alice
2014-01-01
Persevering in problem solving and constructing and critiquing mathematical arguments are some of the mathematical practices included in the Common Core State Standards for Mathematics (CCSSI 2010). To solve unfamiliar problems, students must make sense of the situation and apply current knowledge. Teachers can present such opportunities by…
Polyurethanes: versatile materials and sustainable problem solvers for today's challenges.
Engels, Hans-Wilhelm; Pirkl, Hans-Georg; Albers, Reinhard; Albach, Rolf W; Krause, Jens; Hoffmann, Andreas; Casselmann, Holger; Dormish, Jeff
2013-09-02
Polyurethanes are the only class of polymers that display thermoplastic, elastomeric, and thermoset behavior depending on their chemical and morphological makeup. In addition to compact polyurethanes, foamed variations in particular are very widespread, and they achieve their targeted properties at very low weights. The simple production of sandwich structures and material composites in a single processing step is a key advantage of polyurethane technology. The requirement of energy and resource efficiency increasingly demands lightweight structures. Polyurethanes can serve this requirement by acting as matrix materials or as flexible adhesives for composites. Polyurethanes are indispensable when it comes to high-quality decorative coatings or maintaining the value of numerous objects. They are extremely adaptable and sustainable problem solvers for today's challenges facing our society, all of which impose special demands on materials.
Evaluation of linear solvers for oil reservoir simulation problems. Part 2: The fully implicit case
Joubert, W.; Janardhan, R.
1997-12-01
A previous paper [Joubert/Biswas 1997] contained investigations of linear solver performance for matrices arising from Amoco`s Falcon parallel oil reservoir simulation code using the IMPES formulation (implicit pressure, explicit saturation). In this companion paper, similar issues are explored for linear solvers applied to matrices arising from more difficult fully implicit problems. The results of numerical experiments are given.
Cognitive Distance Learning Problem Solver Reduces Search Cost through Learning Processes
NASA Astrophysics Data System (ADS)
Yamakawa, Hiroshi; Miyamoto, Yuji; Baba, Takayuki; Okada, Hiroyuki
Our proposed cognitive distance learning problem solver generates sequence of actions from initial state to goal states in problem state space. This problem solver learns cognitive distance (path cost) of arbitrary combination of two states. Action generation at each state is selection of next state that has minimum cognitive distance to the goal, like Q-learning agent. In this paper, first, we show that our proposed method reduces search cost than conventional search method by analytical simulation in spherical state space. Second, we show that an average search cost is more reduced more the prior learning term is long and our problem solver is familiar to the environment, by a computer simulation in a tile world state space. Third, we showed that proposed problem solver is superior to the reinforcement learning techniques when goal is changed by a computer simulation. Forth, we found that our simulation result consist with psychological experimental results.
Second-kind integral solvers for TE and TM problems of diffraction by open arcs
NASA Astrophysics Data System (ADS)
Bruno, Oscar P.; Lintner, StéPhane K.
2012-12-01
We present a novel approach for the numerical solution of problems of diffraction by open arcs in two dimensional space. Our methodology relies on composition of weighted versions of the classical integral operators associated with the Dirichlet and Neumann problems (TE and TM polarizations, respectively) together with a generalization to the open-arc case of the well known closed-surface Calderón formulae. When used in conjunction with spectrally accurate discretization rules and Krylov-subspace linear algebra solvers such as GMRES, the new second-kind TE and TM formulations for open arcs produce results of high accuracy in small numbers of iterations—for low and high frequencies alike.
Composing Problem Solvers for Simulation Experimentation: A Case Study on Steady State Estimation
Leye, Stefan; Ewald, Roland; Uhrmacher, Adelinde M.
2014-01-01
Simulation experiments involve various sub-tasks, e.g., parameter optimization, simulation execution, or output data analysis. Many algorithms can be applied to such tasks, but their performance depends on the given problem. Steady state estimation in systems biology is a typical example for this: several estimators have been proposed, each with its own (dis-)advantages. Experimenters, therefore, must choose from the available options, even though they may not be aware of the consequences. To support those users, we propose a general scheme to aggregate such algorithms to so-called synthetic problem solvers, which exploit algorithm differences to improve overall performance. Our approach subsumes various aggregation mechanisms, supports automatic configuration from training data (e.g., via ensemble learning or portfolio selection), and extends the plugin system of the open source modeling and simulation framework James II. We show the benefits of our approach by applying it to steady state estimation for cell-biological models. PMID:24705453
Primitive Variable Solvers for Conservative General Relativistic Magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Noble, Scott C.; Gammie, Charles F.; McKinney, Jonathan C.; Del Zanna, Luca
2006-04-01
Conservative numerical schemes for general relativistic magnetohydrodynamics (GRMHD) require a method for transforming between ``conserved'' variables such as momentum and energy density and ``primitive'' variables such as rest-mass density, internal energy, and components of the four-velocity. The forward transformation (primitive to conserved) has a closed-form solution, but the inverse transformation (conserved to primitive) requires the solution of a set of five nonlinear equations. Here we discuss the mathematical properties of the inverse transformation and present six numerical methods for performing the inversion. The first method solves the full set of five nonlinear equations directly using a Newton-Raphson scheme and a guess from the previous time step. The other methods reduce the five nonlinear equations to either one or two nonlinear equations that are solved numerically. Comparisons between the methods are made using a survey over phase space, a two-dimensional explosion problem, and a general relativistic MHD accretion disk simulation. The run time of the methods is also examined. Code implementing the schemes is available with the electronic edition of the article.
A Riemann solver based on a global existence proof for the Riemann problem
NASA Technical Reports Server (NTRS)
Dutt, P.
1986-01-01
Godunov's method and several other methods for computing solutions to the equations of gas dynamics use Riemann solvers to resolve discontinuities at the interface between cells. A new method is proposed here for solving the Riemann problem based on a global existence proof for the solution to the Riemann problem. The method is found to be very reliable and computationally efficient.
An accurate predictor-corrector HOC solver for the two dimensional Riemann problem of gas dynamics
NASA Astrophysics Data System (ADS)
Gogoi, Bidyut B.
2016-10-01
The work in the present manuscript is concerned with the simulation of twodimensional (2D) Riemann problem of gas dynamics. We extend our recently developed higher order compact (HOC) method from one-dimensional (1D) to 2D solver and simulate the problem on a square geometry with different initial conditions. The method is fourth order accurate in space and second order accurate in time. We then compare our results with the available benchmark results. The comparison shows an excellent agreement of our results with the existing ones in the literature. Being a finite difference solver, it is quite straight-forward and simple.
Black box multigrid solver for definite and indefinite problems
Shapira, Yair
1997-02-01
A two-level analysis method for certain separable problems is introduced. It motivates the definition of improved versions of Black Box Multigrid for diffusion problems with discontinuous coefficients and indefinite Helmholtz equations. For anisotropic problems, it helps in choosing suitable implementations for frequency decomposition multigrid methods. For highly indefinite problems, it provides a way to choose in advance a suitable mesh size for the coarsest grid used. Numerical experiments confirm the analysis and show the advantage of the present methods for several examples.
A Comparison of the Intellectual Abilities of Good and Poor Problem Solvers: An Exploratory Study.
ERIC Educational Resources Information Center
Meyer, Ruth Ann
This study examined a selected sample of fourth-grade students who had been previously identified as good or poor problem solvers. The pupils were compared on variables considered as "reference tests" for Verbal, Induction, Numerical, Word Fluency, Memory, Spatial Visualization, and Perceptual Speed abilities. The data were compiled to…
Parallel satellite orbital situational problems solver for space missions design and control
NASA Astrophysics Data System (ADS)
Atanassov, Atanas Marinov
2016-11-01
Solving different scientific problems for space applications demands implementation of observations, measurements or realization of active experiments during time intervals in which specific geometric and physical conditions are fulfilled. The solving of situational problems for determination of these time intervals when the satellite instruments work optimally is a very important part of all activities on every stage of preparation and realization of space missions. The elaboration of universal, flexible and robust approach for situation analysis, which is easily portable toward new satellite missions, is significant for reduction of missions' preparation times and costs. Every situation problem could be based on one or more situation conditions. Simultaneously solving different kinds of situation problems based on different number and types of situational conditions, each one of them satisfied on different segments of satellite orbit requires irregular calculations. Three formal approaches are presented. First one is related to situation problems description that allows achieving flexibility in situation problem assembling and presentation in computer memory. The second formal approach is connected with developing of situation problem solver organized as processor that executes specific code for every particular situational condition. The third formal approach is related to solver parallelization utilizing threads and dynamic scheduling based on "pool of threads" abstraction and ensures a good load balance. The developed situation problems solver is intended for incorporation in the frames of multi-physics multi-satellite space mission's design and simulation tools.
Equity and Access: All Students Are Mathematical Problem Solvers
ERIC Educational Resources Information Center
Franz, Dana Pompkyl; Ivy, Jessica; McKissick, Bethany R.
2016-01-01
Often mathematical instruction for students with disabilities, especially those with learning disabilities, includes an overabundance of instruction on mathematical computation and does not include high-quality instruction on mathematical reasoning and problem solving. In fact, it is a common misconception that students with learning disabilities…
Fast solvers for optimal control problems from pattern formation
NASA Astrophysics Data System (ADS)
Stoll, Martin; Pearson, John W.; Maini, Philip K.
2016-01-01
The modeling of pattern formation in biological systems using various models of reaction-diffusion type has been an active research topic for many years. We here look at a parameter identification (or PDE-constrained optimization) problem where the Schnakenberg and Gierer-Meinhardt equations, two well-known pattern formation models, form the constraints to an objective function. Our main focus is on the efficient solution of the associated nonlinear programming problems via a Lagrange-Newton scheme. In particular we focus on the fast and robust solution of the resulting large linear systems, which are of saddle point form. We illustrate this by considering several two- and three-dimensional setups for both models. Additionally, we discuss an image-driven formulation that allows us to identify parameters of the model to match an observed quantity obtained from an image.
An Efficient Solver of Elasto-plastic Problems in Mechanics Based on TFETI Domain Decomposition
NASA Astrophysics Data System (ADS)
Čermák, M.; Kozubek, T.; Markopoulos, A.
2011-09-01
This paper illustrates how to implement efficiently solvers for elasto-plastic problems. We consider the time step problems formulated by nonlinear variational equations in terms of displacements. To treat nonlinearity and nonsmoothnes we use semismooth Newton method. In each Newton iteration we have to solve linear system of algebraic equations and for its numerical solution we use TFETI domain decomposition method. In our benchmark we demonstrate our approach on von Mises plasticity with isotropic hardening using the return mapping concept.
Little, Max A.; Jones, Nick S.
2011-01-01
Removing noise from piecewise constant (PWC) signals is a challenging signal processing problem arising in many practical contexts. For example, in exploration geosciences, noisy drill hole records need to be separated into stratigraphic zones, and in biophysics, jumps between molecular dwell states have to be extracted from noisy fluorescence microscopy signals. Many PWC denoising methods exist, including total variation regularization, mean shift clustering, stepwise jump placement, running medians, convex clustering shrinkage and bilateral filtering; conventional linear signal processing methods are fundamentally unsuited. This paper (part I, the first of two) shows that most of these methods are associated with a special case of a generalized functional, minimized to achieve PWC denoising. The minimizer can be obtained by diverse solver algorithms, including stepwise jump placement, convex programming, finite differences, iterated running medians, least angle regression, regularization path following and coordinate descent. In the second paper, part II, we introduce novel PWC denoising methods, and comparisons between these methods performed on synthetic and real signals, showing that the new understanding of the problem gained in part I leads to new methods that have a useful role to play. PMID:22003312
Little, Max A; Jones, Nick S
2011-11-08
Removing noise from piecewise constant (PWC) signals is a challenging signal processing problem arising in many practical contexts. For example, in exploration geosciences, noisy drill hole records need to be separated into stratigraphic zones, and in biophysics, jumps between molecular dwell states have to be extracted from noisy fluorescence microscopy signals. Many PWC denoising methods exist, including total variation regularization, mean shift clustering, stepwise jump placement, running medians, convex clustering shrinkage and bilateral filtering; conventional linear signal processing methods are fundamentally unsuited. This paper (part I, the first of two) shows that most of these methods are associated with a special case of a generalized functional, minimized to achieve PWC denoising. The minimizer can be obtained by diverse solver algorithms, including stepwise jump placement, convex programming, finite differences, iterated running medians, least angle regression, regularization path following and coordinate descent. In the second paper, part II, we introduce novel PWC denoising methods, and comparisons between these methods performed on synthetic and real signals, showing that the new understanding of the problem gained in part I leads to new methods that have a useful role to play.
NASA Astrophysics Data System (ADS)
Reimer, Ashton S.; Cheviakov, Alexei F.
2013-03-01
A Matlab-based finite-difference numerical solver for the Poisson equation for a rectangle and a disk in two dimensions, and a spherical domain in three dimensions, is presented. The solver is optimized for handling an arbitrary combination of Dirichlet and Neumann boundary conditions, and allows for full user control of mesh refinement. The solver routines utilize effective and parallelized sparse vector and matrix operations. Computations exhibit high speeds, numerical stability with respect to mesh size and mesh refinement, and acceptable error values even on desktop computers. Catalogue identifier: AENQ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENQ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License v3.0 No. of lines in distributed program, including test data, etc.: 102793 No. of bytes in distributed program, including test data, etc.: 369378 Distribution format: tar.gz Programming language: Matlab 2010a. Computer: PC, Macintosh. Operating system: Windows, OSX, Linux. RAM: 8 GB (8, 589, 934, 592 bytes) Classification: 4.3. Nature of problem: To solve the Poisson problem in a standard domain with “patchy surface”-type (strongly heterogeneous) Neumann/Dirichlet boundary conditions. Solution method: Finite difference with mesh refinement. Restrictions: Spherical domain in 3D; rectangular domain or a disk in 2D. Unusual features: Choice between mldivide/iterative solver for the solution of large system of linear algebraic equations that arise. Full user control of Neumann/Dirichlet boundary conditions and mesh refinement. Running time: Depending on the number of points taken and the geometry of the domain, the routine may take from less than a second to several hours to execute.
General Flow-Solver Code for Turbomachinery Applications
NASA Technical Reports Server (NTRS)
Dorney, Daniel; Sondak, Douglas
2006-01-01
Phantom is a computer code intended primarily for real-fluid turbomachinery problems. It is based on Corsair, an ideal-gas turbomachinery code, developed by the same authors, which evolved from the ROTOR codes from NASA Ames. Phantom is applicable to real and ideal fluids, both compressible and incompressible, flowing at subsonic, transonic, and supersonic speeds. It utilizes structured, overset, O- and H-type zonal grids to discretize flow fields and represent relative motions of components. Values on grid boundaries are updated at each time step by bilinear interpolation from adjacent grids. Inviscid fluxes are calculated to third-order spatial accuracy using Roe s scheme. Viscous fluxes are calculated using second-order-accurate central differences. The code is second-order accurate in time. Turbulence is represented by a modified Baldwin-Lomax algebraic model. The code offers two options for determining properties of fluids: One is based on equations of state, thermodynamic departure functions, and corresponding state principles. The other, which is more efficient, is based on splines generated from tables of properties of real fluids. Phantom currently contains fluid-property routines for water, hydrogen, oxygen, nitrogen, kerosene, methane, and carbon monoxide as well as ideal gases.
Larger groups of passerines are more efficient problem solvers in the wild.
Morand-Ferron, Julie; Quinn, John L
2011-09-20
Group living commonly helps organisms face challenging environmental conditions. Although a known phenomenon in humans, recent findings suggest that a benefit of group living in animals generally might be increased innovative problem-solving efficiency. This benefit has never been demonstrated in a natural context, however, and the mechanisms underlying improved efficiency are largely unknown. We examined the problem-solving performance of great and blue tits at automated devices and found that efficiency increased with flock size. This relationship held when restricting the analysis to naive individuals, demonstrating that larger groups increased innovation efficiency. In addition to this effect of naive flock size, the presence of at least one experienced bird increased the frequency of solving, and larger flocks were more likely to contain experienced birds. These findings provide empirical evidence for the "pool of competence" hypothesis in nonhuman animals. The probability of success also differed consistently between individuals, a necessary condition for the pool of competence hypothesis. Solvers had a higher probability of success when foraging with a larger number of companions and when using devices located near rather than further from protective tree cover, suggesting a role for reduced predation risk on problem-solving efficiency. In contrast to traditional group living theory, individuals joining larger flocks benefited from a higher seed intake, suggesting that group living facilitated exploitation of a novel food source through improved problem-solving efficiency. Together our results suggest that both ecological and social factors, through reduced predation risk and increased pool of competence, mediate innovation in natural populations.
NASA Astrophysics Data System (ADS)
Yamasaki, Tadashi; Houseman, Gregory; Hamling, Ian; Postek, Elek
2010-05-01
We have developed a new parallelized 3-D numerical code, OREGANO_VE, for the solution of the general visco-elastic problem in a rectangular block domain. The mechanical equilibrium equation is solved using the finite element method for a (non-)linear Maxwell visco-elastic rheology. Time-dependent displacement and/or traction boundary conditions can be applied. Matrix assembly is based on a tetrahedral element defined by 4 vertex nodes and 6 nodes located at the midpoints of the edges, and within which displacement is described by a quadratic interpolation function. For evaluating viscoelastic relaxation, an explicit time-stepping algorithm (Zienkiewicz and Cormeau, Int. J. Num. Meth. Eng., 8, 821-845, 1974) is employed. We test the accurate implementation of the OREGANO_VE by comparing numerical and analytic (or semi-analytic half-space) solutions to different problems in a range of applications: (1) equilibration of stress in a constant density layer after gravity is switched on at t = 0 tests the implementation of spatially variable viscosity and non-Newtonian viscosity; (2) displacement of the welded interface between two blocks of differing viscosity tests the implementation of viscosity discontinuities, (3) displacement of the upper surface of a layer under applied normal load tests the implementation of time-dependent surface tractions (4) visco-elastic response to dyke intrusion (compared with the solution in a half-space) tests the implementation of all aspects. In each case, the accuracy of the code is validated subject to use of a sufficiently small time step, providing assurance that the OREGANO_VE code can be applied to a range of visco-elastic relaxation processes in three dimensions, including post-seismic deformation and post-glacial uplift. The OREGANO_VE code includes a capability for representation of prescribed fault slip on an internal fault. The surface displacement associated with large earthquakes can be detected by some geodetic observations
NASA Astrophysics Data System (ADS)
Bruno, Oscar P.; Lintner, Stéphane K.
2013-11-01
We present a novel methodology for the numerical solution of problems of diffraction by infinitely thin screens in three-dimensional space. Our approach relies on new integral formulations as well as associated high-order quadrature rules. The new integral formulations involve weighted versions of the classical integral operators related to the thin-screen Dirichlet and Neumann problems as well as a generalization to the open-surface problem of the classical Calderón formulae. The high-order quadrature rules we introduce for these operators, in turn, resolve the multiple Green function and edge singularities (which occur at arbitrarily close distances from each other, and which include weakly singular as well as hypersingular kernels) and thus give rise to super-algebraically fast convergence as the discretization sizes are increased. When used in conjunction with Krylov-subspace linear algebra solvers such as GMRES, the resulting solvers produce results of high accuracy in small numbers of iterations for low and high frequencies alike. We demonstrate our methodology with a variety of numerical results for screen and aperture problems at high frequencies-including simulation of classical experiments such as the diffraction by a circular disc (featuring in particular the famous Poisson spot), evaluation of interference fringes resulting from diffraction across two nearby circular apertures, as well as solution of problems of scattering by more complex geometries consisting of multiple scatterers and cavities.
Bruno, Oscar P. Lintner, Stéphane K.
2013-11-01
We present a novel methodology for the numerical solution of problems of diffraction by infinitely thin screens in three-dimensional space. Our approach relies on new integral formulations as well as associated high-order quadrature rules. The new integral formulations involve weighted versions of the classical integral operators related to the thin-screen Dirichlet and Neumann problems as well as a generalization to the open-surface problem of the classical Calderón formulae. The high-order quadrature rules we introduce for these operators, in turn, resolve the multiple Green function and edge singularities (which occur at arbitrarily close distances from each other, and which include weakly singular as well as hypersingular kernels) and thus give rise to super-algebraically fast convergence as the discretization sizes are increased. When used in conjunction with Krylov-subspace linear algebra solvers such as GMRES, the resulting solvers produce results of high accuracy in small numbers of iterations for low and high frequencies alike. We demonstrate our methodology with a variety of numerical results for screen and aperture problems at high frequencies—including simulation of classical experiments such as the diffraction by a circular disc (featuring in particular the famous Poisson spot), evaluation of interference fringes resulting from diffraction across two nearby circular apertures, as well as solution of problems of scattering by more complex geometries consisting of multiple scatterers and cavities.
Analysis, tuning and comparison of two general sparse solvers for distributed memory computers
Amestoy, P.R.; Duff, I.S.; L'Excellent, J.-Y.; Li, X.S.
2000-06-30
We describe the work performed in the context of a Franco-Berkeley funded project between NERSC-LBNL located in Berkeley (USA) and CERFACS-ENSEEIHT located in Toulouse (France). We discuss both the tuning and performance analysis of two distributed memory sparse solvers (superlu from Berkeley and mumps from Toulouse) on the 512 processor Cray T3E from NERSC (Lawrence Berkeley National Laboratory). This project gave us the opportunity to improve the algorithms and add new features to the codes. We then quite extensively analyze and compare the two approaches on a set of large problems from real applications. We further explain the main differences in the behavior of the approaches on artificial regular grid problems. As a conclusion to this activity report, we mention a set of parallel sparse solvers on which this type of study should be extended.
ERIC Educational Resources Information Center
Starkman, Neal
2007-01-01
US students continue to lag behind the rest of the world in science, technology, engineering, and math--taken together, STEM. Even as the US falls further and further behind other countries in these four critical academic areas, not everyone sees it as a crisis. Fortunately, there are those who do. One organization out front on the issue is,…
NASA Astrophysics Data System (ADS)
Mena, Andres; Ferrero, Jose M.; Rodriguez Matas, Jose F.
2015-11-01
Solving the electric activity of the heart possess a big challenge, not only because of the structural complexities inherent to the heart tissue, but also because of the complex electric behaviour of the cardiac cells. The multi-scale nature of the electrophysiology problem makes difficult its numerical solution, requiring temporal and spatial resolutions of 0.1 ms and 0.2 mm respectively for accurate simulations, leading to models with millions degrees of freedom that need to be solved for thousand time steps. Solution of this problem requires the use of algorithms with higher level of parallelism in multi-core platforms. In this regard the newer programmable graphic processing units (GPU) has become a valid alternative due to their tremendous computational horsepower. This paper presents results obtained with a novel electrophysiology simulation software entirely developed in Compute Unified Device Architecture (CUDA). The software implements fully explicit and semi-implicit solvers for the monodomain model, using operator splitting. Performance is compared with classical multi-core MPI based solvers operating on dedicated high-performance computer clusters. Results obtained with the GPU based solver show enormous potential for this technology with accelerations over 50 × for three-dimensional problems.
NASA Technical Reports Server (NTRS)
Voigt, Kerstin
1992-01-01
We present MENDER, a knowledge based system that implements software design techniques that are specialized to automatically compile generate-and-patch problem solvers that satisfy global resource assignments problems. We provide empirical evidence of the superior performance of generate-and-patch over generate-and-test: even with constrained generation, for a global constraint in the domain of '2D-floorplanning'. For a second constraint in '2D-floorplanning' we show that even when it is possible to incorporate the constraint into a constrained generator, a generate-and-patch problem solver may satisfy the constraint more rapidly. We also briefly summarize how an extended version of our system applies to a constraint in the domain of 'multiprocessor scheduling'.
Wu, Jiayang; Cao, Pan; Hu, Xiaofeng; Jiang, Xinhong; Pan, Ting; Yang, Yuxing; Qiu, Ciyuan; Tremblay, Christine; Su, Yikai
2014-10-20
We propose and experimentally demonstrate an all-optical temporal differential-equation solver that can be used to solve ordinary differential equations (ODEs) characterizing general linear time-invariant (LTI) systems. The photonic device implemented by an add-drop microring resonator (MRR) with two tunable interferometric couplers is monolithically integrated on a silicon-on-insulator (SOI) wafer with a compact footprint of ~60 μm × 120 μm. By thermally tuning the phase shifts along the bus arms of the two interferometric couplers, the proposed device is capable of solving first-order ODEs with two variable coefficients. The operation principle is theoretically analyzed, and system testing of solving ODE with tunable coefficients is carried out for 10-Gb/s optical Gaussian-like pulses. The experimental results verify the effectiveness of the fabricated device as a tunable photonic ODE solver.
Evaluation of parallel direct sparse linear solvers in electromagnetic geophysical problems
NASA Astrophysics Data System (ADS)
Puzyrev, Vladimir; Koric, Seid; Wilkin, Scott
2016-04-01
High performance computing is absolutely necessary for large-scale geophysical simulations. In order to obtain a realistic image of a geologically complex area, industrial surveys collect vast amounts of data making the computational cost extremely high for the subsequent simulations. A major computational bottleneck of modeling and inversion algorithms is solving the large sparse systems of linear ill-conditioned equations in complex domains with multiple right hand sides. Recently, parallel direct solvers have been successfully applied to multi-source seismic and electromagnetic problems. These methods are robust and exhibit good performance, but often require large amounts of memory and have limited scalability. In this paper, we evaluate modern direct solvers on large-scale modeling examples that previously were considered unachievable with these methods. Performance and scalability tests utilizing up to 65,536 cores on the Blue Waters supercomputer clearly illustrate the robustness, efficiency and competitiveness of direct solvers compared to iterative techniques. Wide use of direct methods utilizing modern parallel architectures will allow modeling tools to accurately support multi-source surveys and 3D data acquisition geometries, thus promoting a more efficient use of the electromagnetic methods in geophysics.
NASA Astrophysics Data System (ADS)
Gurr, Henry
2014-03-01
Princeton Physicist J. J. Hopfield's Mathematical Model of the Mammalian Brain, (Similar To Ising Glass Model of a crystal of magnetic spin particles) says our Brain-Work for Memory, Perception, Language, Thinking, etc, (Even the AHA-EUREKA-Flash Of Insight Type Problem Solving), is achieved by our massively inter-connected CNS Neurons ... working together ... MINIMIZING an analog of physical energy ... thus yielding Optimal Solutions: These ``best'' answers, correspond to highest mental coherence, for most facets organism response, beit mental (eg: perception, memory, ideas, thinking, etc) or physical-muscular-actions (eg speaking, tool using, trail following, etc). Our brain is this way, because living creature, MUST be evolved, so they will find & use the best actions, for survival!!! Our human heritage, is to instantly compute near optimal future plans, (mental & physical-muscular), and be able to accomplish plans reliably & efficiently. If you know of book or articles in these topic areas, please email to HenryG--USCA.edu How to work well, with your own ``self'', called mind-body, will follow!! Conjectures: Who is the ``I'' that appears to make decisions? Am ``I'' the master of my domain? Is there an ``I'' or am ``I'' merely an illusion of reality.
Dumbser, Michael; Balsara, Dinshaw S.
2016-01-01
In this paper a new, simple and universal formulation of the HLLEM Riemann solver (RS) is proposed that works for general conservative and non-conservative systems of hyperbolic equations. For non-conservative PDE, a path-conservative formulation of the HLLEM RS is presented for the first time in this paper. The HLLEM Riemann solver is built on top of a novel and very robust path-conservative HLL method. It thus naturally inherits the positivity properties and the entropy enforcement of the underlying HLL scheme. However, with just the slight additional cost of evaluating eigenvectors and eigenvalues of intermediate characteristic fields, we can represent linearly degenerate intermediate waves with a minimum of smearing. For conservative systems, our paper provides the easiest and most seamless path for taking a pre-existing HLL RS and quickly and effortlessly converting it to a RS that provides improved results, comparable with those of an HLLC, HLLD, Osher or Roe-type RS. This is done with minimal additional computational complexity, making our variant of the HLLEM RS also a very fast RS that can accurately represent linearly degenerate discontinuities. Our present HLLEM RS also transparently extends these advantages to non-conservative systems. For shallow water-type systems, the resulting method is proven to be well-balanced. Several test problems are presented for shallow water-type equations and two-phase flow models, as well as for gas dynamics with real equation of state, magnetohydrodynamics (MHD & RMHD), and nonlinear elasticity. Since our new formulation accommodates multiple intermediate waves and has a broader applicability than the original HLLEM method, it could alternatively be called the HLLI Riemann solver, where the “I” stands for the intermediate characteristic fields that can be accounted for. -- Highlights: •New simple and general path-conservative formulation of the HLLEM Riemann solver. •Application to general conservative and non
Robust parallel iterative solvers for linear and least-squares problems, Final Technical Report
Saad, Yousef
2014-01-16
The primary goal of this project is to study and develop robust iterative methods for solving linear systems of equations and least squares systems. The focus of the Minnesota team is on algorithms development, robustness issues, and on tests and validation of the methods on realistic problems. 1. The project begun with an investigation on how to practically update a preconditioner obtained from an ILU-type factorization, when the coefficient matrix changes. 2. We investigated strategies to improve robustness in parallel preconditioners in a specific case of a PDE with discontinuous coefficients. 3. We explored ways to adapt standard preconditioners for solving linear systems arising from the Helmholtz equation. These are often difficult linear systems to solve by iterative methods. 4. We have also worked on purely theoretical issues related to the analysis of Krylov subspace methods for linear systems. 5. We developed an effective strategy for performing ILU factorizations for the case when the matrix is highly indefinite. The strategy uses shifting in some optimal way. The method was extended to the solution of Helmholtz equations by using complex shifts, yielding very good results in many cases. 6. We addressed the difficult problem of preconditioning sparse systems of equations on GPUs. 7. A by-product of the above work is a software package consisting of an iterative solver library for GPUs based on CUDA. This was made publicly available. It was the first such library that offers complete iterative solvers for GPUs. 8. We considered another form of ILU which blends coarsening techniques from Multigrid with algebraic multilevel methods. 9. We have released a new version on our parallel solver - called pARMS [new version is version 3]. As part of this we have tested the code in complex settings - including the solution of Maxwell and Helmholtz equations and for a problem of crystal growth.10. As an application of polynomial preconditioning we considered the
Analysis Tools for CFD Multigrid Solvers
NASA Technical Reports Server (NTRS)
Mineck, Raymond E.; Thomas, James L.; Diskin, Boris
2004-01-01
Analysis tools are needed to guide the development and evaluate the performance of multigrid solvers for the fluid flow equations. Classical analysis tools, such as local mode analysis, often fail to accurately predict performance. Two-grid analysis tools, herein referred to as Idealized Coarse Grid and Idealized Relaxation iterations, have been developed and evaluated within a pilot multigrid solver. These new tools are applicable to general systems of equations and/or discretizations and point to problem areas within an existing multigrid solver. Idealized Relaxation and Idealized Coarse Grid are applied in developing textbook-efficient multigrid solvers for incompressible stagnation flow problems.
General Solution of the Kenamond HE Problem 3
Kaul, Ann
2015-12-15
A general solution for programmed burn calculations of the light times produced by a singlepoint initiation of a single HE region surrounding an inert region has been developed. In contrast to the original solutions proposed in References 1 and 2, the detonator is no longer restricted to a location on a Cartesian axis and can be located at any point inside the HE region. This general solution has been implemented in the ExactPack suite of exact solvers for verification problems.
dftatom: A robust and general Schrödinger and Dirac solver for atomic structure calculations
NASA Astrophysics Data System (ADS)
Čertík, Ondřej; Pask, John E.; Vackář, Jiří
2013-07-01
A robust and general solver for the radial Schrödinger, Dirac, and Kohn-Sham equations is presented. The formulation admits general potentials and meshes: uniform, exponential, or other defined by nodal distribution and derivative functions. For a given mesh type, convergence can be controlled systematically by increasing the number of grid points. Radial integrations are carried out using a combination of asymptotic forms, Runge-Kutta, and implicit Adams methods. Eigenfunctions are determined by a combination of bisection and perturbation methods for robustness and speed. An outward Poisson integration is employed to increase accuracy in the core region, allowing absolute accuracies of 10-8 Hartree to be attained for total energies of heavy atoms such as uranium. Detailed convergence studies are presented and computational parameters are provided to achieve accuracies commonly required in practice. Comparisons to analytic and current-benchmark density-functional results for atomic number Z=1-92 are presented, verifying and providing a refinement to current benchmarks. An efficient, modular Fortran 95 implementation, dftatom, is provided as open source, including examples, tests, and wrappers for interface to other languages; wherein particular emphasis is placed on the independence (no global variables), reusability, and generality of the individual routines. Program summaryProgram title:dftatom Catalogue identifier: AEPA_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEPA_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: MIT license No. of lines in distributed program, including test data, etc.: 14122 No. of bytes in distributed program, including test data, etc.: 157453 Distribution format: tar.gz Programming language: Fortran 95 with interfaces to Python and C. Computer: Any computer with a Fortran 95 compiler. Operating system: Any OS with a Fortran 95 compiler. RAM: 500 MB
High-resolution coupled physics solvers for analysing fine-scale nuclear reactor design problems.
Mahadevan, Vijay S; Merzari, Elia; Tautges, Timothy; Jain, Rajeev; Obabko, Aleksandr; Smith, Michael; Fischer, Paul
2014-08-06
An integrated multi-physics simulation capability for the design and analysis of current and future nuclear reactor models is being investigated, to tightly couple neutron transport and thermal-hydraulics physics under the SHARP framework. Over several years, high-fidelity, validated mono-physics solvers with proven scalability on petascale architectures have been developed independently. Based on a unified component-based architecture, these existing codes can be coupled with a mesh-data backplane and a flexible coupling-strategy-based driver suite to produce a viable tool for analysts. The goal of the SHARP framework is to perform fully resolved coupled physics analysis of a reactor on heterogeneous geometry, in order to reduce the overall numerical uncertainty while leveraging available computational resources. The coupling methodology and software interfaces of the framework are presented, along with verification studies on two representative fast sodium-cooled reactor demonstration problems to prove the usability of the SHARP framework.
High-resolution coupled physics solvers for analysing fine-scale nuclear reactor design problems
Mahadevan, Vijay S.; Merzari, Elia; Tautges, Timothy; Jain, Rajeev; Obabko, Aleksandr; Smith, Michael; Fischer, Paul
2014-01-01
An integrated multi-physics simulation capability for the design and analysis of current and future nuclear reactor models is being investigated, to tightly couple neutron transport and thermal-hydraulics physics under the SHARP framework. Over several years, high-fidelity, validated mono-physics solvers with proven scalability on petascale architectures have been developed independently. Based on a unified component-based architecture, these existing codes can be coupled with a mesh-data backplane and a flexible coupling-strategy-based driver suite to produce a viable tool for analysts. The goal of the SHARP framework is to perform fully resolved coupled physics analysis of a reactor on heterogeneous geometry, in order to reduce the overall numerical uncertainty while leveraging available computational resources. The coupling methodology and software interfaces of the framework are presented, along with verification studies on two representative fast sodium-cooled reactor demonstration problems to prove the usability of the SHARP framework. PMID:24982250
Thevenot, Catherine; Barrouillet, Pierre; Castel, Caroline; Jimenez, Sonia
2011-11-01
This paper addresses the relationship between basic numerical processes and higher level numerical abilities in normal achieving adults. In the first experiment we inferred the elementary numerical abilities of university students from the time they needed to encode numerical information involved in complex additions and subtractions. We interpreted the shorter encoding times in good arithmetic problem solvers as revealing clearer or more accessible representations of numbers. The second experiment shows that these results cannot be due to the fact that lower skilled individuals experience more maths anxiety or put more cognitive efforts into calculations than do higher skilled individuals. Moreover, the third experiment involving non-numerical information supports the hypothesis that these interindividual differences are specific to number processing. The possible causal relationships between basic and higher level numerical abilities are discussed.
NASA Technical Reports Server (NTRS)
Harvey, Jason; Moore, Michael
2013-01-01
The General-Use Nodal Network Solver (GUNNS) is a modeling software package that combines nodal analysis and the hydraulic-electric analogy to simulate fluid, electrical, and thermal flow systems. GUNNS is developed by L-3 Communications under the TS21 (Training Systems for the 21st Century) project for NASA Johnson Space Center (JSC), primarily for use in space vehicle training simulators at JSC. It has sufficient compactness and fidelity to model the fluid, electrical, and thermal aspects of space vehicles in real-time simulations running on commodity workstations, for vehicle crew and flight controller training. It has a reusable and flexible component and system design, and a Graphical User Interface (GUI), providing capability for rapid GUI-based simulator development, ease of maintenance, and associated cost savings. GUNNS is optimized for NASA's Trick simulation environment, but can be run independently of Trick.
Problem Solvers: Problem--Light It up! and Solutions--Flags by the Numbers
ERIC Educational Resources Information Center
Hall, Shaun
2009-01-01
A simple circuit is created by the continuous flow of electricity through conductors (copper wires) from a source of electrical energy (batteries). "Completing a circuit" means that electricity flows from the energy source through the circuit and, in the case described in this month's problem, causes the light bulb tolight up. The presence of…
NASA Astrophysics Data System (ADS)
Kaus, Boris; Popov, Anton; Püsök, Adina
2014-05-01
In order to solve high-resolution 3D problems in computational geodynamics it is crucial to use multigrid solvers in combination with parallel computers. A number of approaches are currently in use in the community, which can broadly be divided into coupled and decoupled approaches. In the decoupled approach, an algebraic or geometric multigrid method is used as a preconditioner for the velocity equations only while an iterative approach such as Schur complement reduction used to solve the outer velocity-pressure equations. In the coupled approach, on the other hand, a multigrid approach is applied to both the velocity and pressure equations. The coupled multigrid approaches are typically employed in combination with staggered finite difference discretizations, whereas the decoupled approach is the method of choice in many of the existing finite element codes. Yet, it is unclear whether there are differences in speed between the two approaches, and if so, how this depends on the initial guess. Here, we implemented both approaches in combination with a staggered finite difference discretization and test the robustness of the two approaches with respect to large jumps in viscosity contrast, as well as their computational efficiency as a function of the initial guess. Acknowledgements. Funding was provided by the European Research Council under the European Community's Seventh Framework Program (FP7/2007-2013) / ERC Grant agreement #258830. Numerical computations have been performed on JUQUEEN of the Jülich high-performance computing center.
Problem Solving with General Semantics.
ERIC Educational Resources Information Center
Hewson, David
1996-01-01
Discusses how to use general semantics formulations to improve problem solving at home or at work--methods come from the areas of artificial intelligence/computer science, engineering, operations research, and psychology. (PA)
General aviation IFR operational problems
NASA Technical Reports Server (NTRS)
Bolz, E. H.; Eisele, J. E.
1979-01-01
Operational problems of general aviation IFR operators (particularly single pilot operators) were studied. Several statistical bases were assembled and utilized to identify the more serious problems and to demonstrate their magnitude. These bases include official activity projections, historical accident data and delay data, among others. The GA operating environment and cockpit environment were analyzed in detail. Solutions proposed for each of the problem areas identified are based on direct consideration of currently planned enhancements to the ATC system, and on a realistic assessment of the present and future limitations of general aviation avionics. A coordinated set of research program is suggested which would provide the developments necessary to implement the proposed solutions.
NASA Astrophysics Data System (ADS)
Isakari, Hiroshi; Kondo, Toyohiro; Takahashi, Toru; Matsumoto, Toshiro
2017-03-01
This paper presents a structural optimisation method in three-dimensional acoustic-elastic coupled problems. The proposed optimisation method finds an optimal allocation of elastic materials which reduces the sound level on some fixed observation points. In the process of the optimisation, configuration of the elastic materials is expressed with a level set function, and the distribution of the level set function is iteratively updated with the help of the topological derivative. The topological derivative is associated with state and adjoint variables which are the solutions of the acoustic-elastic coupled problems. In this paper, the acoustic-elastic coupled problems are solved by a BEM-FEM coupled solver, in which the fast multipole method (FMM) and a multi-frontal solver for sparse matrices are efficiently combined. Along with the detailed formulations for the topological derivative and the BEM-FEM coupled solver, we present some numerical examples of optimal designs of elastic sound scatterer to manipulate sound waves, from which we confirm the effectiveness of the present method.
A fast parallel solver for the forward problem in electrical impedance tomography.
Jehl, Markus; Dedner, Andreas; Betcke, Timo; Aristovich, Kirill; Klöfkorn, Robert; Holder, David
2015-01-01
Electrical impedance tomography (EIT) is a noninvasive imaging modality, where imperceptible currents are applied to the skin and the resulting surface voltages are measured. It has the potential to distinguish between ischaemic and haemorrhagic stroke with a portable and inexpensive device. The image reconstruction relies on an accurate forward model of the experimental setup. Because of the relatively small signal in stroke EIT, the finite-element modeling requires meshes of more than 10 million elements. To study the requirements in the forward modeling in EIT and also to reduce the time for experimental image acquisition, it is necessary to reduce the run time of the forward computation. We show the implementation of a parallel forward solver for EIT using the Dune-Fem C++ library and demonstrate its performance on many CPU's of a computer cluster. For a typical EIT application a direct solver was significantly slower and not an alternative to iterative solvers with multigrid preconditioning. With this new solver, we can compute the forward solutions and the Jacobian matrix of a typical EIT application with 30 electrodes on a 15-million element mesh in less than 15 min. This makes it a valuable tool for simulation studies and EIT applications with high precision requirements. It is freely available for download.
Training Tomorrow's Environmental Problem Solvers: An Integrative Approach to Graduate Education
ERIC Educational Resources Information Center
Moslemi, Jennifer M.; Capps, Krista A.; Johnson, Mark S.; Maul, Jude; McIntyre, Peter B.; Melvin, April M.; Vadas, Timothy M.; Vallano, Dena M.; Watkins, James M.; Weiss, Marissa
2009-01-01
Environmental problems are generally complex and blind to disciplinary boundaries. Efforts to devise long-term solutions require collaborative research that integrates knowledge across historically disparate fields, yet the traditional model for training new scientists emphasizes personal independence and disciplinary focus. Growing awareness of…
An Exact, Compressible One-Dimensional Riemann Solver for General, Convex Equations of State
Kamm, James Russell
2015-03-05
This note describes an algorithm with which to compute numerical solutions to the one- dimensional, Cartesian Riemann problem for compressible flow with general, convex equations of state. While high-level descriptions of this approach are to be found in the literature, this note contains most of the necessary details required to write software for this problem. This explanation corresponds to the approach used in the source code that evaluates solutions for the 1D, Cartesian Riemann problem with a JWL equation of state in the ExactPack package [16, 29]. Numerical examples are given with the proposed computational approach for a polytropic equation of state and for the JWL equation of state.
NASA Astrophysics Data System (ADS)
Koldan, Jelena; Puzyrev, Vladimir; de la Puente, Josep; Houzeaux, Guillaume; Cela, José María
2014-06-01
We present an elaborate preconditioning scheme for Krylov subspace methods which has been developed to improve the performance and reduce the execution time of parallel node-based finite-element (FE) solvers for 3-D electromagnetic (EM) numerical modelling in exploration geophysics. This new preconditioner is based on algebraic multigrid (AMG) that uses different basic relaxation methods, such as Jacobi, symmetric successive over-relaxation (SSOR) and Gauss-Seidel, as smoothers and the wave front algorithm to create groups, which are used for a coarse-level generation. We have implemented and tested this new preconditioner within our parallel nodal FE solver for 3-D forward problems in EM induction geophysics. We have performed series of experiments for several models with different conductivity structures and characteristics to test the performance of our AMG preconditioning technique when combined with biconjugate gradient stabilized method. The results have shown that, the more challenging the problem is in terms of conductivity contrasts, ratio between the sizes of grid elements and/or frequency, the more benefit is obtained by using this preconditioner. Compared to other preconditioning schemes, such as diagonal, SSOR and truncated approximate inverse, the AMG preconditioner greatly improves the convergence of the iterative solver for all tested models. Also, when it comes to cases in which other preconditioners succeed to converge to a desired precision, AMG is able to considerably reduce the total execution time of the forward-problem code-up to an order of magnitude. Furthermore, the tests have confirmed that our AMG scheme ensures grid-independent rate of convergence, as well as improvement in convergence regardless of how big local mesh refinements are. In addition, AMG is designed to be a black-box preconditioner, which makes it easy to use and combine with different iterative methods. Finally, it has proved to be very practical and efficient in the
NASA Astrophysics Data System (ADS)
Hintermüller, M.
2008-06-01
An output-least-squares formulation for a class of parameter identification problems for elliptic variational inequalities is considered. Based on the concept of C-stationarity an active set type solver with feasibility restoration is introduced. It is shown that the new method relates to the so-called implicit programming techniques in the context of mathematical programs with equilibrium constraints. In the discrete setting, in order to overcome the ill-posedness of the problem, the parameter of interest is discretized on a coarser mesh than the state of the system. In addition, if the parameter corresponds to the coefficient in the bilinear form of the underlying differential operator, an interior-point treatment is employed to maintain the coercivity of the elliptic operator. Moreover, the computational domain for the coefficient depends on the measurement data. The paper ends with a report on numerical tests including an application to a simplified lubrication problem in a rolling element device.
Framework for a Robust General Purpose Navier-Stokes Solver on Unstructured Meshes
NASA Astrophysics Data System (ADS)
Xiao, Cheng-Nian; Denner, Fabian; van Wachem, Berend G. M.
2016-11-01
A numerical framework for a pressure-based all-speeds flow solver operating on unstructured meshes, which is robust for a broad range of flow configurations, is proposed. The distinct features of our framework are the full coupling of the momentum and continuity equations as well as the use of an energy equation in conservation form to relate the thermal quantities with the flow field. In order to overcome the well-documented instability occurring while coupling the thermal energy to the remaining flow variables, a multistage iteration cycle has been devised which exhibits excellent convergence behavior without requiring any numerical relaxation parameters. Different spatial schemes for accurate shock resolution as well as complex thermodynamic gas models are also seamlessly incorporated into the framework. The solver is directly applicable to stationary and transient flows in all Mach number regimes (sub-, trans-, supersonic), exhibits strong robustness and accurately predicts flow and thermal variables at all speeds across shocks of different strengths. We present a wide range of results for both steady and transient compressible flows with vastly different Mach numbers and thermodynamic conditions in complex geometries represented by different types of unstructured meshes. The authors are grateful for the financial support provided by Shell.
An evaluation of parallel multigrid as a solver and a preconditioner for singular perturbed problems
Oosterlee, C.W.; Washio, T.
1996-12-31
In this paper we try to achieve h-independent convergence with preconditioned GMRES and BiCGSTAB for 2D singular perturbed equations. Three recently developed multigrid methods are adopted as a preconditioner. They are also used as solution methods in order to compare the performance of the methods as solvers and as preconditioners. Two of the multigrid methods differ only in the transfer operators. One uses standard matrix- dependent prolongation operators from. The second uses {open_quotes}upwind{close_quotes} prolongation operators, developed. Both employ the Galerkin coarse grid approximation and an alternating zebra line Gauss-Seidel smoother. The third method is based on the block LU decomposition of a matrix and on an approximate Schur complement. This multigrid variant is presented in. All three multigrid algorithms are algebraic methods.
Fast Multilevel Solvers for a Class of Discrete Fourth Order Parabolic Problems
Zheng, Bin; Chen, Luoping; Hu, Xiaozhe; Chen, Long; Nochetto, Ricardo H.; Xu, Jinchao
2016-03-05
In this paper, we study fast iterative solvers for the solution of fourth order parabolic equations discretized by mixed finite element methods. We propose to use consistent mass matrix in the discretization and use lumped mass matrix to construct efficient preconditioners. We provide eigenvalue analysis for the preconditioned system and estimate the convergence rate of the preconditioned GMRes method. Furthermore, we show that these preconditioners only need to be solved inexactly by optimal multigrid algorithms. Our numerical examples indicate that the proposed preconditioners are very efficient and robust with respect to both discretization parameters and diffusion coefficients. We also investigate the performance of multigrid algorithms with either collective smoothers or distributive smoothers when solving the preconditioner systems.
A More General Solution of the Kenamond HE Problem 2
Kaul, Ann
2015-12-15
A more general solution for programmed burn calculations of the light times produced by an unobstructed line-of-sight, multi-point initiation of a composite HE region has been developed. The equations describing the interfaces between detonation fronts have also been included. In contrast to the original solutions proposed in References 1 and 2, four of the detonators are no longer restricted to specific locations on a Cartesian axis and can be located at any point inside the HE region. For the proposed solution, one detonator must be located at the origin. The more general solution for any locations on the 2D y-axis or 3D z-axis has been implemented in the ExactPack suite of exact solvers for verification problems. It could easily be changed to the most general case outlined above.
NASA Astrophysics Data System (ADS)
Seth, Priyanka; Krivenko, Igor; Ferrero, Michel; Parcollet, Olivier
2016-03-01
We present TRIQS/CTHYB, a state-of-the art open-source implementation of the continuous-time hybridisation expansion quantum impurity solver of the TRIQS package. This code is mainly designed to be used with the TRIQS library in order to solve the self-consistent quantum impurity problem in a multi-orbital dynamical mean field theory approach to strongly-correlated electrons, in particular in the context of realistic electronic structure calculations. It is implemented in C++ for efficiency and is provided with a high-level Python interface. The code ships with a new partitioning algorithm that divides the local Hilbert space without any user knowledge of the symmetries and quantum numbers of the Hamiltonian. Furthermore, we implement higher-order configuration moves and show that such moves are necessary to ensure ergodicity of the Monte Carlo in common Hamiltonians even without symmetry-breaking.
Bakhos, Tania; Saibaba, Arvind K.; Kitanidis, Peter K.
2015-10-15
We consider the problem of estimating parameters in large-scale weakly nonlinear inverse problems for which the underlying governing equations is a linear, time-dependent, parabolic partial differential equation. A major challenge in solving these inverse problems using Newton-type methods is the computational cost associated with solving the forward problem and with repeated construction of the Jacobian, which represents the sensitivity of the measurements to the unknown parameters. Forming the Jacobian can be prohibitively expensive because it requires repeated solutions of the forward and adjoint time-dependent parabolic partial differential equations corresponding to multiple sources and receivers. We propose an efficient method based on a Laplace transform-based exponential time integrator combined with a flexible Krylov subspace approach to solve the resulting shifted systems of equations efficiently. Our proposed solver speeds up the computation of the forward and adjoint problems, thus yielding significant speedup in total inversion time. We consider an application from Transient Hydraulic Tomography (THT), which is an imaging technique to estimate hydraulic parameters related to the subsurface from pressure measurements obtained by a series of pumping tests. The algorithms discussed are applied to a synthetic example taken from THT to demonstrate the resulting computational gains of this proposed method.
NASA Technical Reports Server (NTRS)
Keyes, David E.; Smooke, Mitchell D.
1987-01-01
A parallelized finite difference code based on the Newton method for systems of nonlinear elliptic boundary value problems in two dimensions is analyzed in terms of computational complexity and parallel efficiency. An approximate cost function depending on 15 dimensionless parameters is derived for algorithms based on stripwise and boxwise decompositions of the domain and a one-to-one assignment of the strip or box subdomains to processors. The sensitivity of the cost functions to the parameters is explored in regions of parameter space corresponding to model small-order systems with inexpensive function evaluations and also a coupled system of nineteen equations with very expensive function evaluations. The algorithm was implemented on the Intel Hypercube, and some experimental results for the model problems with stripwise decompositions are presented and compared with the theory. In the context of computational combustion problems, multiprocessors of either message-passing or shared-memory type may be employed with stripwise decompositions to realize speedup of O(n), where n is mesh resolution in one direction, for reasonable n.
Parallel Multigrid Equation Solver
Adams, Mark
2001-09-07
Prometheus is a fully parallel multigrid equation solver for matrices that arise in unstructured grid finite element applications. It includes a geometric and an algebraic multigrid method and has solved problems of up to 76 mullion degrees of feedom, problems in linear elasticity on the ASCI blue pacific and ASCI red machines.
Boosting Stochastic Problem Solvers Through Online Self-Analysis of Performance
2003-07-21
locally optimal peek is reached and then 19 Figure 2.2: Example of a local search algorithm for a four city TSP: an initial state modified by a sequence of...will be discussed in detail later in a specific problem domain context. Since each iteration of a hill-climbing search finds a locally optimal peek in...last t steps. This wandering around while disallowing some moves is a very aggressive way of avoiding local optima . For example, consider a case
Inverse transport problem solvers based on regularized and compressive sensing techniques
Cheng, Y.; Cao, L.; Wu, H.; Zhang, H.
2012-07-01
According to the direct exposure measurements from flash radiographic image, regularized-based method and compressive sensing (CS)-based method for inverse transport equation are presented. The linear absorption coefficients and interface locations of objects are reconstructed directly at the same time. With a large number of measurements, least-square method is utilized to complete the reconstruction. Owing to the ill-posedness of the inverse problems, regularized algorithm is employed. Tikhonov method is applied with an appropriate posterior regularization parameter to get a meaningful solution. However, it's always very costly to obtain enough measurements. With limited measurements, CS sparse reconstruction technique Orthogonal Matching Pursuit (OMP) is applied to obtain the sparse coefficients by solving an optimization problem. This paper constructs and takes the forward projection matrix rather than Gauss matrix as measurement matrix. In the CS-based algorithm, Fourier expansion and wavelet expansion are adopted to convert an underdetermined system to a well-posed system. Simulations and numerical results of regularized method with appropriate regularization parameter and that of CS-based agree well with the reference value, furthermore, both methods avoid amplifying the noise. (authors)
NASA Astrophysics Data System (ADS)
Mitchell, Lawrence; Müller, Eike Hermann
2016-12-01
The implementation of efficient multigrid preconditioners for elliptic partial differential equations (PDEs) is a challenge due to the complexity of the resulting algorithms and corresponding computer code. For sophisticated (mixed) finite element discretisations on unstructured grids an efficient implementation can be very time consuming and requires the programmer to have in-depth knowledge of the mathematical theory, parallel computing and optimisation techniques on manycore CPUs. In this paper we show how the development of bespoke multigrid preconditioners can be simplified significantly by using a framework which allows the expression of the each component of the algorithm at the correct abstraction level. Our approach (1) allows the expression of the finite element problem in a language which is close to the mathematical formulation of the problem, (2) guarantees the automatic generation and efficient execution of parallel optimised low-level computer code and (3) is flexible enough to support different abstraction levels and give the programmer control over details of the preconditioner. We use the composable abstractions of the Firedrake/PyOP2 package to demonstrate the efficiency of this approach for the solution of strongly anisotropic PDEs in atmospheric modelling. The weak formulation of the PDE is expressed in Unified Form Language (UFL) and the lower PyOP2 abstraction layer allows the manual design of computational kernels for a bespoke geometric multigrid preconditioner. We compare the performance of this preconditioner to a single-level method and hypre's BoomerAMG algorithm. The Firedrake/PyOP2 code is inherently parallel and we present a detailed performance analysis for a single node (24 cores) on the ARCHER supercomputer. Our implementation utilises a significant fraction of the available memory bandwidth and shows very good weak scaling on up to 6,144 compute cores.
Software-engineering challenges of building and deploying reusable problem solvers
O’CONNOR, MARTIN J.; NYULAS, CSONGOR; TU, SAMSON; BUCKERIDGE, DAVID L.; OKHMATOVSKAIA, ANNA; MUSEN, MARK A.
2012-01-01
Problem solving methods (PSMs) are software components that represent and encode reusable algorithms. They can be combined with representations of domain knowledge to produce intelligent application systems. A goal of research on PSMs is to provide principled methods and tools for composing and reusing algorithms in knowledge-based systems. The ultimate objective is to produce libraries of methods that can be easily adapted for use in these systems. Despite the intuitive appeal of PSMs as conceptual building blocks, in practice, these goals are largely unmet. There are no widely available tools for building applications using PSMs and no public libraries of PSMs available for reuse. This paper analyzes some of the reasons for the lack of widespread adoptions of PSM techniques and illustrate our analysis by describing our experiences developing a complex, high-throughput software system based on PSM principles. We conclude that many fundamental principles in PSM research are useful for building knowledge-based systems. In particular, the task–method decomposition process, which provides a means for structuring knowledge-based tasks, is a powerful abstraction for building systems of analytic methods. However, despite the power of PSMs in the conceptual modeling of knowledge-based systems, software engineering challenges have been seriously underestimated. The complexity of integrating control knowledge modeled by developers using PSMs with the domain knowledge that they model using ontologies creates a barrier to widespread use of PSM-based systems. Nevertheless, the surge of recent interest in ontologies has led to the production of comprehensive domain ontologies and of robust ontology-authoring tools. These developments present new opportunities to leverage the PSM approach. PMID:23565031
On-line generalized Steiner problem
Awerbuch, B.; Azar, Y.; Bartal, Y.
1996-12-31
The Generalized Steiner Problem (GSP) is defined as follows. We are given a graph with non-negative weights and a set of pairs of vertices. The algorithm has to construct minimum weight subgraph such that the two nodes of each pair are connected by a path. We consider the on-line generalized Steiner problem, in which pairs of vertices arrive on-line and are needed to be connected immediately. We give a simple O(log{sup 2} n) competitive deterministic on-line algorithm. The previous best online algorithm (by Westbrook and Yan) was O({radical}n log n) competitive. We also consider the network connectivity leasing problem which is a generalization of the GSP. Here edges of the graph can be either bought or leased for different costs. We provide simple randomized O(log{sup 2} n) competitive algorithm based on the on-line generalized Steiner problem result.
Two Solvers for Tractable Temporal Constraints with Preferences
NASA Technical Reports Server (NTRS)
Rossi, F.; Khatib,L.; Morris, P.; Morris, R.; Clancy, Daniel (Technical Monitor)
2002-01-01
A number of reasoning problems involving the manipulation of temporal information can naturally be viewed as implicitly inducing an ordering of potential local decisions involving time on the basis of preferences. Soft temporal constraints problems allow to describe in a natural way scenarios where events happen over time and preferences are associated to event distances and durations. In general, solving soft temporal problems require exponential time in the worst case, but there are interesting subclasses of problems which are polynomially solvable. We describe two solvers based on two different approaches for solving the same tractable subclass. For each solver we present the theoretical results it stands on, a description of the algorithm and some experimental results. The random generator used to build the problems on which tests are performed is also described. Finally, we compare the two solvers highlighting the tradeoff between performance and representational power.
NASA Astrophysics Data System (ADS)
Toro, Eleuterio F.; Montecinos, Gino I.
2015-12-01
We present a semi-analytical, implicit solution to the generalized Riemann problem (GRP) for non-linear systems of hyperbolic balance laws with stiff source terms. The solution method is based on an implicit, time Taylor series expansion and the Cauchy-Kowalewskaya procedure, along with the solution of a sequence of classical Riemann problems. Our new GRP solver is then used to construct locally implicit ADER methods of arbitrary accuracy in space and time for solving the general initial-boundary value problem for non-linear systems of hyperbolic balance laws with stiff source terms. Analysis of the method for model problems is carried out and empirical convergence rate studies for suitable tests problems are performed, confirming the theoretically expected high order of accuracy.
T2CG1, a package of preconditioned conjugate gradient solvers for TOUGH2
Moridis, G.; Pruess, K.; Antunez, E.
1994-03-01
Most of the computational work in the numerical simulation of fluid and heat flows in permeable media arises in the solution of large systems of linear equations. The simplest technique for solving such equations is by direct methods. However, because of large storage requirements and accumulation of roundoff errors, the application of direct solution techniques is limited, depending on matrix bandwidth, to systems of a few hundred to at most a few thousand simultaneous equations. T2CG1, a package of preconditioned conjugate gradient solvers, has been added to TOUGH2 to complement its direct solver and significantly increase the size of problems tractable on PCs. T2CG1 includes three different solvers: a Bi-Conjugate Gradient (BCG) solver, a Bi-Conjugate Gradient Squared (BCGS) solver, and a Generalized Minimum Residual (GMRES) solver. Results from six test problems with up to 30,000 equations show that T2CG1 (1) is significantly (and invariably) faster and requires far less memory than the MA28 direct solver, (2) it makes possible the solution of very large three-dimensional problems on PCs, and (3) that the BCGS solver is the fastest of the three in the tested problems. Sample problems are presented related to heat and fluid flow at Yucca Mountain and WIPP, environmental remediation by the Thermal Enhanced Vapor Extraction System, and geothermal resources.
Anton, Luis; MartI, Jose M; Ibanez, Jose M; Aloy, Miguel A.; Mimica, Petar; Miralles, Juan A.
2010-05-01
We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wave front in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, and can be seen as a relativistic generalization of earlier work performed in classical MHD. Based on the full wave decomposition (FWD) provided by the renormalized set of eigenvectors in conserved variables, we have also developed a linearized (Roe-type) Riemann solver. Extensive testing against one- and two-dimensional standard numerical problems allows us to conclude that our solver is very robust. When compared with a family of simpler solvers that avoid the knowledge of the full characteristic structure of the equations in the computation of the numerical fluxes, our solver turns out to be less diffusive than HLL and HLLC, and comparable in accuracy to the HLLD solver. The amount of operations needed by the FWD solver makes it less efficient computationally than those of the HLL family in one-dimensional problems. However, its relative efficiency increases in multidimensional simulations.
NASA Astrophysics Data System (ADS)
Antón, Luis; Miralles, Juan A.; Martí, José M.; Ibáñez, José M.; Aloy, Miguel A.; Mimica, Petar
2010-05-01
We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wave front in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, and can be seen as a relativistic generalization of earlier work performed in classical MHD. Based on the full wave decomposition (FWD) provided by the renormalized set of eigenvectors in conserved variables, we have also developed a linearized (Roe-type) Riemann solver. Extensive testing against one- and two-dimensional standard numerical problems allows us to conclude that our solver is very robust. When compared with a family of simpler solvers that avoid the knowledge of the full characteristic structure of the equations in the computation of the numerical fluxes, our solver turns out to be less diffusive than HLL and HLLC, and comparable in accuracy to the HLLD solver. The amount of operations needed by the FWD solver makes it less efficient computationally than those of the HLL family in one-dimensional problems. However, its relative efficiency increases in multidimensional simulations.
Lobb's Generalization of Catalan's Parenthesization Problem
ERIC Educational Resources Information Center
Koshy, Thomas
2009-01-01
A. Lobb discovered an interesting generalization of Catalan's parenthesization problem, namely: Find the number L(n, m) of arrangements of n + m positive ones and n - m negative ones such that every partial sum is nonnegative, where 0 = m = n. This article uses Lobb's formula, L(n, m) = (2m + 1)/(n + m + 1) C(2n, n + m), where C is the usual…
Amestoy, Patrick R.; Duff, Iain S.; L'Excellent, Jean-Yves; Li, Xiaoye S.
2001-10-10
We examine the mechanics of the send and receive mechanism of MPI and in particular how we can implement message passing in a robust way so that our performance is not significantly affected by changes to the MPI system. This leads us to using the Isend/Irecv protocol which will entail sometimes significant algorithmic changes. We discuss this within the context of two different algorithms for sparse Gaussian elimination that we have parallelized. One is a multifrontal solver called MUMPS, the other is a supernodal solver called SuperLU. Both algorithms are difficult to parallelize on distributed memory machines. Our initial strategies were based on simple MPI point-to-point communication primitives. With such approaches, the parallel performance of both codes are very sensitive to the MPI implementation, the way MPI internal buffers are used in particular. We then modified our codes to use more sophisticated nonblocking versions of MPI communication. This significantly improved the performance robustness (independent of the MPI buffering mechanism) and scalability, but at the cost of increased code complexity.
NASA Technical Reports Server (NTRS)
Ferencz, Donald C.; Viterna, Larry A.
1991-01-01
ALPS is a computer program which can be used to solve general linear program (optimization) problems. ALPS was designed for those who have minimal linear programming (LP) knowledge and features a menu-driven scheme to guide the user through the process of creating and solving LP formulations. Once created, the problems can be edited and stored in standard DOS ASCII files to provide portability to various word processors or even other linear programming packages. Unlike many math-oriented LP solvers, ALPS contains an LP parser that reads through the LP formulation and reports several types of errors to the user. ALPS provides a large amount of solution data which is often useful in problem solving. In addition to pure linear programs, ALPS can solve for integer, mixed integer, and binary type problems. Pure linear programs are solved with the revised simplex method. Integer or mixed integer programs are solved initially with the revised simplex, and the completed using the branch-and-bound technique. Binary programs are solved with the method of implicit enumeration. This manual describes how to use ALPS to create, edit, and solve linear programming problems. Instructions for installing ALPS on a PC compatible computer are included in the appendices along with a general introduction to linear programming. A programmers guide is also included for assistance in modifying and maintaining the program.
Finite Element Interface to Linear Solvers
Williams, Alan
2005-03-18
Sparse systems of linear equations arise in many engineering applications, including finite elements, finite volumes, and others. The solution of linear systems is often the most computationally intensive portion of the application. Depending on the complexity of problems addressed by the application, there may be no single solver capable of solving all of the linear systems that arise. This motivates the desire to switch an application from one solver librwy to another, depending on the problem being solved. The interfaces provided by solver libraries differ greatly, making it difficult to switch an application code from one library to another. The amount of library-specific code in an application Can be greatly reduced by having an abstraction layer between solver libraries and the application, putting a common "face" on various solver libraries. One such abstraction layer is the Finite Element Interface to Linear Solvers (EEl), which has seen significant use by finite element applications at Sandia National Laboratories and Lawrence Livermore National Laboratory.
Doctoral training in behavior analysis: Training generalized problem-solving skills
Chase, Philip N.; Wylie, Ruth G.
1985-01-01
This essay provides guidelines for designing a doctoral program in behavior analysis. First, we propose a general accomplishment for all behavior analytic doctoral students: that they be able to solve problems concerning individual behavior within a range of environments. Second, in order to achieve this goal, we propose that students be trained in conceptual and experimental analysis of behavior, the application of behavioral principles and the administration of behavioral programs. This training should include class work, but it should emphasize the immersion of students in a variety of environments in which they are required to use behavior analytic strategies. Third, we provide an example of a hypothetical graduate program that involves the proposed training. Finally, an evaluation plan is suggested for determining whether a training program is in fact producing students who are generalized problem-solvers. At each step, we justify our point of view from a perspective that combines principles from behavior analysis and educational systems design. PMID:22478633
Solution of the Generalized Noah's Ark Problem.
Billionnet, Alain
2013-01-01
The phylogenetic diversity (PD) of a set of species is a measure of the evolutionary distance among the species in the collection, based on a phylogenetic tree. Such a tree is composed of a root, internal nodes, and leaves that correspond to the set of taxa under study. With each edge of the tree is associated a non-negative branch length (evolutionary distance). If a particular survival probability is associated with each taxon, the PD measure becomes the expected PD measure. In the Noah's Ark Problem (NAP) introduced by Weitzman (1998), these survival probabilities can be increased at some cost. The problem is to determine how best to allocate a limited amount of resources to maximize the expected PD of the considered species. It is easy to formulate the NAP as a (difficult) nonlinear 0-1 programming problem. The aim of this article is to show that a general version of the NAP (GNAP) can be solved simply and efficiently with any set of edge weights and any set of survival probabilities by using standard mixed-integer linear programming software. The crucial point to move from a nonlinear program in binary variables to a mixed-integer linear program, is to approximate the logarithmic function by the lower envelope of a set of tangents to the curve. Solving the obtained mixed-integer linear program provides not only a near-optimal solution but also an upper bound on the value of the optimal solution. We also applied this approach to a generalization of the nature reserve problem (GNRP) that consists of selecting a set of regions to be conserved so that the expected PD of the set of species present in these regions is maximized. In this case, the survival probabilities of different taxa are not independent of each other. Computational results are presented to illustrate potentialities of the approach. Near-optimal solutions with hypothetical phylogenetic trees comprising about 4000 taxa are obtained in a few seconds or minutes of computing time for the GNAP, and in
A Projection free method for Generalized Eigenvalue Problem with a nonsmooth Regularizer.
Hwang, Seong Jae; Collins, Maxwell D; Ravi, Sathya N; Ithapu, Vamsi K; Adluru, Nagesh; Johnson, Sterling C; Singh, Vikas
2015-12-01
Eigenvalue problems are ubiquitous in computer vision, covering a very broad spectrum of applications ranging from estimation problems in multi-view geometry to image segmentation. Few other linear algebra problems have a more mature set of numerical routines available and many computer vision libraries leverage such tools extensively. However, the ability to call the underlying solver only as a "black box" can often become restrictive. Many 'human in the loop' settings in vision frequently exploit supervision from an expert, to the extent that the user can be considered a subroutine in the overall system. In other cases, there is additional domain knowledge, side or even partial information that one may want to incorporate within the formulation. In general, regularizing a (generalized) eigenvalue problem with such side information remains difficult. Motivated by these needs, this paper presents an optimization scheme to solve generalized eigenvalue problems (GEP) involving a (nonsmooth) regularizer. We start from an alternative formulation of GEP where the feasibility set of the model involves the Stiefel manifold. The core of this paper presents an end to end stochastic optimization scheme for the resultant problem. We show how this general algorithm enables improved statistical analysis of brain imaging data where the regularizer is derived from other 'views' of the disease pathology, involving clinical measurements and other image-derived representations.
A Projection free method for Generalized Eigenvalue Problem with a nonsmooth Regularizer
Hwang, Seong Jae; Collins, Maxwell D.; Ravi, Sathya N.; Ithapu, Vamsi K.; Adluru, Nagesh; Johnson, Sterling C.; Singh, Vikas
2016-01-01
Eigenvalue problems are ubiquitous in computer vision, covering a very broad spectrum of applications ranging from estimation problems in multi-view geometry to image segmentation. Few other linear algebra problems have a more mature set of numerical routines available and many computer vision libraries leverage such tools extensively. However, the ability to call the underlying solver only as a “black box” can often become restrictive. Many ‘human in the loop’ settings in vision frequently exploit supervision from an expert, to the extent that the user can be considered a subroutine in the overall system. In other cases, there is additional domain knowledge, side or even partial information that one may want to incorporate within the formulation. In general, regularizing a (generalized) eigenvalue problem with such side information remains difficult. Motivated by these needs, this paper presents an optimization scheme to solve generalized eigenvalue problems (GEP) involving a (nonsmooth) regularizer. We start from an alternative formulation of GEP where the feasibility set of the model involves the Stiefel manifold. The core of this paper presents an end to end stochastic optimization scheme for the resultant problem. We show how this general algorithm enables improved statistical analysis of brain imaging data where the regularizer is derived from other ‘views’ of the disease pathology, involving clinical measurements and other image-derived representations. PMID:27081374
Cinema, Fermi problems and general education
NASA Astrophysics Data System (ADS)
Efthimiou, C. J.; Llewellyn, R. A.
2007-05-01
During the past few years the authors have developed a new approach to the teaching of physical science, a general education course typically found in the curricula of nearly every college and university. This approach, called Physics in Films (Efthimiou and Llewellyn 2006 Phys. Teach. 44 28-33), uses scenes from popular films to illustrate physical principles and has excited student interest and improved student performance. A similar approach at the senior/high-school level, nicknamed Hollywood Physics, has been developed by Chandler (2006 Phys. Teach. 44 290-2 2002 Phys. Teach. 40 420-4). The two approaches may be considered complementary as they target different student groups. The analyses of many of the scenes in Physics in Films are a direct application of Fermi calculations—estimates and approximations designed to make solutions of complex and seemingly intractable problems understandable to the student non-specialist. The intent of this paper is to provide instructors with examples they can use to develop skill in recognizing Fermi problems and making Fermi calculations in their own courses.
Approximations for generalized bilevel programming problem
Morgan, J.; Lignola, M.B.
1994-12-31
The following mathematical programming with variational inequality constraints, also called {open_quotes}Generalized bilevel programming problem{close_quotes}, is considered: minimize f(x, y) subject to x {element_of} U and y {element_of} S(x) where S(x) is the solution set of a parametrized variational inequality; i.e., S(x) = {l_brace}y {element_of} U(x): F(x, y){sup T} (y-z){<=} 0 {forall}z {element_of} U (x){r_brace} with f : R{sup n} {times} R{sup m} {yields} {bar R}, F : R{sup n} {times} R{sup m} - R{sup n} and U(x) = {l_brace}y {element_of} {Gamma}{sup T} c{sub i} (x, y) {<=} 0 for 1 = 1, p{r_brace} with c : R{sup n} {times} R{sup m} {yields} R and U{sub ad}, {Gamma} be compact subsets of R{sup m} and R{sup n} respectively. Approximations will be presented to guarantee not only existence of solutions but also convergence of them under perturbations of the data. Connections with previous results obtained when the lower level problem is an optimization one, will be given.
Generalized quasi-variational inequality and implicit complementarity problems
Yao, Jen-Chih.
1989-10-01
A new problem called the generalized quasi-variational inequality problem is introduced. This new formulation extends all kinds of variational inequality problem formulations that have been introduced and enlarges the class of problems that can be approached by the variational inequality problem formulation. Existence results without convexity assumptions are established and topological properties of the solution set are investigated. A new problem called the generalized implicit complementarity problem is also introduced which generalizes all the complementarity problem formulations that have been introduced. Applications of generalized quasi-variational inequality and implicit complementarity problems are given. 43 refs.
ERIC Educational Resources Information Center
Foley, Greg
2014-01-01
A problem that illustrates two ways of computing the break-even radius of insulation is outlined. The problem is suitable for students who are taking an introductory module in heat transfer or transport phenomena and who have some previous knowledge of the numerical solution of non- linear algebraic equations. The potential for computer algebra,…
ERIC Educational Resources Information Center
Cantor, Alida; DeLauer, Verna; Martin, Deborah; Rogan, John
2015-01-01
Management of "wicked problems", messy real-world problems that defy resolution, requires thinkers who can transcend disciplinary boundaries, work collaboratively, and handle complexity and obstacles. This paper explores how educators can train undergraduates in these skills through applied community-based research, using the example of…
Scalable Parallel Algebraic Multigrid Solvers
Bank, R; Lu, S; Tong, C; Vassilevski, P
2005-03-23
The authors propose a parallel algebraic multilevel algorithm (AMG), which has the novel feature that the subproblem residing in each processor is defined over the entire partition domain, although the vast majority of unknowns for each subproblem are associated with the partition owned by the corresponding processor. This feature ensures that a global coarse description of the problem is contained within each of the subproblems. The advantages of this approach are that interprocessor communication is minimized in the solution process while an optimal order of convergence rate is preserved; and the speed of local subproblem solvers can be maximized using the best existing sequential algebraic solvers.
The generalized pole assignment problem. [dynamic output feedback problems
NASA Technical Reports Server (NTRS)
Djaferis, T. E.; Mitter, S. K.
1979-01-01
Two dynamic output feedback problems for a linear, strictly proper system are considered, along with their interrelationships. The problems are formulated in the frequency domain and investigated in terms of linear equations over rings of polynomials. Necessary and sufficient conditions are expressed using genericity.
Huang, Kuo -Ling; Mehrotra, Sanjay
2016-11-08
We present a homogeneous algorithm equipped with a modified potential function for the monotone complementarity problem. We show that this potential function is reduced by at least a constant amount if a scaled Lipschitz condition (SLC) is satisfied. A practical algorithm based on this potential function is implemented in a software package named iOptimize. The implementation in iOptimize maintains global linear and polynomial time convergence properties, while achieving practical performance. It either successfully solves the problem, or concludes that the SLC is not satisfied. When compared with the mature software package MOSEK (barrier solver version 6.0.0.106), iOptimize solves convex quadraticmore » programming problems, convex quadratically constrained quadratic programming problems, and general convex programming problems in fewer iterations. Moreover, several problems for which MOSEK fails are solved to optimality. In addition, we also find that iOptimize detects infeasibility more reliably than the general nonlinear solvers Ipopt (version 3.9.2) and Knitro (version 8.0).« less
Huang, Kuo -Ling; Mehrotra, Sanjay
2016-11-08
We present a homogeneous algorithm equipped with a modified potential function for the monotone complementarity problem. We show that this potential function is reduced by at least a constant amount if a scaled Lipschitz condition (SLC) is satisfied. A practical algorithm based on this potential function is implemented in a software package named iOptimize. The implementation in iOptimize maintains global linear and polynomial time convergence properties, while achieving practical performance. It either successfully solves the problem, or concludes that the SLC is not satisfied. When compared with the mature software package MOSEK (barrier solver version 6.0.0.106), iOptimize solves convex quadratic programming problems, convex quadratically constrained quadratic programming problems, and general convex programming problems in fewer iterations. Moreover, several problems for which MOSEK fails are solved to optimality. In addition, we also find that iOptimize detects infeasibility more reliably than the general nonlinear solvers Ipopt (version 3.9.2) and Knitro (version 8.0).
Generalized Kepler problems. I. Without magnetic charges
Meng, Guowu
2013-01-15
For each simple euclidean Jordan algebra V of rank {rho} and degree {delta}, we introduce a family of classical dynamic problems. These dynamical problems all share the characteristic features of the Kepler problem for planetary motions, such as the existence of Laplace-Runge-Lenz vector and hidden symmetry. After suitable quantizations, a family of quantum dynamic problems, parametrized by the nontrivial Wallach parameter {nu}, is obtained. Here, {nu} Element-Of W(V):={l_brace}k({delta}/2) Double-Vertical-Line k=1,...,({rho}-1){r_brace} Union (({rho}-1)({delta}/2),{infinity}) and was introduced by N. Wallach to parametrize the set of nontrivial scalar-type unitary lowest weight representations of the conformal group of V. For the quantum dynamic problem labelled by {nu}, the bound state spectra is -(1/2/(I+{nu}({rho}/2)){sup 2}), I= 0, 1, Horizontal-Ellipsis and its Hilbert space of bound states gives a new realization for the afore-mentioned representation labelled by {nu}. A few results in the literature about these representations become more explicit and more refined. The Lagrangian for a classical Kepler-type dynamic problem introduced here is still of the simple form: (1/2) parallel x parallel {sup 2}+(1/r). Here, x is the velocity of a unit-mass particle moving on the space consisting of V's semi-positive elements of a fixed rank, and r is the inner product of x with the identity element of V.
General Problem Solving: Navy Requirements and Solutions.
1985-03-01
Karat, 1982; Lukas, et. al., 1971; Pitt, 1983; Post and Brennan, 1976; Reif and Heller, 1982; Schwieger , 1° 4; Speedie, et. al., 1973; Thor- son...bVo°o ,o. 4*** h ° . . .. - - o. . . . o. , ’ Schwieger , Ruben Don, A Component Analysis of Mathematical Problem Solving, Ph.D
NASA Astrophysics Data System (ADS)
Sun, Rui; Xiao, Heng
2016-04-01
With the growth of available computational resource, CFD-DEM (computational fluid dynamics-discrete element method) becomes an increasingly promising and feasible approach for the study of sediment transport. Several existing CFD-DEM solvers are applied in chemical engineering and mining industry. However, a robust CFD-DEM solver for the simulation of sediment transport is still desirable. In this work, the development of a three-dimensional, massively parallel, and open-source CFD-DEM solver SediFoam is detailed. This solver is built based on open-source solvers OpenFOAM and LAMMPS. OpenFOAM is a CFD toolbox that can perform three-dimensional fluid flow simulations on unstructured meshes; LAMMPS is a massively parallel DEM solver for molecular dynamics. Several validation tests of SediFoam are performed using cases of a wide range of complexities. The results obtained in the present simulations are consistent with those in the literature, which demonstrates the capability of SediFoam for sediment transport applications. In addition to the validation test, the parallel efficiency of SediFoam is studied to test the performance of the code for large-scale and complex simulations. The parallel efficiency tests show that the scalability of SediFoam is satisfactory in the simulations using up to O(107) particles.
Cinema, Fermi Problems and General Education
ERIC Educational Resources Information Center
Efthimiou, C. J.; Llewellyn, R. A.
2007-01-01
During the past few years the authors have developed a new approach to the teaching of physical science, a general education course typically found in the curricula of nearly every college and university. This approach, called "Physics in Films" (Efthimiou and Llewellyn 2006 Phys. Teach. 44 28-33), uses scenes from popular films to illustrate…
Using a general problem-solving strategy to promote transfer.
Youssef-Shalala, Amina; Ayres, Paul; Schubert, Carina; Sweller, John
2014-09-01
Cognitive load theory was used to hypothesize that a general problem-solving strategy based on a make-as-many-moves-as-possible heuristic could facilitate problem solutions for transfer problems. In four experiments, school students were required to learn about a topic through practice with a general problem-solving strategy, through a conventional problem solving strategy or by studying worked examples. In Experiments 1 and 2 using junior high school students learning geometry, low knowledge students in the general problem-solving group scored significantly higher on near or far transfer tests than the conventional problem-solving group. In Experiment 3, an advantage for a general problem-solving group over a group presented worked examples was obtained on far transfer tests using the same curriculum materials, again presented to junior high school students. No differences between conditions were found in Experiments 1, 2, or 3 using test problems similar to the acquisition problems. Experiment 4 used senior high school students studying economics and found the general problem-solving group scored significantly higher than the conventional problem-solving group on both similar and transfer tests. It was concluded that the general problem-solving strategy was helpful for novices, but not for students that had access to domain-specific knowledge.
A Wavelet Technique For Multi-grid Solver For Large Linear Systems
NASA Astrophysics Data System (ADS)
Keller, W.
In general, large systems of linear equations cannot be solved directly. An iterative solver has to be applied instead. Unfortunately, iterative solvers have a notouriously slow convergence rate, which in the worst case can prevent convergence at all, due to the inavoidable rounding errors. Multi-grid iteration schemes are meant to guarantee a sufficiently high convergence rate, independent from the dimension of the linear system. The idea behind the multi-grid solvers is that the traditional iterative solvers eliminate only the short-wavelength error constituents in the initial guess for the solution. For the elimination of the remaining long-wavelength error constituents a much coarser grid is sufficient. On the coarse grid the dimension of the problem is much smaller so that the elimination can be done by a direct solver. The paper shows that wavelet techniques successfully can be applied for following steps of a multi-grid procedure: · Generation of an approximation of the proplem on a coarse grid from a given approximation on the fine grid. · Restriction of a signal on a fine grid to its approximation on a co grid. · Uplift of a signal from the coarse to the fine grid. The paper starts with a theoretical explanation of the links between wavelets and multi-grid solvers. Based on this investigation the class o operators, which are suitable for a multi-grid solution strategy can be characterized. The numerical efficiency of the approach will be tested for the Planar Stokes problem.
NASA Astrophysics Data System (ADS)
Kordy, M.; Wannamaker, P.; Maris, V.; Cherkaev, E.; Hill, G.
2016-01-01
We have developed an algorithm, which we call HexMT, for 3-D simulation and inversion of magnetotelluric (MT) responses using deformable hexahedral finite elements that permit incorporation of topography. Direct solvers parallelized on symmetric multiprocessor (SMP), single-chassis workstations with large RAM are used throughout, including the forward solution, parameter Jacobians and model parameter update. In Part I, the forward simulator and Jacobian calculations are presented. We use first-order edge elements to represent the secondary electric field (E), yielding accuracy O(h) for E and its curl (magnetic field). For very low frequencies or small material admittivities, the E-field requires divergence correction. With the help of Hodge decomposition, the correction may be applied in one step after the forward solution is calculated. This allows accurate E-field solutions in dielectric air. The system matrix factorization and source vector solutions are computed using the MKL PARDISO library, which shows good scalability through 24 processor cores. The factorized matrix is used to calculate the forward response as well as the Jacobians of electromagnetic (EM) field and MT responses using the reciprocity theorem. Comparison with other codes demonstrates accuracy of our forward calculations. We consider a popular conductive/resistive double brick structure, several synthetic topographic models and the natural topography of Mount Erebus in Antarctica. In particular, the ability of finite elements to represent smooth topographic slopes permits accurate simulation of refraction of EM waves normal to the slopes at high frequencies. Run-time tests of the parallelized algorithm indicate that for meshes as large as 176 × 176 × 70 elements, MT forward responses and Jacobians can be calculated in ˜1.5 hr per frequency. Together with an efficient inversion parameter step described in Part II, MT inversion problems of 200-300 stations are computable with total run times
Parallel Symmetric Eigenvalue Problem Solvers
2015-05-01
7 2.2 Condensed matter physics . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 Spectral reordering...working precision in floating-point arithmetic due to the fact that rotational masses are omitted [1]. 2.2 Condensed matter physics In 1958, P.W...the plot more intuitive, we have chosen to refer to our updated vector as v = x+ d rather than v = x− d. 19 quantity is smallest, and the dark blue
ERIC Educational Resources Information Center
Figarella-Garcia, Frances V.; Velazquez-Rivera, Lizzette M.; Santiago-Rivera, Teresita
2004-01-01
Imagine--you must bring water to a hurricane-ravaged area. There is only one bridge and only one truck, and the bridge can only hold so much weight. Your calculations determine if the truck--and its load of water--can make it safely over the bridge. This is a typical challenge during two-week summer camps for third-through fourth-grade students…
Parallel Symmetric Eigenvalue Problem Solvers
2015-05-01
graduate school. Debugging somebody else’s MPI code is an immensely frustrating experience, but he would regularly stay late at the oce to assist me...cessfully. In addition, I will describe the parallel kernels required by my code . 5 The next sections will describe my Fortran-based implementations of...Sandia’s publicly available Trace- Min code . Each of the methods has its own unique advantages and disadvantages, summarized in table 3.1. In short, I
A Vectorized General Sparsity Solver.
1982-10-01
726. S5] Woo, P.T., et at, "Application of Sparse Matrix Techniques to Reservoir Simulation ," in Spare Matrix Computations, ed. by J. R. Bunch and D. J...Rose, Academic Press, 1976, pp. 427-438. [6] Price, H.S., and K.H. Coates, "Direct Methods in Reservoir Simulation ," Soc. Pet. Engrs. Jour., vol. 14...for 2- D Grids," Proc. 6th Symposium on Reservoir Simulation , New Orleans, Feb. 1-2, 1982, pp. t89-506. I 4 0 Appendix A Program Listing C-. LmC- Cv
A STUDY OF PROBLEM DRINKERS IN A GENERAL HOSPITAL
Babu, R. Sateesh; Sengupta, S.N.
1997-01-01
349 new admissions in the wards of Medicine, General Surgery & Orthopedics in a general hospital were screened with MAST & AUDIT for problem use of alcohol. Problem drinking was present in 14.6% of the inpatients. The severity and the need for additional treatment were measured with Addiction Severity Index (ASI). Majority of the patients had problems in more than one ar?a. Nevertheless, only one fourth of the patients were referred for psychiatric treatment. The findings indicate the need to develop services towards the recognition and referrals of the problem drinkers in general hospitals PMID:21584037
The generalized quadratic knapsack problem. A neuronal network approach.
Talaván, Pedro M; Yáñez, Javier
2006-05-01
The solution of an optimization problem through the continuous Hopfield network (CHN) is based on some energy or Lyapunov function, which decreases as the system evolves until a local minimum value is attained. A new energy function is proposed in this paper so that any 0-1 linear constrains programming with quadratic objective function can be solved. This problem, denoted as the generalized quadratic knapsack problem (GQKP), includes as particular cases well-known problems such as the traveling salesman problem (TSP) and the quadratic assignment problem (QAP). This new energy function generalizes those proposed by other authors. Through this energy function, any GQKP can be solved with an appropriate parameter setting procedure, which is detailed in this paper. As a particular case, and in order to test this generalized energy function, some computational experiments solving the traveling salesman problem are also included.
Error control of iterative linear solvers for integrated groundwater models.
Dixon, Matthew F; Bai, Zhaojun; Brush, Charles F; Chung, Francis I; Dogrul, Emin C; Kadir, Tariq N
2011-01-01
An open problem that arises when using modern iterative linear solvers, such as the preconditioned conjugate gradient method or Generalized Minimum RESidual (GMRES) method, is how to choose the residual tolerance in the linear solver to be consistent with the tolerance on the solution error. This problem is especially acute for integrated groundwater models, which are implicitly coupled to another model, such as surface water models, and resolve both multiple scales of flow and temporal interaction terms, giving rise to linear systems with variable scaling. This article uses the theory of "forward error bound estimation" to explain the correspondence between the residual error in the preconditioned linear system and the solution error. Using examples of linear systems from models developed by the US Geological Survey and the California State Department of Water Resources, we observe that this error bound guides the choice of a practical measure for controlling the error in linear systems. We implemented a preconditioned GMRES algorithm and benchmarked it against the Successive Over-Relaxation (SOR) method, the most widely known iterative solver for nonsymmetric coefficient matrices. With forward error control, GMRES can easily replace the SOR method in legacy groundwater modeling packages, resulting in the overall simulation speedups as large as 7.74×. This research is expected to broadly impact groundwater modelers through the demonstration of a practical and general approach for setting the residual tolerance in line with the solution error tolerance and presentation of GMRES performance benchmarking results.
NONLINEAR MULTIGRID SOLVER EXPLOITING AMGe COARSE SPACES WITH APPROXIMATION PROPERTIES
Christensen, Max La Cour; Villa, Umberto E.; Engsig-Karup, Allan P.; Vassilevski, Panayot S.
2016-01-22
The paper introduces a nonlinear multigrid solver for mixed nite element discretizations based on the Full Approximation Scheme (FAS) and element-based Algebraic Multigrid (AMGe). The main motivation to use FAS for unstruc- tured problems is the guaranteed approximation property of the AMGe coarse spaces that were developed recently at Lawrence Livermore National Laboratory. These give the ability to derive stable and accurate coarse nonlinear discretization problems. The previous attempts (including ones with the original AMGe method, [5, 11]), were less successful due to lack of such good approximation properties of the coarse spaces. With coarse spaces with approximation properties, our FAS approach on un- structured meshes should be as powerful/successful as FAS on geometrically re ned meshes. For comparison, Newton's method and Picard iterations with an inner state-of-the-art linear solver is compared to FAS on a nonlinear saddle point problem with applications to porous media ow. It is demonstrated that FAS is faster than Newton's method and Picard iterations for the experiments considered here. Due to the guaranteed approximation properties of our AMGe, the coarse spaces are very accurate, providing a solver with the potential for mesh-independent convergence on general unstructured meshes.
A chemical reaction network solver for the astrophysics code NIRVANA
NASA Astrophysics Data System (ADS)
Ziegler, U.
2016-02-01
Context. Chemistry often plays an important role in astrophysical gases. It regulates thermal properties by changing species abundances and via ionization processes. This way, time-dependent cooling mechanisms and other chemistry-related energy sources can have a profound influence on the dynamical evolution of an astrophysical system. Modeling those effects with the underlying chemical kinetics in realistic magneto-gasdynamical simulations provide the basis for a better link to observations. Aims: The present work describes the implementation of a chemical reaction network solver into the magneto-gasdynamical code NIRVANA. For this purpose a multispecies structure is installed, and a new module for evolving the rate equations of chemical kinetics is developed and coupled to the dynamical part of the code. A small chemical network for a hydrogen-helium plasma was constructed including associated thermal processes which is used in test problems. Methods: Evolving a chemical network within time-dependent simulations requires the additional solution of a set of coupled advection-reaction equations for species and gas temperature. Second-order Strang-splitting is used to separate the advection part from the reaction part. The ordinary differential equation (ODE) system representing the reaction part is solved with a fourth-order generalized Runge-Kutta method applicable for stiff systems inherent to astrochemistry. Results: A series of tests was performed in order to check the correctness of numerical and technical implementation. Tests include well-known stiff ODE problems from the mathematical literature in order to confirm accuracy properties of the solver used as well as problems combining gasdynamics and chemistry. Overall, very satisfactory results are achieved. Conclusions: The NIRVANA code is now ready to handle astrochemical processes in time-dependent simulations. An easy-to-use interface allows implementation of complex networks including thermal processes
NASA Technical Reports Server (NTRS)
Ilin, Andrew V.
2006-01-01
The Magnetic Field Solver computer program calculates the magnetic field generated by a group of collinear, cylindrical axisymmetric electromagnet coils. Given the current flowing in, and the number of turns, axial position, and axial and radial dimensions of each coil, the program calculates matrix coefficients for a finite-difference system of equations that approximates a two-dimensional partial differential equation for the magnetic potential contributed by the coil. The program iteratively solves these finite-difference equations by use of the modified incomplete Cholesky preconditioned-conjugate-gradient method. The total magnetic potential as a function of axial (z) and radial (r) position is then calculated as a sum of the magnetic potentials of the individual coils, using a high-accuracy interpolation scheme. Then the r and z components of the magnetic field as functions of r and z are calculated from the total magnetic potential by use of a high-accuracy finite-difference scheme. Notably, for the finite-difference calculations, the program generates nonuniform two-dimensional computational meshes from nonuniform one-dimensional meshes. Each mesh is generated in such a way as to minimize the numerical error for a benchmark one-dimensional magnetostatic problem.
Problem drug users known to Bristol general practitioners
Parker, Julie; Gay, Martyn
1987-01-01
A 12-month prospective survey was undertaken of all 239 problem drug users known to general practitioners in Bristol and the doctors' attitudes towards them. The drug users were predominantly young, aged 15-35 years, and males outnumbered females by approximately two to one. Seventy-eight per cent had problems associated with opiates, almost invariably heroin, 10% had problems with stimulants (mainly amphetamine powder), and others had problems with hallucinogens, cannabis, barbiturates and solvents. Opiate dependence was the commonest single problem but ill health, hepatitis, psychiatric illnesses, relationship problems, work and financial difficulties were also frequently mentioned. There was a wide variation in the numbers of problem drug users seen by individual practices, which related both to the situation of the practice and the widely varying attitudes of the partners towards drug users and drug problems. General practitioners were aware of the grapevine that transmits news of their treatment to other users, and individual practices had typically evolved a general strategy for all drug users, to minimize arguments. General practitioners were asked their views about specialist services: they thought that services in the area for drug users were inadequate to help them and their patients in 58% of cases. Several suggestions were made for additional services which were needed. PMID:3448214
Local Conjecturing Process in the Solving of Pattern Generalization Problem
ERIC Educational Resources Information Center
Sutarto; Nusantara, Toto; Subanji; Sisworo
2016-01-01
This aim of this study is to describe the process of local conjecturing in generalizing patterns based on Action, Process, Object, Schema (APOS) theory. The subjects were 16 grade 8 students from a junior high school. Data collection used Pattern Generalization Problem (PGP) and interviews. In the first stage, students completed PGP; in the second…
Monotonicity Formula and Regularity for General Free Discontinuity Problems
NASA Astrophysics Data System (ADS)
Bucur, Dorin; Luckhaus, Stephan
2014-02-01
We give a general monotonicity formula for local minimizers of free discontinuity problems which have a critical deviation from minimality, of order d - 1. This result allows us to prove partial regularity results (that is closure and density estimates for the jump set) for a large class of free discontinuity problems involving general energies associated to the jump set, as for example free boundary problems with Robin conditions. In particular, we give a short proof to the De Giorgi-Carriero-Leaci result for the Mumford-Shah functional.
[Problems of general surgery in the cardiosurgical patient].
Emanuele, B; Bonardi, O; Garrone, C; De Michelis, M; Cantore, R; Viziale, G
1980-08-25
The preoperative problem is analysed with proposal of a heart risk index table and assessment of the manifold problems involved. Stress is thenn laid on the importance of careful postoperative treatment, establishing rules of surgical and resuscitatory behaviour to be followed in the general surgery of the heart patient. These rules of behaviour permit prevention of surgical complications, which are fully illustrated. Particular attention is paid to the selection of those conditions of pertinence to general surgery which have treatment of choice prior to heart surgery. Personal experience of 75 general surgery operations between 1977 and 1979 in the Villa Pia Clinic is then reviewed.
A parallel PCG solver for MODFLOW.
Dong, Yanhui; Li, Guomin
2009-01-01
In order to simulate large-scale ground water flow problems more efficiently with MODFLOW, the OpenMP programming paradigm was used to parallelize the preconditioned conjugate-gradient (PCG) solver with in this study. Incremental parallelization, the significant advantage supported by OpenMP on a shared-memory computer, made the solver transit to a parallel program smoothly one block of code at a time. The parallel PCG solver, suitable for both MODFLOW-2000 and MODFLOW-2005, is verified using an 8-processor computer. Both the impact of compilers and different model domain sizes were considered in the numerical experiments. Based on the timing results, execution times using the parallel PCG solver are typically about 1.40 to 5.31 times faster than those using the serial one. In addition, the simulation results are the exact same as the original PCG solver, because the majority of serial codes were not changed. It is worth noting that this parallelizing approach reduces cost in terms of software maintenance because only a single source PCG solver code needs to be maintained in the MODFLOW source tree.
NASA Technical Reports Server (NTRS)
Bittker, David A.; Radhakrishnan, Krishnan
1994-01-01
LSENS, the Lewis General Chemical Kinetics and Sensitivity Analysis Code, has been developed for solving complex, homogeneous, gas-phase chemical kinetics problems and contains sensitivity analysis for a variety of problems, including nonisothermal situations. This report is part 3 of a series of three reference publications that describe LSENS, provide a detailed guide to its usage, and present many example problems. Part 3 explains the kinetics and kinetics-plus-sensitivity analysis problems supplied with LSENS and presents sample results. These problems illustrate the various capabilities of, and reaction models that can be solved by, the code and may provide a convenient starting point for the user to construct the problem data file required to execute LSENS. LSENS is a flexible, convenient, accurate, and efficient solver for chemical reaction problems such as static system; steady, one-dimensional, inviscid flow; reaction behind incident shock wave, including boundary layer correction; and perfectly stirred (highly backmixed) reactor. In addition, the chemical equilibrium state can be computed for the following assigned states: temperature and pressure, enthalpy and pressure, temperature and volume, and internal energy and volume. For static problems the code computes the sensitivity coefficients of the dependent variables and their temporal derivatives with respect to the initial values of the dependent variables and/or the three rate coefficient parameters of the chemical reactions.
Global flow in the generalized Buckingham's two-body problem
NASA Astrophysics Data System (ADS)
Popescu, E.; Pricopi, D.
2017-04-01
In this paper, we consider the generalized Buckingham potential. Using the McGehee's regularizing transformations, we study the global flow for the two-body problem associated to this potential. By making vary the angular momentum constant in the three cases of negative, zero, and positive energy, we analyze all possible situations. In each case, we obtain the global flow of the problem, exhibiting a great variety of orbits. All phase portraits are interpreted in terms of physical trajectories.
Many body generalization of the Landau-Zener problem.
Altland, Alexander; Gurarie, V
2008-02-15
We formulate and approximately solve a specific many body generalization of the Landau-Zener problem. Unlike with the single particle Landau-Zener problem, our system does not abide in the adiabatic ground state, even at very slow driving rates. The structure of the theory suggests that this finding reflects a more general phenomenon in the physics of adiabatically driven many particle systems. Our solution can be used to understand, for example, the behavior of two-level systems coupled to an electromagnetic field, as realized in cavity QED experiments.
Wavelet-based Poisson Solver for use in Particle-In-CellSimulations
Terzic, B.; Mihalcea, D.; Bohn, C.L.; Pogorelov, I.V.
2005-05-13
We report on a successful implementation of a wavelet based Poisson solver for use in 3D particle-in-cell (PIC) simulations. One new aspect of our algorithm is its ability to treat the general(inhomogeneous) Dirichlet boundary conditions (BCs). The solver harnesses advantages afforded by the wavelet formulation, such as sparsity of operators and data sets, existence of effective preconditioners, and the ability simultaneously to remove numerical noise and further compress relevant data sets. Having tested our method as a stand-alone solver on two model problems, we merged it into IMPACT-T to obtain a fully functional serial PIC code. We present and discuss preliminary results of application of the new code to the modeling of the Fermilab/NICADD and AES/JLab photoinjectors.
Solving a generalized distance geometry problem for protein structure determination.
Sit, Atilla; Wu, Zhijun
2011-12-01
We propose a new approach to the problem of determining an ensemble of protein structures with a set of interatomic distance bounds in NMR protein modeling. Similarly to X-ray crystallography, we assume that the protein has an equilibrium structure and the atoms fluctuate around their equilibrium positions. Then, the problem can be formulated as a generalized distance geometry problem, to find the equilibrium positions and maximal possible fluctuation radii for the atoms in the protein, subject to the condition that the fluctuations should be within the given distance bounds. We describe the scientific background of the work, the motivation of the new approach and the formulation of the problem. We develop a geometric buildup algorithm for an approximate solution to the problem and present some preliminary test results as a first step concept proofing. We also discuss related theoretical and computational issues and potential impacts of this work in NMR protein modeling.
LOGO and the Development of General Problem-Solving Skills.
ERIC Educational Resources Information Center
Krasnor, Linda R.; Mitterer, John O.
1984-01-01
Provides framework for assessing the extent to which problem-solving skills learned through LOGO, a children's graphics-oriented-structured computer language, may be transferred to other contexts. Examines principles governing generalization of learning. Discusses learning transfer and components of the LOGO experience that may affect transfer.…
Equation solvers for distributed-memory computers
NASA Technical Reports Server (NTRS)
Storaasli, Olaf O.
1994-01-01
A large number of scientific and engineering problems require the rapid solution of large systems of simultaneous equations. The performance of parallel computers in this area now dwarfs traditional vector computers by nearly an order of magnitude. This talk describes the major issues involved in parallel equation solvers with particular emphasis on the Intel Paragon, IBM SP-1 and SP-2 processors.
A real-time impurity solver for DMFT
NASA Astrophysics Data System (ADS)
Kim, Hyungwon; Aron, Camille; Han, Jong E.; Kotliar, Gabriel
Dynamical mean-field theory (DMFT) offers a non-perturbative approach to problems with strongly correlated electrons. The method heavily relies on the ability to numerically solve an auxiliary Anderson-type impurity problem. While powerful Matsubara-frequency solvers have been developed over the past two decades to tackle equilibrium situations, the status of real-time impurity solvers that could compete with Matsubara-frequency solvers and be readily generalizable to non-equilibrium situations is still premature. We present a real-time solver which is based on a quantum Master equation description of the dissipative dynamics of the impurity and its exact diagonalization. As a benchmark, we illustrate the strengths of our solver in the context of the equilibrium Mott-insulator transition of the one-band Hubbard model and compare it with iterative perturbation theory (IPT) method. Finally, we discuss its direct application to a nonequilibrium situation.
Generalized Hill Climbing Algorithms For Discrete Optimization Problems
2011-07-21
the Solution of the n/m/Cmax Flowshop Problem," Computers and Operations Research, 17 (3): 243-253. Papadimitriou , C.H. and K. Steiglitz [1982...model, whereby deteriorating moves are accepted according to a general random variable. Computational results are reported that illustrate...optimal solutions. Sangiovanni-Vincentelli [1991] separates heuristic methods into two conceptual classes: a class that computes the best solution
Lonigan, Christopher J; Spiegel, Jamie A; Goodrich, J Marc; Morris, Brittany M; Osborne, Colleen M; Lerner, Matthew D; Phillips, Beth M
2017-01-27
Findings from prior research have consistently indicated significant associations between self-regulation and externalizing behaviors. Significant associations have also been reported between children's language skills and both externalizing behaviors and self-regulation. Few studies to date, however, have examined these relations longitudinally, simultaneously, or with respect to unique clusters of externalizing problems. The current study examined the influence of preschool self-regulation on general and specific externalizing behavior problems in early elementary school and whether these relations were independent of associations between language, self-regulation, and externalizing behaviors in a sample of 815 children (44% female). Additionally, given a general pattern of sex differences in the presentations of externalizing behavior problems, self-regulation, and language skills, sex differences for these associations were examined. Results indicated unique relations of preschool self-regulation and language with both general externalizing behavior problems and specific problems of inattention. In general, self-regulation was a stronger longitudinal correlate of externalizing behavior for boys than it was for girls, and language was a stronger longitudinal predictor of hyperactive/impulsive behavior for girls than it was for boys.
Sensitivity analysis and approximation methods for general eigenvalue problems
NASA Technical Reports Server (NTRS)
Murthy, D. V.; Haftka, R. T.
1986-01-01
Optimization of dynamic systems involving complex non-hermitian matrices is often computationally expensive. Major contributors to the computational expense are the sensitivity analysis and reanalysis of a modified design. The present work seeks to alleviate this computational burden by identifying efficient sensitivity analysis and approximate reanalysis methods. For the algebraic eigenvalue problem involving non-hermitian matrices, algorithms for sensitivity analysis and approximate reanalysis are classified, compared and evaluated for efficiency and accuracy. Proper eigenvector normalization is discussed. An improved method for calculating derivatives of eigenvectors is proposed based on a more rational normalization condition and taking advantage of matrix sparsity. Important numerical aspects of this method are also discussed. To alleviate the problem of reanalysis, various approximation methods for eigenvalues are proposed and evaluated. Linear and quadratic approximations are based directly on the Taylor series. Several approximation methods are developed based on the generalized Rayleigh quotient for the eigenvalue problem. Approximation methods based on trace theorem give high accuracy without needing any derivatives. Operation counts for the computation of the approximations are given. General recommendations are made for the selection of appropriate approximation technique as a function of the matrix size, number of design variables, number of eigenvalues of interest and the number of design points at which approximation is sought.
Shape reanalysis and sensitivities utilizing preconditioned iterative boundary solvers
NASA Technical Reports Server (NTRS)
Guru Prasad, K.; Kane, J. H.
1992-01-01
The computational advantages associated with the utilization of preconditined iterative equation solvers are quantified for the reanalysis of perturbed shapes using continuum structural boundary element analysis (BEA). Both single- and multi-zone three-dimensional problems are examined. Significant reductions in computer time are obtained by making use of previously computed solution vectors and preconditioners in subsequent analyses. The effectiveness of this technique is demonstrated for the computation of shape response sensitivities required in shape optimization. Computer times and accuracies achieved using the preconditioned iterative solvers are compared with those obtained via direct solvers and implicit differentiation of the boundary integral equations. It is concluded that this approach employing preconditioned iterative equation solvers in reanalysis and sensitivity analysis can be competitive with if not superior to those involving direct solvers.
General bounds for electrode mislocation on the EEG inverse problem.
Beltrachini, L; von Ellenrieder, N; Muravchik, C H
2011-07-01
We analyze the effect of electrode mislocation on the electroencephalography (EEG) inverse problem using the Cramér-Rao bound (CRB) for single dipolar source parameters. We adopt a realistic head shape model, and solve the forward problem using the Boundary Element Method; the use of the CRB allows us to obtain general results which do not depend on the algorithm used for solving the inverse problem. We consider two possible causes for the electrode mislocation, errors in the measurement of the electrode positions and an imperfect registration between the electrodes and the scalp surfaces. For 120 electrodes placed in the scalp according to the 10-20 standard, and errors on the electrode location with a standard deviation of 5mm, the lower bound on the standard deviation in the source depth estimation is approximately 1mm in the worst case. Therefore, we conclude that errors in the electrode location may be tolerated since their effect on the EEG inverse problem are negligible from a practical point of view.
A semi-direct solver for compressible 3-dimensional rotational flow
NASA Technical Reports Server (NTRS)
Chang, S. C.; Adamczyk, J. J.
1983-01-01
An iterative procedure is presented for solving steady inviscid 3-D subsonic rotational flow problems. The procedure combines concepts from classical secondary flow theory with an extension to 3-D of a novel semi-direct Cauchy-Riemann solver. It is developed for generalized coordinates and can be exercised using standard finite difference procedures. The stability criterion of the iterative procedure is discussed along with its ability to capture the evolution of inviscid secondary flow in a turning channel.
A semi-direct solver for compressible three-dimensional rotational flow
NASA Technical Reports Server (NTRS)
Chang, S.-C.; Adamczyk, J. J.
1983-01-01
An iterative procedure is presented for solving steady inviscid 3-D subsonic rotational flow problems. The procedure combines concepts from classical secondary flow theory with an extension to 3-D of a novel semi-direct Cauchy-Riemann solver. It is developed for generalized coordinates and can be exercised using standard finite difference procedures. The stability criterion of the iterative procedure is discussed along with its ability to capture the evolution of inviscid secondary flow in a turning channel.
Extracting Embedded Generalized Networks from Linear Programming Problems.
1984-09-01
E EXTRACTING EMBEDDED GENERALIZED NETWORKS FROM LINEAR PROGRAMMING PROBLEMS by Gerald G. Brown * . ___Richard D. McBride * R. Kevin Wood LcL7...authorized. EA Gerald ’Brown Richar-rD. McBride 46;val Postgrduate School University of Southern California Monterey, California 93943 Los Angeles...REOT UBE . OV S.SF- PERFOING’ CAORG soN UER. 7. AUTNOR(a) S. CONTRACT ON GRANT NUME111() Gerald G. Brown Richard D. McBride S. PERFORMING ORGANIZATION
A parallel Lanczos method for symmetric generalized eigenvalue problems
Wu, K.; Simon, H.D.
1997-12-01
Lanczos algorithm is a very effective method for finding extreme eigenvalues of symmetric matrices. It requires less arithmetic operations than similar algorithms, such as, the Arnoldi method. In this paper, the authors present their parallel version of the Lanczos method for symmetric generalized eigenvalue problem, PLANSO. PLANSO is based on a sequential package called LANSO which implements the Lanczos algorithm with partial re-orthogonalization. It is portable to all parallel machines that support MPI and easy to interface with most parallel computing packages. Through numerical experiments, they demonstrate that it achieves similar parallel efficiency as PARPACK, but uses considerably less time.
Computational results for flows over 2-D ramp and 3-D obstacle with an upwind Navier-Stokes solver
NASA Technical Reports Server (NTRS)
Venkatapathy, Ethiraj
1990-01-01
An implicit, finite-difference, upwind, full Navier-Stokes solver was applied to supersonic/hypersonic flows over two-dimensional ramps and three-dimensional obstacle. Some of the computed results are presented. The numerical scheme used in the study is an implicit, spacially second order accurate, upwind, LU-ADI scheme based on Roe's approximate Reimann solver with MUSCL differencing of Van Leer. An algebraic grid generation scheme based on generalized interpolation scheme was used in generating the grids for the various 2-D and 3-D problems.
Computational results for 2-D and 3-D ramp flows with an upwind Navier-Stokes solver
NASA Technical Reports Server (NTRS)
Venkatapathy, Ethiraj
1991-01-01
An implicit, finite-difference, upwind, full Navier-Stokes solver was applied to supersonic/hypersonic flows over two-dimensional ramps and three-dimensional obstacle. Some of the computed results are presented. The numerical scheme used in the study is an implicit, spatially second order accurate, upwind, LU-ADI scheme based on Roe's approximate Reimann solver with MUSCL differencing of Van Leer. An algebraic grid generation scheme based on generalized interpolation scheme was used in generating the grids for the various 2-D and 3-D problems.
Scalable solvers and applications
Ribbens, C J
2000-10-27
The purpose of this report is to summarize research activities carried out under Lawrence Livermore National Laboratory (LLNL) research subcontract B501073. This contract supported the principal investigator (P1), Dr. Calvin Ribbens, during his sabbatical visit to LLNL from August 1999 through June 2000. Results and conclusions from the work are summarized below in two major sections. The first section covers contributions to the Scalable Linear Solvers and hypre projects in the Center for Applied Scientific Computing (CASC). The second section describes results from collaboration with Patrice Turchi of LLNL's Chemistry and Materials Science Directorate (CMS). A list of publications supported by this subcontract appears at the end of the report.
NASA Astrophysics Data System (ADS)
Aricò, Costanza; Lo Re, Carlo
2016-12-01
We extend a recently proposed 2D depth-integrated Finite Volume solver for the nonlinear shallow water equations with non-hydrostatic pressure distribution. The proposed model is aimed at simulating both nonlinear and dispersive shallow water processes. We split the total pressure into its hydrostatic and dynamic components and solve a hydrostatic problem and a non-hydrostatic problem sequentially, in the framework of a fractional time step procedure. The dispersive properties are achieved by incorporating the non-hydrostatic pressure component in the governing equations. The governing equations are the depth-integrated continuity equation and the depth-integrated momentum equations along the x, y and z directions. Unlike the previous non-hydrostatic shallow water solver, in the z momentum equation, we retain both the vertical local and convective acceleration terms. In the former solver, we keep only the local vertical acceleration term. In this paper, we investigate the effects of these convective terms and the possible improvements of the computed solution when these terms are not neglected in the governing equations, especially in strongly nonlinear processes. The presence of the convective terms in the vertical momentum equation leads to a numerical solution procedure, which is quite different from the one of the previous solver, in both the hydrostatic and dynamic steps. We discretize the spatial domain using unstructured triangular meshes satisfying the Generalized Delaunay property. The numerical solver is shock capturing and easily addresses wetting/drying problems, without any additional equation to solve at wet/dry interfaces. We present several numerical applications for challenging flooding processes encountered in practical aspects over irregular topography, including a new set of experiments carried out at the Hydraulics Laboratory of the University of Palermo.
Comparison of open-source linear programming solvers.
Gearhart, Jared Lee; Adair, Kristin Lynn; Durfee, Justin David.; Jones, Katherine A.; Martin, Nathaniel; Detry, Richard Joseph
2013-10-01
When developing linear programming models, issues such as budget limitations, customer requirements, or licensing may preclude the use of commercial linear programming solvers. In such cases, one option is to use an open-source linear programming solver. A survey of linear programming tools was conducted to identify potential open-source solvers. From this survey, four open-source solvers were tested using a collection of linear programming test problems and the results were compared to IBM ILOG CPLEX Optimizer (CPLEX) [1], an industry standard. The solvers considered were: COIN-OR Linear Programming (CLP) [2], [3], GNU Linear Programming Kit (GLPK) [4], lp_solve [5] and Modular In-core Nonlinear Optimization System (MINOS) [6]. As no open-source solver outperforms CPLEX, this study demonstrates the power of commercial linear programming software. CLP was found to be the top performing open-source solver considered in terms of capability and speed. GLPK also performed well but cannot match the speed of CLP or CPLEX. lp_solve and MINOS were considerably slower and encountered issues when solving several test problems.
Origins and development of the Cauchy problem in general relativity
NASA Astrophysics Data System (ADS)
Ringström, Hans
2015-06-01
The seminal work of Yvonne Choquet-Bruhat published in 1952 demonstrates that it is possible to formulate Einstein's equations as an initial value problem. The purpose of this article is to describe the background to and impact of this achievement, as well as the result itself. In some respects, the idea of viewing the field equations of general relativity as a system of evolution equations goes back to Einstein himself; in an argument justifying that gravitational waves propagate at the speed of light, Einstein used a special choice of coordinates to derive a system of wave equations for the linear perturbations on a Minkowski background. Over the following decades, Hilbert, de Donder, Lanczos, Darmois and many others worked to put Einstein's ideas on a more solid footing. In fact, the issue of local uniqueness (giving a rigorous justification for the statement that the speed of propagation of the gravitational field is bounded by that of light) was already settled in the 1930s by the work of Stellmacher. However, the first person to demonstrate both local existence and uniqueness in a setting in which the notion of finite speed of propagation makes sense was Yvonne Choquet-Bruhat. In this sense, her work lays the foundation for the formulation of Einstein's equations as an initial value problem. Following a description of the results of Choquet-Bruhat, we discuss the development of three research topics that have their origin in her work. The first one is local existence. One reason for addressing it is that it is at the heart of the original paper. Moreover, it is still an active and important research field, connected to the problem of characterizing the asymptotic behaviour of solutions that blow up in finite time. As a second topic, we turn to the questions of global uniqueness and strong cosmic censorship. These questions are of fundamental importance to anyone interested in justifying that the Cauchy problem makes sense globally. They are also closely
Advanced Multigrid Solvers for Fluid Dynamics
NASA Technical Reports Server (NTRS)
Brandt, Achi
1999-01-01
The main objective of this project has been to support the development of multigrid techniques in computational fluid dynamics that can achieve "textbook multigrid efficiency" (TME), which is several orders of magnitude faster than current industrial CFD solvers. Toward that goal we have assembled a detailed table which lists every foreseen kind of computational difficulty for achieving it, together with the possible ways for resolving the difficulty, their current state of development, and references. We have developed several codes to test and demonstrate, in the framework of simple model problems, several approaches for overcoming the most important of the listed difficulties that had not been resolved before. In particular, TME has been demonstrated for incompressible flows on one hand, and for near-sonic flows on the other hand. General approaches were advanced for the relaxation of stagnation points and boundary conditions under various situations. Also, new algebraic multigrid techniques were formed for treating unstructured grid formulations. More details on all these are given below.
A generalized stochastic perturbation technique for plasticity problems
NASA Astrophysics Data System (ADS)
Kamiński, Marcin Marek
2010-03-01
The main aim of this paper is to present an algorithm and the solution to the nonlinear plasticity problems with random parameters. This methodology is based on the finite element method covering physical and geometrical nonlinearities and, on the other hand, on the generalized nth order stochastic perturbation method. The perturbation approach resulting from the Taylor series expansion with uncertain parameters is provided in two different ways: (i) via the straightforward differentiation of the initial incremental equation and (ii) using the modified response surface method. This methodology is illustrated with the analysis of the elasto-plastic plane truss with random Young’s modulus leading to the determination of the probabilistic moments by the hybrid stochastic symbolic-finite element method computations.
Turovets, Sergei; Volkov, Vasily; Zherdetsky, Aleksej; Prakonina, Alena; Malony, Allen D
2014-01-01
The Electrical Impedance Tomography (EIT) and electroencephalography (EEG) forward problems in anisotropic inhomogeneous media like the human head belongs to the class of the three-dimensional boundary value problems for elliptic equations with mixed derivatives. We introduce and explore the performance of several new promising numerical techniques, which seem to be more suitable for solving these problems. The proposed numerical schemes combine the fictitious domain approach together with the finite-difference method and the optimally preconditioned Conjugate Gradient- (CG-) type iterative method for treatment of the discrete model. The numerical scheme includes the standard operations of summation and multiplication of sparse matrices and vector, as well as FFT, making it easy to implement and eligible for the effective parallel implementation. Some typical use cases for the EIT/EEG problems are considered demonstrating high efficiency of the proposed numerical technique.
A perspective on unstructured grid flow solvers
NASA Technical Reports Server (NTRS)
Venkatakrishnan, V.
1995-01-01
This survey paper assesses the status of compressible Euler and Navier-Stokes solvers on unstructured grids. Different spatial and temporal discretization options for steady and unsteady flows are discussed. The integration of these components into an overall framework to solve practical problems is addressed. Issues such as grid adaptation, higher order methods, hybrid discretizations and parallel computing are briefly discussed. Finally, some outstanding issues and future research directions are presented.
An efficient iterative method for the generalized Stokes problem
Sameh, A.; Sarin, V.
1996-12-31
This paper presents an efficient iterative scheme for the generalized Stokes problem, which arises frequently in the simulation of time-dependent Navier-Stokes equations for incompressible fluid flow. The general form of the linear system is where A = {alpha}M + vT is an n x n symmetric positive definite matrix, in which M is the mass matrix, T is the discrete Laplace operator, {alpha} and {nu} are positive constants proportional to the inverses of the time-step {Delta}t and the Reynolds number Re respectively, and B is the discrete gradient operator of size n x k (k < n). Even though the matrix A is symmetric and positive definite, the system is indefinite due to the incompressibility constraint (B{sup T}u = 0). This causes difficulties both for iterative methods and commonly used preconditioners. Moreover, depending on the ratio {alpha}/{nu}, A behaves like the mass matrix M at one extreme and the Laplace operator T at the other, thus complicating the issue of preconditioning.
Turinsky, P.J.; Al-Chalabi, R.M.K.; Engrand, P.; Sarsour, H.N.; Faure, F.X.; Guo, W.
1994-06-01
NESTLE is a FORTRAN77 code that solves the few-group neutron diffusion equation utilizing the Nodal Expansion Method (NEM). NESTLE can solve the eigenvalue (criticality); eigenvalue adjoint; external fixed-source steady-state; or external fixed-source. or eigenvalue initiated transient problems. The code name NESTLE originates from the multi-problem solution capability, abbreviating Nodal Eigenvalue, Steady-state, Transient, Le core Evaluator. The eigenvalue problem allows criticality searches to be completed, and the external fixed-source steady-state problem can search to achieve a specified power level. Transient problems model delayed neutrons via precursor groups. Several core properties can be input as time dependent. Two or four energy groups can be utilized, with all energy groups being thermal groups (i.e. upscatter exits) if desired. Core geometries modelled include Cartesian and Hexagonal. Three, two and one dimensional models can be utilized with various symmetries. The non-linear iterative strategy associated with the NEM method is employed. An advantage of the non-linear iterative strategy is that NSTLE can be utilized to solve either the nodal or Finite Difference Method representation of the few-group neutron diffusion equation.
The development of a robust, efficient solver for spectral and spectral-element time discretizations
NASA Astrophysics Data System (ADS)
Mundis, Nathan L.
This work examines alternative time discretizations for the Euler equations and methods for the robust and efficient solution of these discretizations. Specifically, the time-spectral method (TS), quasi-periodic time-spectral method (BDFTS), and spectral-element method in time (SEMT) are derived and examined in detail. For the two time-spectral based methods, focus is given to expanding these methods for more complicated problems than have been typically solved by other authors, including problems with spectral content in a large number of harmonics, gust response problems, and aeroelastic problems. To solve these more complicated problems, it was necessary to implement the flexible variant of the Generalized Minimal Residual method (FGMRES), utilizing the full second-order accurate spatial Jacobian, complete temporal coupling of the chosen time discretization, and fully-implicit coupling of the aeroelastic equations in the cases where they are needed. The FGMRES solver developed utilizes a block-colored Gauss-Seidel (BCGS) preconditioner augmented by a defect-correction process to increase its effectiveness. Exploration of more efficient preconditioners for the FGMRES solver is an anticipated topic for future work in this field. It was a logical extension to apply this already developed FGMRES solver to the spectral-element method in time, which has some advantages over the spectral methods already discussed. Unlike purely-spectral methods, SEMT allows for bothh- and p-refinement. This property could allow for element clustering around areas of sharp gradients and discontinuities, which in turn could make SEMT more efficient than TS for periodic problems that contain these sharp gradients and would require many time instances to produce a precise solution using the TS method. As such, a preliminary investigation of the SEMT method applied to the Euler equations is conducted and some areas for needed improvement in future work are identified. In this work, it is
NASA Technical Reports Server (NTRS)
McCormick, S.; Ruge, John W.
1998-01-01
This work represents a part of a project to develop an atmospheric general circulation model based on the semi-Lagrangian advection of potential vorticity (PC) with divergence as the companion prognostic variable.
Koteras, J.R.
1996-01-01
The prediction of stresses and displacements around tunnels buried deep within the earth is an important class of geomechanics problems. The material behavior immediately surrounding the tunnel is typically nonlinear. The surrounding mass, even if it is nonlinear, can usually be characterized by a simple linear elastic model. The finite element method is best suited for modeling nonlinear materials of limited volume, while the boundary element method is well suited for modeling large volumes of linear elastic material. A computational scheme that couples the finite element and boundary element methods would seem particularly useful for geomechanics problems. A variety of coupling schemes have been proposed, but they rely on direct solution methods. Direct solution techniques have large storage requirements that become cumbersome for large-scale three-dimensional problems. An alternative to direct solution methods is iterative solution techniques. A scheme has been developed for coupling the finite element and boundary element methods that uses an iterative solution method. This report shows that this coupling scheme is valid for problems where nonlinear material behavior occurs in the finite element region.
Implicit Riemann solvers for the Pn equations.
Mehlhorn, Thomas Alan; McClarren, Ryan; Brunner, Thomas A.; Holloway, James Paul
2005-03-01
The spherical harmonics (P{sub n}) approximation to the transport equation for time dependent problems has previously been treated using Riemann solvers and explicit time integration. Here we present an implicit time integration method for the P n equations using Riemann solvers. Both first-order and high-resolution spatial discretization schemes are detailed. One facet of the high-resolution scheme is that a system of nonlinear equations must be solved at each time step. This nonlinearity is the result of slope reconstruction techniques necessary to avoid the introduction of artifical extrema in the numerical solution. Results are presented that show auspicious agreement with analytical solutions using time steps well beyond the CFL limit.
General heuristics algorithms for solving capacitated arc routing problem
NASA Astrophysics Data System (ADS)
Fadzli, Mohammad; Najwa, Nurul; Masran, Hafiz
2015-05-01
In this paper, we try to determine the near-optimum solution for the capacitated arc routing problem (CARP). In general, NP-hard CARP is a special graph theory specifically arises from street services such as residential waste collection and road maintenance. By purpose, the design of the CARP model and its solution techniques is to find optimum (or near-optimum) routing cost for a fleet of vehicles involved in operation. In other words, finding minimum-cost routing is compulsory in order to reduce overall operation cost that related with vehicles. In this article, we provide a combination of various heuristics algorithm to solve a real case of CARP in waste collection and benchmark instances. These heuristics work as a central engine in finding initial solutions or near-optimum in search space without violating the pre-setting constraints. The results clearly show that these heuristics algorithms could provide good initial solutions in both real-life and benchmark instances.
A robust multilevel simultaneous eigenvalue solver
NASA Technical Reports Server (NTRS)
Costiner, Sorin; Taasan, Shlomo
1993-01-01
Multilevel (ML) algorithms for eigenvalue problems are often faced with several types of difficulties such as: the mixing of approximated eigenvectors by the solution process, the approximation of incomplete clusters of eigenvectors, the poor representation of solution on coarse levels, and the existence of close or equal eigenvalues. Algorithms that do not treat appropriately these difficulties usually fail, or their performance degrades when facing them. These issues motivated the development of a robust adaptive ML algorithm which treats these difficulties, for the calculation of a few eigenvectors and their corresponding eigenvalues. The main techniques used in the new algorithm include: the adaptive completion and separation of the relevant clusters on different levels, the simultaneous treatment of solutions within each cluster, and the robustness tests which monitor the algorithm's efficiency and convergence. The eigenvectors' separation efficiency is based on a new ML projection technique generalizing the Rayleigh Ritz projection, combined with a technique, the backrotations. These separation techniques, when combined with an FMG formulation, in many cases lead to algorithms of O(qN) complexity, for q eigenvectors of size N on the finest level. Previously developed ML algorithms are less focused on the mentioned difficulties. Moreover, algorithms which employ fine level separation techniques are of O(q(sub 2)N) complexity and usually do not overcome all these difficulties. Computational examples are presented where Schrodinger type eigenvalue problems in 2-D and 3-D, having equal and closely clustered eigenvalues, are solved with the efficiency of the Poisson multigrid solver. A second order approximation is obtained in O(qN) work, where the total computational work is equivalent to only a few fine level relaxations per eigenvector.
Kim, Hyo-Joong; Furukawa, Yoshihiro; Kakegawa, Takeshi; Bita, Andrei; Scorei, Romulus; Benner, Steven A
2016-12-19
RNA is currently thought to have been the first biopolymer to support Darwinian natural selection on Earth. However, the phosphate esters in RNA and its precursors, and the many sites at which phosphorylation might occur in ribonucleosides under conditions that make it possible, challenge prebiotic chemists. Moreover, free inorganic phosphate may have been scarce on early Earth owing to its sequestration by calcium in the unreactive mineral hydroxyapatite. Herein, it is shown that these problems can be mitigated by a particular geological environment that contains borate, magnesium, sulfate, calcium, and phosphate in evaporite deposits. Actual geological environments, reproduced here, show that Mg(2+) and borate sequester phosphate from calcium to form the mineral lüneburgite. Ribonucleosides stabilized by borate mobilize borate and phosphate from lüneburgite, and are then regiospecifically phosphorylated by the mineral. Thus, in addition to guiding carbohydrate pre-metabolism, borate minerals in evaporite geoorganic contexts offer a solution to the phosphate problem in the "RNA first" model for the origins of life.
Parallel iterative solvers and preconditioners using approximate hierarchical methods
Grama, A.; Kumar, V.; Sameh, A.
1996-12-31
In this paper, we report results of the performance, convergence, and accuracy of a parallel GMRES solver for Boundary Element Methods. The solver uses a hierarchical approximate matrix-vector product based on a hybrid Barnes-Hut / Fast Multipole Method. We study the impact of various accuracy parameters on the convergence and show that with minimal loss in accuracy, our solver yields significant speedups. We demonstrate the excellent parallel efficiency and scalability of our solver. The combined speedups from approximation and parallelism represent an improvement of several orders in solution time. We also develop fast and paralellizable preconditioners for this problem. We report on the performance of an inner-outer scheme and a preconditioner based on truncated Green`s function. Experimental results on a 256 processor Cray T3D are presented.
1984-04-01
sd*l it (S.AX) 31 Stfm d fe VOO 2em. Twied7y. Os Md tdliM WaaIn~psla. (X y)m - 22 Y isWI .3. to solve the qpa fy-disctized two- and three-dimensional...to compute F,(JP) an each tera- tio. For larg problems, the evaluation of the Jacobian May be very ezpensiv, and, 2 A fe .. I i f4d. -eadm l 008m p et...301" Of*r 6 Set pe -,f&g voM 1-0 STW 1 UNTI couverpunce DO Solveft -Ape. dk4 - ( Fe -Ie141 l p -0 f5 14p EmD FOR 11pm 3.1.h The Pteomuditiomed Coujuget
ALPS - A LINEAR PROGRAM SOLVER
NASA Technical Reports Server (NTRS)
Viterna, L. A.
1994-01-01
Linear programming is a widely-used engineering and management tool. Scheduling, resource allocation, and production planning are all well-known applications of linear programs (LP's). Most LP's are too large to be solved by hand, so over the decades many computer codes for solving LP's have been developed. ALPS, A Linear Program Solver, is a full-featured LP analysis program. ALPS can solve plain linear programs as well as more complicated mixed integer and pure integer programs. ALPS also contains an efficient solution technique for pure binary (0-1 integer) programs. One of the many weaknesses of LP solvers is the lack of interaction with the user. ALPS is a menu-driven program with no special commands or keywords to learn. In addition, ALPS contains a full-screen editor to enter and maintain the LP formulation. These formulations can be written to and read from plain ASCII files for portability. For those less experienced in LP formulation, ALPS contains a problem "parser" which checks the formulation for errors. ALPS creates fully formatted, readable reports that can be sent to a printer or output file. ALPS is written entirely in IBM's APL2/PC product, Version 1.01. The APL2 workspace containing all the ALPS code can be run on any APL2/PC system (AT or 386). On a 32-bit system, this configuration can take advantage of all extended memory. The user can also examine and modify the ALPS code. The APL2 workspace has also been "packed" to be run on any DOS system (without APL2) as a stand-alone "EXE" file, but has limited memory capacity on a 640K system. A numeric coprocessor (80X87) is optional but recommended. The standard distribution medium for ALPS is a 5.25 inch 360K MS-DOS format diskette. IBM, IBM PC and IBM APL2 are registered trademarks of International Business Machines Corporation. MS-DOS is a registered trademark of Microsoft Corporation.
A simplified analysis of the multigrid V-cycle as a fast elliptic solver
NASA Technical Reports Server (NTRS)
Decker, Naomi H.; Taasan, Shlomo
1988-01-01
For special model problems, Fourier analysis gives exact convergence rates for the two-grid multigrid cycle and, for more general problems, provides estimates of the two-grid convergence rates via local mode analysis. A method is presented for obtaining mutigrid convergence rate estimates for cycles involving more than two grids (using essentially the same analysis as for the two-grid cycle). For the simple cast of the V-cycle used as a fast Laplace solver on the unit square, the k-grid convergence rate bounds obtained by this method are sharper than the bounds predicted by the variational theory. Both theoretical justification and experimental evidence are presented.
A basic theorem of complementarity for the generalized variational-like inequality problem
Yao, Jen-Chih.
1989-11-01
In this report, a basic theorem of complementarity is established for the generalized variational-like inequality problem introduced by Parida and Sen. Some existence results for both generalized variational inequality and complementarity problems are established by employing this basic theorem of complementarity. In particular, some sets of conditions that are normally satisfied by a nonsolvable generalized complementarity problem are investigated. 16 refs.
A GPU-enabled Finite Volume solver for global magnetospheric simulations on unstructured grids
NASA Astrophysics Data System (ADS)
Lani, Andrea; Yalim, Mehmet Sarp; Poedts, Stefaan
2014-10-01
This paper describes an ideal Magnetohydrodynamics (MHD) solver for global magnetospheric simulations based on a B1 +B0 splitting approach, which has been implemented within the COOLFluiD platform and adapted to run on modern heterogeneous architectures featuring General Purpose Graphical Processing Units (GPGPUs). The code is based on a state-of-the-art Finite Volume discretization for unstructured grids and either explicit or implicit time integration, suitable for both steady and time accurate problems. Innovative object-oriented design and coding techniques mixing C++ and CUDA are discussed. Performance results of the modified code on single and multiple processors are presented and compared with those provided by the original solver.
AN ADAPTIVE PARTICLE-MESH GRAVITY SOLVER FOR ENZO
Passy, Jean-Claude; Bryan, Greg L.
2014-11-01
We describe and implement an adaptive particle-mesh algorithm to solve the Poisson equation for grid-based hydrodynamics codes with nested grids. The algorithm is implemented and extensively tested within the astrophysical code Enzo against the multigrid solver available by default. We find that while both algorithms show similar accuracy for smooth mass distributions, the adaptive particle-mesh algorithm is more accurate for the case of point masses, and is generally less noisy. We also demonstrate that the two-body problem can be solved accurately in a configuration with nested grids. In addition, we discuss the effect of subcycling, and demonstrate that evolving all the levels with the same timestep yields even greater precision.
Towards general information theoretical representations of database problems
Joslyn, C.
1997-06-01
General database systems are described from the General Systems Theoretical (GST) framework. In this context traditional information theoretical (statistical) and general information theoretical (fuzzy measure and set theoretical, possibilistic, and random set theoretical) representations are derived. A preliminary formal framework is introduced.
A Generalized Orienteering Problem for Optimal Search and Interdiction Planning
2013-09-01
exploit this resource trade-o through a specialized branch -and- bound algorithm that relies on partial path relaxation problems , which often yield tight...computing inexpensive upper bounds based on a binary knapsack problem . This is possible because the arc lengths and rewards are xed values...algorithm that relies on partial path relaxation problems , which often yield tight bounds and lead to substantial pruning in the enumeration tree. We
A multigrid solver for the semiconductor equations
NASA Technical Reports Server (NTRS)
Bachmann, Bernhard
1993-01-01
We present a multigrid solver for the exponential fitting method. The solver is applied to the current continuity equations of semiconductor device simulation in two dimensions. The exponential fitting method is based on a mixed finite element discretization using the lowest-order Raviart-Thomas triangular element. This discretization method yields a good approximation of front layers and guarantees current conservation. The corresponding stiffness matrix is an M-matrix. 'Standard' multigrid solvers, however, cannot be applied to the resulting system, as this is dominated by an unsymmetric part, which is due to the presence of strong convection in part of the domain. To overcome this difficulty, we explore the connection between Raviart-Thomas mixed methods and the nonconforming Crouzeix-Raviart finite element discretization. In this way we can construct nonstandard prolongation and restriction operators using easily computable weighted L(exp 2)-projections based on suitable quadrature rules and the upwind effects of the discretization. The resulting multigrid algorithm shows very good results, even for real-world problems and for locally refined grids.
Quantitative analysis of numerical solvers for oscillatory biomolecular system models
Quo, Chang F; Wang, May D
2008-01-01
Background This article provides guidelines for selecting optimal numerical solvers for biomolecular system models. Because various parameters of the same system could have drastically different ranges from 10-15 to 1010, the ODEs can be stiff and ill-conditioned, resulting in non-unique, non-existing, or non-reproducible modeling solutions. Previous studies have not examined in depth how to best select numerical solvers for biomolecular system models, which makes it difficult to experimentally validate the modeling results. To address this problem, we have chosen one of the well-known stiff initial value problems with limit cycle behavior as a test-bed system model. Solving this model, we have illustrated that different answers may result from different numerical solvers. We use MATLAB numerical solvers because they are optimized and widely used by the modeling community. We have also conducted a systematic study of numerical solver performances by using qualitative and quantitative measures such as convergence, accuracy, and computational cost (i.e. in terms of function evaluation, partial derivative, LU decomposition, and "take-off" points). The results show that the modeling solutions can be drastically different using different numerical solvers. Thus, it is important to intelligently select numerical solvers when solving biomolecular system models. Results The classic Belousov-Zhabotinskii (BZ) reaction is described by the Oregonator model and is used as a case study. We report two guidelines in selecting optimal numerical solver(s) for stiff, complex oscillatory systems: (i) for problems with unknown parameters, ode45 is the optimal choice regardless of the relative error tolerance; (ii) for known stiff problems, both ode113 and ode15s are good choices under strict relative tolerance conditions. Conclusions For any given biomolecular model, by building a library of numerical solvers with quantitative performance assessment metric, we show that it is possible
Possible solution of strong CP problem in generalized unimodular gravity
Frampton, P.H.; Ng, Y.J.; Van Dam, H. )
1992-11-01
It was recently pointed out how constrained gravitational dynamics offers a possible solution of the cosmological constant problem at the quantum level. Here we point out that the same theory may be used to solve the strong CP problem without recourse to wormholes or to the introduction of any new particle.
Using Data Analysis Problems in a Large General Microbiology Course.
ERIC Educational Resources Information Center
Deutch, Charles E.
1997-01-01
Argues that data analysis problems can be used successfully in large introductory microbiology courses, even when exams consist entirely of multiple-choice questions and out-of-class contact with the instructor is limited. Discusses course organization, problem structure, student performance and response, advantages of using data analysis…
Overset Techniques for Hypersonic Multibody Configurations with the DPLR Solver
NASA Technical Reports Server (NTRS)
Hyatt, Andrew James; Prabhu, Dinesh K.; Boger, David A.
2010-01-01
Three unit problems in shock-shock/shock-boundary layer interactions are considered in the evaluation overset techniques with the Data Parallel Line Relaxation (DPLR) computational fluid dynamics solver, a three dimensional Navier-Stokes solver . The unit problems considered are those of two stacked hemispherical cylinders (of different diameters and lengths, and at various orientations relative to each other or relative to the nozzle axis) tested in a hypersonic wind tunnel. These problems are taken as representative of a Two-Stage-To-Orbit design. The objective of the present presentation would be to discuss the techniques used to develop suitable overset grid systems and then evaluate their respective solutions by comparing to corresponding point matched grid solutions and experimental data. Both successful and unsuccessful techniques would be discussed. All solutions would be calculated using the DPLR solver and SUGGAR will be used to develop the domain connectivity information.
Problems with Single Interest Scales: Implications of the General Factor
ERIC Educational Resources Information Center
Tracey, Terence J. G.
2012-01-01
The presence of the general factor in interest and self-efficacy assessment and its meaning are reviewed. The general factor is found in all interest and self-efficacy assessment and has been viewed as (a) a nuisance factor with little effect on assessment, (b) a variable having substantive meaning and thus worthy of including in interpretation,…
NASA Technical Reports Server (NTRS)
Eidson, T. M.; Erlebacher, G.
1994-01-01
While parallel computers offer significant computational performance, it is generally necessary to evaluate several programming strategies. Two programming strategies for a fairly common problem - a periodic tridiagonal solver - are developed and evaluated. Simple model calculations as well as timing results are presented to evaluate the various strategies. The particular tridiagonal solver evaluated is used in many computational fluid dynamic simulation codes. The feature that makes this algorithm unique is that these simulation codes usually require simultaneous solutions for multiple right-hand-sides (RHS) of the system of equations. Each RHS solutions is independent and thus can be computed in parallel. Thus a Gaussian elimination type algorithm can be used in a parallel computation and the more complicated approaches such as cyclic reduction are not required. The two strategies are a transpose strategy and a distributed solver strategy. For the transpose strategy, the data is moved so that a subset of all the RHS problems is solved on each of the several processors. This usually requires significant data movement between processor memories across a network. The second strategy attempts to have the algorithm allow the data across processor boundaries in a chained manner. This usually requires significantly less data movement. An approach to accomplish this second strategy in a near-perfect load-balanced manner is developed. In addition, an algorithm will be shown to directly transform a sequential Gaussian elimination type algorithm into the parallel chained, load-balanced algorithm.
Simulating underwater propulsion using an immersed boundary method based open-source solver
NASA Astrophysics Data System (ADS)
Senturk, Utku; Hemmati, Arman; Smits, Alexander J.
2016-11-01
The performance of a newly developed Immersed Boundary Method (IBM) incorporated into a finite volume solver is examined using foam-extend-3.2. IBM uses a discrete forcing approach based on the weighted least squares interpolation to preserve the sharpness of the boundary, which decreases the computational complexity of the problem. Initially, four case studies with gradually increasing complexities are considered to verify the accuracy of the IBM approach. These include the flow past 2D stationary and transversely oscillating cylinders and 3D wake of stationary and pitching flat plates with aspect ratio 1.0 at Re=2000. The primary objective of this study, which is pursued by an ongoing simulation of the wake formed behind a pitching deformable 3D flat plate, is to investigate the underwater locomotion of a fish at Re=10000. The results of the IBM based solver are compared to the experimental results, which suggest that the force computations are accurate in general. Spurious oscillations in the forces are observed for problems with moving bodies which change based on spatial and temporal grid resolutions. Although it still has the full advantage of the main code features, the IBM-based solver in foam-extend-3.2 requires further development to be exploited for complex grids. The work was supported by ONR under MURI Grant N00014-14-1-0533.
Cultivating Creative Problem Solvers: The PBL Style
ERIC Educational Resources Information Center
Hung, Woei
2015-01-01
After decades of research, we now know that creativity is a multidimensional construct that involves variables from the domains of personality, environment, and cognition. A construct with such level of complexity, as we know from past research, cannot be effectively learned through traditional lecture-based instruction. Rather, the formation of…
Needed: A New Generation of Problem Solvers
ERIC Educational Resources Information Center
McArthur, John W.; Sachs, Jeffrey
2009-01-01
Amid the global economic crisis dominating policy makers' recent attention, the world faces many other equal if not greater long-term challenges that will require concerted and highly skilled policy efforts in coming years. Those interwoven challenges include the mitigation of climate change, the control of emerging diseases, the reduction of…
Linear iterative solvers for implicit ODE methods
NASA Technical Reports Server (NTRS)
Saylor, Paul E.; Skeel, Robert D.
1990-01-01
The numerical solution of stiff initial value problems, which lead to the problem of solving large systems of mildly nonlinear equations are considered. For many problems derived from engineering and science, a solution is possible only with methods derived from iterative linear equation solvers. A common approach to solving the nonlinear equations is to employ an approximate solution obtained from an explicit method. The error is examined to determine how it is distributed among the stiff and non-stiff components, which bears on the choice of an iterative method. The conclusion is that error is (roughly) uniformly distributed, a fact that suggests the Chebyshev method (and the accompanying Manteuffel adaptive parameter algorithm). This method is described, also commenting on Richardson's method and its advantages for large problems. Richardson's method and the Chebyshev method with the Mantueffel algorithm are applied to the solution of the nonlinear equations by Newton's method.
Boundary conditions and generalized functions in a transition radiation problem
NASA Astrophysics Data System (ADS)
Villavicencio, M.; Jiménez, J. L.
2017-03-01
The aim of this work is to show how all the components of the electromagnetic field involved in the transition radiation problem can be obtained using distribution functions. The handling of the products and derivatives of distributions appearing in the differential equations governing transition radiation, allows to obtain the necessary boundary conditions, additional to those implied by Maxwell's equations, in order to exactly determine the longitudinal components of the electromagnetic field. It is shown that this method is not only useful but it is really convenient to achieve a full analysis of the problem.
Brittle Solvers: Lessons and insights into effective solvers for visco-plasticity in geodynamics
NASA Astrophysics Data System (ADS)
Spiegelman, M. W.; May, D.; Wilson, C. R.
2014-12-01
Plasticity/Fracture and rock failure are essential ingredients in geodynamic models as terrestrial rocks do not possess an infinite yield strength. Numerous physical mechanisms have been proposed to limit the strength of rocks, including low temperature plasticity and brittle fracture. While ductile and creep behavior of rocks at depth is largely accepted, the constitutive relations associated with brittle failure, or shear localisation, are more controversial. Nevertheless, there are really only a few macroscopic constitutive laws for visco-plasticity that are regularly used in geodynamics models. Independent of derivation, all of these can be cast as simple effective viscosities which act as stress limiters with different choices for yield surfaces; the most common being a von Mises (constant yield stress) or Drucker-Prager (pressure dependent yield-stress) criterion. The choice of plasticity model, however, can have significant consequences for the degree of non-linearity in a problem and the choice and efficiency of non-linear solvers. Here we describe a series of simplified 2 and 3-D model problems to elucidate several issues associated with obtaining accurate description and solution of visco-plastic problems. We demonstrate that1) Picard/Successive substitution schemes for solution of the non-linear problems can often stall at large values of the non-linear residual, thus producing spurious solutions2) Combined Picard/Newton schemes can be effective for a range of plasticity models, however, they can produce serious convergence problems for strongly pressure dependent plasticity models such as Drucker-Prager.3) Nevertheless, full Drucker-Prager may not be the plasticity model of choice for strong materials as the dynamic pressures produced in these layers can develop pathological behavior with Drucker-Prager, leading to stress strengthening rather than stress weakening behavior.4) In general, for any incompressible Stoke's problem, it is highly advisable to
Complexity of the Generalized Mover’s Problem.
1985-01-01
problem by workers in the robotics fields and in artificial intellegence , (for example [Nilson, 69], [Paul, 72], (Udupa, 77], [Widdoes, 74], [Lozano-Perez...Nilsson, "A mobile automation: An application of artificial intelligence techniques," Proceedings TJCAI-69, 509-520, 1969. . -7-- -17- C. O’Dunlaing, M
Awareness during general anesthesia: new technology for an old problem.
Halliburton, J R
1998-05-01
The possibility of awareness during general anesthesia causes apprehension for the patient and the Certified Registered Nurse Anesthetist (CRNA). The goals of general anesthesia are to prevent the sensation of pain and produce a state of sedation, hypnosis, and unconsciousness so the patient will not remember the surgical procedure. An inadequate level of anesthesia can result in patient awareness during surgery. The current practice of anesthesia relies on indirect hemodynamic measurements such as blood pressure and heart rate to monitor the sedative hypnotic state of the patient's brain during general anesthesia. Hemodynamic responses are not reliable for predicting awareness just as blood pressure and heart rate are not indicative of consciousness. Electroencephalogram (EEG) waveforms are known to be affected by anesthetics. Characteristic EEG waveforms are a direct indication of the patient's level of consciousness. Unprocessed and computer-processed EEG recordings have been used in an attempt to monitor the patient's level of consciousness during general anesthesia. A raw or unprocessed EEG recording to monitor the level of consciousness during general anesthesia is problematic. The EEG signal is complex, affected by artifact, and it requires a dedicated interpreter. Conventional processed EEG monitoring systems are problematic because of the complexity of the equipment and technical difficulty of reading the EEG recording. The purpose of this article is to describe the history of awareness during anesthesia and introduce a new processed EEG monitor, the Bispectral Index (BIS) (Aspect Medical Systems, Inc., Natick, MA) with implications for future clinical use and research.
General aviation aircraft interior noise problem: Some suggested solutions
NASA Technical Reports Server (NTRS)
Roskam, J.; Navaneethan, R.
1984-01-01
Laboratory investigation of sound transmission through panels and the use of modern data analysis techniques applied to actual aircraft is used to determine methods to reduce general aviation interior noise. The experimental noise reduction characteristics of stiffened flat and curved panels with damping treatment are discussed. The experimental results of double-wall panels used in the general aviation industry are given. The effects of skin panel material, fiberglass insulation and trim panel material on the noise reduction characteristics of double-wall panels are investigated. With few modifications, the classical sound transmission theory can be used to design the interior noise control treatment of aircraft. Acoustic intensity and analysis procedures are included.
The novel high-performance 3-D MT inverse solver
NASA Astrophysics Data System (ADS)
Kruglyakov, Mikhail; Geraskin, Alexey; Kuvshinov, Alexey
2016-04-01
We present novel, robust, scalable, and fast 3-D magnetotelluric (MT) inverse solver. The solver is written in multi-language paradigm to make it as efficient, readable and maintainable as possible. Separation of concerns and single responsibility concepts go through implementation of the solver. As a forward modelling engine a modern scalable solver extrEMe, based on contracting integral equation approach, is used. Iterative gradient-type (quasi-Newton) optimization scheme is invoked to search for (regularized) inverse problem solution, and adjoint source approach is used to calculate efficiently the gradient of the misfit. The inverse solver is able to deal with highly detailed and contrasting models, allows for working (separately or jointly) with any type of MT responses, and supports massive parallelization. Moreover, different parallelization strategies implemented in the code allow optimal usage of available computational resources for a given problem statement. To parameterize an inverse domain the so-called mask parameterization is implemented, which means that one can merge any subset of forward modelling cells in order to account for (usually) irregular distribution of observation sites. We report results of 3-D numerical experiments aimed at analysing the robustness, performance and scalability of the code. In particular, our computational experiments carried out at different platforms ranging from modern laptops to HPC Piz Daint (6th supercomputer in the world) demonstrate practically linear scalability of the code up to thousands of nodes.
Generalized Householder transformations for the complex symmetric eigenvalue problem
NASA Astrophysics Data System (ADS)
Noble, J. H.; Lubasch, M.; Jentschura, U. D.
2013-08-01
We present an intuitive and scalable algorithm for the diagonalization of complex symmetric matrices, which arise from the projection of pseudo-Hermitian and complex scaled Hamiltonians onto a suitable basis set of "trial" states. The algorithm diagonalizes complex and symmetric (non-Hermitian) matrices and is easily implemented in modern computer languages. It is based on generalized Householder transformations and relies on iterative similarity transformations T → T' = Q T T Q, where Q is a complex and orthogonal, but not unitary, matrix, i.e. Q T = Q -1 but Q + ≠ Q -1. We present numerical reference data to support the scalability of the algorithm. We construct the generalized Householder transformations from the notion that the conserved scalar product of eigenstates Ψ n and Ψ m of a pseudo-Hermitian quantum mechanical Hamiltonian can be reformulated in terms of the generalized indefinite inner product ∫ d x Ψ n ( x, t) Ψ m ( x, t), where the integrand is locally defined, and complex conjugation is avoided. A few example calculations are described which illustrate the physical origin of the ideas used in the construction of the algorithm.
Optimising a parallel conjugate gradient solver
Field, M.R.
1996-12-31
This work arises from the introduction of a parallel iterative solver to a large structural analysis finite element code. The code is called FEX and it was developed at Hitachi`s Mechanical Engineering Laboratory. The FEX package can deal with a large range of structural analysis problems using a large number of finite element techniques. FEX can solve either stress or thermal analysis problems of a range of different types from plane stress to a full three-dimensional model. These problems can consist of a number of different materials which can be modelled by a range of material models. The structure being modelled can have the load applied at either a point or a surface, or by a pressure, a centrifugal force or just gravity. Alternatively a thermal load can be applied with a given initial temperature. The displacement of the structure can be constrained by having a fixed boundary or by prescribing the displacement at a boundary.
ERIC Educational Resources Information Center
Cook, Ellen Piel; And Others
1984-01-01
Surveyed perceptions of personal problems, appropriate help sources, and general attitudes about counseling in college students (N=738). Results indicated areas of concern, conservative preferences for intervention, generally favorable attitudes about counseling, and some sex differences. (Author/LLL)
Multilevel solvers of first-order system least-squares for Stokes equations
Lai, Chen-Yao G.
1996-12-31
Recently, The use of first-order system least squares principle for the approximate solution of Stokes problems has been extensively studied by Cai, Manteuffel, and McCormick. In this paper, we study multilevel solvers of first-order system least-squares method for the generalized Stokes equations based on the velocity-vorticity-pressure formulation in three dimensions. The least-squares functionals is defined to be the sum of the L{sup 2}-norms of the residuals, which is weighted appropriately by the Reynolds number. We develop convergence analysis for additive and multiplicative multilevel methods applied to the resulting discrete equations.
Matrix general relativity: a new look at old problems
NASA Astrophysics Data System (ADS)
Avramidi, Ivan G.
2004-01-01
We develop a novel approach to gravity that we call 'matrix general relativity' (MGR) or 'gravitational chromodynamics' (GCD or GQCD for the quantum version). Gravity is described in this approach not by one Riemannian metric (i.e. a symmetric two-tensor field) but by a multiplet of such fields, or by a matrix-valued symmetric two-tensor field that satisfies certain conditions. We define the matrix extensions of standard constructions of differential geometry including connections and curvatures, and finally, an invariant functional of the new field that reduces to the standard Einstein action functional in the commutative (diagonal) case. Our main idea is the analogy with Yang Mills theory (QCD and the standard model). We call the new degrees of freedom of gravity associated with the matrix structure 'gravitational colour' or simply 'gravicolour' and introduce a new gauge symmetry associated with this degree of freedom. As in the standard model there are two possibilities. First of all, it is possible that at high energies (say at the Planckian scale) this symmetry is exact (symmetric phase), but at low energies it is badly broken, so that one tensor field remains massless (and gives general relativity) and the other ones become massive with masses of Planckian scale. The second possibility is that the additional degrees of freedom of the gravitational field are confined to the Planckian scale. What one sees at large distances are singlets (invariants) of the new gauge symmetry.
A Radiation Transfer Solver for Athena Using Short Characteristics
NASA Astrophysics Data System (ADS)
Davis, Shane W.; Stone, James M.; Jiang, Yan-Fei
2012-03-01
We describe the implementation of a module for the Athena magnetohydrodynamics (MHD) code that solves the time-independent, multi-frequency radiative transfer (RT) equation on multidimensional Cartesian simulation domains, including scattering and non-local thermodynamic equilibrium (LTE) effects. The module is based on well known and well tested algorithms developed for modeling stellar atmospheres, including the method of short characteristics to solve the RT equation, accelerated Lambda iteration to handle scattering and non-LTE effects, and parallelization via domain decomposition. The module serves several purposes: it can be used to generate spectra and images, to compute a variable Eddington tensor (VET) for full radiation MHD simulations, and to calculate the heating and cooling source terms in the MHD equations in flows where radiation pressure is small compared with gas pressure. For the latter case, the module is combined with the standard MHD integrators using operator splitting: we describe this approach in detail, including a new constraint on the time step for stability due to radiation diffusion modes. Implementation of the VET method for radiation pressure dominated flows is described in a companion paper. We present results from a suite of test problems for both the RT solver itself and for dynamical problems that include radiative heating and cooling. These tests demonstrate that the radiative transfer solution is accurate and confirm that the operator split method is stable, convergent, and efficient for problems of interest. We demonstrate there is no need to adopt ad hoc assumptions of questionable accuracy to solve RT problems in concert with MHD: the computational cost for our general-purpose module for simple (e.g., LTE gray) problems can be comparable to or less than a single time step of Athena's MHD integrators, and only few times more expensive than that for more general (non-LTE) problems.
A RADIATION TRANSFER SOLVER FOR ATHENA USING SHORT CHARACTERISTICS
Davis, Shane W.; Stone, James M.; Jiang Yanfei
2012-03-01
We describe the implementation of a module for the Athena magnetohydrodynamics (MHD) code that solves the time-independent, multi-frequency radiative transfer (RT) equation on multidimensional Cartesian simulation domains, including scattering and non-local thermodynamic equilibrium (LTE) effects. The module is based on well known and well tested algorithms developed for modeling stellar atmospheres, including the method of short characteristics to solve the RT equation, accelerated Lambda iteration to handle scattering and non-LTE effects, and parallelization via domain decomposition. The module serves several purposes: it can be used to generate spectra and images, to compute a variable Eddington tensor (VET) for full radiation MHD simulations, and to calculate the heating and cooling source terms in the MHD equations in flows where radiation pressure is small compared with gas pressure. For the latter case, the module is combined with the standard MHD integrators using operator splitting: we describe this approach in detail, including a new constraint on the time step for stability due to radiation diffusion modes. Implementation of the VET method for radiation pressure dominated flows is described in a companion paper. We present results from a suite of test problems for both the RT solver itself and for dynamical problems that include radiative heating and cooling. These tests demonstrate that the radiative transfer solution is accurate and confirm that the operator split method is stable, convergent, and efficient for problems of interest. We demonstrate there is no need to adopt ad hoc assumptions of questionable accuracy to solve RT problems in concert with MHD: the computational cost for our general-purpose module for simple (e.g., LTE gray) problems can be comparable to or less than a single time step of Athena's MHD integrators, and only few times more expensive than that for more general (non-LTE) problems.
NASA Technical Reports Server (NTRS)
Hersey, Mayo D
1923-01-01
This report is intended as a technical introduction to the series of reports on aeronautic instruments. It presents a discussion of those subjects which are common to all instruments. First, a general classification is given, embracing all types of instruments used in aeronautics. Finally, a classification is given of the various problems confronted by the instrument expert and investigator. In this way the following groups of problems are brought up for consideration: problems of mechanical design, human factor, manufacturing problems, supply and selection of instruments, problems concerning the technique of testing, problems of installation, problems concerning the use of instruments, problems of maintenance, and physical research problems. This enumeration of problems which are common to instruments in general serves to indicate the different points of view which should be kept in mind in approaching the study of any particular instrument.
Robust and Efficient Riemann Solvers for MHD
NASA Astrophysics Data System (ADS)
Miyoshi, T.; Kusano, K.
2008-04-01
Robust and efficient approximate Riemann solvers for magnetohydrodynamics (MHD) are constructed. Particularly, a family of positively conservative Harten-Lax-van Leer (HLL)-type Riemann solvers, the so-called HLLD (`D' denotes Discontinuities), HLLR (`R' denotes Rotational), HLLC (`C' denotes Contact), and HLL solvers, is systematically considered.
Time-varying Riemann solvers for conservation laws on networks
NASA Astrophysics Data System (ADS)
Garavello, Mauro; Piccoli, Benedetto
We consider a conservation law on a network and generic Riemann solvers at nodes depending on parameters, which can be seen as control functions. Assuming that the parameters have bounded variation as functions of time, we prove existence of solutions to Cauchy problems on the whole network.
Numerical System Solver Developed for the National Cycle Program
NASA Technical Reports Server (NTRS)
Binder, Michael P.
1999-01-01
As part of the National Cycle Program (NCP), a powerful new numerical solver has been developed to support the simulation of aeropropulsion systems. This software uses a hierarchical object-oriented design. It can provide steady-state and time-dependent solutions to nonlinear and even discontinuous problems typically encountered when aircraft and spacecraft propulsion systems are simulated. It also can handle constrained solutions, in which one or more factors may limit the behavior of the engine system. Timedependent simulation capabilities include adaptive time-stepping and synchronization with digital control elements. The NCP solver is playing an important role in making the NCP a flexible, powerful, and reliable simulation package.
A robust HLLC-type Riemann solver for strong shock
NASA Astrophysics Data System (ADS)
Shen, Zhijun; Yan, Wei; Yuan, Guangwei
2016-03-01
It is well known that for the Eulerian equations the numerical schemes that can accurately capture contact discontinuity usually suffer from some disastrous carbuncle phenomenon, while some more dissipative schemes, such as the HLL scheme, are free from this kind of shock instability. Hybrid schemes to combine a dissipative flux with a less dissipative flux can cure the shock instability, but also may lead to other problems, such as certain arbitrariness of choosing switching parameters or contact interface becoming smeared. In order to overcome these drawbacks, this paper proposes a simple and robust HLLC-type Riemann solver for inviscid, compressible gas flows, which is capable of preserving sharp contact surface and is free from instability. The main work is to construct a HLL-type Riemann solver and a HLLC-type Riemann solver by modifying the shear viscosity of the original HLL and HLLC methods. Both of the two new schemes are positively conservative under some typical wavespeed estimations. Moreover, a linear matrix stability analysis for the proposed schemes is accomplished, which illustrates the HLLC-type solver with shear viscosity is stable whereas the HLL-type solver with vorticity wave is unstable. Our arguments and numerical experiments demonstrate that the inadequate dissipation associated to the shear wave may be a unique reason to cause the instability.
ERIC Educational Resources Information Center
Ekici, Didem Inel
2016-01-01
This study aimed to determine Turkish junior high-school students' perceptions of the general problem-solving process. The Turkish junior high-school students' perceptions of the general problem-solving process were examined in relation to their gender, grade level, age and their grade point with regards to the science course identified in the…
Subspace differential coexpression analysis: problem definition and a general approach.
Fang, Gang; Kuang, Rui; Pandey, Gaurav; Steinbach, Michael; Myers, Chad L; Kumar, Vipin
2010-01-01
In this paper, we study methods to identify differential coexpression patterns in case-control gene expression data. A differential coexpression pattern consists of a set of genes that have substantially different levels of coherence of their expression profiles across the two sample-classes, i.e., highly coherent in one class, but not in the other. Biologically, a differential coexpression patterns may indicate the disruption of a regulatory mechanism possibly caused by disregulation of pathways or mutations of transcription factors. A common feature of all the existing approaches for differential coexpression analysis is that the coexpression of a set of genes is measured on all the samples in each of the two classes, i.e., over the full-space of samples. Hence, these approaches may miss patterns that only cover a subset of samples in each class, i.e., subspace patterns, due to the heterogeneity of the subject population and disease causes. In this paper, we extend differential coexpression analysis by defining a subspace differential coexpression pattern, i.e., a set of genes that are coexpressed in a relatively large percent of samples in one class, but in a much smaller percent of samples in the other class. We propose a general approach based upon association analysis framework that allows exhaustive yet efficient discovery of subspace differential coexpression patterns. This approach can be used to adapt a family of biclustering algorithms to obtain their corresponding differential versions that can directly discover differential coexpression patterns. Using a recently developed biclustering algorithm as illustration, we perform experiments on cancer datasets which demonstrates the existence of subspace differential coexpression patterns. Permutation tests demonstrate the statistical significance for a large number of discovered subspace patterns, many of which can not be discovered if they are measured over all the samples in each of the classes
Coordinate Projection-based Solver for ODE with Invariants
Serban, Radu
2008-04-08
CPODES is a general purpose (serial and parallel) solver for systems of ordinary differential equation (ODE) with invariants. It implements a coordinate projection approach using different types of projection (orthogonal or oblique) and one of several methods for the decompositon of the Jacobian of the invariant equations.
Performance Models for the Spike Banded Linear System Solver
Manguoglu, Murat; Saied, Faisal; Sameh, Ahmed; ...
2011-01-01
With availability of large-scale parallel platforms comprised of tens-of-thousands of processors and beyond, there is significant impetus for the development of scalable parallel sparse linear system solvers and preconditioners. An integral part of this design process is the development of performance models capable of predicting performance and providing accurate cost models for the solvers and preconditioners. There has been some work in the past on characterizing performance of the iterative solvers themselves. In this paper, we investigate the problem of characterizing performance and scalability of banded preconditioners. Recent work has demonstrated the superior convergence properties and robustness of banded preconditioners,more » compared to state-of-the-art ILU family of preconditioners as well as algebraic multigrid preconditioners. Furthermore, when used in conjunction with efficient banded solvers, banded preconditioners are capable of significantly faster time-to-solution. Our banded solver, the Truncated Spike algorithm is specifically designed for parallel performance and tolerance to deep memory hierarchies. Its regular structure is also highly amenable to accurate performance characterization. Using these characteristics, we derive the following results in this paper: (i) we develop parallel formulations of the Truncated Spike solver, (ii) we develop a highly accurate pseudo-analytical parallel performance model for our solver, (iii) we show excellent predication capabilities of our model – based on which we argue the high scalability of our solver. Our pseudo-analytical performance model is based on analytical performance characterization of each phase of our solver. These analytical models are then parameterized using actual runtime information on target platforms. An important consequence of our performance models is that they reveal underlying performance bottlenecks in both serial and parallel formulations. All of our results are validated
ERIC Educational Resources Information Center
Limon, Margarita
2006-01-01
Research on epistemological beliefs has clearly increased in the last decade. Even though the construct is clearer and relevant data are being collected, there are important theoretical and methodological issues that need further clarification. One of them is the debate about the domain generality-specificity of epistemological beliefs. I argue…
A Look at the Generalized Heron Problem through the Lens of Majorization-Minimization
Chi, Eric C.; Lange, Kenneth
2013-01-01
In a recent issue of this journal, Mordukhovich, Nam, and Salinas pose and solve an interesting non-differentiable generalization of the Heron problem in the framework of modern convex analysis. In the generalized Heron problem, one is given k + 1 closed convex sets in ℝd equipped with its Euclidean norm and asked to find the point in the last set such that the sum of the distances to the first k sets is minimal. In later work, the authors generalize the Heron problem even further, relax its convexity assumptions, study its theoretical properties, and pursue subgradient algorithms for solving the convex case. Here, we revisit the original problem solely from the numerical perspective. By exploiting the majorization-minimization (MM) principle of computational statistics and rudimentary techniques from differential calculus, we are able to construct a very fast algorithm for solving the Euclidean version of the generalized Heron problem. PMID:25242816
High-performance equation solvers and their impact on finite element analysis
NASA Technical Reports Server (NTRS)
Poole, Eugene L.; Knight, Norman F., Jr.; Davis, D. Dale, Jr.
1990-01-01
The role of equation solvers in modern structural analysis software is described. Direct and iterative equation solvers which exploit vectorization on modern high-performance computer systems are described and compared. The direct solvers are two Cholesky factorization methods. The first method utilizes a novel variable-band data storage format to achieve very high computation rates and the second method uses a sparse data storage format designed to reduce the number of operations. The iterative solvers are preconditioned conjugate gradient methods. Two different preconditioners are included; the first uses a diagonal matrix storage scheme to achieve high computation rates and the second requires a sparse data storage scheme and converges to the solution in fewer iterations that the first. The impact of using all of the equation solvers in a common structural analysis software system is demonstrated by solving several representative structural analysis problems.
Robust large-scale parallel nonlinear solvers for simulations.
Bader, Brett William; Pawlowski, Roger Patrick; Kolda, Tamara Gibson
2005-11-01
This report documents research to develop robust and efficient solution techniques for solving large-scale systems of nonlinear equations. The most widely used method for solving systems of nonlinear equations is Newton's method. While much research has been devoted to augmenting Newton-based solvers (usually with globalization techniques), little has been devoted to exploring the application of different models. Our research has been directed at evaluating techniques using different models than Newton's method: a lower order model, Broyden's method, and a higher order model, the tensor method. We have developed large-scale versions of each of these models and have demonstrated their use in important applications at Sandia. Broyden's method replaces the Jacobian with an approximation, allowing codes that cannot evaluate a Jacobian or have an inaccurate Jacobian to converge to a solution. Limited-memory methods, which have been successful in optimization, allow us to extend this approach to large-scale problems. We compare the robustness and efficiency of Newton's method, modified Newton's method, Jacobian-free Newton-Krylov method, and our limited-memory Broyden method. Comparisons are carried out for large-scale applications of fluid flow simulations and electronic circuit simulations. Results show that, in cases where the Jacobian was inaccurate or could not be computed, Broyden's method converged in some cases where Newton's method failed to converge. We identify conditions where Broyden's method can be more efficient than Newton's method. We also present modifications to a large-scale tensor method, originally proposed by Bouaricha, for greater efficiency, better robustness, and wider applicability. Tensor methods are an alternative to Newton-based methods and are based on computing a step based on a local quadratic model rather than a linear model. The advantage of Bouaricha's method is that it can use any existing linear solver, which makes it simple to write
General theory of spherically symmetric boundary-value problems of the linear transport theory.
NASA Technical Reports Server (NTRS)
Kanal, M.
1972-01-01
A general theory of spherically symmetric boundary-value problems of the one-speed neutron transport theory is presented. The formulation is also applicable to the 'gray' problems of radiative transfer. The Green's function for the purely absorbing medium is utilized in obtaining the normal mode expansion of the angular densities for both interior and exterior problems. As the integral equations for unknown coefficients are regular, a general class of reduction operators is introduced to reduce such regular integral equations to singular ones with a Cauchy-type kernel. Such operators then permit one to solve the singular integral equations by the standard techniques due to Muskhelishvili. We discuss several spherically symmetric problems. However, the treatment is kept sufficiently general to deal with problems lacking azimuthal symmetry. In particular the procedure seems to work for regions whose boundary coincides with one of the coordinate surfaces for which the Helmholtz equation is separable.
A general resolution of intractable problems in polynomial time through DNA Computing.
Sanches, C A A; Soma, N Y
2016-12-01
Based on a set of known biological operations, a general resolution of intractable problems in polynomial time through DNA Computing is presented. This scheme has been applied to solve two NP-Hard problems (Minimization of Open Stacks Problem and Matrix Bandwidth Minimization Problem) and three co-NP-Complete problems (associated with Hamiltonian Path, Traveling Salesman and Hamiltonian Circuit), which have not been solved with this model. Conclusions and open questions concerning the computational capacity of this model are presented, and research topics are suggested.
A High-Order Direct Solver for Helmholtz Equations with Neumann Boundary Conditions
NASA Technical Reports Server (NTRS)
Sun, Xian-He; Zhuang, Yu
1997-01-01
In this study, a compact finite-difference discretization is first developed for Helmholtz equations on rectangular domains. Special treatments are then introduced for Neumann and Neumann-Dirichlet boundary conditions to achieve accuracy and separability. Finally, a Fast Fourier Transform (FFT) based technique is used to yield a fast direct solver. Analytical and experimental results show this newly proposed solver is comparable to the conventional second-order elliptic solver when accuracy is not a primary concern, and is significantly faster than that of the conventional solver if a highly accurate solution is required. In addition, this newly proposed fourth order Helmholtz solver is parallel in nature. It is readily available for parallel and distributed computers. The compact scheme introduced in this study is likely extendible for sixth-order accurate algorithms and for more general elliptic equations.
Choreographic solution to the general-relativistic three-body problem.
Imai, Tatsunori; Chiba, Takamasa; Asada, Hideki
2007-05-18
We reexamine the three-body problem in the framework of general relativity. The Newtonian N-body problem admits choreographic solutions, where a solution is called choreographic if every massive particle moves periodically in a single closed orbit. One is a stable figure-eight orbit for a three-body system, which was found first by Moore (1993) and rediscovered with its existence proof by Chenciner and Montgomery (2000). In general relativity, however, the periastron shift prohibits a binary system from orbiting in a single closed curve. Therefore, it is unclear whether general-relativistic effects admit choreography such as the figure eight. We examine general-relativistic corrections to initial conditions so that an orbit for a three-body system can be choreographic and a figure eight. This illustration suggests that the general-relativistic N-body problem also may admit a certain class of choreographic solutions.
Choreographic Solution to the General-Relativistic Three-Body Problem
NASA Astrophysics Data System (ADS)
Imai, Tatsunori; Chiba, Takamasa; Asada, Hideki
2007-05-01
We reexamine the three-body problem in the framework of general relativity. The Newtonian N-body problem admits choreographic solutions, where a solution is called choreographic if every massive particle moves periodically in a single closed orbit. One is a stable figure-eight orbit for a three-body system, which was found first by Moore (1993) and rediscovered with its existence proof by Chenciner and Montgomery (2000). In general relativity, however, the periastron shift prohibits a binary system from orbiting in a single closed curve. Therefore, it is unclear whether general-relativistic effects admit choreography such as the figure eight. We examine general-relativistic corrections to initial conditions so that an orbit for a three-body system can be choreographic and a figure eight. This illustration suggests that the general-relativistic N-body problem also may admit a certain class of choreographic solutions.
Parallel Performance of Linear Solvers and Preconditioners
2014-01-01
MUMPS libraries to identify the combination with the shortest wall clock time for large-scale linear systems. The linear system of equations in this...during initialization. Our results show that for system sizes of less than three million degrees of freedom (DOF), the MUMPS direct solver is 20...solver with various iterative solver – preconditioner combinations. Both solve time and setup time for MUMPS are included. Ideal refers to the solve
Creative Problem Solving for General Education Intervention Teams: A Two-Year Evaluation Study
ERIC Educational Resources Information Center
Bahr, Michael W.; Walker, Kenneth; Hampton, Eric M.; Buddle, Bonita S.; Freeman, Tamyra; Ruschman, Nancy; Sears, Jennifer; McKinney, Angela; Miller, Maurice; Littlejohn, William
2006-01-01
Creative problem solving (CPS) is an approach for identifying solutions to problems within a structured, facilitated process. In the current studies, CPS was customized for general education intervention (GEI) teams in elementary schools. In the first study, 24 GEI teams were randomly assigned either to a CPS for GEI training condition or to a…
Cauchy problem of the generalized Zakharov type system in [Formula: see text].
You, Shujun; Ning, Xiaoqi
2017-01-01
In this paper, we consider the initial value problem for a two-dimensional generalized Zakharov system with quantum effects. We prove the existence and uniqueness of global smooth solutions to the initial value problem in the Sobolev space through making a priori integral estimates and the Galerkin method.
Teaching Problem Solving: Don't Forget the Problem Solver(s)
ERIC Educational Resources Information Center
Ranade, Saidas M.; Corrales, Angela
2013-01-01
The importance of intrapersonal and interpersonal intelligences has long been known but educators have debated whether to and how to incorporate those topics in an already crowded engineering curriculum. In 2010, the authors used the classroom as a laboratory to observe the usefulness of including selected case studies and exercises from the…
Migration of vectorized iterative solvers to distributed memory architectures
Pommerell, C.; Ruehl, R.
1994-12-31
Both necessity and opportunity motivate the use of high-performance computers for iterative linear solvers. Necessity results from the size of the problems being solved-smaller problems are often better handled by direct methods. Opportunity arises from the formulation of the iterative methods in terms of simple linear algebra operations, even if this {open_quote}natural{close_quotes} parallelism is not easy to exploit in irregularly structured sparse matrices and with good preconditioners. As a result, high-performance implementations of iterative solvers have attracted a lot of interest in recent years. Most efforts are geared to vectorize or parallelize the dominating operation-structured or unstructured sparse matrix-vector multiplication, or to increase locality and parallelism by reformulating the algorithm-reducing global synchronization in inner products or local data exchange in preconditioners. Target architectures for iterative solvers currently include mostly vector supercomputers and architectures with one or few optimized (e.g., super-scalar and/or super-pipelined RISC) processors and hierarchical memory systems. More recently, parallel computers with physically distributed memory and a better price/performance ratio have been offered by vendors as a very interesting alternative to vector supercomputers. However, programming comfort on such distributed memory parallel processors (DMPPs) still lags behind. Here the authors are concerned with iterative solvers and their changing computing environment. In particular, they are considering migration from traditional vector supercomputers to DMPPs. Application requirements force one to use flexible and portable libraries. They want to extend the portability of iterative solvers rather than reimplementing everything for each new machine, or even for each new architecture.
NASA Astrophysics Data System (ADS)
Alipova, B. N.; Alexeyeva, L. A.; Dadayeva, A. N.
2017-01-01
Generalized solutions of coupled thermoelastodynamics equations are considered. By use of generalized functions theory, the conditions on jumps of stresses, velocities, temperature gradients and energy density on their fronts are received. The statements of four non-stationary boundary value problems of coupled thermoelasticity are given, for which uniqueness of decisions are proved by influence of shock thermoelastic waves.
NASA Astrophysics Data System (ADS)
Gorskii, A. V.; Gorskii, P. V.
2008-10-01
Relations for two-dimensional ideal plasticity problems under the full plasticity condition are determined with material anisotropy, inhomogeneity, and compressibility properties taken into account. These properties are determined by the direction cosines of the principal stress, the coordinates of points in space, and the mean stress. For the yield strength we take a function of the form k = k( σ, n 1, n 2, n 3, x, y, z). The desired relations are determined for the general plane ideal plasticity problem. The relations thus obtained are generalized to the cases of axisymmetric and spherical plasticity problems.
Pelanti, Marica; Bouchut, Francois; Mangeney, Anne
2011-02-01
We present a Riemann solver derived by a relaxation technique for classical single-phase shallow flow equations and for a two-phase shallow flow model describing a mixture of solid granular material and fluid. Our primary interest is the numerical approximation of this two-phase solid/fluid model, whose complexity poses numerical difficulties that cannot be efficiently addressed by existing solvers. In particular, we are concerned with ensuring a robust treatment of dry bed states. The relaxation system used by the proposed solver is formulated by introducing auxiliary variables that replace the momenta in the spatial gradients of the original model systems. The resulting relaxation solver is related to Roe solver in that its Riemann solution for the flow height and relaxation variables is formally computed as Roe's Riemann solution. The relaxation solver has the advantage of a certain degree of freedom in the specification of the wave structure through the choice of the relaxation parameters. This flexibility can be exploited to handle robustly vacuum states, which is a well known difficulty of standard Roe's method, while maintaining Roe's low diffusivity. For the single-phase model positivity of flow height is rigorously preserved. For the two-phase model positivity of volume fractions in general is not ensured, and a suitable restriction on the CFL number might be needed. Nonetheless, numerical experiments suggest that the proposed two-phase flow solver efficiently models wet/dry fronts and vacuum formation for a large range of flow conditions. As a corollary of our study, we show that for single-phase shallow flow equations the relaxation solver is formally equivalent to the VFRoe solver with conservative variables of Gallouet and Masella [T. Gallouet, J.-M. Masella, Un schema de Godunov approche C.R. Acad. Sci. Paris, Serie I, 323 (1996) 77-84]. The relaxation interpretation allows establishing positivity conditions for this VFRoe method.
A general architecture for intelligent tutoring of diagnostic classification problem solving.
Crowley, Rebecca S; Medvedeva, Olga
2003-01-01
We report on a general architecture for creating knowledge-based medical training systems to teach diagnostic classification problem solving. The approach is informed by our previous work describing the development of expertise in classification problem solving in Pathology. The architecture envelops the traditional Intelligent Tutoring System design within the Unified Problem-solving Method description Language (UPML) architecture, supporting component modularity and reuse. Based on the domain ontology, domain task ontology and case data, the abstract problem-solving methods of the expert model create a dynamic solution graph. Student interaction with the solution graph is filtered through an instructional layer, which is created by a second set of abstract problem-solving methods and pedagogic ontologies, in response to the current state of the student model. We outline the advantages and limitations of this general approach, and describe it's implementation in SlideTutor - a developing Intelligent Tutoring System in Dermatopathology.
Development of multiphase CFD flow solver in OpenFOAM
NASA Astrophysics Data System (ADS)
Rollins, Chad; Luo, Hong; Dinh, Nam
2016-11-01
We are developing a pressure-based multiphase (Eulerian) CFD solver using OpenFOAM with Reynolds-averaged turbulence stress modeling. Our goal is the evaluation and improvement of the current OpenFOAM two-fluid (Eulerian) solver in boiling channels with a motivation to produce a more consistent modeling and numerics treatment. The difficulty lies in the prescense of the many forces and models that are tightly non-linearly coupled in the solver. Therefore, the solver platform will allow not only the modeling, but the tracking as well, of the effects of the individual components (various interfacial forces/heat transfer models) and their interactions. This is essential for the development of a robust and efficient solution method. There has be a lot of work already performed in related areas that generally indicates a lack of robustness of the solution methods. The objective here is therefore to identify and develop remedies for numerical/modeling issues through a systematic approach to verification and validation, taking advantage of the open source nature of OpenFOAM. The presentation will discuss major findings, and suggest strategies for robust and consistent modeling (probably, a more consistent treatment of heat transfer models with two-fluid models in the near-wall cells).
The general form of 0-1 programming problem based on DNA computing.
ZhiXiang, Yin; Fengyue, Zhang; Jin, Xu
2003-06-01
DNA computing is a novel method of solving a class of intractable computational problems, in which the computing speeds up exponentially with the problem size. Up to now, many accomplishments have been made to improve its performance and increase its reliability. In this paper, we solved the general form of 0-1 programming problem with fluorescence labeling techniques based on surface chemistry by attempting to apply DNA computing to a programming problem. Our method has some significant advantages such as simple encoding, low cost, and short operating time.
Zhao, Yingfeng; Liu, Sanyang
2016-01-01
We present a practical branch and bound algorithm for globally solving generalized linear multiplicative programming problem with multiplicative constraints. To solve the problem, a relaxation programming problem which is equivalent to a linear programming is proposed by utilizing a new two-phase relaxation technique. In the algorithm, lower and upper bounds are simultaneously obtained by solving some linear relaxation programming problems. Global convergence has been proved and results of some sample examples and a small random experiment show that the proposed algorithm is feasible and efficient.
Elliptic Solvers with Adaptive Mesh Refinement on Complex Geometries
Phillip, B.
2000-07-24
Adaptive Mesh Refinement (AMR) is a numerical technique for locally tailoring the resolution computational grids. Multilevel algorithms for solving elliptic problems on adaptive grids include the Fast Adaptive Composite grid method (FAC) and its parallel variants (AFAC and AFACx). Theory that confirms the independence of the convergence rates of FAC and AFAC on the number of refinement levels exists under certain ellipticity and approximation property conditions. Similar theory needs to be developed for AFACx. The effectiveness of multigrid-based elliptic solvers such as FAC, AFAC, and AFACx on adaptively refined overlapping grids is not clearly understood. Finally, a non-trivial eye model problem will be solved by combining the power of using overlapping grids for complex moving geometries, AMR, and multilevel elliptic solvers.
Intrusive Method for Uncertainty Quantification in a Multiphase Flow Solver
NASA Astrophysics Data System (ADS)
Turnquist, Brian; Owkes, Mark
2016-11-01
Uncertainty quantification (UQ) is a necessary, interesting, and often neglected aspect of fluid flow simulations. To determine the significance of uncertain initial and boundary conditions, a multiphase flow solver is being created which extends a single phase, intrusive, polynomial chaos scheme into multiphase flows. Reliably estimating the impact of input uncertainty on design criteria can help identify and minimize unwanted variability in critical areas, and has the potential to help advance knowledge in atomizing jets, jet engines, pharmaceuticals, and food processing. Use of an intrusive polynomial chaos method has been shown to significantly reduce computational cost over non-intrusive collocation methods such as Monte-Carlo. This method requires transforming the model equations into a weak form through substitution of stochastic (random) variables. Ultimately, the model deploys a stochastic Navier Stokes equation, a stochastic conservative level set approach including reinitialization, as well as stochastic normals and curvature. By implementing these approaches together in one framework, basic problems may be investigated which shed light on model expansion, uncertainty theory, and fluid flow in general. NSF Grant Number 1511325.
Solvers for $\\mathcal{O} (N)$ Electronic Structure in the Strong Scaling Limit
Bock, Nicolas; Challacombe, William M.; Kale, Laxmikant
2016-01-26
Here we present a hybrid OpenMP/Charm\\tt++ framework for solving the $\\mathcal{O} (N)$ self-consistent-field eigenvalue problem with parallelism in the strong scaling regime, $P\\gg{N}$, where $P$ is the number of cores, and $N$ is a measure of system size, i.e., the number of matrix rows/columns, basis functions, atoms, molecules, etc. This result is achieved with a nested approach to spectral projection and the sparse approximate matrix multiply [Bock and Challacombe, SIAM J. Sci. Comput., 35 (2013), pp. C72--C98], and involves a recursive, task-parallel algorithm, often employed by generalized $N$-Body solvers, to occlusion and culling of negligible products in the case of matrices with decay. Lastly, employing classic technologies associated with generalized $N$-Body solvers, including overdecomposition, recursive task parallelism, orderings that preserve locality, and persistence-based load balancing, we obtain scaling beyond hundreds of cores per molecule for small water clusters ([H${}_2$O]${}_N$, $N \\in \\{ 30, 90, 150 \\}$, $P/N \\approx \\{ 819, 273, 164 \\}$) and find support for an increasingly strong scalability with increasing system size $N$.
Solvers for $$\\mathcal{O} (N)$$ Electronic Structure in the Strong Scaling Limit
Bock, Nicolas; Challacombe, William M.; Kale, Laxmikant
2016-01-26
Here we present a hybrid OpenMP/Charm\\tt++ framework for solving themore » $$\\mathcal{O} (N)$$ self-consistent-field eigenvalue problem with parallelism in the strong scaling regime, $$P\\gg{N}$$, where $P$ is the number of cores, and $N$ is a measure of system size, i.e., the number of matrix rows/columns, basis functions, atoms, molecules, etc. This result is achieved with a nested approach to spectral projection and the sparse approximate matrix multiply [Bock and Challacombe, SIAM J. Sci. Comput., 35 (2013), pp. C72--C98], and involves a recursive, task-parallel algorithm, often employed by generalized $N$-Body solvers, to occlusion and culling of negligible products in the case of matrices with decay. Lastly, employing classic technologies associated with generalized $N$-Body solvers, including overdecomposition, recursive task parallelism, orderings that preserve locality, and persistence-based load balancing, we obtain scaling beyond hundreds of cores per molecule for small water clusters ([H$${}_2$$O]$${}_N$$, $$N \\in \\{ 30, 90, 150 \\}$$, $$P/N \\approx \\{ 819, 273, 164 \\}$$) and find support for an increasingly strong scalability with increasing system size $N$.« less
MACSYMA's symbolic ordinary differential equation solver
NASA Technical Reports Server (NTRS)
Golden, J. P.
1977-01-01
The MACSYMA's symbolic ordinary differential equation solver ODE2 is described. The code for this routine is delineated, which is of interest because it is written in top-level MACSYMA language, and may serve as a good example of programming in that language. Other symbolic ordinary differential equation solvers are mentioned.
Multiscale Universal Interface: A concurrent framework for coupling heterogeneous solvers
NASA Astrophysics Data System (ADS)
Tang, Yu-Hang; Kudo, Shuhei; Bian, Xin; Li, Zhen; Karniadakis, George Em
2015-09-01
Concurrently coupled numerical simulations using heterogeneous solvers are powerful tools for modeling multiscale phenomena. However, major modifications to existing codes are often required to enable such simulations, posing significant difficulties in practice. In this paper we present a C++ library, i.e. the Multiscale Universal Interface (MUI), which is capable of facilitating the coupling effort for a wide range of multiscale simulations. The library adopts a header-only form with minimal external dependency and hence can be easily dropped into existing codes. A data sampler concept is introduced, combined with a hybrid dynamic/static typing mechanism, to create an easily customizable framework for solver-independent data interpretation. The library integrates MPI MPMD support and an asynchronous communication protocol to handle inter-solver information exchange irrespective of the solvers' own MPI awareness. Template metaprogramming is heavily employed to simultaneously improve runtime performance and code flexibility. We validated the library by solving three different multiscale problems, which also serve to demonstrate the flexibility of the framework in handling heterogeneous models and solvers. In the first example, a Couette flow was simulated using two concurrently coupled Smoothed Particle Hydrodynamics (SPH) simulations of different spatial resolutions. In the second example, we coupled the deterministic SPH method with the stochastic Dissipative Particle Dynamics (DPD) method to study the effect of surface grafting on the hydrodynamics properties on the surface. In the third example, we consider conjugate heat transfer between a solid domain and a fluid domain by coupling the particle-based energy-conserving DPD (eDPD) method with the Finite Element Method (FEM).
Multiscale Universal Interface: A concurrent framework for coupling heterogeneous solvers
Tang, Yu-Hang; Kudo, Shuhei; Bian, Xin; Li, Zhen; Karniadakis, George Em
2015-09-15
Graphical abstract: - Abstract: Concurrently coupled numerical simulations using heterogeneous solvers are powerful tools for modeling multiscale phenomena. However, major modifications to existing codes are often required to enable such simulations, posing significant difficulties in practice. In this paper we present a C++ library, i.e. the Multiscale Universal Interface (MUI), which is capable of facilitating the coupling effort for a wide range of multiscale simulations. The library adopts a header-only form with minimal external dependency and hence can be easily dropped into existing codes. A data sampler concept is introduced, combined with a hybrid dynamic/static typing mechanism, to create an easily customizable framework for solver-independent data interpretation. The library integrates MPI MPMD support and an asynchronous communication protocol to handle inter-solver information exchange irrespective of the solvers' own MPI awareness. Template metaprogramming is heavily employed to simultaneously improve runtime performance and code flexibility. We validated the library by solving three different multiscale problems, which also serve to demonstrate the flexibility of the framework in handling heterogeneous models and solvers. In the first example, a Couette flow was simulated using two concurrently coupled Smoothed Particle Hydrodynamics (SPH) simulations of different spatial resolutions. In the second example, we coupled the deterministic SPH method with the stochastic Dissipative Particle Dynamics (DPD) method to study the effect of surface grafting on the hydrodynamics properties on the surface. In the third example, we consider conjugate heat transfer between a solid domain and a fluid domain by coupling the particle-based energy-conserving DPD (eDPD) method with the Finite Element Method (FEM)
Decision Engines for Software Analysis Using Satisfiability Modulo Theories Solvers
NASA Technical Reports Server (NTRS)
Bjorner, Nikolaj
2010-01-01
The area of software analysis, testing and verification is now undergoing a revolution thanks to the use of automated and scalable support for logical methods. A well-recognized premise is that at the core of software analysis engines is invariably a component using logical formulas for describing states and transformations between system states. The process of using this information for discovering and checking program properties (including such important properties as safety and security) amounts to automatic theorem proving. In particular, theorem provers that directly support common software constructs offer a compelling basis. Such provers are commonly called satisfiability modulo theories (SMT) solvers. Z3 is a state-of-the-art SMT solver. It is developed at Microsoft Research. It can be used to check the satisfiability of logical formulas over one or more theories such as arithmetic, bit-vectors, lists, records and arrays. The talk describes some of the technology behind modern SMT solvers, including the solver Z3. Z3 is currently mainly targeted at solving problems that arise in software analysis and verification. It has been applied to various contexts, such as systems for dynamic symbolic simulation (Pex, SAGE, Vigilante), for program verification and extended static checking (Spec#/Boggie, VCC, HAVOC), for software model checking (Yogi, SLAM), model-based design (FORMULA), security protocol code (F7), program run-time analysis and invariant generation (VS3). We will describe how it integrates support for a variety of theories that arise naturally in the context of the applications. There are several new promising avenues and the talk will touch on some of these and the challenges related to SMT solvers. Proceedings
Recent Enhancements To The FUN3D Flow Solver For Moving-Mesh Applications
NASA Technical Reports Server (NTRS)
Biedron, Robert T,; Thomas, James L.
2009-01-01
An unsteady Reynolds-averaged Navier-Stokes solver for unstructured grids has been extended to handle general mesh movement involving rigid, deforming, and overset meshes. Mesh deformation is achieved through analogy to elastic media by solving the linear elasticity equations. A general method for specifying the motion of moving bodies within the mesh has been implemented that allows for inherited motion through parent-child relationships, enabling simulations involving multiple moving bodies. Several example calculations are shown to illustrate the range of potential applications. For problems in which an isolated body is rotating with a fixed rate, a noninertial reference-frame formulation is available. An example calculation for a tilt-wing rotor is used to demonstrate that the time-dependent moving grid and noninertial formulations produce the same results in the limit of zero time-step size.
The problem of general Radon representation for an arbitrary Hausdorff space
NASA Astrophysics Data System (ADS)
Zakharov, V. K.; Mikhalev, A. V.
1999-10-01
After the fundamental work of Riesz, Radon and Hausdorff in the period 1909-1914, the following problem of general Radon representation emerged: for any Hausdorff space find the space of linear functionals that are integrally representable by Radon measures. In the early 1950s, a partial solution of this problem (the bijective version) for locally compact spaces was obtained by Halmos, Hewitt, Edwards, Bourbaki and others. For bounded Radon measures on a Tychonoff space, the problem of isomorphic Radon representation was solved in 1956 by Prokhorov. In this paper we give a possible solution of the problem of general Radon representation. To do this, we use the family of metasemicontinuous functions with compact support and the class of thin functionals. We present bijective and isomorphic versions of the solution (Theorems 1 and 2 of §2.5). To get the isomorphic version, we introduce the family of Radon bimeasures.
Cai, Yunfeng; Bai, Zhaojun; Pask, John E.; Sukumar, N.
2013-12-15
The iterative diagonalization of a sequence of large ill-conditioned generalized eigenvalue problems is a computational bottleneck in quantum mechanical methods employing a nonorthogonal basis for ab initio electronic structure calculations. We propose a hybrid preconditioning scheme to effectively combine global and locally accelerated preconditioners for rapid iterative diagonalization of such eigenvalue problems. In partition-of-unity finite-element (PUFE) pseudopotential density-functional calculations, employing a nonorthogonal basis, we show that the hybrid preconditioned block steepest descent method is a cost-effective eigensolver, outperforming current state-of-the-art global preconditioning schemes, and comparably efficient for the ill-conditioned generalized eigenvalue problems produced by PUFE as the locally optimal block preconditioned conjugate-gradient method for the well-conditioned standard eigenvalue problems produced by planewave methods.
Detwiler, R.L.; Mehl, S.; Rajaram, H.; Cheung, W.W.
2002-01-01
Numerical solution of large-scale ground water flow and transport problems is often constrained by the convergence behavior of the iterative solvers used to solve the resulting systems of equations. We demonstrate the ability of an algebraic multigrid algorithm (AMG) to efficiently solve the large, sparse systems of equations that result from computational models of ground water flow and transport in large and complex domains. Unlike geometric multigrid methods, this algorithm is applicable to problems in complex flow geometries, such as those encountered in pore-scale modeling of two-phase flow and transport. We integrated AMG into MODFLOW 2000 to compare two- and three-dimensional flow simulations using AMG to simulations using PCG2, a preconditioned conjugate gradient solver that uses the modified incomplete Cholesky preconditioner and is included with MODFLOW 2000. CPU times required for convergence with AMG were up to 140 times faster than those for PCG2. The cost of this increased speed was up to a nine-fold increase in required random access memory (RAM) for the three-dimensional problems and up to a four-fold increase in required RAM for the two-dimensional problems. We also compared two-dimensional numerical simulations of steady-state transport using AMG and the generalized minimum residual method with an incomplete LU-decomposition preconditioner. For these transport simulations, AMG yielded increased speeds of up to 17 times with only a 20% increase in required RAM. The ability of AMG to solve flow and transport problems in large, complex flow systems and its ready availability make it an ideal solver for use in both field-scale and pore-scale modeling.
Wavelet-based Poisson solver for use in particle-in-cell simulations.
Terzić, Balsa; Pogorelov, Ilya V
2005-06-01
We report on a successful implementation of a wavelet-based Poisson solver for use in three-dimensional particle-in-cell simulations. Our method harnesses advantages afforded by the wavelet formulation, such as sparsity of operators and data sets, existence of effective preconditioners, and the ability simultaneously to remove numerical noise and additional compression of relevant data sets. We present and discuss preliminary results relating to the application of the new solver to test problems in accelerator physics and astrophysics.
Cherpitel, C J
1991-01-01
While problem drinking is believed to be over-represented in primary care practice, additional research in this area is needed. A probability sample of 394 patients attending all county-operated primary care clinics in Contra Costa County, California, were breathalyzed and interviewed regarding drinking patterns and alcohol problems. These data are compared with those obtained from a representative general population sample of over 3000 respondents living in the same county. While the clinic population reported higher rates of abstinence compared with the general population (38 versus 17%), among drinkers the clinic sample reported higher rates of heavy drinking. In the clinic sample 14% reported a physical health problem related to drinking and 22% reported three or more symptoms of alcohol dependence during the last year, compared with 3 and 10%, respectively, in the general population. The clinic sample was demographically different from those in the general population which could account, in part, for differences in heavy drinking and alcohol-related problems between the two populations. The prevalence of heavy and problem drinking in this primary care practice suggests the potential of primary care settings for early identification and treatment of alcohol-misusing patients.
Study to determine the IFR operational profile and problems of the general aviation single pilot
NASA Technical Reports Server (NTRS)
Weislogel, G. S.
1983-01-01
General aviation single pilot operating under instrument flight rules (GA SPIFR) was studied. The objectives of the study were to (1) develop a GA SPIFR operational profile, (2) identify problems experienced by the GA SPIFR pilot, and (3) identify research tasks which have the potential for eliminating or reducing the severity of the problems. To obtain the information necessary to accomplish these objectives, a mail questionnaire survey of instrument rated pilots was conducted. The general aviation IFR single pilot operational profile and selected data analysis examples are presented.
NASA Astrophysics Data System (ADS)
Liang, Li-Fu; Liu, Zong-Min; Guo, Qing-Yong
2009-03-01
The fluid-solid coupling theory, an interdisciplinary science between hydrodynamics and solid mechanics, is an important tool for response analysis and direct design of structures in naval architecture and ocean engineering. By applying the corresponding relations between generalized forces and generalized displacements, convolutions were performed between the basic equations of elasto-dynamics in the primary space and corresponding virtual quantities. The results were integrated and then added algebraically. In light of the fact that body forces and surface forces are both follower forces, the generalized quasi-complementary energy principle with two kinds of variables for an initial value problem is established in non-conservative systems. Using the generalized quasi-complementary energy principle to deal with the fluid-solid coupling problem and to analyze the dynamic response of structures, a method for using two kinds of variables simultaneously for calculation of force and displacement was derived.
Elliptic Solvers for Adaptive Mesh Refinement Grids
Quinlan, D.J.; Dendy, J.E., Jr.; Shapira, Y.
1999-06-03
We are developing multigrid methods that will efficiently solve elliptic problems with anisotropic and discontinuous coefficients on adaptive grids. The final product will be a library that provides for the simplified solution of such problems. This library will directly benefit the efforts of other Laboratory groups. The focus of this work is research on serial and parallel elliptic algorithms and the inclusion of our black-box multigrid techniques into this new setting. The approach applies the Los Alamos object-oriented class libraries that greatly simplify the development of serial and parallel adaptive mesh refinement applications. In the final year of this LDRD, we focused on putting the software together; in particular we completed the final AMR++ library, we wrote tutorials and manuals, and we built example applications. We implemented the Fast Adaptive Composite Grid method as the principal elliptic solver. We presented results at the Overset Grid Conference and other more AMR specific conferences. We worked on optimization of serial and parallel performance and published several papers on the details of this work. Performance remains an important issue and is the subject of continuing research work.
Development of a New and Fast Linear Solver for Multi-component Reactive Transport Simulation
NASA Astrophysics Data System (ADS)
Qiao, C.; Li, L.; Bao, C.; Hu, X.; Johns, R.; Xu, J.
2013-12-01
Reactive transport models (RTM) have been extensively used to understand the coupling between solute transport and (bio) geochemical reactions in complex earth systems. RTM typically involves a large number of primary and secondary species with a complex reaction network in large domains. The computational expenses increase significantly with the number of grid blocks and the number of chemical species. Within both the operator splitting approach (OS) and the global implicit approach (GI) that are commonly used, the steps that involve Newton-Raphson method are typically one of the most time-consuming parts (up to 80% to 90% of CPU times). Under such circumstances, accelerating reactive transport simulation is very essential. In this research, we present a physics-based linear system solution strategy for general reactive transport models with many species. We observed up to five times speed up for the linear solver portion of the simulations in our test cases. Our new linear solver takes advantage of the sparsity of the Jacobian matrix arising from the reaction network. The Jacobian matrix for the speciation problem is typically considered as a dense matrix and solved with a direct method such as Gaussian elimination. For the reactive transport problem, the graph of the local Jacobian matrix has a one-to-one correspondence to the reaction network graph. The Jacobian matrix is commonly sparse and has the same sparsity structure for the same reaction network. We developed a strategy that performs a minimum degree of reordering and symbolic factorization to determine the non-zero pattern at the beginning of the OS and GI simulation. During the speciation calculation in OS, we calculate the L and U factors and solve the triangular matrices according to the non-zero pattern. For GI, our strategy can be applied to inverse the diagonal blocks in the block-Jacobi preconditioner and smoothers of the multigrid preconditioners in iterative solvers. Our strategy is naturally
Oasis: A high-level/high-performance open source Navier-Stokes solver
NASA Astrophysics Data System (ADS)
Mortensen, Mikael; Valen-Sendstad, Kristian
2015-03-01
Oasis is a high-level/high-performance finite element Navier-Stokes solver written from scratch in Python using building blocks from the FEniCS project (fenicsproject.org). The solver is unstructured and targets large-scale applications in complex geometries on massively parallel clusters. Oasis utilizes MPI and interfaces, through FEniCS, to the linear algebra backend PETSc. Oasis advocates a high-level, programmable user interface through the creation of highly flexible Python modules for new problems. Through the high-level Python interface the user is placed in complete control of every aspect of the solver. A version of the solver, that is using piecewise linear elements for both velocity and pressure, is shown to reproduce very well the classical, spectral, turbulent channel simulations of Moser et al. (1999). The computational speed is strongly dominated by the iterative solvers provided by the linear algebra backend, which is arguably the best performance any similar implicit solver using PETSc may hope for. Higher order accuracy is also demonstrated and new solvers may be easily added within the same framework.
The impact of improved sparse linear solvers on industrial engineering applications
Heroux, M.; Baddourah, M.; Poole, E.L.; Yang, Chao Wu
1996-12-31
There are usually many factors that ultimately determine the quality of computer simulation for engineering applications. Some of the most important are the quality of the analytical model and approximation scheme, the accuracy of the input data and the capability of the computing resources. However, in many engineering applications the characteristics of the sparse linear solver are the key factors in determining how complex a problem a given application code can solve. Therefore, the advent of a dramatically improved solver often brings with it dramatic improvements in our ability to do accurate and cost effective computer simulations. In this presentation we discuss the current status of sparse iterative and direct solvers in several key industrial CFD and structures codes, and show the impact that recent advances in linear solvers have made on both our ability to perform challenging simulations and the cost of those simulations. We also present some of the current challenges we have and the constraints we face in trying to improve these solvers. Finally, we discuss future requirements for sparse linear solvers on high performance architectures and try to indicate the opportunities that exist if we can develop even more improvements in linear solver capabilities.
NASA Astrophysics Data System (ADS)
Marshall, David D.
With the renewed interest in Cartesian gridding methodologies for the ease and speed of gridding complex geometries in addition to the simplicity of the control volumes used in the computations, it has become important to investigate ways of extending the existing Cartesian grid solver functionalities. This includes developing methods of modeling the viscous effects in order to utilize Cartesian grids solvers for accurate drag predictions and addressing the issues related to the distributed memory parallelization of Cartesian solvers. This research presents advances in two areas of interest in Cartesian grid solvers, viscous effects modeling and MPI parallelization. The development of viscous effects modeling using solely Cartesian grids has been hampered by the widely varying control volume sizes associated with the mesh refinement and the cut cells associated with the solid surface. This problem is being addressed by using physically based modeling techniques to update the state vectors of the cut cells and removing them from the finite volume integration scheme. This work is performed on a new Cartesian grid solver, NASCART-GT, with modifications to its cut cell functionality. The development of MPI parallelization addresses issues associated with utilizing Cartesian solvers on distributed memory parallel environments. This work is performed on an existing Cartesian grid solver, CART3D, with modifications to its parallelization methodology.
NASA Astrophysics Data System (ADS)
Malmivuo, Jaakko
2010-04-01
Though the principle of reciprocity was invented by Hermann von Helmholtz already over 150 years ago, and though it is a very powerful tool in solving various important problems in bioelectromagnetism, it is not generally used. In impedance tomography the measurement sensitivity distribution has generally been misunderstood. This can be easily demonstrated with the principle of reciprocity. Some other applications of the principle of reciprocity are also discussed.
NASA Astrophysics Data System (ADS)
Raskin, Cody; Owen, J. Michael
2016-11-01
We discuss a generalization of the classic Keplerian disk test problem allowing for both pressure and rotational support, as a method of testing astrophysical codes incorporating both gravitation and hydrodynamics. We argue for the inclusion of pressure in rotating disk simulations on the grounds that realistic, astrophysical disks exhibit non-negligible pressure support. We then apply this test problem to examine the performance of various smoothed particle hydrodynamics (SPH) methods incorporating a number of improvements proposed over the years to address problems noted in modeling the classical gravitation-only Keplerian disk. We also apply this test to a newly developed extension of SPH based on reproducing kernels called CRKSPH. Counterintuitively, we find that pressure support worsens the performance of traditional SPH on this problem, causing unphysical collapse away from the steady-state disk solution even more rapidly than the purely gravitational problem, whereas CRKSPH greatly reduces this error.
Code Verification of the HIGRAD Computational Fluid Dynamics Solver
Van Buren, Kendra L.; Canfield, Jesse M.; Hemez, Francois M.; Sauer, Jeremy A.
2012-05-04
The purpose of this report is to outline code and solution verification activities applied to HIGRAD, a Computational Fluid Dynamics (CFD) solver of the compressible Navier-Stokes equations developed at the Los Alamos National Laboratory, and used to simulate various phenomena such as the propagation of wildfires and atmospheric hydrodynamics. Code verification efforts, as described in this report, are an important first step to establish the credibility of numerical simulations. They provide evidence that the mathematical formulation is properly implemented without significant mistakes that would adversely impact the application of interest. Highly accurate analytical solutions are derived for four code verification test problems that exercise different aspects of the code. These test problems are referred to as: (i) the quiet start, (ii) the passive advection, (iii) the passive diffusion, and (iv) the piston-like problem. These problems are simulated using HIGRAD with different levels of mesh discretization and the numerical solutions are compared to their analytical counterparts. In addition, the rates of convergence are estimated to verify the numerical performance of the solver. The first three test problems produce numerical approximations as expected. The fourth test problem (piston-like) indicates the extent to which the code is able to simulate a 'mild' discontinuity, which is a condition that would typically be better handled by a Lagrangian formulation. The current investigation concludes that the numerical implementation of the solver performs as expected. The quality of solutions is sufficient to provide credible simulations of fluid flows around wind turbines. The main caveat associated to these findings is the low coverage provided by these four problems, and somewhat limited verification activities. A more comprehensive evaluation of HIGRAD may be beneficial for future studies.
The development of an intelligent interface to a computational fluid dynamics flow-solver code
NASA Technical Reports Server (NTRS)
Williams, Anthony D.
1988-01-01
Researchers at NASA Lewis are currently developing an 'intelligent' interface to aid in the development and use of large, computational fluid dynamics flow-solver codes for studying the internal fluid behavior of aerospace propulsion systems. This paper discusses the requirements, design, and implementation of an intelligent interface to Proteus, a general purpose, 3-D, Navier-Stokes flow solver. The interface is called PROTAIS to denote its introduction of artificial intelligence (AI) concepts to the Proteus code.
The development of an intelligent interface to a computational fluid dynamics flow-solver code
NASA Technical Reports Server (NTRS)
Williams, Anthony D.
1988-01-01
Researchers at NASA Lewis are currently developing an 'intelligent' interface to aid in the development and use of large, computational fluid dynamics flow-solver codes for studying the internal fluid behavior of aerospace propulsion systems. This paper discusses the requirements, design, and implementation of an intelligent interface to Proteus, a general purpose, three-dimensional, Navier-Stokes flow solver. The interface is called PROTAIS to denote its introduction of artificial intelligence (AI) concepts to the Proteus code.
A spectral Poisson solver for kinetic plasma simulation
NASA Astrophysics Data System (ADS)
Szeremley, Daniel; Obberath, Jens; Brinkmann, Ralf
2011-10-01
Plasma resonance spectroscopy is a well established plasma diagnostic method, realized in several designs. One of these designs is the multipole resonance probe (MRP). In its idealized - geometrically simplified - version it consists of two dielectrically shielded, hemispherical electrodes to which an RF signal is applied. A numerical tool is under development which is capable of simulating the dynamics of the plasma surrounding the MRP in electrostatic approximation. In this contribution we concentrate on the specialized Poisson solver for that tool. The plasma is represented by an ensemble of point charges. By expanding both the charge density and the potential into spherical harmonics, a largely analytical solution of the Poisson problem can be employed. For a practical implementation, the expansion must be appropriately truncated. With this spectral solver we are able to efficiently solve the Poisson equation in a kinetic plasma simulation without the need of introducing a spatial discretization.
On improving linear solver performance: a block variant of GMRES
Baker, A H; Dennis, J M; Jessup, E R
2004-05-10
The increasing gap between processor performance and memory access time warrants the re-examination of data movement in iterative linear solver algorithms. For this reason, we explore and establish the feasibility of modifying a standard iterative linear solver algorithm in a manner that reduces the movement of data through memory. In particular, we present an alternative to the restarted GMRES algorithm for solving a single right-hand side linear system Ax = b based on solving the block linear system AX = B. Algorithm performance, i.e. time to solution, is improved by using the matrix A in operations on groups of vectors. Experimental results demonstrate the importance of implementation choices on data movement as well as the effectiveness of the new method on a variety of problems from different application areas.
GARDNER, P.R.
2006-04-01
Sudoku, also known as Number Place, is a logic-based placement puzzle. The aim of the puzzle is to enter a numerical digit from 1 through 9 in each cell of a 9 x 9 grid made up of 3 x 3 subgrids (called ''regions''), starting with various digits given in some cells (the ''givens''). Each row, column, and region must contain only one instance of each numeral. Completing the puzzle requires patience and logical ability. Although first published in a U.S. puzzle magazine in 1979, Sudoku initially caught on in Japan in 1986 and attained international popularity in 2005. Last fall, after noticing Sudoku puzzles in some newspapers and magazines, I attempted a few just to see how hard they were. Of course, the difficulties varied considerably. ''Obviously'' one could use Trial and Error but all the advice was to ''Use Logic''. Thinking to flex, and strengthen, those powers, I began to tackle the puzzles systematically. That is, when I discovered a new tactical rule, I would write it down, eventually generating a list of ten or so, with some having overlap. They served pretty well except for the more difficult puzzles, but even then I managed to develop an additional three rules that covered all of them until I hit the Oregonian puzzle shown. With all of my rules, I could not seem to solve that puzzle. Initially putting my failure down to rapid mental fatigue (being unable to hold a sufficient quantity of information in my mind at one time), I decided to write a program to implement my rules and see what I had failed to notice earlier. The solver, too, failed. That is, my rules were insufficient to solve that particular puzzle. I happened across a book written by a fellow who constructs such puzzles and who claimed that, sometimes, the only tactic left was trial and error. With a trial and error routine implemented, my solver successfully completed the Oregonian puzzle, and has successfully solved every puzzle submitted to it since.
NASA Technical Reports Server (NTRS)
Hedgley, D. R., Jr.
1982-01-01
The requirements for computer-generated perspective projections of three dimensional objects has escalated. A general solution was developed. The theoretical solution to this problem is presented. The method is very efficient as it minimizes the selection of points and comparison of line segments and hence avoids the devastation of square-law growth.
ERIC Educational Resources Information Center
de Villiers, Michael
2017-01-01
This paper discusses an interesting, classic problem that provides a nice classroom investigation for dynamic geometry, and which can easily be explained (proved) with transformation geometry. The deductive explanation (proof) provides insight into why it is true, leading to an immediate generalization, thus illustrating the discovery function of…
General Problem-Solving Skills: Relations between Metacognition and Strategic Processing.
ERIC Educational Resources Information Center
Borkowski, John G.
1989-01-01
A metacognition model that can help understand general problem-solving deficits in learning disabled students is presented. Two components of metacognition are highlighted: executive processes and attributional beliefs. An educational package combining these components with specific strategy training is illustrated as an approach to improving…
A Review of Studies on the General Problem of Knowledge Production and Utilization.
ERIC Educational Resources Information Center
Short, Edmund C.
The growing complexity of society has resulted in increased attention to the problem of knowledge production and utilization. This review of the scholarship pertaining to this subject traces the topic in its most general sense. Three fields of interest have received attention from researchers: 1) the relation of research to practice; 2) the nature…
Promoting Student Learning through Group Problem Solving in General Chemistry Recitations
ERIC Educational Resources Information Center
Mahalingam, Madhu; Schaefer, Fred; Morlino, Elisabeth
2008-01-01
We describe the implementation and effects of group problem solving in recitation sections associated with the general chemistry course at a small private science university. Recitation sections of approximately 45 students are used to supplement large (approximately 180 students) lecture sections. The primary goal of recitation is working in…
Existence Result for the Kinetic Neutron Transport Problem with a General Albedo Boundary Condition
NASA Astrophysics Data System (ADS)
Sanchez, Richard; Bourhrara, Lahbib
2011-09-01
We present an existence result for the kinetic neutron transport equation with a general albedo boundary condition. The proof is constructive in the sense that we build a sequence that converges to the solution of the problem by iterating on the albedo term. Both nonhomogeneous and albedo boundary conditions are studied.
Problem Solving Videos for General Chemistry Review: Students' Perceptions and Use Patterns
ERIC Educational Resources Information Center
Richards-Babb, Michelle; Curtis, Reagan; Smith, Valerie J.; Xu, Mingming
2014-01-01
We examined the use of problem solving videos (PSVs) as a substitute for general chemistry exam review sessions. We investigated student perceptions of course aspects regarding usefulness for supporting their learning of chemistry content. We also examined "how" students used the PSVs to further their learning. Students ranked the PSVs…
Baker, J.R.; Budinger, T.F.; Huesman, R.H.
1992-10-01
A major limitation in tomographic inverse problems is inadequate computation speed, which frequently impedes the application of engineering ideas and principles in medical science more than in the physical and engineering sciences. Medical problems are computationally taxing because a minimum description of the system often involves 5 dimensions (3 space, 1 energy, 1 time), with the range of each space coordinate requiring up to 512 samples. The computational tasks for this problem can be simply expressed by posing the problem as one in which the tomograph system response function is spatially invariant, and the noise is additive and Gaussian. Under these assumptions, a number of reconstruction methods have been implemented with generally satisfactory results for general medical imaging purposes. However, if the system response function of the tomograph is assumed more realistically to be spatially variant and the noise to be Poisson, the computational problem becomes much more difficult. Some of the algorithms being studied to compensate for position dependent resolution and statistical fluctuations in the data acquisition process, when expressed in canonical form, are not practical for clinical applications because the number of computations necessary exceeds the capabilities of high performance computer systems currently available. Reconstruction methods based on natural pixels, specifically orthonormal natural pixels, preserve symmetries in the data acquisition process. Fast implementations of orthonormal natural pixel algorithms can achieve orders of magnitude speedup relative to general implementations. Thus, specialized thought in algorithm development can lead to more significant increases in performance than can be achieved through hardware improvements alone.
SIERRA framework version 4 : solver services.
Williams, Alan B.
2005-02-01
Several SIERRA applications make use of third-party libraries to solve systems of linear and nonlinear equations, and to solve eigenproblems. The classes and interfaces in the SIERRA framework that provide linear system assembly services and access to solver libraries are collectively referred to as solver services. This paper provides an overview of SIERRA's solver services including the design goals that drove the development, and relationships and interactions among the various classes. The process of assembling and manipulating linear systems will be described, as well as access to solution methods and other operations.
A generalized version of a two point boundary value problem guidance algorithm
NASA Astrophysics Data System (ADS)
Kelly, W. D.
An iterative guidance algorithm known as a minimum Hamiltonian method is used for performance analyses of launch vehicles in personal-computer trajectory simulations. Convergence in this application is rapid for a minimum-time-of-flight upper-stage solution. Examination of the coded algorithm resulted in a reformulation in which problem-specific portions of the code were separated from portions that were shared by problems in general. More generalized problem inputs were included to operate the algorithm based on varied numbers of state variables, terminal constraints, and controls, preparing for other applications the basic algorithm applied to ascent guidance. In most cases, including entry, the compact form of the algorithm along with the capability to converge rapidly makes it a contender for autonomous guidance aboard a powered flight vehicle.
Nakai, Minori; Hotta, Hiroshi; Ootsuru, Taku; Hiejima, Shigeto; Murakami, Masaru; Yuzuriha, Takefumi; Kondo, Tsuyoshi
2013-04-01
In Japan, many problems related to alcohol are pointed out from before. We believe that there is a unique drinking culture in Okinawa, such as a large amount of alcohol. Therefore, we estimate many people in Okinawa have a drinking problem. We conducted a survey of patients who visited general hospital (medical or surgical or orthopedic) in 2007. The purpose of this study is to collect basic data for introducing alcoholics to specialized treatment as early as possible, detecting the person who drink large amounts of alcohol, performing early intervention for people who drink large amount of alcohol, and advancing cooperation with specialized medical agencies of alcohol. As a result, Among the patients who visited general hospital in Okinawa, many problem drinkers are concentrated in the young age. and they have strong fears of health. The possibility of early intervention with intervention techniques, such as brief intervention, has been suggested.
Generalized solutions of initial-boundary value problems for second-order hyperbolic systems
NASA Astrophysics Data System (ADS)
Alexeyeva, L. A.; Zakir'yanova, G. K.
2011-07-01
The method of boundary integral equations is developed as applied to initial-boundary value problems for strictly hyperbolic systems of second-order equations characteristic of anisotropic media dynamics. Based on the theory of distributions (generalized functions), solutions are constructed in the space of generalized functions followed by passing to integral representations and classical solutions. Solutions are considered in the class of singular functions with discontinuous derivatives, which are typical of physical problems describing shock waves. The uniqueness of the solutions to the initial-boundary value problems is proved under certain smoothness conditions imposed on the boundary functions. The Green's matrix of the system and new fundamental matrices based on it are used to derive integral analogues of the Gauss, Kirchhoff, and Green formulas for solutions and solving singular boundary integral equations.
Dowsing, Paul; Murray, Alison; Sandler, Jonathan
2015-03-01
Fixed appliance treatment is a popular treatment modality with a burgeoning increase in the numbers of children and adults realizing the benefits that can be gained. Appliance breakage is an unavoidable nuisance which is at best inconvenient, and at worst may result in significant pain or discomfort for the patient. General dental practitioners (GDPs) should have the practical knowledge of how to provide timely and appropriate orthodontic 'emergency treatment'. This will significantly reduce the sometimes considerable inconvenience and discomfort for both the patient and his/her parents, and the inevitable frustration for the clinician providing ongoing care. This first paper will deal with general orthodontic problems that commonly present, as well as some issues specific to fixed appliances. The second paper will deal with the other orthodontic appliances that may be encountered by GDPs in their daily practice. Clinical Relevance: Appropriate handling of an orthodontic 'emergency' by the general practitioner will, on many occasions, provide immediate relief of pain and distress for the patient. This will in turn allow treatment to continue moving in the right direction, thus allowing more efficient and effective use of valuable resources.
A Survey of Solver-Related Geometry and Meshing Issues
NASA Technical Reports Server (NTRS)
Masters, James; Daniel, Derick; Gudenkauf, Jared; Hine, David; Sideroff, Chris
2016-01-01
There is a concern in the computational fluid dynamics community that mesh generation is a significant bottleneck in the CFD workflow. This is one of several papers that will help set the stage for a moderated panel discussion addressing this issue. Although certain general "rules of thumb" and a priori mesh metrics can be used to ensure that some base level of mesh quality is achieved, inadequate consideration is often given to the type of solver or particular flow regime on which the mesh will be utilized. This paper explores how an analyst may want to think differently about a mesh based on considerations such as if a flow is compressible vs. incompressible or hypersonic vs. subsonic or if the solver is node-centered vs. cell-centered. This paper is a high-level investigation intended to provide general insight into how considering the nature of the solver or flow when performing mesh generation has the potential to increase the accuracy and/or robustness of the solution and drive the mesh generation process to a state where it is no longer a hindrance to the analysis process.
A Nonlinear Modal Aeroelastic Solver for FUN3D
NASA Technical Reports Server (NTRS)
Goldman, Benjamin D.; Bartels, Robert E.; Biedron, Robert T.; Scott, Robert C.
2016-01-01
A nonlinear structural solver has been implemented internally within the NASA FUN3D computational fluid dynamics code, allowing for some new aeroelastic capabilities. Using a modal representation of the structure, a set of differential or differential-algebraic equations are derived for general thin structures with geometric nonlinearities. ODEPACK and LAPACK routines are linked with FUN3D, and the nonlinear equations are solved at each CFD time step. The existing predictor-corrector method is retained, whereby the structural solution is updated after mesh deformation. The nonlinear solver is validated using a test case for a flexible aeroshell at transonic, supersonic, and hypersonic flow conditions. Agreement with linear theory is seen for the static aeroelastic solutions at relatively low dynamic pressures, but structural nonlinearities limit deformation amplitudes at high dynamic pressures. No flutter was found at any of the tested trajectory points, though LCO may be possible in the transonic regime.
NASA Astrophysics Data System (ADS)
Guda, A. A.; Guda, S. A.; Soldatov, M. A.; Lomachenko, K. A.; Bugaev, A. L.; Lamberti, C.; Gawelda, W.; Bressler, C.; Smolentsev, G.; Soldatov, A. V.; Joly, Y.
2016-05-01
Finite difference method (FDM) implemented in the FDMNES software [Phys. Rev. B, 2001, 63, 125120] was revised. Thorough analysis shows, that the calculated diagonal in the FDM matrix consists of about 96% zero elements. Thus a sparse solver would be more suitable for the problem instead of traditional Gaussian elimination for the diagonal neighbourhood. We have tried several iterative sparse solvers and the direct one MUMPS solver with METIS ordering turned out to be the best. Compared to the Gaussian solver present method is up to 40 times faster and allows XANES simulations for complex systems already on personal computers. We show applicability of the software for metal-organic [Fe(bpy)3]2+ complex both for low spin and high spin states populated after laser excitation.
NASA Astrophysics Data System (ADS)
Klibanov, Michael V.; Romanov, Vladimir G.
2016-01-01
The 3D inverse scattering problem of the reconstruction of the unknown dielectric permittivity in the generalized Helmholtz equation is considered. Applications are in imaging of nanostructures and biological cells. The main difference with the conventional inverse scattering problems is that only the modulus of the scattering wave field is measured. The phase is not measured. The initializing wave field is the incident plane wave. On the other hand, in the previous recent works of the authors about the ‘phaseless topic’ the case of the point source was considered (Klibanov and Romanov 2015 J. Inverse Ill-Posed Problem 23 415-28 J. Inverse Ill-Posed Problem 23 187-93). Two reconstruction procedures are developed.
Plasma wave simulation based on a versatile FEM solver on Alcator C-Mod
NASA Astrophysics Data System (ADS)
Shiraiwa, Syun'ichi
2009-11-01
A new efficient full wave simulation code of the lower hybrid (LH) wave was developed using the finite element method (FEM). A dielectric tensor consisting of the cold plasma contribution and the electron Landau damping (ELD) was used. The non-trivial problem of introducing non-local hot plasma effects into an FEM solver was addressed by iteratively solving the coupled problem of the Maxwell's equations with the convolution integral. With this approach, the EM problem is numerically sparse, and the computational requirements are reduced significantly compared to spectral domain solvers [1]. The simulation of an Alcator C-Mod scale plasma has been done on a desktop computer, suggesting the possibility of an ITER scale plasma simulation. The algorithm was implemented using a general purpose FEM software, COMSOL Multiphysics, and the simulation results of a Maxwellian tokamak plasma showed good agreement with ray tracing calculations in the strong single pass absorption regime. Integration of a Fokker-Planck calculation for a more realistic non-Maxwellian plasma is underway and initial results show reasonable shift of the power absorption towards the plasma edge [2]. Importantly, the FEM approach allows seamless handling of the core, SOL, and antenna regions. This flexibility has been exploited to address issues of antenna-plasma coupling in the LH and ICRF frequency ranges. Techniques to use the FEM package for this purpose were validated by solving the LH grill antenna coupling problem whose analytic solution is known. The code has been applied to a new Alcator C-Mod ICRF antenna to assess the antenna near field pattern [3]. [4pt] [1] J. C. Wright, et. al., Comput. Phys. 4, 545 (2008) [0pt] [2] O. Meneghini, et. al., this conference [0pt] [3] M. Garrett, et. al., this conference
A Simple Quantum Integro-Differential Solver (SQuIDS)
NASA Astrophysics Data System (ADS)
Argüelles Delgado, Carlos A.; Salvado, Jordi; Weaver, Christopher N.
2015-11-01
Simple Quantum Integro-Differential Solver (SQuIDS) is a C++ code designed to solve semi-analytically the evolution of a set of density matrices and scalar functions. This is done efficiently by expressing all operators in an SU(N) basis. SQuIDS provides a base class from which users can derive new classes to include new non-trivial terms from the right hand sides of density matrix equations. The code was designed in the context of solving neutrino oscillation problems, but can be applied to any problem that involves solving the quantum evolution of a collection of particles with Hilbert space of dimension up to six.
Solution strategies for constant acceleration problems
NASA Astrophysics Data System (ADS)
Wheaton, S. M.; Binder, P.-M.
2017-03-01
We discuss strategies for the general solution of single-step 1D constant acceleration problems. In a slightly restricted form, these problems have five variables (Δx, v 0, v, a and t) and two independent equations, so three variables must be given to solve for the other two, giving 10 cases. Instead of the haphazard solution of individual problems, we advocate teaching a strategy for tackling the entire class of problems. We enumerate the possible strategies, and present in detail one which reveals a number of interesting special cases and also allows the possibility of developing an automatic problem generator and solver.
Parallelizing alternating direction implicit solver on GPUs
Technology Transfer Automated Retrieval System (TEKTRAN)
We present a parallel Alternating Direction Implicit (ADI) solver on GPUs. Our implementation significantly improves existing implementations in two aspects. First, we address the scalability issue of existing Parallel Cyclic Reduction (PCR) implementations by eliminating their hardware resource con...
Max-product algorithms for the generalized multiple-fault diagnosis problem.
Le, Tung; Hadjicostis, Christoforos N
2007-12-01
In this paper, we study the application of the max-product algorithm (MPA) to the generalized multiple-fault diagnosis (GMFD) problem, which consists of components (to be diagnosed) and alarms/connections that can be unreliable. The MPA and the improved sequential MPA (SMPA) that we develop in this paper are local-message-passing algorithms that operate on the bipartite diagnosis graph (BDG) associated with the GMFD problem and converge to the maximum a posteriori probability (MAP) solution if this graph is acyclic (in addition, the MPA requires the MAP solution to be unique). Our simulations suggest that both the MPA and the SMPA perform well in more general systems that may exhibit cycles in the associated BDGs (the SMPA also appears to outperform the MPA in these more general systems). In this paper, we provide analytical results for acyclic BDGs and also assess the performance of both algorithms under particular patterns of alarm observations in general graphs; this allows us to obtain analytical bounds on the probability of making erroneous diagnosis with respect to the MAP solution. We also evaluate the performance of the MPA and the SMPA algorithms via simulations, and provide comparisons with previously developed heuristics for this type of diagnosis problems. We conclude that the MPA and the SMPA perform well under reasonable computational complexity when the underlying diagnosis graph is sparse.
Generalized CNF satisfiability, local reductions and complexity of succinctly specified problems
Marathe, M.V.; Hunt, H.B. III; Stearns, R.E.; Radhakrishnan, V.
1995-02-01
We, study the complexity and efficient approximability of various decision, counting and optimization problems when instances are specified using (1) the 1-dimensional finite periodic narrow specifications of Wanke, (2) the 2-way infinite 1-dimensional narrow periodic (sometimes called dynamic) specifications of Karp and Orlin et al., and (3) the hierarchical specification language of Lengauer et al. We outline how generalized CNF satisfiability problems and local reductions can be used to obtain both hardness and easiness results for a number of decision, counting, optimization and approximate optimization problems when instances are specified as in (1), (2) or (3). As corollaries we obtain a number of new PSPACE-hardness and {number_sign}PSPACE-hardness,9 results and a number of new polynomial time approximation algorithms for natural PSPACE-hard optimization problems. In particular assuming P {ne} PSPACE, we characterize completely the complexities of the generalized CNF satisfiability problems SAT(S) of Schaefer [Sc78], when instances are specified as in (1), (2) or (3).
User's Manual for PCSMS (Parallel Complex Sparse Matrix Solver). Version 1.
NASA Technical Reports Server (NTRS)
Reddy, C. J.
2000-01-01
PCSMS (Parallel Complex Sparse Matrix Solver) is a computer code written to make use of the existing real sparse direct solvers to solve complex, sparse matrix linear equations. PCSMS converts complex matrices into real matrices and use real, sparse direct matrix solvers to factor and solve the real matrices. The solution vector is reconverted to complex numbers. Though, this utility is written for Silicon Graphics (SGI) real sparse matrix solution routines, it is general in nature and can be easily modified to work with any real sparse matrix solver. The User's Manual is written to make the user acquainted with the installation and operation of the code. Driver routines are given to aid the users to integrate PCSMS routines in their own codes.
The Rayleigh-Stokes problem for an edge in a generalized Oldroyd-B fluid
NASA Astrophysics Data System (ADS)
Fetecau, Corina; Jamil, Muhammad; Fetecau, Constantin; Vieru, Dumitru
2009-09-01
The velocity field corresponding to the Rayleigh-Stokes problem for an edge, in an incompressible generalized Oldroyd-B fluid has been established by means of the double Fourier sine and Laplace transforms. The fractional calculus approach is used in the constitutive relationship of the fluid model. The obtained solution, written in terms of the generalized G-functions, is presented as a sum of the Newtonian solution and the corresponding non-Newtonian contribution. The solution for generalized Maxwell fluids, as well as those for ordinary Maxwell and Oldroyd-B fluids, performing the same motion, is obtained as a limiting case of the present solution. This solution can be also specialized to give the similar solution for generalized second grade fluids. However, for simplicity, a new and simpler exact solution is established for these fluids. For β → 1, this last solution reduces to a previous solution obtained by a different technique.
Improved Stiff ODE Solvers for Combustion CFD
NASA Astrophysics Data System (ADS)
Imren, A.; Haworth, D. C.
2016-11-01
Increasingly large chemical mechanisms are needed to predict autoignition, heat release and pollutant emissions in computational fluid dynamics (CFD) simulations of in-cylinder processes in compression-ignition engines and other applications. Calculation of chemical source terms usually dominates the computational effort, and several strategies have been proposed to reduce the high computational cost associated with realistic chemistry in CFD. Central to most strategies is a stiff ordinary differential equation (ODE) solver to compute the change in composition due to chemical reactions over a computational time step. Most work to date on stiff ODE solvers for computational combustion has focused on backward differential formula (BDF) methods, and has not explicitly considered the implications of how the stiff ODE solver couples with the CFD algorithm. In this work, a fresh look at stiff ODE solvers is taken that includes how the solver is integrated into a turbulent combustion CFD code, and the advantages of extrapolation-based solvers in this regard are demonstrated. Benefits in CPU time and accuracy are demonstrated for homogeneous systems and compression-ignition engines, for chemical mechanisms that range in size from fewer than 50 to more than 7,000 species.
Generalized Dirichlet to Neumann map for moving initial-boundary value problems
Fokas, A. S.; Pelloni, B.
2007-01-15
We present an algorithm for characterizing the generalized Dirichlet to Neumann map for moving initial-boundary value problems. This algorithm is derived by combining the so-called global relation, which couples the initial and boundary values of the problem, with a new method for inverting certain one-dimensional integrals. This new method is based on the spectral analysis of an associated ordinary differantial equation and on the use of the d-bar formalism. As an illustration, the Neumann boundary value for the linearized Schroedinger equation is determined in terms of the Dirichlet boundary value and of the initial conditi0008.
The use of Lanczos's method to solve the large generalized symmetric definite eigenvalue problem
NASA Technical Reports Server (NTRS)
Jones, Mark T.; Patrick, Merrell L.
1989-01-01
The generalized eigenvalue problem, Kx = Lambda Mx, is of significant practical importance, especially in structural enginering where it arises as the vibration and buckling problem. A new algorithm, LANZ, based on Lanczos's method is developed. LANZ uses a technique called dynamic shifting to improve the efficiency and reliability of the Lanczos algorithm. A new algorithm for solving the tridiagonal matrices that arise when using Lanczos's method is described. A modification of Parlett and Scott's selective orthogonalization algorithm is proposed. Results from an implementation of LANZ on a Convex C-220 show it to be superior to a subspace iteration code.
Generalized Thomson problem in arbitrary dimensions and non-euclidean geometries
NASA Astrophysics Data System (ADS)
Batle, J.; Bagdasaryan, Armen; Abdel-Aty, M.; Abdalla, S.
2016-06-01
Systems of identical particles with equal charge are studied under a special type of confinement. These classical particles are free to move inside some convex region S and on the boundary of it Ω (the S d - 1 -sphere, in our case). We shall show how particles arrange themselves under the sole action of the Coulomb repulsion in many dimensions in the usual Euclidean space, therefore generalizing the so called Thomson problem to many dimensions. Also, we explore how the problem varies when non-Euclidean geometries are considered. We shall see that optimal configurations in all cases possess a high degree of symmetry, regardless of the concomitant dimension or geometry.
A note on relative motion in the general three-body problem.
NASA Technical Reports Server (NTRS)
Broucke, R.; Lass, H.
1973-01-01
It is shown that the equations of the general three-body problem take on a very symmetric form when one considers only their relative positions, rather than position vectors relative to some given coordinate system. From these equations one quickly surmises some well known classical properties of the three-body problem, such as the first integrals and the equilateral triangle solutions. Some new Lagrangians with relative coordinates are also obtained. Numerical integration of the new equations of motion is about 10% faster than with barycentric or heliocentric coordinates.
NASA Astrophysics Data System (ADS)
Gainullin, I. K.; Sonkin, M. A.
2015-03-01
A parallelized three-dimensional (3D) time-dependent Schrodinger equation (TDSE) solver for one-electron systems is presented in this paper. The TDSE Solver is based on the finite-difference method (FDM) in Cartesian coordinates and uses a simple and explicit leap-frog numerical scheme. The simplicity of the numerical method provides very efficient parallelization and high performance of calculations using Graphics Processing Units (GPUs). For example, calculation of 106 time-steps on the 1000ṡ1000ṡ1000 numerical grid (109 points) takes only 16 hours on 16 Tesla M2090 GPUs. The TDSE Solver demonstrates scalability (parallel efficiency) close to 100% with some limitations on the problem size. The TDSE Solver is validated by calculation of energy eigenstates of the hydrogen atom (13.55 eV) and affinity level of H- ion (0.75 eV). The comparison with other TDSE solvers shows that a GPU-based TDSE Solver is 3 times faster for the problems of the same size and with the same cost of computational resources. The usage of a non-regular Cartesian grid or problem-specific non-Cartesian coordinates increases this benefit up to 10 times. The TDSE Solver was applied to the calculation of the resonant charge transfer (RCT) in nanosystems, including several related physical problems, such as electron capture during H+-H0 collision and electron tunneling between H- ion and thin metallic island film.
NITSOL: A Newton iterative solver for nonlinear systems
Pernice, M.; Walker, H.F.
1996-12-31
Newton iterative methods, also known as truncated Newton methods, are implementations of Newton`s method in which the linear systems that characterize Newton steps are solved approximately using iterative linear algebra methods. Here, we outline a well-developed Newton iterative algorithm together with a Fortran implementation called NITSOL. The basic algorithm is an inexact Newton method globalized by backtracking, in which each initial trial step is determined by applying an iterative linear solver until an inexact Newton criterion is satisfied. In the implementation, the user can specify inexact Newton criteria in several ways and select an iterative linear solver from among several popular {open_quotes}transpose-free{close_quotes} Krylov subspace methods. Jacobian-vector products used by the Krylov solver can be either evaluated analytically with a user-supplied routine or approximated using finite differences of function values. A flexible interface permits a wide variety of preconditioning strategies and allows the user to define a preconditioner and optionally update it periodically. We give details of these and other features and demonstrate the performance of the implementation on a representative set of test problems.
The Effect of New Vocabulary on Problem Solving in Novice Physics Students.
ERIC Educational Resources Information Center
Sobolewski, Stanley J.
One of the difficulties encountered by novice problem solvers in introductory physics is in the area of problem solving. It has been shown in other studies that poor problem solvers are affected by the surface aspects of the problem in contrast with more efficient problem solvers who are capable of constructing a mental model of the physical…
NASA Astrophysics Data System (ADS)
Acker, A.
Under reasonably general assumptions, we prove the existence of convex classical solutions for the Prandtl-Batchelor free boundary problem in fluid dynamics, in which a flow of constant vorticity density is embedded in a potential flow, with a vortex sheet of constant vorticity density as the flow interface. These results apply to Batchelor flows which are confined to a bounded, convex vessel, and for which the limiting interior flow-speed exceeds the limiting exterior flow-speed along the interface.
NASA Astrophysics Data System (ADS)
Scapellato, Andrea
2017-01-01
Aim of this study is to obtain an interior estimate for the solution of the Dirichlet problem for a linear elliptic partial differential equations having the coefficients of the principal part that belong to the Sarason class VMO of functions with vanishing mean oscillation. In order to obtain the desidered result we use some estimates for singular integral operators and commutators on Generalized Local Morrey Spaces.
QED multi-dimensional vacuum polarization finite-difference solver
NASA Astrophysics Data System (ADS)
Carneiro, Pedro; Grismayer, Thomas; Silva, Luís; Fonseca, Ricardo
2015-11-01
The Extreme Light Infrastructure (ELI) is expected to deliver peak intensities of 1023 - 1024 W/cm2 allowing to probe nonlinear Quantum Electrodynamics (QED) phenomena in an unprecedented regime. Within the framework of QED, the second order process of photon-photon scattering leads to a set of extended Maxwell's equations [W. Heisenberg and H. Euler, Z. Physik 98, 714] effectively creating nonlinear polarization and magnetization terms that account for the nonlinear response of the vacuum. To model this in a self-consistent way, we present a multi dimensional generalized Maxwell equation finite difference solver with significantly enhanced dispersive properties, which was implemented in the OSIRIS particle-in-cell code [R.A. Fonseca et al. LNCS 2331, pp. 342-351, 2002]. We present a detailed numerical analysis of this electromagnetic solver. As an illustration of the properties of the solver, we explore several examples in extreme conditions. We confirm the theoretical prediction of vacuum birefringence of a pulse propagating in the presence of an intense static background field [arXiv:1301.4918 [quant-ph
Irrelevance in Problem Solving
NASA Technical Reports Server (NTRS)
Levy, Alon Y.
1992-01-01
The notion of irrelevance underlies many different works in AI, such as detecting redundant facts, creating abstraction hierarchies and reformulation and modeling physical devices. However, in order to design problem solvers that exploit the notion of irrelevance, either by automatically detecting irrelevance or by being given knowledge about irrelevance, a formal treatment of the notion is required. In this paper we present a general framework for analyzing irrelevance. We discuss several properties of irrelevance and show how they vary in a space of definitions outlined by the framework. We show how irrelevance claims can be used to justify the creation of abstractions thereby suggesting a new view on the work on abstraction.
Three-dimensional crack and contact problems with a general geometric configuration
NASA Astrophysics Data System (ADS)
Yong, Z.; Hanson, M. T.
1994-02-01
A NEW METHOD, based on point set theory and properties of orthogonal functions, is developed for determining exact solutions to three-dimensional crack and contact problems with complicated geometric configurations (e.g. a star-convex domain) in an infinite linear elastic medium. The governing equation is a two-dimensional Fredholm integral equation of the first kind. The central idea of this method is the chain extension of an exact solution from a regular subdomain to an irregular entire domain. Examples are given illustrating how this solution procedure can be used to obtain exact closed form solutions for a general Hertz contact problem and various crack problems in an inhomogeneous isotropic medium with an elastic modulus which is a power function of depth.
Stathopoulos, A.; Fischer, C.F.; Saad, Y.
1994-12-31
The solution of the large, sparse, symmetric eigenvalue problem, Ax = {lambda}x, is central to many scientific applications. Among many iterative methods that attempt to solve this problem, the Lanczos and the Generalized Davidson (GD) are the most widely used methods. The Lanczos method builds an orthogonal basis for the Krylov subspace, from which the required eigenvectors are approximated through a Rayleigh-Ritz procedure. Each Lanczos iteration is economical to compute but the number of iterations may grow significantly for difficult problems. The GD method can be considered a preconditioned version of Lanczos. In each step the Rayleigh-Ritz procedure is solved and explicit orthogonalization of the preconditioned residual ((M {minus} {lambda}I){sup {minus}1}(A {minus} {lambda}I)x) is performed. Therefore, the GD method attempts to improve convergence and robustness at the expense of a more complicated step.
Miller, Gregory H.
2003-08-06
In this paper we present a general iterative method for the solution of the Riemann problem for hyperbolic systems of PDEs. The method is based on the multiple shooting method for free boundary value problems. We demonstrate the method by solving one-dimensional Riemann problems for hyperelastic solid mechanics. Even for conditions representative of routine laboratory conditions and military ballistics, dramatic differences are seen between the exact and approximate Riemann solution. The greatest discrepancy arises from misallocation of energy between compressional and thermal modes by the approximate solver, resulting in nonphysical entropy and temperature estimates. Several pathological conditions arise in common practice, and modifications to the method to handle these are discussed. These include points where genuine nonlinearity is lost, degeneracies, and eigenvector deficiencies that occur upon melting.
A five-wave Harten-Lax-van Leer Riemann solver for relativistic magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Mignone, A.; Ugliano, M.; Bodo, G.
2009-03-01
We present a five-wave Riemann solver for the equations of ideal relativistic magneto-hydrodynamics. Our solver can be regarded as a relativistic extension of the five-wave HLLD Riemann solver initially developed by Miyoshi & Kusano for the equations of ideal magnetohydrodynamics. The solution to the Riemann problem is approximated by a five-wave pattern, comprising two outermost fast shocks, two rotational discontinuities and a contact surface in the middle. The proposed scheme is considerably more elaborate than in the classical case since the normal velocity is no longer constant across the rotational modes. Still, proper closure to the Rankine-Hugoniot jump conditions can be attained by solving a non-linear scalar equation in the total pressure variable which, for the chosen configuration, has to be constant over the whole Riemann fan. The accuracy of the new Riemann solver is validated against one-dimensional tests and multidimensional applications. It is shown that our new solver considerably improves over the popular Harten-Lax-van Leer solver or the recently proposed HLLC schemes.
NASA Astrophysics Data System (ADS)
Cottrill, Gerald C.
A hybrid numerical algorithm combining the Gauss Pseudospectral Method (GPM) with a Generalized Polynomial Chaos (gPC) method to solve nonlinear stochastic optimal control problems with constraint uncertainties is presented. TheGPM and gPC have been shown to be spectrally accurate numerical methods for solving deterministic optimal control problems and stochastic differential equations, respectively. The gPC uses collocation nodes to sample the random space, which are then inserted into the differential equations and solved by applying standard differential equation methods. The resulting set of deterministic solutions is used to characterize the distribution of the solution by constructing a polynomial representation of the output as a function of uncertain parameters. Optimal control problems are especially challenging to solve since they often include path constraints, bounded controls, boundary conditions, and require solutions that minimize a cost functional. Adding random parameters can make these problems even more challenging. The hybrid algorithm presented in this dissertation is the first time the GPM and gPC algorithms have been combined to solve optimal control problems with random parameters. Using the GPM in the gPC construct provides minimum cost deterministic solutions used in stochastic computations that meet path, control, and boundary constraints, thus extending current gPC methods to be applicable to stochastic optimal control problems. The hybrid GPM-gPC algorithm was applied to two concept demonstration problems: a nonlinear optimal control problem with multiplicative uncertain elements and a trajectory optimization problem simulating an aircraft flying through a threat field where exact locations of the threats are unknown. The results show that the expected value, variance, and covariance statistics of the polynomial output function approximations of the state, control, cost, and terminal time variables agree with Monte-Carlo simulation
Kastanya, Doddy Yozef Febrian; Turinsky, Paul J.
2005-05-15
A Newton-Krylov iterative solver has been developed to reduce the CPU execution time of boiling water reactor (BWR) core simulators implemented in the core simulator part of the Fuel Optimization for Reloads Multiple Objectives by Simulated Annealing for BWR (FORMOSA-B) code, which is an in-core fuel management optimization code for BWRs. This new solver utilizes Newton's method to explicitly treat strong nonlinearities in the problem, replacing the traditionally used nested iterative approach. Newton's method provides the solver with a higher-than-linear convergence rate, assuming that good initial estimates of the unknowns are provided. Within each Newton iteration, an appropriately preconditioned Krylov solver is utilized for solving the linearized system of equations. Taking advantage of the higher convergence rate provided by Newton's method and utilizing an efficient preconditioned Krylov solver, we have developed a Newton-Krylov solver to evaluate the three-dimensional, two-group neutron diffusion equations coupled with a two-phase flow model within a BWR core simulator. Numerical tests on the new solver have shown that speedups ranging from 1.6 to 2.1, with reference to the traditional approach of employing nested iterations to treat the nonlinear feedbacks, can be achieved. However, if a preconditioned Krylov solver is employed to complete the inner iterations of the traditional approach, negligible CPU time differences are noted between the Newton-Krylov and traditional (Krylov) approaches.
NASA Astrophysics Data System (ADS)
Kim, D.-J.; Duarte, C. A.; Proenca, S. P.
2012-11-01
The main feature of partition of unity methods such as the generalized or extended finite element method is their ability of utilizing a priori knowledge about the solution of a problem in the form of enrichment functions. However, analytical derivation of enrichment functions with good approximation properties is mostly limited to two-dimensional linear problems. This paper presents a procedure to numerically generate proper enrichment functions for three-dimensional problems with confined plasticity where plastic evolution is gradual. This procedure involves the solution of boundary value problems around local regions exhibiting nonlinear behavior and the enrichment of the global solution space with the local solutions through the partition of unity method framework. This approach can produce accurate nonlinear solutions with a reduced computational cost compared to standard finite element methods since computationally intensive nonlinear iterations can be performed on coarse global meshes after the creation of enrichment functions properly describing localized nonlinear behavior. Several three-dimensional nonlinear problems based on the rate-independent J 2 plasticity theory with isotropic hardening are solved using the proposed procedure to demonstrate its robustness, accuracy and computational efficiency.
Extension of the Time-Spectral Approach to Overset Solvers for Arbitrary Motion
NASA Technical Reports Server (NTRS)
Leffell, Joshua Isaac; Murman, Scott M.; Pulliam, Thomas H.
2012-01-01
demonstrated marked success in reducing the computational costs associated with simulating periodic forced flows, but have yet to be fully applied to overset or Cartesian solvers for arbitrary motion with dynamic hole-cutting. Overset and Cartesian grid methodologies are versatile techniques capable of handling complex geometry configurations in practical engineering applications, and the combination of the Time-Spectral approach with this general capability potentially provides an enabling new design and analysis tool. In an arbitrary moving-body scenario for these approaches, a Lagrangian body moves through a fixed Eulerian mesh and mesh points in the Eulerian mesh interior to the solid body are removed (cut or blanked), leaving a hole in the Eulerian mesh. During the dynamic motion some gridpoints in the domain are blanked and do not have a complete set of time-samples preventing a direct implementation of the Time-Spectral method. Murman[6] demonstrated the Time-Spectral approach for a Cartesian solver with a rigid domain motion, wherein the hole cutting remains constant. Similarly, Custer et al. [15, 16] used the NASA overset OVERFLOW solver and limited the amount of relative motion to ensure static hole-cutting and interpolation. Recently, Mavriplis and Mundis[17] demonstrated a qualitative method for applying the Time-Spectral approach to an unstructured overset solver for arbitrary motion. The goal of the current work is to develop a robust and general method for handling arbitrary motion with the Time-Spectral approach within an overset or Cartesian mesh method, while still approaching the spectral convergence rate of the original Time-Spectral approach. The viscous OVERFLOW solver will be augmented with the new Time-Spectral algorithm and the capability of the method for benchmark problems in rotorcraft and turbomachinery will be demonstrated. This abstract begins with a brief synopsis of the Time-Spectral approach for overset grids and provides details of e current
Evolution of the General Solution of the Restricted Problem Covering Symmetric and Escape Solutions
NASA Astrophysics Data System (ADS)
Goudas, C. L.; Papadakis, K. E.
2006-12-01
The work presented in paper I (Papadakis, K.E., Goudas, C.L.: Astrophys. Space Sci. (2006)) is expanded here to cover the evolution of the approximate general solution of the restricted problem covering symmetric and escape solutions for values of μ in the interval [0, 0.5]. The work is purely numerical, although the available rich theoretical background permits the assertions that most of the theoretical issues related to the numerical treatment of the problem are known. The prime objective of this work is to apply the ‘Last Geometric Theorem of Poincaré’ (Birkhoff, G.D.: Trans. Amer. Math. Soc. 14, 14 (1913); Poincaré, H.: Rend. Cir. Mat. Palermo 33, 375 (1912)) and compute dense sets of axisymmetric periodic family curves covering the initial conditions space of bounded motions for a discrete set of values of the basic parameter μ spread along the entire interval of permissible values. The results obtained for each value of μ, tested for completeness, constitute an approximation of the general solution of the problem related to symmetric motions. The approximate general solution of the same problem related to asymmetric solutions, also computable by application of the same theorem (Poincaré-Birkhoff) is left for a future paper. A secondary objective is identification-computation of the compact space of escape motions of the problem also for selected values of the mass parameter μ. We first present the approximate general solution for the integrable case μ = 0 and then the approximate solution for the nonintegrable case μ = 10-3. We then proceed to presenting the approximate general solutions for the cases μ = 0.1, 0.2, 0.3, 0.4, and 0.5, in all cases building them in four phases, namely, presenting for each value of μ, first all family curves of symmetric periodic solutions that re-enter after 1 oscillation, then adding to it successively, the family curves that re-enter after 2 to 10 oscillations, after 11 to 30 oscillations, after 31 to 50
A general population twin study of conduct problems and the auditory P300 waveform.
Bertoletti, Eleonora; Michelini, Giorgia; Moruzzi, Sara; Ferrer, Giuseppina; Ferini-Strambi, Luigi; Stazi, Maria Antonietta; Ogliari, Anna; Battaglia, Marco
2014-01-01
Reduced amplitude of the P300 event-related potential has been consistently associated with a variety of externalising problems, including conduct disorder. The few available genetically-informative studies of these relationships, however, were conducted among adolescents/adults (i.e., at an age when conduct disorder has typically already become manifest). Among 200 general population twins with a mean age of 9 years (range 6-14 years), we studied the relationship between the P300 waveform elicited by an auditory oddball task and the DSM-oriented conduct problems scale of the Child Behavior Checklist 6-18. Conduct problems scores were negatively and significantly correlated (r = -0.19, p = 0.01) with P300 amplitude; correlations between P300 amplitude and the other DSM-oriented Child Behavior Checklist scales were non-significant, except for oppositional defiant problems (p = 0.01). We found moderate heritability estimates for both P300 amplitude (0.58, CI:0.37;0.73) and conduct problems (0.52, CI:0.25;0.70). Bivariate twin analyses indicated that the covariation between these two phenotypes can be explained by additive genetic factors only, with a genetic correlation of -0.33. An association between reduced P300 amplitude and conduct problems can be substantiated already in childhood, at an age that precedes the most typical onset of conduct disorder. This relationship appears to be genetic in nature. Reduced P300 amplitude can represent a valuable marker for conduct problems, and can contribute to the early identification of children at high-risk for conduct disorder.
Domain decomposed preconditioners with Krylov subspace methods as subdomain solvers
Pernice, M.
1994-12-31
Domain decomposed preconditioners for nonsymmetric partial differential equations typically require the solution of problems on the subdomains. Most implementations employ exact solvers to obtain these solutions. Consequently work and storage requirements for the subdomain problems grow rapidly with the size of the subdomain problems. Subdomain solves constitute the single largest computational cost of a domain decomposed preconditioner, and improving the efficiency of this phase of the computation will have a significant impact on the performance of the overall method. The small local memory available on the nodes of most message-passing multicomputers motivates consideration of the use of an iterative method for solving subdomain problems. For large-scale systems of equations that are derived from three-dimensional problems, memory considerations alone may dictate the need for using iterative methods for the subdomain problems. In addition to reduced storage requirements, use of an iterative solver on the subdomains allows flexibility in specifying the accuracy of the subdomain solutions. Substantial savings in solution time is possible if the quality of the domain decomposed preconditioner is not degraded too much by relaxing the accuracy of the subdomain solutions. While some work in this direction has been conducted for symmetric problems, similar studies for nonsymmetric problems appear not to have been pursued. This work represents a first step in this direction, and explores the effectiveness of performing subdomain solves using several transpose-free Krylov subspace methods, GMRES, transpose-free QMR, CGS, and a smoothed version of CGS. Depending on the difficulty of the subdomain problem and the convergence tolerance used, a reduction in solution time is possible in addition to the reduced memory requirements. The domain decomposed preconditioner is a Schur complement method in which the interface operators are approximated using interface probing.
Still a difficult business? Negotiating alcohol-related problems in general practice consultations.
Rapley, Tim; May, Carl; Frances Kaner, Eileen
2006-11-01
This paper describes general practitioners' (GPs) experiences of detecting and managing alcohol and alcohol-related problems in consultations. We undertook qualitative research in two phases in the North-East of England. Initially, qualitative interviews with 29 GPs explored their everyday work with patients with alcohol-related issues. We then undertook group interviews--two with GPs and one with a primary care team--where they discussed and challenged findings of the interviews. The GPs reported routinely discussing alcohol with patients with a range of alcohol-related problems. GPs believed that this work is important, but felt that until patients were willing to accept that their alcohol consumption was problematic they could achieve very little. They tentatively introduced alcohol as a potential problem, re-introduced the topic periodically, and then waited until the patient decided to change their behaviour. They were aware that they could identify and manage more patients. A lack of time and having to work with the multiple problems that patients brought to consultations were the main factors that stopped GPs managing more risky drinkers. Centrally, we compared the results of our study with [Thom, B., & Tellez, C. (1986). A difficult business-Detecting and managing alcohol-problems in general-practice. British Journal of Addiction, 81, 405-418] seminal study that was undertaken 20 years ago. We show how the intellectual, moral, emotional and practical difficulties that GPs currently face are quite similar to those faced by GPs from 20 years ago. As the definition of what could constitute abnormal alcohol consumption has expanded, so the range of consultations that they may have to negotiate these difficulties in has also expanded.
Inductive ionospheric solver for magnetospheric MHD simulations
NASA Astrophysics Data System (ADS)
Vanhamäki, H.
2011-01-01
We present a new scheme for solving the ionospheric boundary conditions required in magnetospheric MHD simulations. In contrast to the electrostatic ionospheric solvers currently in use, the new solver takes ionospheric induction into account by solving Faraday's law simultaneously with Ohm's law and current continuity. From the viewpoint of an MHD simulation, the new inductive solver is similar to the electrostatic solvers, as the same input data is used (field-aligned current [FAC] and ionospheric conductances) and similar output is produced (ionospheric electric field). The inductive solver is tested using realistic, databased models of an omega-band and westward traveling surge. Although the tests were performed with local models and MHD simulations require a global ionospheric solution, we may nevertheless conclude that the new solution scheme is feasible also in practice. In the test cases the difference between static and electrodynamic solutions is up to ~10 V km-1 in certain locations, or up to 20-40% of the total electric field. This is in agreement with previous estimates. It should also be noted that if FAC is replaced by the ground magnetic field (or ionospheric equivalent current) in the input data set, exactly the same formalism can be used to construct an inductive version of the KRM method originally developed by Kamide et al. (1981).
NASA Technical Reports Server (NTRS)
Martin, E. D.; Lomax, H.
1977-01-01
Revised and extended versions of a fast, direct (noniterative) numerical Cauchy-Riemann solver are presented for solving finite difference approximations of first order systems of partial differential equations. Although the difference operators treated are linear and elliptic, one significant application of these extended direct Cauchy-Riemann solvers is in the fast, semidirect (iterative) solution of fluid dynamic problems governed by the nonlinear mixed elliptic-hyperbolic equations of transonic flow. Different versions of the algorithms are derived and the corresponding FORTRAN computer programs for a simple example problem are described and listed. The algorithms are demonstrated to be efficient and accurate.
NASA Astrophysics Data System (ADS)
Rogovtsov, Nikolai N.; Borovik, Felix
2016-11-01
A brief analysis of different properties and principles of invariance to solve a number of classical problems of the radiation transport theory is presented. The main ideas, constructions, and assertions used in the general invariance relations reduction method are described in outline. The most important distinctive features of this general method of solving a wide enough range of problems of the radiation transport theory and mathematical physics are listed. To illustrate the potential of this method, a number of problems of the scalar radiative transfer theory have been solved rigorously in the article. The main stages of rigorous derivations of asymptotical formulas for the smallest in modulo elements of the discrete spectrum and the eigenfunctions, corresponding to them, of the characteristic equation for the case of an arbitrary phase function and almost conservative scattering are described. Formulas of the same type for the azimuthal averaged reflection function, the plane and spherical albedos have been obtained rigorously. New analytical representations for the reflection function, the plane and spherical albedos have been obtained, and effective algorithms for calculating these values have been offered for the case of a practically arbitrary phase function satisfying the Hölder condition. New analytical representation of the «surface» Green function of the scalar radiative transfer equation for a semi-infinite plane-parallel conservatively scattering medium has been found. The deep regime asymptotics of the "volume" Green function has been obtained for the case of a turbid medium of cylindrical form.
Combinatorial approach to generalized Bell and Stirling numbers and boson normal ordering problem
Mendez, M.A.; Blasiak, P.; Penson, K.A.
2005-08-01
We consider the numbers arising in the problem of normal ordering of expressions in boson creation a{sup {dagger}} and annihilation a operators ([a,a{sup {dagger}}]=1). We treat a general form of a boson string (a{sup {dagger}}){sup r{sub n}}a{sup s{sub n}}...(a{sup {dagger}}){sup r{sub 2}}a{sup s{sub 2}}(a{sup {dagger}}){sup r{sub 1}}a{sup s{sub 1}} which is shown to be associated with generalizations of Stirling and Bell numbers. The recurrence relations and closed-form expressions (Dobinski-type formulas) are obtained for these quantities by both algebraic and combinatorial methods. By extensive use of methods of combinatorial analysis we prove the equivalence of the aforementioned problem to the enumeration of special families of graphs. This link provides a combinatorial interpretation of the numbers arising in this normal ordering problem.
New iterative solvers for the NAG Libraries
Salvini, S.; Shaw, G.
1996-12-31
The purpose of this paper is to introduce the work which has been carried out at NAG Ltd to update the iterative solvers for sparse systems of linear equations, both symmetric and unsymmetric, in the NAG Fortran 77 Library. Our current plans to extend this work and include it in our other numerical libraries in our range are also briefly mentioned. We have added to the Library the new Chapter F11, entirely dedicated to sparse linear algebra. At Mark 17, the F11 Chapter includes sparse iterative solvers, preconditioners, utilities and black-box routines for sparse symmetric (both positive-definite and indefinite) linear systems. Mark 18 will add solvers, preconditioners, utilities and black-boxes for sparse unsymmetric systems: the development of these has already been completed.
Using SPARK as a Solver for Modelica
Wetter, Michael; Wetter, Michael; Haves, Philip; Moshier, Michael A.; Sowell, Edward F.
2008-06-30
Modelica is an object-oriented acausal modeling language that is well positioned to become a de-facto standard for expressing models of complex physical systems. To simulate a model expressed in Modelica, it needs to be translated into executable code. For generating run-time efficient code, such a translation needs to employ algebraic formula manipulations. As the SPARK solver has been shown to be competitive for generating such code but currently cannot be used with the Modelica language, we report in this paper how SPARK's symbolic and numerical algorithms can be implemented in OpenModelica, an open-source implementation of a Modelica modeling and simulation environment. We also report benchmark results that show that for our air flow network simulation benchmark, the SPARK solver is competitive with Dymola, which is believed to provide the best solver for Modelica.
An approximate Riemann solver for hypervelocity flows
NASA Technical Reports Server (NTRS)
Jacobs, Peter A.
1991-01-01
We describe an approximate Riemann solver for the computation of hypervelocity flows in which there are strong shocks and viscous interactions. The scheme has three stages, the first of which computes the intermediate states assuming isentropic waves. A second stage, based on the strong shock relations, may then be invoked if the pressure jump across either wave is large. The third stage interpolates the interface state from the two initial states and the intermediate states. The solver is used as part of a finite-volume code and is demonstrated on two test cases. The first is a high Mach number flow over a sphere while the second is a flow over a slender cone with an adiabatic boundary layer. In both cases the solver performs well.
Beliefs about gambling problems and recovery: results from a general population telephone survey.
Cunningham, John A; Cordingley, Joanne; Hodgins, David C; Toneatto, Tony
2011-12-01
Respondents were asked their beliefs about gambling abuse as part of a general population telephone survey. The random digit dialing survey consisted of 8,467 interviews of adults, 18 years and older, from Ontario, Canada (45% male; mean age = 46.2). The predominant conception of gambling abuse was that of an addiction, similar to drug addiction. More than half of respondents reported that treatment was necessary and almost three-quarters of respondents felt that problem gamblers would have to give up gambling completely in order to overcome their gambling problem. Problem gamblers (past or current) were less likely than non- or social gamblers to believe that treatment was needed, and current problem gamblers were least likely to believe that abstinence was required, as compared to all other respondents. Strong agreement with conceptions of gambling abuse as disease or addiction were positively associated with belief that treatment is needed, while strong agreement with conceptions of disease or wrongdoing were positively associated with belief that abstinence is required.
NASA Astrophysics Data System (ADS)
Guo, Peng; Cheng, Wenming; Wang, Yi
2014-10-01
The quay crane scheduling problem (QCSP) determines the handling sequence of tasks at ship bays by a set of cranes assigned to a container vessel such that the vessel's service time is minimized. A number of heuristics or meta-heuristics have been proposed to obtain the near-optimal solutions to overcome the NP-hardness of the problem. In this article, the idea of generalized extremal optimization (GEO) is adapted to solve the QCSP with respect to various interference constraints. The resulting GEO is termed the modified GEO. A randomized searching method for neighbouring task-to-QC assignments to an incumbent task-to-QC assignment is developed in executing the modified GEO. In addition, a unidirectional search decoding scheme is employed to transform a task-to-QC assignment to an active quay crane schedule. The effectiveness of the developed GEO is tested on a suite of benchmark problems introduced by K.H. Kim and Y.M. Park in 2004 (European Journal of Operational Research, Vol. 156, No. 3). Compared with other well-known existing approaches, the experiment results show that the proposed modified GEO is capable of obtaining the optimal or near-optimal solution in a reasonable time, especially for large-sized problems.
Multigrid method applied to the solution of an elliptic, generalized eigenvalue problem
Alchalabi, R.M.; Turinsky, P.J.
1996-12-31
The work presented in this paper is concerned with the development of an efficient MG algorithm for the solution of an elliptic, generalized eigenvalue problem. The application is specifically applied to the multigroup neutron diffusion equation which is discretized by utilizing the Nodal Expansion Method (NEM). The underlying relaxation method is the Power Method, also known as the (Outer-Inner Method). The inner iterations are completed using Multi-color Line SOR, and the outer iterations are accelerated using Chebyshev Semi-iterative Method. Furthermore, the MG algorithm utilizes the consistent homogenization concept to construct the restriction operator, and a form function as a prolongation operator. The MG algorithm was integrated into the reactor neutronic analysis code NESTLE, and numerical results were obtained from solving production type benchmark problems.
One-dimensional Coulomb-like problem in general case of deformed space with minimal length
NASA Astrophysics Data System (ADS)
Samar, M. I.; Tkachuk, V. M.
2016-08-01
In general case of deformed Heisenberg algebra leading to the minimal length, we present a definition of the inverse of position operator which is linear and two-sided. Our proposal is based on the functional analysis of the position operator. Using this definition, 1D Coulomb-like problem is studied. We find exactly the energy spectrum and the eigenfunctions for the 1D Coulomb-like potential in deformed space with arbitrary function of deformation. We analyze the energy spectrum for different partial cases of deformation function and find that the correction caused by the deformation highly depends on the type of the deformation function.
Some problems of human adaptation and ecology under the aspect of general pathology
NASA Technical Reports Server (NTRS)
Kaznacheyev, V. P.
1980-01-01
The main problems of human adaptation at the level of the body and the population in connection with the features of current morbidity of the population and certain demographic processes are analyzed. The concepts of health and adaptation of the individual and human populations are determined. The importance of the anthropo-ecological approach to the investigation of the adaptation process of human populations is demonstrated. Certain features of the etiopathogenesis of diseases are considered in connection with the population-ecological regularities of human adaptation. The importance of research on general pathology aspects of adaptation and the ecology of man for planning, and organization of public health protection is discussed.
A general model for moving boundary problems -- Application to drying of porous media
Silva, M.A.
2000-03-01
This work presents a general model to describe momentum, heat and mass transfer for moving boundary problems. The equations are obtained supposing an instantaneous superposition of a moving volume with velocity {nu}{sub s} (Lagrangean reference frame) over a stationary volume in the stream velocity {nu} (Eulerian reference frame). The set of equations for multicomponent single-phase systems is applied to porous media (multi-phase systems) using the volume-averaging method. Depending on the assumptions about the behavior of the system, it is possible to obtain the different models proposed in the literature, showing the generality of the model proposed in this work. Numerical results were compared to experimental data of Kaolin drying during the shrinking stage. These results showed a good agreement.
Some problems of the calculation of three-dimensional boundary layer flows on general configurations
NASA Technical Reports Server (NTRS)
Cebeci, T.; Kaups, K.; Mosinskis, G. J.; Rehn, J. A.
1973-01-01
An accurate solution of the three-dimensional boundary layer equations over general configurations such as those encountered in aircraft and space shuttle design requires a very efficient, fast, and accurate numerical method with suitable turbulence models for the Reynolds stresses. The efficiency, speed, and accuracy of a three-dimensional numerical method together with the turbulence models for the Reynolds stresses are examined. The numerical method is the implicit two-point finite difference approach (Box Method) developed by Keller and applied to the boundary layer equations by Keller and Cebeci. In addition, a study of some of the problems that may arise in the solution of these equations for three-dimensional boundary layer flows over general configurations.
Multi-choice stochastic transportation problem involving general form of distributions.
Quddoos, Abdul; Ull Hasan, Md Gulzar; Khalid, Mohammad Masood
2014-01-01
Many authors have presented studies of multi-choice stochastic transportation problem (MCSTP) where availability and demand parameters follow a particular probability distribution (such as exponential, weibull, cauchy or extreme value). In this paper an MCSTP is considered where availability and demand parameters follow general form of distribution and a generalized equivalent deterministic model (GMCSTP) of MCSTP is obtained. It is also shown that all previous models obtained by different authors can be deduced with the help of GMCSTP. MCSTP with pareto, power function or burr-XII distributions are also considered and equivalent deterministic models are obtained. To illustrate the proposed model two numerical examples are presented and solved using LINGO 13.0 software package.
The dynamic generalization of the Eshelby inclusion problem and its static limit
NASA Astrophysics Data System (ADS)
Ni, Luqun; Markenscoff, Xanthippi
2016-07-01
The dynamic generalization of the celebrated Eshelby inclusion with transformation strain is the (subsonically) self-similarly expanding ellipsoidal inclusion starting from the zero dimension. The solution of the governing system of partial differential equations was obtained recently by Ni & Markenscoff (In press. J. Mech. Phys. Solids (doi:10.1016/j.jmps.2016.02.025)) on the basis of the Radon transformation, while here an alternative method is presented. In the self-similarly expanding motion, the Eshelby property of constant constrained strain is valid in the interior domain of the expanding ellipsoid where the particle velocity vanishes (lacuna). The dynamic Eshelby tensor is obtained in integral form. From it, the static Eshelby tensor is obtained by a limiting procedure, as the axes' expansion velocities tend to zero and time to infinity, while their product is equal to the length of the static axis. This makes the Eshelby problem the limit of its dynamic generalization.
Some fast elliptic solvers on parallel architectures and their complexities
NASA Technical Reports Server (NTRS)
Gallopoulos, E.; Saad, Youcef
1989-01-01
The discretization of separable elliptic partial differential equations leads to linear systems with special block triangular matrices. Several methods are known to solve these systems, the most general of which is the Block Cyclic Reduction (BCR) algorithm which handles equations with nonconsistant coefficients. A method was recently proposed to parallelize and vectorize BCR. Here, the mapping of BCR on distributed memory architectures is discussed, and its complexity is compared with that of other approaches, including the Alternating-Direction method. A fast parallel solver is also described, based on an explicit formula for the solution, which has parallel computational complexity lower than that of parallel BCR.
Some fast elliptic solvers on parallel architectures and their complexities
NASA Technical Reports Server (NTRS)
Gallopoulos, E.; Saad, Y.
1989-01-01
The discretization of separable elliptic partial differential equations leads to linear systems with special block tridiagonal matrices. Several methods are known to solve these systems, the most general of which is the Block Cyclic Reduction (BCR) algorithm which handles equations with nonconstant coefficients. A method was recently proposed to parallelize and vectorize BCR. In this paper, the mapping of BCR on distributed memory architectures is discussed, and its complexity is compared with that of other approaches including the Alternating-Direction method. A fast parallel solver is also described, based on an explicit formula for the solution, which has parallel computational compelxity lower than that of parallel BCR.
Hierarchically Parallelized Constrained Nonlinear Solvers with Automated Substructuring
NASA Technical Reports Server (NTRS)
Padovan, Joe; Kwang, Abel
1994-01-01
This paper develops a parallelizable multilevel multiple constrained nonlinear equation solver. The substructuring process is automated to yield appropriately balanced partitioning of each succeeding level. Due to the generality of the procedure,_sequential, as well as partially and fully parallel environments can be handled. This includes both single and multiprocessor assignment per individual partition. Several benchmark examples are presented. These illustrate the robustness of the procedure as well as its capability to yield significant reductions in memory utilization and calculational effort due both to updating and inversion.
Problems of drug abuse, HIV and AIDS: the burden of care in one general practice.
Ronald, P J; Witcomb, J C; Robertson, J R; Roberts, J J; Shishodia, P C; Whittaker, A
1992-01-01
Responsibility for many of the problems of intravenous drug abuse and human immunodeficiency virus (HIV) infection lies with community care agencies, such as general practitioners, community psychiatric and district nurses and drug agencies. It is in general practice that this burden is most clearly observed, given that general practitioners are in charge of the day-to-day care of patients. In an attempt to quantify this workload in an inner city practice with 11,200 patients, data were gathered from several sources relating to drug use and HIV infection. The study identified 432 patients who had consulted with problems of drug abuse and/or HIV infection over the period 1981-90. Among this group of patients 161 (37%) were HIV antibody positive. Among 191 drug abusers who were still registered with the practice in 1990 dihydrocodeine was the most commonly prescribed substitute treatment (130 patients) and only nine patients were prescribed methadone. Forty seven per cent of drug users continued to inject drugs occasionally. However, analysis of urine samples revealed that there was a shift away from injecting mainly heroin to multiple drug use, including benzodiazepines, usually originating from prescribed sources. Drug abusers who were HIV positive consulted their general practitioner significantly more often over one year than those who were not (mean 24.9 versus 15.8 consultations, P < 0.01). However, there was no significant difference between these two groups in terms of days spent in hospital. A total of 61 patients were referred to a community psychiatric nurse over an eight month period.(ABSTRACT TRUNCATED AT 250 WORDS) PMID:1419244
NASA Astrophysics Data System (ADS)
Kabakian, Adour Vahe
1998-12-01
Most time-domain solvers of Maxwell's equations that are applied to electromagnetic wave scattering problems are based on second- or third-order finite-difference and finite-volume schemes. Since linear wave propagation phenomena tend to be very susceptible to numerical dissipation and dispersion errors, they place high accuracy demands on the numerical methods employed. Starting with the premise that the required accuracy can be achieved more efficiently with high-order methods, a new numerical scheme based on spectral collocation is developed for solving Maxwell's equations in the time domain. The three-dimensional method is formulated over generalized curvilinear coordinates. It employs Fourier and Chebyshev spectral collocation for the spatial derivatives, while time advancement is achieved by the explicit third-order Adams-Moulton-Bashforth scheme. A domain decomposition method supplementing the spectral solver is also developed, extending its range of applications to geometries more complex than those traditionally associated with spectral methods. Reflective and absorbing boundary conditions are developed specifically for the spectral scheme. Finally, a grid stretching function is incorporated into the solver, which can be used, when needed, to relieve the stability restriction associated with the Chebyshev spacing of the collocation points, at the expense of only moderate loss in accuracy. The numerical method is applied to solve electromagnetic wave scattering problems from perfectly conducting solid targets, using both single and multi-domain grids. The geometries considered are the circular cylinder, the square cylinder, and the sphere. Solutions are evaluated and validated by the accuracy of the radar cross-section and, in some instances, the surface currents. Compared to commonly used finite-difference and finite-volume solvers, the spectral scheme produces results that are one to two orders of magnitude more accurate, using grids that are an order of
NASA Astrophysics Data System (ADS)
Wei, Jian-Gong; Peng, Zhen; Lee, Jin-Fa
2012-10-01
The implementation details of a fast direct solver is described herein for solving dense matrix equations from the application of surface integral equation methods for electromagnetic field scatterings from non-penetrable targets. The proposed algorithm exploits the smoothness of the far field and computes a low rank decomposition of the off-diagonal coupling blocks of the matrices through a set of skeletonization processes. Moreover, an artificial surface (the Huygens' surface) is introduced for each clustering group to efficiently account for the couplings between well-separated groups. Furthermore, a recursive multilevel version of the algorithm is presented. Although asymptotically the algorithm would not alter the bleak outlook of the complexity of the worst case scenario,O(N3) for required CPU time where N denotes the number of unknowns, for electrically large electromagnetic (EM) problems; through numerical examples, we found that the proposed multilevel direct solver can scale as good as O(N1.3) in memory consumption and O(N1.8) in CPU time for moderate-sized EM problems. Note that our conclusions are drawn based on a few sample examples that we have conducted and should not be taken as a true complexity analysis for general electrodynamic applications. However, for the fixed frequency (h-refinement) scenario, where the discretization size decreases, the computational complexities observed agree well with the theoretical predictions. Namely, the algorithm exhibits O(N) and O(N1.5) complexities for memory consumption and CPU time, respectively.
Application of Aeroelastic Solvers Based on Navier Stokes Equations
NASA Technical Reports Server (NTRS)
Keith, Theo G., Jr.; Srivastava, Rakesh
2001-01-01
The propulsion element of the NASA Advanced Subsonic Technology (AST) initiative is directed towards increasing the overall efficiency of current aircraft engines. This effort requires an increase in the efficiency of various components, such as fans, compressors, turbines etc. Improvement in engine efficiency can be accomplished through the use of lighter materials, larger diameter fans and/or higher-pressure ratio compressors. However, each of these has the potential to result in aeroelastic problems such as flutter or forced response. To address the aeroelastic problems, the Structural Dynamics Branch of NASA Glenn has been involved in the development of numerical capabilities for analyzing the aeroelastic stability characteristics and forced response of wide chord fans, multi-stage compressors and turbines. In order to design an engine to safely perform a set of desired tasks, accurate information of the stresses on the blade during the entire cycle of blade motion is required. This requirement in turn demands that accurate knowledge of steady and unsteady blade loading is available. To obtain the steady and unsteady aerodynamic forces for the complex flows around the engine components, for the flow regimes encountered by the rotor, an advanced compressible Navier-Stokes solver is required. A finite volume based Navier-Stokes solver has been developed at Mississippi State University (MSU) for solving the flow field around multistage rotors. The focus of the current research effort, under NASA Cooperative Agreement NCC3- 596 was on developing an aeroelastic analysis code (entitled TURBO-AE) based on the Navier-Stokes solver developed by MSU. The TURBO-AE code has been developed for flutter analysis of turbomachine components and delivered to NASA and its industry partners. The code has been verified. validated and is being applied by NASA Glenn and by aircraft engine manufacturers to analyze the aeroelastic stability characteristics of modem fans, compressors
ERIC Educational Resources Information Center
Neman, Robert Lynn
This study was designed to assess the effects of the problem-oriented method compared to those of the traditional approach in general chemistry at the college level. The problem-oriented course included topics such as air and water pollution, drug addiction and analysis, tetraethyl-lead additives, insecticides in the environment, and recycling of…
ERIC Educational Resources Information Center
Mataka, Lloyd M.; Cobern, William W.; Grunert, Megan L.; Mutambuki, Jacinta; Akom, George
2014-01-01
This study investigate the effectiveness of adding an "explicit general problem solving teaching strategy" (EGPS) to guided inquiry (GI) on pre-service elementary school teachers' ability to solve heat transfer problems. The pre-service elementary teachers in this study were enrolled in two sections of a chemistry course for pre-service…
A Coupled Finite Volume Solver for Incompressible Flows
NASA Astrophysics Data System (ADS)
Moukalled, F.; Darwish, M.
2008-09-01
This paper reports on a pressure-based coupled algorithm for the solution of laminar incompressible flow problems. The implicit pressure-velocity coupling is accomplished by deriving a pressure equation in a way similar to a segregated SIMPLE algorithm with the extended set of equations solved simultaneously and having diagonally dominant coefficients. The superiority of the coupled approach over the segregated approach is demonstrated by solving the lid-driven flow in a square cavity problem using both methodologies and comparing their computational costs. Results indicate that the number of iterations needed by the coupled solver is grid independent. Moreover, recorded CPU time values reveal that the coupled approach substantially reduces the computational cost with the reduction rate for the problem solved increasing as the grid size increases and reaching a value as high as 115.
Manuscript "Collection of Solved Problems of General Astronomy" by Vojislav Miskovic
NASA Astrophysics Data System (ADS)
Pejovic, N.
2009-09-01
In this paper we present the first university problems book concerning astronomy written in Serbian. The topic is "Zbirka rešenih zadataka iz opšte astronomije" (A Collection of Solved Problems of General Astronomy) by Prof. Vojislav Mi\\vsković. The first part of this collection was published in 1956 in Belgrade. The second one is still in the form of a manuscript. Though completely prepared for publishing, it has never been published. From the methodical point of view the collection was interestingly and nicely arranged. All astronomical notions and formulae are treated in details and well explained so that no complementary textbook is needed. A special attention is devoted to the numerical solution of the problems, which is not only missing in Serbian schools, but also, as said by Mi\\vsković in the Preface, is not properly valued. This paper treats both parts of this Collection which have been digitized and are available in the Virtual Library of the National Digitization Centre (Virtual Library, http://elib.matf.bg.ac.yu:8080/virlib/). By means of the manuscript digitization the second part of the Collection has become available to public use.
Bordner, J.; Saied, F.
1996-12-31
GLab3D is an enhancement of an interactive environment (MGLab) for experimenting with iterative solvers and multigrid algorithms. It is implemented in MATLAB. The new version has built-in 3D elliptic pde`s and several iterative methods and preconditioners that were not available in the original version. A sparse direct solver option has also been included. The multigrid solvers have also been extended to 3D. The discretization and pde domains are restricted to standard finite differences on the unit square/cube. The power of this software studies in the fact that no programming is needed to solve, for example, the convection-diffusion equation in 3D with TFQMR and a customized V-cycle preconditioner, for a variety of problem sizes and mesh Reynolds, numbers. In addition to the graphical user interface, some sample drivers are included to show how experiments can be composed using the underlying suite of problems and solvers.
Hertz-Mindlin problem for arbitrary oblique 2D loading: General solution by memory diagrams
NASA Astrophysics Data System (ADS)
Aleshin, V.; Van Den Abeele, K.
2012-01-01
In this paper we present a new general solution to the fundamental problem of frictional contact of two elastic spheres, also known as the Hertz-Mindlin (HM) problem. The description of spheres in contact is a central topic in contact mechanics. It became a foundation of many applications, such as the friction of rough surfaces and the mechanics of granular materials and rocks, etc. Moreover, it serves as a theoretical background in modern nonlinear acoustics and elasticity, e.g. seismology and nondestructive testing. However, despite many efforts, a rigorous analytical solution for the general case when arbitrary normal and tangential forces are present is still missing, mainly because the traction distribution within the contact zone is convoluted and hardly tractable, even under relatively simple external action. Here, accepting a number of traditional limitations such as 2D loading and the existence of a functional dependence between normal and tangential forces, we propose an original way of replacing the complex traction distributions by simple graphical counterparts called memory diagrams, and we formulate a procedure that enables initiating and maintaining these memory diagrams following an arbitrary loading history. For each memory diagram, the solution can be expressed by closed-form analytical formulas that we have derived using known techniques suggested by Mindlin, Deresiewicz, and others. So far, to the best of our knowledge, arbitrary loading histories have been treated only numerically. Implementation of the proposed memory diagram method provides an easy-to-use computer-assisted analytical solution with a high level of generality. Examples and results illustrate the variety and richness of effects that can be encountered in a geometrically simple system of two contacting spheres.
Rouinfar, Amy; Agra, Elise; Larson, Adam M; Rebello, N Sanjay; Loschky, Lester C
2014-01-01
This study investigated links between visual attention processes and conceptual problem solving. This was done by overlaying visual cues on conceptual physics problem diagrams to direct participants' attention to relevant areas to facilitate problem solving. Participants (N = 80) individually worked through four problem sets, each containing a diagram, while their eye movements were recorded. Each diagram contained regions that were relevant to solving the problem correctly and separate regions related to common incorrect responses. Problem sets contained an initial problem, six isomorphic training problems, and a transfer problem. The cued condition saw visual cues overlaid on the training problems. Participants' verbal responses were used to determine their accuracy. This study produced two major findings. First, short duration visual cues which draw attention to solution-relevant information and aid in the organizing and integrating of it, facilitate both immediate problem solving and generalization of that ability to new problems. Thus, visual cues can facilitate re-representing a problem and overcoming impasse, enabling a correct solution. Importantly, these cueing effects on problem solving did not involve the solvers' attention necessarily embodying the solution to the problem, but were instead caused by solvers attending to and integrating relevant information in the problems into a solution path. Second, this study demonstrates that when such cues are used across multiple problems, solvers can automatize the extraction of problem-relevant information extraction. These results suggest that low-level attentional selection processes provide a necessary gateway for relevant information to be used in problem solving, but are generally not sufficient for correct problem solving. Instead, factors that lead a solver to an impasse and to organize and integrate problem information also greatly facilitate arriving at correct solutions.
NASA Technical Reports Server (NTRS)
Wiggins, R. A.
1972-01-01
The discrete general linear inverse problem reduces to a set of m equations in n unknowns. There is generally no unique solution, but we can find k linear combinations of parameters for which restraints are determined. The parameter combinations are given by the eigenvectors of the coefficient matrix. The number k is determined by the ratio of the standard deviations of the observations to the allowable standard deviations in the resulting solution. Various linear combinations of the eigenvectors can be used to determine parameter resolution and information distribution among the observations. Thus we can determine where information comes from among the observations and exactly how it constraints the set of possible models. The application of such analyses to surface-wave and free-oscillation observations indicates that (1) phase, group, and amplitude observations for any particular mode provide basically the same type of information about the model; (2) observations of overtones can enhance the resolution considerably; and (3) the degree of resolution has generally been overestimated for many model determinations made from surface waves.
NASA Astrophysics Data System (ADS)
Vaneeva, O. O.; Papanicolaou, N. C.; Christou, M. A.; Sophocleous, C.
2014-09-01
The exhaustive group classification of a class of variable coefficient generalized KdV equations is presented, which completes and enhances results existing in the literature. Lie symmetries are used for solving an initial and boundary value problem for certain subclasses of the above class. Namely, the found Lie symmetries are applied in order to reduce the initial and boundary value problem for the generalized KdV equations (which are PDEs) to an initial value problem for nonlinear third-order ODEs. The latter problem is solved numerically using the finite difference method. Numerical solutions are computed and the vast parameter space is studied.
NASA Technical Reports Server (NTRS)
Biedron, Robert T.; Vatsa, Veer N.; Atkins, Harold L.
2005-01-01
We apply an unsteady Reynolds-averaged Navier-Stokes (URANS) solver for unstructured grids to unsteady flows on moving and stationary grids. Example problems considered are relevant to active flow control and stability and control. Computational results are presented using the Spalart-Allmaras turbulence model and are compared to experimental data. The effect of grid and time-step refinement are examined.
Fast methods incorporating direct elliptic solvers for nonlinear applications in fluid dynamics
NASA Technical Reports Server (NTRS)
Martin, E. D.
1977-01-01
Semidirect methods are discussed, their present role, as well as some developments for their application in computational fluid dynamics. A semidirect method is a computational scheme that uses a fast, direct, elliptic solver as the driving algorithm for the iterative solution of finite difference equations. Specific subtopics include: (1) direct Cauchy Riemann solvers for first order elliptic equations; (2) application of the semidirect method to the mixed elliptic hyperbolic problem of steady, inviscid transonic flow; and (3) the treatment of interior conditions, such as those on an airfoil or wing, in semidirect methods.
A generalized number theory problem applied to ideal liquids and to terminological lexis
NASA Astrophysics Data System (ADS)
Maslov, V. P.; Maslova, T. V.
2017-01-01
We consider the notion of number of degrees of freedom in number theory and thermodynamics. This notion is applied to notions of terminology such as terms, slogans, themes, rules, and regulations. Prohibitions are interpreted as restrictions on the number of degrees of freedom. We present a theorem on the small number of degrees of freedom as a consequence of the generalized partitio numerorum problem. We analyze the relationship between thermodynamically ideal liquids with the lexical background that a term acquires in the process of communication. Examples showing how this background may be enhanced are considered. We discuss the question of the coagulation of drops in connection with the forecast of analogs of the gas-ideal liquid phase transition in social-political processes.
Mikami, Katsunaka; Jorge, Ricardo E; Moser, David J; Arndt, Stephan; Jang, Mijin; Solodkin, Ana; Small, Steven L; Fonzetti, Pasquale; Hegel, Mark T; Robinson, Robert G
2014-01-01
This study examined the efficacy of antidepressant treatment for preventing the onset of generalized anxiety disorder (GAD) among patients with recent stroke. Of 799 patients assessed, 176 were randomized, and 149 patients without evidence of GAD at the initial visit were included in this double-blind treatment with escitalopram (N=47) or placebo (N=49) or non-blinded problem-solving therapy (PST; 12 total sessions; N=53). Participants given placebo over 12 months were 4.95 times more likely to develop GAD than patients given escitalopram and 4.00 times more likely to develop GAD than patients given PST. Although these results should be considered preliminary, the authors found that both escitalopram and PST were effective in preventing new onset of post-stroke GAD.
NASA Astrophysics Data System (ADS)
Kuzovkov, V. N.
2011-12-01
The goal of this paper is twofold. First, based on the interpretation of a quantum tight-binding model in terms of a classical Hamiltonian map, we consider the Anderson localization (AL) problem as the Fermi-Pasta-Ulam (FPU) effect in a modified dynamical system containing both stable and unstable (inverted) modes. Delocalized states in the AL are analogous to the stable quasi-periodic motion in FPU, whereas localized states are analogous to thermalization, respectively. The second aim is to use the classical Hamilton map for a simplified derivation of exact equations for the localization operator H(z). The latter was presented earlier (Kuzovkov et al 2002 J. Phys.: Condens. Matter 14 13777) treating the AL as a generalized diffusion in a dynamical system. We demonstrate that counter-intuitive results of our studies of the AL are similar to the FPU counter-intuitivity.
Solving the Linear Balance Equation on the Globe as a Generalized Inverse Problem
NASA Technical Reports Server (NTRS)
Lu, Huei-Iin; Robertson, Franklin R.
1999-01-01
A generalized (pseudo) inverse technique was developed to facilitate a better understanding of the numerical effects of tropical singularities inherent in the spectral linear balance equation (LBE). Depending upon the truncation, various levels of determinancy are manifest. The traditional fully-determined (FD) systems give rise to a strong response, while the under-determined (UD) systems yield a weak response to the tropical singularities. The over-determined (OD) systems result in a modest response and a large residual in the tropics. The FD and OD systems can be alternatively solved by the iterative method. Differences in the solutions of an UD system exist between the inverse technique and the iterative method owing to the non- uniqueness of the problem. A realistic balanced wind was obtained by solving the principal components of the spectral LBE in terms of vorticity in an intermediate resolution. Improved solutions were achieved by including the singular-component solutions which best fit the observed wind data.
LAGRANGE SOLUTIONS TO THE DISCRETE-TIME GENERAL THREE-BODY PROBLEM
Minesaki, Yukitaka
2013-03-15
There is no known integrator that yields exact orbits for the general three-body problem (G3BP). It is difficult to verify whether a numerical procedure yields the correct solutions to the G3BP because doing so requires knowledge of all 11 conserved quantities, whereas only six are known. Without tracking all of the conserved quantities, it is possible to show that the discrete general three-body problem (d-G3BP) yields the correct orbits corresponding to Lagrange solutions of the G3BP. We show that the d-G3BP yields the correct solutions to the G3BP for two special cases: the equilateral triangle and collinear configurations. For the triangular solution, we use the fact that the solution to the three-body case is a superposition of the solutions to the three two-body cases, and we show that the three bodies maintain the same relative distances at all times. To obtain the collinear solution, we assume a specific permutation of the three bodies arranged along a straight rotating line, and we show that the d-G3BP maintains the same distance ratio between two bodies as in the G3BP. Proving that the d-G3BP solutions for these cases are equivalent to those of the G3BP makes it likely that the d-G3BP and G3BP solutions are equivalent in other cases. To our knowledge, this is the first work that proves the equivalence of the discrete solutions and the Lagrange orbits.
NASA Astrophysics Data System (ADS)
Tatsii, R. M.; Pazen, O. Yu.
2016-03-01
A constructive scheme for the construction of a solution of a mixed problem for the heat conduction equation with piecewise-continuous coefficients coordinate-dependent in the final interval is suggested and validated in the present work. The boundary conditions are assumed to be most general. The scheme is based on: the reduction method, the concept of quasi-derivatives, the currently accepted theory of the systems of linear differential equations, the Fourier method, and the modified method of eigenfunctions. The method based on this scheme should be related to direct exact methods of solving mixed problems that do not employ the procedures of constructing Green's functions or integral transformations. Here the theorem of eigenfunction expansion is adapted for the case of coefficients that have discontinuity points of the 1st kind. The results obtained can be used, for example, in investigating the process of heat transfer in a multilayer slab under conditions of ideal thermal contact between the layers. A particular case of piecewise-continuous coefficients is considered. A numerical example of calculation of a temperature field in a real four-layer building slab under boundary conditions of the 3rd kind (conditions of convective heat transfer) that model the phenomenon of fire near one of the external surfaces is given.
A fast and Robust Algorithm for general inequality/equality constrained minimum time problems
Briessen, B.; Sadegh, N.
1995-12-01
This paper presents a new algorithm for solving general inequality/equality constrained minimum time problems. The algorithm`s solution time is linear in the number of Runge-Kutta steps and the number of parameters used to discretize the control input history. The method is being applied to a three link redundant robotic arm with torque bounds, joint angle bounds, and a specified tip path. It solves case after case within a graphical user interface in which the user chooses the initial joint angles and the tip path with a mouse. Solve times are from 30 to 120 seconds on a Hewlett Packard workstation. A zero torque history is always used in the initial guess, and the algorithm has never crashed, indicating its robustness. The algorithm solves for a feasible solution for large trajectory execution time t{sub f} and then reduces t{sub f} and then reduces t{sub f} by a small amount and re-solves. The fixed time re- solve uses a new method of finding a near-minimum-2-norm solution to a set of linear equations and inequalities that achieves quadratic convegence to a feasible solution of the full nonlinear problem.
Collaborative Problem Solving in Shared Space
ERIC Educational Resources Information Center
Lin, Lin; Mills, Leila A.; Ifenthaler, Dirk
2015-01-01
The purpose of this study was to examine collaborative problem solving in a shared virtual space. The main question asked was: How will the performance and processes differ between collaborative problem solvers and independent problem solvers over time? A total of 104 university students (63 female and 41 male) participated in an experimental…
Recruitment and retention of general practitioners in the UK: what are the problems and solutions?
Young, R; Leese, B
1999-01-01
Recruitment and retention of general practitioners (GPs) has become an issue of major concern in recent years. However, much of the evidence is anecdotal and some commentators continue to question the scale of workforce problems. Hence, there is a need to establish a clear picture of those instabilities (i.e. imbalances between demand and supply) that do exist in the GP labour market in the UK. Based on a review of the published literature, we identify problems that stem from: (i) the changing social composition of the workforce and the fact that a large proportion of qualified GPs are significantly underutilized within traditional career structures; and (ii) the considerable differences in the ability of local areas to match labour demand and supply. We argue that one way to address these problems would be to encourage greater flexibility in a number of areas highlighted in the literature: (i) time commitment across the working day and week; (ii) long-term career paths; (iii) training and education; and (iv) remuneration and contract conditions. Overall, although the evidence suggests that the predicted 'crisis' has not yet occurred in the GP labour market as a whole, there is no room for lack of imagination in planning terms. Workforce planners continue to emphasize national changes to the medical school intake as the means to balance labour demand and supply between the specialities; however, better retention and deployment of existing GP labour would arguably produce more effective supply-side solutions. In this context, current policy and practice developments (e.g. Primary Care Groups and Primary Care Act Pilot Sites) offer a unique learning base upon which to move forward. PMID:10885092
A fast parallel Poisson solver on irregular domains applied to beam dynamics simulations
Adelmann, A. Arbenz, P. Ineichen, Y.
2010-06-20
We discuss the scalable parallel solution of the Poisson equation within a Particle-In-Cell (PIC) code for the simulation of electron beams in particle accelerators of irregular shape. The problem is discretized by Finite Differences. Depending on the treatment of the Dirichlet boundary the resulting system of equations is symmetric or 'mildly' nonsymmetric positive definite. In all cases, the system is solved by the preconditioned conjugate gradient algorithm with smoothed aggregation (SA) based algebraic multigrid (AMG) preconditioning. We investigate variants of the implementation of SA-AMG that lead to considerable improvements in the execution times. We demonstrate good scalability of the solver on distributed memory parallel processor with up to 2048 processors. We also compare our iterative solver with an FFT-based solver that is more commonly used for applications in beam dynamics.
dugksFoam: An open source OpenFOAM solver for the Boltzmann model equation
NASA Astrophysics Data System (ADS)
Zhu, Lianhua; Chen, Songze; Guo, Zhaoli
2017-04-01
A deterministic Boltzmann model equation solver called dugksFoam has been developed in the framework of the open source CFD toolbox OpenFOAM. The solver adopts the discrete unified gas kinetic scheme (Guo et al., 2015) with the Shakhov collision model. It has been validated by simulating several test cases covering different flow regimes including the one dimensional shock tube problem, a two dimensional thermal induced flow and the three dimensional lid-driven cavity flow. The solver features a parallel computing ability based on the velocity space decomposition, which is different from the physical space decomposition based approach provided by the OpenFOAM framework. The two decomposition approaches have been compared in both two and three dimensional cases. The parallel performance improves significantly using the newly implemented approach. A speed up by two orders of magnitudes has been observed using 256 cores on a small cluster.
Plasma wave simulation based on versatile FEM solver on Alcator C-mod
Shiraiwa, S.; Meneghini, O.; Parker, R.; Wallace, G.; Wilson, J.
2009-11-26
The finite element method (FEM) has the potential of simulating plasma waves seamlessly from the core to the vacuum and antenna regions. We explored the possibility of using a versatile FEM solver package, COMSOL, for lower hybrid (LH) wave simulation. Special care was paid to boundary conditions to satisfy toroidal symmetry. The non-trivial issue of introducing hot plasma effects was addressed by an iterative algorithm. These techniques are verified both analytically and numerically. In the lower hybrid (LH) grill antenna coupling problem, the FEM solver successfully reproduced the solution that was obtained analytically. Propagation of LH waves on the Alcator C and Alcator C-MOD plasmas was compared with a ray-tracing code, showing good consistency. The approach based on the FEM is computationally less intensive compared to spectral domain solvers, and more suitable for the simulation of larger device such as ITER.
George, D.L.
2011-01-01
The simulation of advancing flood waves over rugged topography, by solving the shallow-water equations with well-balanced high-resolution finite volume methods and block-structured dynamic adaptive mesh refinement (AMR), is described and validated in this paper. The efficiency of block-structured AMR makes large-scale problems tractable, and allows the use of accurate and stable methods developed for solving general hyperbolic problems on quadrilateral grids. Features indicative of flooding in rugged terrain, such as advancing wet-dry fronts and non-stationary steady states due to balanced source terms from variable topography, present unique challenges and require modifications such as special Riemann solvers. A well-balanced Riemann solver for inundation and general (non-stationary) flow over topography is tested in this context. The difficulties of modeling floods in rugged terrain, and the rationale for and efficacy of using AMR and well-balanced methods, are presented. The algorithms are validated by simulating the Malpasset dam-break flood (France, 1959), which has served as a benchmark problem previously. Historical field data, laboratory model data and other numerical simulation results (computed on static fitted meshes) are shown for comparison. The methods are implemented in GEOCLAW, a subset of the open-source CLAWPACK software. All the software is freely available at. Published in 2010 by John Wiley & Sons, Ltd.
Heather, Nick; Campion, Peter D.; Neville, Ronald G.; Maccabe, David
1987-01-01
Sixteen general practitioners participated in a controlled trial of the Scottish Health Education Group's DRAMS (drinking reasonably and moderately with self-control) scheme. The scheme was evaluated by randomly assigning 104 heavy or problem drinkers to three groups – a group participating in the DRAMS scheme (n = 34), a group given simple advice only (n = 32) and a non-intervention control group (n = 38). Six month follow-up information was obtained for 91 subjects (87.5% of initial sample). There were no significant differences between the groups in reduction in alcohol consumption, but patients in the DRAMS group showed a significantly greater reduction in a logarithmic measure of serum gamma-glutamyl-transpeptidase than patients in the group receiving advice only. Only 14 patients in the DRAMS group completed the full DRAMS procedure. For the sample as a whole, there was a significant reduction in alcohol consumption, a significant improvement on a measure of physical health and well-being, and significant reductions in the logarithmic measure of serum gamma-glutamyl transpeptidase and in mean corpuscular volume. The implications of these findings for future research into controlled drinking minimal interventions in general practice are discussed. PMID:3448228
Overweight in adolescent, psychiatric inpatients: A problem of general or food-specific impulsivity?
Deux, Natalie; Schlarb, Angelika A; Martin, Franziska; Holtmann, Martin; Hebebrand, Johannes; Legenbauer, Tanja
2017-05-01
Adolescent psychiatric patients are vulnerable to weight problems and show an overrepresentation of overweight compared to the healthy population. One potential factor that can contribute to the etiology of overweight is higher impulsivity. As of yet, it is unclear whether it is a general impulse control deficit or weight-related aspects such as lower impulse control in response to food that have an impact on body weight. As this may have therapeutic implications, the current study investigated differences between overweight and non-overweight adolescent psychiatric inpatients (N = 98; aged 12-20) in relation to trait impulsivity and behavioral inhibition performance. The Barratt Impulsiveness Scale and two go/no-go paradigms with neutral and food-related stimulus materials were applied. Results indicated no significant differences concerning trait impulsivity, but revealed that overweight inpatients had significantly more difficulties in inhibition performance (i.e. they reacted more impulsively) in response to both food and neutral stimuli compared to non-overweight inpatients. Furthermore, no specific inhibition deficit for high-caloric vs. low-caloric food cues emerged in overweight inpatients, whereas non-overweight participants showed significantly lower inhibition skills in response to high-caloric than low-caloric food stimuli. The results highlight a rather general, non-food-specific reduced inhibition performance in an overweight adolescent psychiatric population. Further research is necessary to enhance the understanding of the role of impulsivity in terms of body weight status in this high-risk group of adolescent inpatients.
Progress in developing Poisson-Boltzmann equation solvers
Li, Chuan; Li, Lin; Petukh, Marharyta; Alexov, Emil
2013-01-01
This review outlines the recent progress made in developing more accurate and efficient solutions to model electrostatics in systems comprised of bio-macromolecules and nano-objects, the last one referring to objects that do not have biological function themselves but nowadays are frequently used in biophysical and medical approaches in conjunction with bio-macromolecules. The problem of modeling macromolecular electrostatics is reviewed from two different angles: as a mathematical task provided the specific definition of the system to be modeled and as a physical problem aiming to better capture the phenomena occurring in the real experiments. In addition, specific attention is paid to methods to extend the capabilities of the existing solvers to model large systems toward applications of calculations of the electrostatic potential and energies in molecular motors, mitochondria complex, photosynthetic machinery and systems involving large nano-objects. PMID:24199185
Algorithms for parallel flow solvers on message passing architectures
NASA Technical Reports Server (NTRS)
Vanderwijngaart, Rob F.
1995-01-01
The purpose of this project has been to identify and test suitable technologies for implementation of fluid flow solvers -- possibly coupled with structures and heat equation solvers -- on MIMD parallel computers. In the course of this investigation much attention has been paid to efficient domain decomposition strategies for ADI-type algorithms. Multi-partitioning derives its efficiency from the assignment of several blocks of grid points to each processor in the parallel computer. A coarse-grain parallelism is obtained, and a near-perfect load balance results. In uni-partitioning every processor receives responsibility for exactly one block of grid points instead of several. This necessitates fine-grain pipelined program execution in order to obtain a reasonable load balance. Although fine-grain parallelism is less desirable on many systems, especially high-latency networks of workstations, uni-partition methods are still in wide use in production codes for flow problems. Consequently, it remains important to achieve good efficiency with this technique that has essentially been superseded by multi-partitioning for parallel ADI-type algorithms. Another reason for the concentration on improving the performance of pipeline methods is their applicability in other types of flow solver kernels with stronger implied data dependence. Analytical expressions can be derived for the size of the dynamic load imbalance incurred in traditional pipelines. From these it can be determined what is the optimal first-processor retardation that leads to the shortest total completion time for the pipeline process. Theoretical predictions of pipeline performance with and without optimization match experimental observations on the iPSC/860 very well. Analysis of pipeline performance also highlights the effect of uncareful grid partitioning in flow solvers that employ pipeline algorithms. If grid blocks at boundaries are not at least as large in the wall-normal direction as those
NASA Astrophysics Data System (ADS)
Balsara, Dinshaw S.; Kim, Jinho
2016-05-01
The relativistic magnetohydrodynamics (RMHD) set of equations has recently seen an increased use in astrophysical computations. Even so, RMHD codes remain fragile. The reconstruction can sometimes yield superluminal velocities in certain parts of the mesh. The current generation of RMHD codes does not have any particularly good strategy for avoiding such an unphysical situation. In this paper we present a reconstruction strategy that overcomes this problem by making a single conservative to primitive transformation per cell followed by higher order WENO reconstruction on a carefully chosen set of primitives that guarantee subluminal reconstruction of the flow variables. For temporal evolution via a predictor step we also present second, third and fourth order accurate ADER methods that keep the velocity subluminal during the predictor step. The methods presented here are very general and should apply to other PDE systems where physical realizability is most easily asserted in the primitive variables. The RMHD system also requires the magnetic field to be evolved in a divergence-free fashion. In the treatment of classical numerical MHD the analogous issue has seen much recent progress with the advent of multidimensional Riemann solvers. By developing multidimensional Riemann solvers for RMHD, we show that similar advances extend to RMHD. As a result, the face-centered magnetic fields can be evolved much more accurately using the edge-centered electric fields in the corrector step. Those edge-centered electric fields come from a multidimensional Riemann solver for RMHD which we present in this paper. The overall update results in a one-step, fully conservative scheme that is suited for AMR. In this paper we also develop several new test problems for RMHD. We show that RMHD vortices can be designed that propagate on the computational mesh as self-preserving structures. These RMHD vortex test problems provide a means to do truly multidimensional accuracy testing for
Wu, Jue; Chung, Albert C S
2005-01-01
This paper introduces a novel solver, namely cross entropy (CE), into the MRF theory for medical image segmentation. The solver, which is based on the theory of rare event simulation, is general and stochastic. Unlike some popular optimization methods such as belief propagation and graph cuts, CE makes no assumption on the form of objective functions and thus can be applied to any type of MRF models. Furthermore, it achieves higher performance of finding more global optima because of its stochastic property. In addition, it is more efficient than other stochastic methods like simulated annealing. We tested the new solver in 4 series of segmentation experiments on synthetic and clinical, vascular and cerebral images. The experiments show that CE can give more accurate segmentation results.
Domain Decomposition for the SPN Solver MINOS
NASA Astrophysics Data System (ADS)
Jamelot, Erell; Baudron, Anne-Marie; Lautard, Jean-Jacques
2012-12-01
In this article we present a domain decomposition method for the mixed SPN equations, discretized with Raviart-Thomas-Nédélec finite elements. This domain decomposition is based on the iterative Schwarz algorithm with Robin interface conditions to handle communications. After having described this method, we give details on how to optimize the convergence. Finally, we give some numerical results computed in a realistic 3D domain. The computations are done with the MINOS solver of the APOLLO3® code.
Domain decomposition for the SPN solver MINOS
Jamelot, Erell; Baudron, Anne-Marie; Lautard, Jean-Jacques
2012-07-01
In this article we present a domain decomposition method for the mixed SPN equations, discretized with Raviart-Thomas-Nedelec finite elements. This domain decomposition is based on the iterative Schwarz algorithm with Robin interface conditions to handle communications. After having described this method, we give details on how to optimize the convergence. Finally, we give some numerical results computed in a realistic 3D domain. The computations are done with the MINOS solver of the APOLLO3 (R) code. (authors)
ERIC Educational Resources Information Center
Baeza-Baeza, Juan J.; Garcia-Alvarez-Coque, M. Celia
2012-01-01
A general systematic approach including ionic strength effects is proposed for the numerical calculation of concentrations of chemical species in multiequilibrium problems. This approach extends the versatility of the approach presented in a previous article and is applied using the Solver option of the Excel spreadsheet to solve real problems…
Generalized Uncertainty Quantification for Linear Inverse Problems in X-ray Imaging
Fowler, Michael James
2014-04-25
In industrial and engineering applications, X-ray radiography has attained wide use as a data collection protocol for the assessment of material properties in cases where direct observation is not possible. The direct measurement of nuclear materials, particularly when they are under explosive or implosive loading, is not feasible, and radiography can serve as a useful tool for obtaining indirect measurements. In such experiments, high energy X-rays are pulsed through a scene containing material of interest, and a detector records a radiograph by measuring the radiation that is not attenuated in the scene. One approach to the analysis of these radiographs is to model the imaging system as an operator that acts upon the object being imaged to produce a radiograph. In this model, the goal is to solve an inverse problem to reconstruct the values of interest in the object, which are typically material properties such as density or areal density. The primary objective in this work is to provide quantitative solutions with uncertainty estimates for three separate applications in X-ray radiography: deconvolution, Abel inversion, and radiation spot shape reconstruction. For each problem, we introduce a new hierarchical Bayesian model for determining a posterior distribution on the unknowns and develop efficient Markov chain Monte Carlo (MCMC) methods for sampling from the posterior. A Poisson likelihood, based on a noise model for photon counts at the detector, is combined with a prior tailored to each application: an edge-localizing prior for deconvolution; a smoothing prior with non-negativity constraints for spot reconstruction; and a full covariance sampling prior based on a Wishart hyperprior for Abel inversion. After developing our methods in a general setting, we demonstrate each model on both synthetically generated datasets, including those from a well known radiation transport code, and real high energy radiographs taken at two U. S. Department of Energy
ERIC Educational Resources Information Center
Paraschiv, Irina; Olley, J. Gregory
This paper describes the "Problem Solving for Life" training program which trains adolescents and adults with mental retardation in skills for solving social problems. The program requires group participants to solve social problems by practicing two prerequisite skills (relaxation and positive self-statements) and four problem solving steps: (1)…
LORENE: Spectral methods differential equations solver
NASA Astrophysics Data System (ADS)
Gourgoulhon, Eric; Grandclément, Philippe; Marck, Jean-Alain; Novak, Jérôme; Taniguchi, Keisuke
2016-08-01
LORENE (Langage Objet pour la RElativité NumériquE) solves various problems arising in numerical relativity, and more generally in computational astrophysics. It is a set of C++ classes and provides tools to solve partial differential equations by means of multi-domain spectral methods. LORENE classes implement basic structures such as arrays and matrices, but also abstract mathematical objects, such as tensors, and astrophysical objects, such as stars and black holes.
On some generalization of the area theorem with applications to the problem of rolling balls
NASA Astrophysics Data System (ADS)
Chaplygin, Sergey A.
2012-04-01
This publication contributes to the series of RCD translations of Sergey Alexeevich Chaplygin's scientific heritage. Earlier we published three of his papers on non-holonomic dynamics (vol. 7, no. 2; vol. 13, no. 4) and two papers on hydrodynamics (vol. 12, nos. 1, 2). The present paper deals with mechanical systems that consist of several spheres and discusses generalized conditions for the existence of integrals of motion (linear in velocities) in such systems. First published in 1897 and awarded by the Gold Medal of Russian Academy of Sciences, this work has not lost its scientific significance and relevance. (In particular, its principal ideas are further developed and extended in the recent article "Two Non-holonomic Integrable Problems Tracing Back to Chaplygin", published in this issue, see p. 191). Note that non-holonomic models for rolling motion of spherical shells, including the case where the shells contain intricate mechanisms inside, are currently of particular interest in the context of their application in the design of ball-shaped mobile robots. We hope that this classical work will be estimated at its true worth by the English-speaking world.
NASA Astrophysics Data System (ADS)
Vozmishcheva, Tatiana
2016-09-01
The connection between the problems of celestial mechanics: the Kepler problem, the two-center problem and the two body problem in spaces of constant curvature with the generalized Kepler and Hooke potentials is investigated. The limit passage in the two-center and two body problems in the Lobachevsky space and on a sphere is carried out as λto0 (λ is the curvature of the corresponding space) for the two potentials. The potentials and metrics in spaces under study are written in the gnomonic coordinates. It is shown that as the curvature radius tends to infinity, the generalized gravitational and elastic potentials transform to the Kepler and Hooke forms in the Euclidean space.
Kinugawa, Tohru
2014-02-15
This paper presents a simple but nontrivial generalization of Abel's mechanical problem, based on the extended isochronicity condition and the superposition principle. There are two primary aims. The first one is to reveal the linear relation between the transit-time T and the travel-length X hidden behind the isochronicity problem that is usually discussed in terms of the nonlinear equation of motion (d{sup 2}X)/(dt{sup 2}) +(dU)/(dX) =0 with U(X) being an unknown potential. Second, the isochronicity condition is extended for the possible Abel-transform approach to designing the isochronous trajectories of charged particles in spectrometers and/or accelerators for time-resolving experiments. Our approach is based on the integral formula for the oscillatory motion by Landau and Lifshitz [Mechanics (Pergamon, Oxford, 1976), pp. 27–29]. The same formula is used to treat the non-periodic motion that is driven by U(X). Specifically, this unknown potential is determined by the (linear) Abel transform X(U) ∝ A[T(E)], where X(U) is the inverse function of U(X), A=(1/√(π))∫{sub 0}{sup E}dU/√(E−U) is the so-called Abel operator, and T(E) is the prescribed transit-time for a particle with energy E to spend in the region of interest. Based on this Abel-transform approach, we have introduced the extended isochronicity condition: typically, τ = T{sub A}(E) + T{sub N}(E) where τ is a constant period, T{sub A}(E) is the transit-time in the Abel type [A-type] region spanning X > 0 and T{sub N}(E) is that in the Non-Abel type [N-type] region covering X < 0. As for the A-type region in X > 0, the unknown inverse function X{sub A}(U) is determined from T{sub A}(E) via the Abel-transform relation X{sub A}(U) ∝ A[T{sub A}(E)]. In contrast, the N-type region in X < 0 does not ensure this linear relation: the region is covered with a predetermined potential U{sub N}(X) of some arbitrary choice, not necessarily obeying the Abel-transform relation. In discussing
Preconditioned implicit solvers for the Navier-Stokes equations on distributed-memory machines
NASA Technical Reports Server (NTRS)
Ajmani, Kumud; Liou, Meng-Sing; Dyson, Rodger W.
1994-01-01
The GMRES method is parallelized, and combined with local preconditioning to construct an implicit parallel solver to obtain steady-state solutions for the Navier-Stokes equations of fluid flow on distributed-memory machines. The new implicit parallel solver is designed to preserve the convergence rate of the equivalent 'serial' solver. A static domain-decomposition is used to partition the computational domain amongst the available processing nodes of the parallel machine. The SPMD (Single-Program Multiple-Data) programming model is combined with message-passing tools to develop the parallel code on a 32-node Intel Hypercube and a 512-node Intel Delta machine. The implicit parallel solver is validated for internal and external flow problems, and is found to compare identically with flow solutions obtained on a Cray Y-MP/8. A peak computational speed of 2300 MFlops/sec has been achieved on 512 nodes of the Intel Delta machine,k for a problem size of 1024 K equations (256 K grid points).
A Tensor-Train accelerated solver for integral equations in complex geometries
NASA Astrophysics Data System (ADS)
Corona, Eduardo; Rahimian, Abtin; Zorin, Denis
2017-04-01
We present a framework using the Quantized Tensor Train (QTT) decomposition to accurately and efficiently solve volume and boundary integral equations in three dimensions. We describe how the QTT decomposition can be used as a hierarchical compression and inversion scheme for matrices arising from the discretization of integral equations. For a broad range of problems, computational and storage costs of the inversion scheme are extremely modest O (log N) and once the inverse is computed, it can be applied in O (Nlog N) . We analyze the QTT ranks for hierarchically low rank matrices and discuss its relationship to commonly used hierarchical compression techniques such as FMM and HSS. We prove that the QTT ranks are bounded for translation-invariant systems and argue that this behavior extends to non-translation invariant volume and boundary integrals. For volume integrals, the QTT decomposition provides an efficient direct solver requiring significantly less memory compared to other fast direct solvers. We present results demonstrating the remarkable performance of the QTT-based solver when applied to both translation and non-translation invariant volume integrals in 3D. For boundary integral equations, we demonstrate that using a QTT decomposition to construct preconditioners for a Krylov subspace method leads to an efficient and robust solver with a small memory footprint. We test the QTT preconditioners in the iterative solution of an exterior elliptic boundary value problem (Laplace) formulated as a boundary integral equation in complex, multiply connected geometries.
The School Problem-Solver's Guide to Distance Education.
ERIC Educational Resources Information Center
Levinson, Cynthia Y.
Many administrators are meeting specific instructional needs of their students without always or solely relying on classroom teachers by utilizing distance education, i.e., instruction that takes place while the learner is physically distant from the instructor and/or the materials. Distance education is particularly appropriate in rural and small…
Opening up the Collaborative Problem-Solving Process to Solvers
ERIC Educational Resources Information Center
Robison, Tyler
2013-01-01
In software systems, having features of openness means that some of the internal components of the system are made available for examination by users. Researchers have looked at different effects of open systems a great deal in the area of educational technology, but also in areas outside of education. Properly used, openness has the potential to…
A fast solver for systems of reaction-diffusion equations.
Garbey, M.; Kaper, H. G.; Romanyukha, N.
2001-04-20
In this paper we present a fast algorithm for the numerical solution of systems of reaction-diffusion equations, {partial_derivative}{sub t} u + a {center_dot} {del}u = {Delta}u + f(x,t,u), and x element of {Omega} contained in R{sup 3}, t > 0. Here, u is a vector-valued function, u triple bond u(x,t) element of R{sup m} is large, and the corresponding system of ODEs, {partial_derivative}{sub t}u = F(x,t,u), is stiff. Typical examples arise in air pollution studies, where a is the given wind field and the nonlinear function F models the atmospheric chemistry. The time integration of Eq. (1) is best handled by the method of characteristics. The problem is thus reduced to designing for the reaction-diffusion part a fast solver that has good stability properties for the given time step and does not require the computation of the full Jacobi matrix. An operator-splitting technique, even a high-order one, combining a fast nonlinear ODE solver with an efficient solver for the diffusion operator is less effective when the reaction term is stiff. In fact, the classical Strang splitting method may underperform a first-order source splitting method. The algorithm we propose in this paper uses an a posteriori filtering technique to stabilize the computation of the diffusion term. The algorithm parallelizes well, because the solution of the large system of ODEs is done pointwise; however, the integration of the chemistry may lead to load-balancing problems. The Tchebycheff acceleration technique proposed in offers an alternative that complements the approach presented here. To facilitate the presentation, we limit the discussion to domains {Omega} that either admit a regular discretization grid or decompose into subdomains that admit regular discretization grids. We describe the algorithm for one-dimensional domains in Section 2 and for multidimensional domains in Section 3. Section 4 briefly outlines future work.
GPU accelerated FDTD solver and its application in MRI.
Chi, J; Liu, F; Jin, J; Mason, D G; Crozier, S
2010-01-01
The finite difference time domain (FDTD) method is a popular technique for computational electromagnetics (CEM). The large computational power often required, however, has been a limiting factor for its applications. In this paper, we will present a graphics processing unit (GPU)-based parallel FDTD solver and its successful application to the investigation of a novel B1 shimming scheme for high-field magnetic resonance imaging (MRI). The optimized shimming scheme exhibits considerably improved transmit B(1) profiles. The GPU implementation dramatically shortened the runtime of FDTD simulation of electromagnetic field compared with its CPU counterpart. The acceleration in runtime has made such investigation possible, and will pave the way for other studies of large-scale computational electromagnetic problems in modern MRI which were previously impractical.
Large-scale linear nonparallel support vector machine solver.
Tian, Yingjie; Ping, Yuan
2014-02-01
Twin support vector machines (TWSVMs), as the representative nonparallel hyperplane classifiers, have shown the effectiveness over standard SVMs from some aspects. However, they still have some serious defects restricting their further study and real applications: (1) They have to compute and store the inverse matrices before training, it is intractable for many applications where data appear with a huge number of instances as well as features; (2) TWSVMs lost the sparseness by using a quadratic loss function making the proximal hyperplane close enough to the class itself. This paper proposes a Sparse Linear Nonparallel Support Vector Machine, termed as L1-NPSVM, to deal with large-scale data based on an efficient solver-dual coordinate descent (DCD) method. Both theoretical analysis and experiments indicate that our method is not only suitable for large scale problems, but also performs as good as TWSVMs and SVMs.
Performance evaluation of a parallel sparse lattice Boltzmann solver
Axner, L. Bernsdorf, J. Zeiser, T. Lammers, P. Linxweiler, J. Hoekstra, A.G.
2008-05-01
We develop a performance prediction model for a parallelized sparse lattice Boltzmann solver and present performance results for simulations of flow in a variety of complex geometries. A special focus is on partitioning and memory/load balancing strategy for geometries with a high solid fraction and/or complex topology such as porous media, fissured rocks and geometries from medical applications. The topology of the lattice nodes representing the fluid fraction of the computational domain is mapped on a graph. Graph decomposition is performed with both multilevel recursive-bisection and multilevel k-way schemes based on modified Kernighan-Lin and Fiduccia-Mattheyses partitioning algorithms. Performance results and optimization strategies are presented for a variety of platforms, showing a parallel efficiency of almost 80% for the largest problem size. A good agreement between the performance model and experimental results is demonstrated.
ERIC Educational Resources Information Center
Lower, Stephen K.
A brief overview of CHEMEX--a problem-solving, tutorial style computer-assisted instructional course--is provided and sample problems are offered. In CHEMEX, students receive problems in advance and attempt to solve them before moving through the computer program, which assists them in overcoming difficulties and serves as a review mechanism.…
Implementation of generalized optimality criteria in a multidisciplinary environment
NASA Technical Reports Server (NTRS)
Canfield, R. A.; Venkayya, V. B.
1989-01-01
A generalized optimality criterion method consisting of a dual problem solver combined with a compound scaling algorithm was implemented in the multidisciplinary design tool, ASTROS. This method enables, for the first time in a production design tool, the determination of a minimum weight design using thousands of independent structural design variables while simultaneously considering constraints on response quantities in several disciplines. Even for moderately large examples, the computational efficiency is improved significantly relative to the conventional approach.
Basten, Maartje; Tiemeier, Henning; Althoff, Robert R; van de Schoot, Rens; Jaddoe, Vincent W V; Hofman, Albert; Hudziak, James J; Verhulst, Frank C; van der Ende, Jan
2016-02-01
This study examined the stability of internalizing and externalizing problems from age 1.5 to 6 years, while taking into account developmental changes in the presentation of problems. The study comprised a population-based cohort of 7,206 children (50.4 % boys). At ages 1.5, 3, and 6 years, mothers reported on problem behavior using the Child Behavior Checklist/1.5-5 (CBCL/1.5-5). At each age we performed latent profile analysis on the CBCL/1.5-5 scales. Latent transition analysis (LTA) was applied to study the stability of problem behavior. Profiles of problem behavior varied across ages. At each age, 82-87 % of the children did not have problems whereas approximately 2 % showed a profile of co-occurring internalizing and externalizing problems. This profile was more severe (with higher scores) at 6 years than at earlier ages. A predominantly internalizing profile only emerged at 6 years, while a profile with externalizing problems and emotional reactivity was present at each age. LTA showed that, based on profiles at 1.5 and 3 years, it was difficult to predict the type of profile at 6 years. Children with a profile of co-occurring internalizing and externalizing problems early in life were most likely to show problem behavior at 6 years. This study shows that the presentation of problem behavior changes across the preschool period and that heterotypic continuity of problems is very common among preschoolers. Children with co-occurring internalizing and externalizing problems were most likely to show persisting problems. The use of evidence-based treatment for these young children may prevent psychiatric problems across the life course.
ERIC Educational Resources Information Center
Donoghue, John R.
2015-01-01
At the heart of van der Linden's approach to automated test assembly (ATA) is a linear programming/integer programming (LP/IP) problem. A variety of IP solvers are available, ranging in cost from free to hundreds of thousands of dollars. In this paper, I compare several approaches to solving the underlying IP problem. These approaches range from…
Stevens, D.E.; Bretherton, S.
1996-12-01
This paper presents a new forward-in-time advection method for nearly incompressible flow, MU, and its application to an adaptive multilevel flow solver for atmospheric flows. MU is a modification of Leonard et al.`s UTOPIA scheme. MU, like UTOPIA, is based on third-order accurate semi-Lagrangian multidimensional upwinding for constant velocity flows. for varying velocity fields, MU is a second-order conservative method. MU has greater stability and accuracy than UTOPIA and naturally decomposes into a monotone low-order method and a higher-order accurate correction for use with flux limiting. Its stability and accuracy make it a computationally efficient alternative to current finite-difference advection methods. We present a fully second-order accurate flow solver for the anelastic equations, a prototypical low Mach number flow. The flow solver is based on MU which is used for both momentum and scalar transport equations. This flow solver can also be implemented with any forward-in-time advection scheme. The multilevel flow solver conserves discrete global integrals of advected quantities and includes adaptive mesh refinements. Its second-order accuracy is verified using a nonlinear energy conservation integral for the anelastic equations. For a typical geophysical problem in which the flow is most rapidly varying in a small part of the domain, the multilevel flow solver achieves global accuracy comparable to uniform-resolution simulation for 10% of the computational cost. 36 refs., 10 figs.
AQUASOL: An efficient solver for the dipolar Poisson–Boltzmann–Langevin equation
Koehl, Patrice; Delarue, Marc
2010-01-01
The Poisson–Boltzmann (PB) formalism is among the most popular approaches to modeling the solvation of molecules. It assumes a continuum model for water, leading to a dielectric permittivity that only depends on position in space. In contrast, the dipolar Poisson–Boltzmann–Langevin (DPBL) formalism represents the solvent as a collection of orientable dipoles with nonuniform concentration; this leads to a nonlinear permittivity function that depends both on the position and on the local electric field at that position. The differences in the assumptions underlying these two models lead to significant differences in the equations they generate. The PB equation is a second order, elliptic, nonlinear partial differential equation (PDE). Its response coefficients correspond to the dielectric permittivity and are therefore constant within each subdomain of the system considered (i.e., inside and outside of the molecules considered). While the DPBL equation is also a second order, elliptic, nonlinear PDE, its response coefficients are nonlinear functions of the electrostatic potential. Many solvers have been developed for the PB equation; to our knowledge, none of these can be directly applied to the DPBL equation. The methods they use may adapt to the difference; their implementations however are PBE specific. We adapted the PBE solver originally developed by Holst and Saied [J. Comput. Chem. 16, 337 (1995)] to the problem of solving the DPBL equation. This solver uses a truncated Newton method with a multigrid preconditioner. Numerical evidences suggest that it converges for the DPBL equation and that the convergence is superlinear. It is found however to be slow and greedy in memory requirement for problems commonly encountered in computational biology and computational chemistry. To circumvent these problems, we propose two variants, a quasi-Newton solver based on a simplified, inexact Jacobian and an iterative self-consistent solver that is based directly on
NASA Astrophysics Data System (ADS)
Lochon, H.; Daude, F.; Galon, P.; Hérard, J.-M.
2016-12-01
The computation of compressible two-phase flows with the Baer-Nunziato model is addressed. Only the convective part of the model that exhibits non-conservative products is considered and the source terms of the model that represent the exchange between phases are neglected. Based on the solver proposed by Tokareva & Toro [1], a new HLLC-type Riemann solver is built. The key idea of this new solver lies in an approximation of the two-phase contact discontinuity of the model. Thus the Riemann invariants of the wave are approximated in the "subsonic" case. A major consequence of this approximation is that the resulting solver can deal with any Equation Of State. It also allows to bypass the resolution of a non-linear equation based on those Riemann invariants. We assess the solver and compare it with others on 1D Riemann problems including grid convergence and efficiency studies. The ability of the proposed solver to deal with complex Equations Of State is also investigated. Finally, the different solvers have been compared on challenging 2D test-cases due to the presence of both material interfaces and shock waves: a shock-bubble interaction and underwater explosions. When compared with others, the present solver appears to be accurate, efficient and robust.
Updates to the NEQAIR Radiation Solver
NASA Technical Reports Server (NTRS)
Cruden, Brett A.; Brandis, Aaron M.
2014-01-01
The NEQAIR code is one of the original heritage solvers for radiative heating prediction in aerothermal environments, and is still used today for mission design purposes. This paper discusses the implementation of the first major revision to the NEQAIR code in the last five years, NEQAIR v14.0. The most notable features of NEQAIR v14.0 are the parallelization of the radiation computation, reducing runtimes by about 30×, and the inclusion of mid-wave CO2 infrared radiation.
Three-Dimensional Inverse Transport Solver Based on Compressive Sensing Technique
NASA Astrophysics Data System (ADS)
Cheng, Yuxiong; Wu, Hongchun; Cao, Liangzhi; Zheng, Youqi
2013-09-01
According to the direct exposure measurements from flash radiographic image, a compressive sensing-based method for three-dimensional inverse transport problem is presented. The linear absorption coefficients and interface locations of objects are reconstructed directly at the same time. It is always very expensive to obtain enough measurements. With limited measurements, compressive sensing sparse reconstruction technique orthogonal matching pursuit is applied to obtain the sparse coefficients by solving an optimization problem. A three-dimensional inverse transport solver is developed based on a compressive sensing-based technique. There are three features in this solver: (1) AutoCAD is employed as a geometry preprocessor due to its powerful capacity in graphic. (2) The forward projection matrix rather than Gauss matrix is constructed by the visualization tool generator. (3) Fourier transform and Daubechies wavelet transform are adopted to convert an underdetermined system to a well-posed system in the algorithm. Simulations are performed and numerical results in pseudo-sine absorption problem, two-cube problem and two-cylinder problem when using compressive sensing-based solver agree well with the reference value.
A finite different field solver for dipole modes
Nelson, E.M.
1992-08-01
A finite element field solver for dipole modes in axisymmetric structures has been written. The second-order elements used in this formulation yield accurate mode frequencies with no spurious modes. Quasi-periodic boundaries are included to allow travelling waves in periodic structures. The solver is useful in applications requiring precise frequency calculations such as detuned accelerator structures for linear colliders. Comparisons are made with measurements and with the popular but less accurate field solver URMEL.
Piping benchmark problems for the General Electric Advanced Boiling Water Reactor
Bezler, P.; DeGrassi, G.; Braverman, J.; Wang, Y.K.
1993-08-01
To satisfy the need for verification of the computer programs and modeling techniques that will be used to perform the final piping analyses for an advanced boiling water reactor standard design, three benchmark problems were developed. The problems are representative piping systems subjected to representative dynamic loads with solutions developed using the methods being proposed for analysis for the advanced reactor standard design. It will be required that the combined license holders demonstrate that their solutions to these problems are in agreement with the benchmark problem set.
A 3D approximate maximum likelihood localization solver
2016-09-23
A robust three-dimensional solver was needed to accurately and efficiently estimate the time sequence of locations of fish tagged with acoustic transmitters and vocalizing marine mammals to describe in sufficient detail the information needed to assess the function of dam-passage design alternatives and support Marine Renewable Energy. An approximate maximum likelihood solver was developed using measurements of time difference of arrival from all hydrophones in receiving arrays on which a transmission was detected. Field experiments demonstrated that the developed solver performed significantly better in tracking efficiency and accuracy than other solvers described in the literature.
Jia, Jingfei
2015-01-01
It is well known that radiative transfer equation (RTE) provides more accurate tomographic results than its diffusion approximation (DA). However, RTE-based tomographic reconstruction codes have limited applicability in practice due to their high computational cost. In this article, we propose a new efficient method for solving the RTE forward problem with multiple light sources in an all-at-once manner instead of solving it for each source separately. To this end, we introduce here a novel linear solver called block biconjugate gradient stabilized method (block BiCGStab) that makes full use of the shared information between different right hand sides to accelerate solution convergence. Two parallelized block BiCGStab methods are proposed for additional acceleration under limited threads situation. We evaluate the performance of this algorithm with numerical simulation studies involving the Delta-Eddington approximation to the scattering phase function. The results show that the single threading block RTE solver proposed here reduces computation time by a factor of 1.5~3 as compared to the traditional sequential solution method and the parallel block solver by a factor of 1.5 as compared to the traditional parallel sequential method. This block linear solver is, moreover, independent of discretization schemes and preconditioners used; thus further acceleration and higher accuracy can be expected when combined with other existing discretization schemes or preconditioners. PMID:26345531
Lipnikov, Konstantin; Moulton, David; Svyatskiy, Daniil
2016-04-29
We develop a new approach for solving the nonlinear Richards’ equation arising in variably saturated flow modeling. The growing complexity of geometric models for simulation of subsurface flows leads to the necessity of using unstructured meshes and advanced discretization methods. Typically, a numerical solution is obtained by first discretizing PDEs and then solving the resulting system of nonlinear discrete equations with a Newton-Raphson-type method. Efficiency and robustness of the existing solvers rely on many factors, including an empiric quality control of intermediate iterates, complexity of the employed discretization method and a customized preconditioner. We propose and analyze a new preconditioningmore » strategy that is based on a stable discretization of the continuum Jacobian. We will show with numerical experiments for challenging problems in subsurface hydrology that this new preconditioner improves convergence of the existing Jacobian-free solvers 3-20 times. Furthermore, we show that the Picard method with this preconditioner becomes a more efficient nonlinear solver than a few widely used Jacobian-free solvers.« less
NASA Astrophysics Data System (ADS)
Lipnikov, Konstantin; Moulton, David; Svyatskiy, Daniil
2016-08-01
We develop a new approach for solving the nonlinear Richards' equation arising in variably saturated flow modeling. The growing complexity of geometric models for simulation of subsurface flows leads to the necessity of using unstructured meshes and advanced discretization methods. Typically, a numerical solution is obtained by first discretizing PDEs and then solving the resulting system of nonlinear discrete equations with a Newton-Raphson-type method. Efficiency and robustness of the existing solvers rely on many factors, including an empiric quality control of intermediate iterates, complexity of the employed discretization method and a customized preconditioner. We propose and analyze a new preconditioning strategy that is based on a stable discretization of the continuum Jacobian. We will show with numerical experiments for challenging problems in subsurface hydrology that this new preconditioner improves convergence of the existing Jacobian-free solvers 3-20 times. We also show that the Picard method with this preconditioner becomes a more efficient nonlinear solver than a few widely used Jacobian-free solvers.
Lipnikov, Konstantin; Moulton, David; Svyatskiy, Daniil
2016-04-29
We develop a new approach for solving the nonlinear Richards’ equation arising in variably saturated flow modeling. The growing complexity of geometric models for simulation of subsurface flows leads to the necessity of using unstructured meshes and advanced discretization methods. Typically, a numerical solution is obtained by first discretizing PDEs and then solving the resulting system of nonlinear discrete equations with a Newton-Raphson-type method. Efficiency and robustness of the existing solvers rely on many factors, including an empiric quality control of intermediate iterates, complexity of the employed discretization method and a customized preconditioner. We propose and analyze a new preconditioning strategy that is based on a stable discretization of the continuum Jacobian. We will show with numerical experiments for challenging problems in subsurface hydrology that this new preconditioner improves convergence of the existing Jacobian-free solvers 3-20 times. Furthermore, we show that the Picard method with this preconditioner becomes a more efficient nonlinear solver than a few widely used Jacobian-free solvers.
Jia, Jingfei; Kim, Hyun K; Hielscher, Andreas H
2015-12-01
It is well known that radiative transfer equation (RTE) provides more accurate tomographic results than its diffusion approximation (DA). However, RTE-based tomographic reconstruction codes have limited applicability in practice due to their high computational cost. In this article, we propose a new efficient method for solving the RTE forward problem with multiple light sources in an all-at-once manner instead of solving it for each source separately. To this end, we introduce here a novel linear solver called block biconjugate gradient stabilized method (block BiCGStab) that makes full use of the shared information between different right hand sides to accelerate solution convergence. Two parallelized block BiCGStab methods are proposed for additional acceleration under limited threads situation. We evaluate the performance of this algorithm with numerical simulation studies involving the Delta-Eddington approximation to the scattering phase function. The results show that the single threading block RTE solver proposed here reduces computation time by a factor of 1.5~3 as compared to the traditional sequential solution method and the parallel block solver by a factor of 1.5 as compared to the traditional parallel sequential method. This block linear solver is, moreover, independent of discretization schemes and preconditioners used; thus further acceleration and higher accuracy can be expected when combined with other existing discretization schemes or preconditioners.
Cuddeback, Gary S.; Scheyett, Anna; Pettus-Davis, Carrie; Morrissey, Joseph P.
2010-01-01
Objective Persons with severe mental illness have higher rates of chronic general medical illness compared with the general population. Similarly, compared with the general population, incarcerated persons have higher rates of chronic medical illness; however, there is little information about the synergy between severe mental illness and incarceration and the general medical problems of consumers. To address this gap in the literature this study addresses the following question: are consumers with a history of incarceration at greater risk of general medical problems compared with consumers without such a history? Methods Administrative data were used to compare the medical problems of 3,690 persons with severe mental illness with a history of incarceration and 2,042 persons with severe mental illness with no such history. Results Consumers with a history of incarceration were more likely than those with no such history to have infectious, blood, and skin diseases and a history of injury. Furthermore, when analyses controlled for gender, race, age, and substance use disorders, consumers with an incarceration history were 40% more likely to have any general medical problem and 30% more likely to have multiple medical problems. Conclusions The findings presented here call for better communication among local public health and mental health providers and jails and better integration of primary care and behavioral health care among community mental health providers. Also, research on evidence-based interventions designed to divert persons with severe mental illness from the criminal justice system and facilitate community reentry for persons with severe mental illness who are released from jails and prisons should be accelerated. PMID:20044417
Ma, Guodong; Zhang, Yufeng; Liu, Meixing
2017-01-01
Combining the techniques of the working set identification and generalized gradient projection, we present a new generalized gradient projection algorithm for minimax optimization problems with inequality constraints. In this paper, we propose a new optimal identification function, from which we provide a new working set. At each iteration, the improved search direction is generated by only one generalized gradient projection explicit formula, which is simple and could reduce the computational cost. Under some mild assumptions, the algorithm possesses the global and strong convergence. Finally, the numerical results show that the proposed algorithm is promising.
The number radial coherent states for the generalized MICZ-Kepler problem
NASA Astrophysics Data System (ADS)
Salazar-Ramírez, M.; Ojeda-Guillén, D.; Mota, R. D.
2016-02-01
We study the radial part of the McIntosh-Cisneros-Zwanziger (MICZ)-Kepler problem in an algebraic way by using the 𝔰𝔲(1, 1) Lie algebra. We obtain the energy spectrum and the eigenfunctions of this problem from the 𝔰𝔲(1, 1) theory of unitary representations and the tilting transformation to the stationary Schrödinger equation. We construct the physical Perelomov number coherent states for this problem and compute some expectation values. Also, we obtain the time evolution of these coherent states.
A general algorithm for control problems with variable parameters and quasi-linear models
NASA Astrophysics Data System (ADS)
Bayón, L.; Grau, J. M.; Ruiz, M. M.; Suárez, P. M.
2015-12-01
This paper presents an algorithm that is able to solve optimal control problems in which the modelling of the system contains variable parameters, with the added complication that, in certain cases, these parameters can lead to control problems governed by quasi-linear equations. Combining the techniques of Pontryagin's Maximum Principle and the shooting method, an algorithm has been developed that is not affected by the values of the parameters, being able to solve conventional problems as well as cases in which the optimal solution is shown to be bang-bang with singular arcs.
ERIC Educational Resources Information Center
Gladman, Justin; Perkins, David
2013-01-01
Context and Objective: Australian rural general practitioners (GPs) require public health knowledge. This study explored the suitability of teaching complex public health issues related to Aboriginal health by way of a hybrid problem-based learning (PBL) model within an intensive training retreat for GP registrars, when numerous trainees have no…
ERIC Educational Resources Information Center
Nygaard, Egil; Jensen, Tine K.; Dyb, Grete
2012-01-01
The aim of this study was to evaluate the structure of posttraumatic stress reaction factors and their relation to general mental health problems in Norwegian children exposed to the tsunami on December 26, 2004. A total of 133 children and adolescents (ages 6-17) were interviewed 10 months posttsunami using the UCLA PTSD Reaction Index, and 104…
Hinz, Andreas; Zenger, Markus; Brähler, Elmar; Spitzer, Silvia; Scheuch, Klaus; Seibt, Reingard
2016-08-01
High degrees of premature retirement among teachers warrant investigating the occupational burden and the mental health status of this profession. A sample of 1074 German teachers participated in this study. Two samples of the general population (N = 824 and N = 792) were used as comparison groups. Work distress was assessed with the Effort-Reward-Imbalance questionnaire, and mental health problems were measured with the General Health Questionnaire (GHQ-12). Teachers reported more effort-reward imbalance (M = 0.64) compared with the general population (M = 0.57), and they perceived more mental health problems (GHQ: M = 12.1) than the comparison group (M = 9.5). School type was not associated with work stress and mental health. Teachers with leading functions perceived high degrees of effort and reward, resulting in a moderate effort-reward ratio and no heightened mental health problems. Teachers working full time reported more effort than teachers working part time, but the reward mean values of both groups were similar. This results in a somewhat unfavourable effort-reward ratio of teachers working full time. Moreover, teachers working full time reported more mental health problems. The results support the appropriateness of the effort-reward conception, applied to the profession of teachers. The higher degree of effort-reward imbalance and the level of mental health problems warrant preventive measures. Copyright © 2014 John Wiley & Sons, Ltd.
Flowfield Comparisons from Three Navier-Stokes Solvers for an Axisymmetric Separate Flow Jet
NASA Technical Reports Server (NTRS)
Koch, L. Danielle; Bridges, James; Khavaran, Abbas
2002-01-01
To meet new noise reduction goals, many concepts to enhance mixing in the exhaust jets of turbofan engines are being studied. Accurate steady state flowfield predictions from state-of-the-art computational fluid dynamics (CFD) solvers are needed as input to the latest noise prediction codes. The main intent of this paper was to ascertain that similar Navier-Stokes solvers run at different sites would yield comparable results for an axisymmetric two-stream nozzle case. Predictions from the WIND and the NPARC codes are compared to previously reported experimental data and results from the CRAFT Navier-Stokes solver. Similar k-epsilon turbulence models were employed in each solver, and identical computational grids were used. Agreement between experimental data and predictions from each code was generally good for mean values. All three codes underpredict the maximum value of turbulent kinetic energy. The predicted locations of the maximum turbulent kinetic energy were farther downstream than seen in the data. A grid study was conducted using the WIND code, and comments about convergence criteria and grid requirements for CFD solutions to be used as input for noise prediction computations are given. Additionally, noise predictions from the MGBK code, using the CFD results from the CRAFT code, NPARC, and WIND as input are compared to data.
Induction as an Empirical Problem: How Students Generalize during Practical Work.
ERIC Educational Resources Information Center
Wickman, Per-Olof; Ostman, Leif
2002-01-01
Examines how university students made generalizations when making morphological insect observations. Results showed students rarely made generalizations in terms of universal statements: they did not use induction or produce hypotheses for testing in an analytic philosophical sense but used induction in more familiar contexts. Discusses the…
Induction as an empirical problem: how students generalize during practical work
NASA Astrophysics Data System (ADS)
Wickman, Per-Olof
2002-05-01
We examined how university students made generalizations when making morphological observations of insects. Five groups of two or three students working together were audio recorded. The results were analysed by an approach based on the work of Wittgenstein and on a pragmatic and sociocultural perspective. Results showed that students rarely made generalizations in terms of universal statements and they did not use induction or produced hypotheses for testing in an analytic philosophical sense. The few generalizations they made of this kind were taken from zoological authorities like textbooks or lectures. However, students used induction when in more familiar contexts. Moreover, when generalizations were analysed in the sense of Dewey, it became evident that students are fully capable of making generalizations by transferring meaning from one experience to another. The implications of these results for using induction and hypotheses testing in instruction are discussed.
An unstructured-grid, parallel, projection solver for computing low-speed flows
Christon, M.A.; Carroll, D.E.
1998-08-01
This paper presents an overview of the issues associated with applying a domain-decomposition message-passing paradigm to the parallel implementation of both explicit and semi-implicit projection algorithms. The use of an element-based domain decomposition with an efficient solution strategy for the pressure field is shown to yield a scalable, parallel solution method capable of treating complex flow problems where high-resolution grids are required. In addition, the use of an SSOR or Jacobi preconditioned conjugate gradient solver with an A-conjugate projection reduces the computational time for the solution of the pressure field, and yields parallel efficiencies above 80% for computations with O(250) elements per processor. The parallel projection solver is verified using a series of 2-D and 3-D benchmarks designed to evaluate time-accurate flow solution methods. Finally, the extension of the projection algorithm to reacting flows is demonstrated for a time-dependent vortex-shedding problem.
An approximate Riemann solver for magnetohydrodynamics (that works in more than one dimension)
NASA Technical Reports Server (NTRS)
Powell, Kenneth G.
1994-01-01
An approximate Riemann solver is developed for the governing equations of ideal magnetohydrodynamics (MHD). The Riemann solver has an eight-wave structure, where seven of the waves are those used in previous work on upwind schemes for MHD, and the eighth wave is related to the divergence of the magnetic field. The structure of the eighth wave is not immediately obvious from the governing equations as they are usually written, but arises from a modification of the equations that is presented in this paper. The addition of the eighth wave allows multidimensional MHD problems to be solved without the use of staggered grids or a projection scheme, one or the other of which was necessary in previous work on upwind schemes for MHD. A test problem made up of a shock tube with rotated initial conditions is solved to show that the two-dimensional code yields answers consistent with the one-dimensional methods developed previously.
Parallel performance of a preconditioned CG solver for unstructured finite element applications
Shadid, J.N.; Hutchinson, S.A.; Moffat, H.K.
1994-12-31
A parallel unstructured finite element (FE) implementation designed for message passing MIMD machines is described. This implementation employs automated problem partitioning algorithms for load balancing unstructured grids, a distributed sparse matrix representation of the global finite element equations and a parallel conjugate gradient (CG) solver. In this paper a number of issues related to the efficient implementation of parallel unstructured mesh applications are presented. These include the differences between structured and unstructured mesh parallel applications, major communication kernels for unstructured CG solvers, automatic mesh partitioning algorithms, and the influence of mesh partitioning metrics on parallel performance. Initial results are presented for example finite element (FE) heat transfer analysis applications on a 1024 processor nCUBE 2 hypercube. Results indicate over 95% scaled efficiencies are obtained for some large problems despite the required unstructured data communication.
NASA Astrophysics Data System (ADS)
Zhang, Chenglong; Gamba, Irene M.
2016-11-01
We propose a deterministic conservative solver for the inhomogeneous Fokker-Planck-Landau equation coupled with Poisson equation. Through time-splitting scheme, a Vlasov-Poisson (collisionless) problem and a homogeneous Landau (collisional) problem are obtained. These two subproblems can be treated separately. We use operator splitting where the transport dynamics for Runge-Kutta Discontinuous Galerkin (RK-DG) method and the collisional dynamics for homogeneous conservative spectral method are adopted respectively. Since two different numerical schemes are applied separately, we have designed a new conservation correction process such that, after projecting the conservative spectral solution onto the DG mesh, there is no loss of moment consvervation. Parallelization is readily implemented. To verify our solver, numerical experiments on linear and nonlinear Landau damping are provided.
Generalized Airy functions for use in one-dimensional quantum mechanical problems
NASA Technical Reports Server (NTRS)
Eaves, J. O.
1972-01-01
The solution of the one dimensional, time independent, Schroedinger equation in which the energy minus the potential varies as the nth power of the distance is obtained from proper linear combinations of Bessel functions. The linear combinations called generalized Airy functions, reduce to the usual Airy functions Ai(x) and Bi(x) when n equals 1 and have the same type of simple asymptotic behavior. Expressions for the generalized Airy functions which can be evaluated by the method of generalized Gaussian quadrature are obtained.
A Newton-Krylov Solver for Implicit Solution of Hydrodynamics in Core Collapse Supernovae
Reynolds, D R; Swesty, F D; Woodward, C S
2008-06-12
This paper describes an implicit approach and nonlinear solver for solution of radiation-hydrodynamic problems in the context of supernovae and proto-neutron star cooling. The robust approach applies Newton-Krylov methods and overcomes the difficulties of discontinuous limiters in the discretized equations and scaling of the equations over wide ranges of physical behavior. We discuss these difficulties, our approach for overcoming them, and numerical results demonstrating accuracy and efficiency of the method.
Hybrid MPI+OpenMP Programming of an Overset CFD Solver and Performance Investigations
NASA Technical Reports Server (NTRS)
Djomehri, M. Jahed; Jin, Haoqiang H.; Biegel, Bryan (Technical Monitor)
2002-01-01
This report describes a two level parallelization of a Computational Fluid Dynamic (CFD) solver with multi-zone overset structured grids. The approach is based on a hybrid MPI+OpenMP programming model suitable for shared memory and clusters of shared memory machines. The performance investigations of the hybrid application on an SGI Origin2000 (O2K) machine is reported using medium and large scale test problems.
Large-scale 3D EM modeling with a Block Low-Rank multifrontal direct solver
NASA Astrophysics Data System (ADS)
Shantsev, Daniil V.; Jaysaval, Piyoosh; de la Kethulle de Ryhove, Sébastien; Amestoy, Patrick R.; Buttari, Alfredo; L'Excellent, Jean-Yves; Mary, Theo
2017-03-01
We put forward the idea of using a Block Low-Rank (BLR) multifrontal direct solver to efficiently solve the linear systems of equations arising from a finite-difference discretization of the frequency-domain Maxwell equations for 3D electromagnetic (EM) problems. The solver uses a low-rank representation for the off-diagonal blocks of the intermediate dense matrices arising in the multifrontal method to reduce the computational load. A numerical threshold, the so called BLR threshold, controlling the accuracy of low-rank representations was optimized by balancing errors in the computed EM fields against savings in floating point operations (flops). Simulations were carried out over large-scale 3D resistivity models representing typical scenarios for marine controlled-source EM surveys, and in particular the SEG SEAM model which contains an irregular salt body. The flop count, size of factor matrices and elapsed run time for matrix factorization are reduced dramatically by using BLR representations and can go down to, respectively, 10%, 30% and 40% of their full rank values for our largest system with N = 20.6 million unknowns. The reductions are almost independent of the number of MPI tasks and threads at least up to 90 × 10 = 900 cores. The BLR savings increase for larger systems, which reduces the factorization flop complexity from O( {{N^2}} ) for the full-rank solver to O( {{N^m}} ) with m = 1.4 - 1.6 . The BLR savings are significantly larger for deep-water environments that exclude the highly resistive air layer from the computational domain. A study in a scenario where simulations are required at multiple source locations shows that the BLR solver can become competitive in comparison to iterative solvers as an engine for 3D CSEM Gauss-Newton inversion that requires forward modelling for a few thousand right-hand sides.
A new algorithm for constrained nonlinear least-squares problems, part 1
NASA Technical Reports Server (NTRS)
Hanson, R. J.; Krogh, F. T.
1983-01-01
A Gauss-Newton algorithm is presented for solving nonlinear least squares problems. The problem statement may include simple bounds or more general constraints on the unknowns. The algorithm uses a trust region that allows the objective function to increase with logic for retreating to best values. The computations for the linear problem are done using a least squares system solver that allows for simple bounds and linear constraints. The trust region limits are defined by a box around the current point. In its current form the algorithm is effective only for problems with small residuals, linear constraints and dense Jacobian matrices. Results on a set of test problems are encouraging.
Newton's method as applied to the Riemann problem for media with general equations of state
NASA Astrophysics Data System (ADS)
Moiseev, N. Ya.; Mukhamadieva, T. A.
2008-06-01
An approach based on Newton’s method is proposed for solving the Riemann problem for media with normal equations of state. The Riemann integrals are evaluated using a cubic approximation of an isentropic curve that is superior to the Simpson method in terms of accuracy, convergence rate, and efficiency. The potentials of the approach are demonstrated by solving problems for media obeying the Mie-Grüneisen equation of state. The algebraic equation of the isentropic curve and some exact solutions for configurations with rarefaction waves are explicitly given.
A comparison of SuperLU solvers on the intel MIC architecture
NASA Astrophysics Data System (ADS)
Tuncel, Mehmet; Duran, Ahmet; Celebi, M. Serdar; Akaydin, Bora; Topkaya, Figen O.
2016-10-01
In many science and engineering applications, problems may result in solving a sparse linear system AX=B. For example, SuperLU_MCDT, a linear solver, was used for the large penta-diagonal matrices for 2D problems and hepta-diagonal matrices for 3D problems, coming from the incompressible blood flow simulation (see [1]). It is important to test the status and potential improvements of state-of-the-art solvers on new technologies. In this work, sequential, multithreaded and distributed versions of SuperLU solvers (see [2]) are examined on the Intel Xeon Phi coprocessors using offload programming model at the EURORA cluster of CINECA in Italy. We consider a portfolio of test matrices containing patterned matrices from UFMM ([3]) and randomly located matrices. This architecture can benefit from high parallelism and large vectors. We find that the sequential SuperLU benefited up to 45 % performance improvement from the offload programming depending on the sparse matrix type and the size of transferred and processed data.
Using Problem-Centered Learning for Teaching Collaboration in a General Methods Course
ERIC Educational Resources Information Center
Memory, David M.; Yoder, Carol Y.; Williams, Robert O.
2003-01-01
The Interstate New Teacher Assessment and Support Consortium's (INTASC's) (1992) standards for beginning teachers and the National Board for Professional Teaching Standards' core propositions highlight the importance of collaborative problem solving for teachers. They suggest teachers work together with other school professionals, parents, and…
In-Home Generalization of Social Interactions in Families of Adolescents with Behavior Problems.
ERIC Educational Resources Information Center
Serna, Loretta A.; And Others
1991-01-01
A communication program was implemented with the families of three adolescents with behavior problems. Skill teaching resulted in parent-adolescent dyads learning to use the skills in the teaching setting, but competent use of the skills in the home was not observed until an in-home family conference phase was implemented. (Author/JDD)
A Generalized Approach to the Two Sample Problem: The Quantile Approach.
1981-04-01
Tests for the Two Sample Problem and Their Power," I, II, III, Indagationes Math., 14, 453-458, 15, 303-310, 15, 80. Wald , A. and Wolfowitz , J. (1940...where 0 < p < q < 1 or use p,q an inner product based on the censored observations. Other directions to go include the Wald andWolfowitz (1940) runs
Alcohol Problems and the Differentiation of Partner, Stranger, and General Violence
ERIC Educational Resources Information Center
Cogan, Rosemary; Ballinger, Bud C., III
2006-01-01
To explore the relationship between alcohol problems and physical violence with partners and strangers, 457 college men and 958 college women with low, intermediate, or high scores on the Short Michigan Alcohol Screening Test reported conflict tactics on the Conflict Tactics Scale in the past year to and by partners and strangers. More men than…
ERIC Educational Resources Information Center
Bazo, Plácido; Rodríguez, Romén; Fumero, Dácil
2016-01-01
In this paper, we will introduce an innovative software platform that can be especially useful in a Content and Language Integrated Learning (CLIL) context. This tool is called Vocabulary Notebook, and has been developed to solve all the problems that traditional (paper) vocabulary notebooks have. This tool keeps focus on the personalisation of…
Parallelization of Unsteady Adaptive Mesh Refinement for Unstructured Navier-Stokes Solvers
NASA Technical Reports Server (NTRS)
Schwing, Alan M.; Nompelis, Ioannis; Candler, Graham V.
2014-01-01
This paper explores the implementation of the MPI parallelization in a Navier-Stokes solver using adaptive mesh re nement. Viscous and inviscid test problems are considered for the purpose of benchmarking, as are implicit and explicit time advancement methods. The main test problem for comparison includes e ects from boundary layers and other viscous features and requires a large number of grid points for accurate computation. Ex- perimental validation against double cone experiments in hypersonic ow are shown. The adaptive mesh re nement shows promise for a staple test problem in the hypersonic com- munity. Extension to more advanced techniques for more complicated ows is described.
Performance of the block-Krylov energy group solvers in Jaguar
Watson, A. M.; Kennedy, R. A.
2012-07-01
A new method of coupling the inner and outer iterations for deterministic transport problems is proposed. This method is termed the Multigroup Energy Blocking Method (MEBM) and has been implemented in the deterministic transport solver Jaguar, which is currently under development at KAPL. The method is derived for both fixed-source and eigenvalue problems. The method is then applied to a PWR pin cell model, both in fixed-source mode and eigenvalue mode. The results show that the MEBM improves the convergence of both types of problems when applied to the thermal (up-scattering) groups. (authors)
Transonic Drag Prediction on a DLR-F6 Transport Configuration Using Unstructured Grid Solvers
NASA Technical Reports Server (NTRS)
Lee-Rausch, E. M.; Frink, N. T.; Mavriplis, D. J.; Rausch, R. D.; Milholen, W. E.
2004-01-01
A second international AIAA Drag Prediction Workshop (DPW-II) was organized and held in Orlando Florida on June 21-22, 2003. The primary purpose was to inves- tigate the code-to-code uncertainty. address the sensitivity of the drag prediction to grid size and quantify the uncertainty in predicting nacelle/pylon drag increments at a transonic cruise condition. This paper presents an in-depth analysis of the DPW-II computational results from three state-of-the-art unstructured grid Navier-Stokes flow solvers exercised on similar families of tetrahedral grids. The flow solvers are USM3D - a tetrahedral cell-centered upwind solver. FUN3D - a tetrahedral node-centered upwind solver, and NSU3D - a general element node-centered central-differenced solver. For the wingbody, the total drag predicted for a constant-lift transonic cruise condition showed a decrease in code-to-code variation with grid refinement as expected. For the same flight condition, the wing/body/nacelle/pylon total drag and the nacelle/pylon drag increment predicted showed an increase in code-to-code variation with grid refinement. Although the range in total drag for the wingbody fine grids was only 5 counts, a code-to-code comparison of surface pressures and surface restricted streamlines indicated that the three solvers were not all converging to the same flow solutions- different shock locations and separation patterns were evident. Similarly, the wing/body/nacelle/pylon solutions did not appear to be converging to the same flow solutions. Overall, grid refinement did not consistently improve the correlation with experimental data for either the wingbody or the wing/body/nacelle pylon configuration. Although the absolute values of total drag predicted by two of the solvers for the medium and fine grids did not compare well with the experiment, the incremental drag predictions were within plus or minus 3 counts of the experimental data. The correlation with experimental incremental drag was not
Honea, R.B.; Baxter, F.P.
1984-07-01
In 1977 Congress passed the Surface Mining Control and Reclamation Act, which provided for the abatement of abandoned mine land (AML) problems through a reclamation program funded by a severance tax on current mining. AML was defined as any land, including associated buildings, equipment, and affected areas, that was no longer being used for coal mining by August 1977. This act also created the Office of Surface Mining (OSM) in the Department of the Interior to administer the AML program and to assume other regulatory and research responsibilities. This report documents the design, implementation, and results of a National inventory of the most serious problems associated with past mining practices. One of the objectives of the Inventory was to help OSM and the participating states locate, identify, and rank AML problems and estimate their reclamation costs. Other objectives were to encourage states and Indian tribes to collect such data and to provide OSM with the information necessary to guide its decision-making processes and to quantify the progress of the reclamation program. Because only limited funds were available to design and implement the National inventory and because the reclamation fund established by the Act may never be sufficient to correct all AML problems, OSM has focused on only the top-priority problems. It is stressed that this is not an inventory of AML features but rather an inventory of AML impacts. It should be noted that the data and analysis contained in this report are based on a data collection effort conducted by the states, Indian tribes, and OSM contractors between 1979 and mid-1982.
Common mental health problems in immigrants and refugees: general approach in primary care
Kirmayer, Laurence J.; Narasiah, Lavanya; Munoz, Marie; Rashid, Meb; Ryder, Andrew G.; Guzder, Jaswant; Hassan, Ghayda; Rousseau, Cécile; Pottie, Kevin
2011-01-01
Background: Recognizing and appropriately treating mental health problems among new immigrants and refugees in primary care poses a challenge because of differences in language and culture and because of specific stressors associated with migration and resettlement. We aimed to identify risk factors and strategies in the approach to mental health assessment and to prevention and treatment of common mental health problems for immigrants in primary care. Methods: We searched and compiled literature on prevalence and risk factors for common mental health problems related to migration, the effect of cultural influences on health and illness, and clinical strategies to improve mental health care for immigrants and refugees. Publications were selected on the basis of relevance, use of recent data and quality in consultation with experts in immigrant and refugee mental health. Results: The migration trajectory can be divided into three components: premigration, migration and postmigration resettlement. Each phase is associated with specific risks and exposures. The prevalence of specific types of mental health problems is influenced by the nature of the migration experience, in terms of adversity experienced before, during and after resettlement. Specific challenges in migrant mental health include communication difficulties because of language and cultural differences; the effect of cultural shaping of symptoms and illness behaviour on diagnosis, coping and treatment; differences in family structure and process affecting adaptation, acculturation and intergenerational conflict; and aspects of acceptance by the receiving society that affect employment, social status and integration. These issues can be addressed through specific inquiry, the use of trained interpreters and culture brokers, meetings with families, and consultation with community organizations. Interpretation: Systematic inquiry into patients’ migration trajectory and subsequent follow-up on culturally
NASA Astrophysics Data System (ADS)
Turyshev, S. G.
2009-01-01
Einstein's general theory of relativity is the standard theory of gravity, especially where the needs of astronomy, astrophysics, cosmology, and fundamental physics are concerned. As such, this theory is used for many practical purposes involving spacecraft navigation, geodesy, and time transfer. We review the foundations of general relativity, discuss recent progress in tests of relativistic gravity, and present motivations for the new generation of high-accuracy tests of new physics beyond general relativity. Space-based experiments in fundamental physics are presently capable of uniquely addressing important questions related to the fundamental laws of nature. We discuss the advances in our understanding of fundamental physics that are anticipated in the near future and evaluate the discovery potential of a number of recently proposed space-based gravitational experiments.
ERIC Educational Resources Information Center
Cor, Ken; Alves, Cecilia; Gierl, Mark J.
2008-01-01
This review describes and evaluates a software add-in created by Frontline Systems, Inc., that can be used with Microsoft Excel 2007 to solve large, complex test assembly problems. The combination of Microsoft Excel 2007 with the Frontline Systems Premium Solver Platform is significant because Microsoft Excel is the most commonly used spreadsheet…
An extension of the QZ algorithm for solving the generalized matrix eigenvalue problem
NASA Technical Reports Server (NTRS)
Ward, R. C.
1973-01-01
This algorithm is an extension of Moler and Stewart's QZ algorithm with some added features for saving time and operations. Also, some additional properties of the QR algorithm which were not practical to implement in the QZ algorithm can be generalized with the combination shift QZ algorithm. Numerous test cases are presented to give practical application tests for algorithm. Based on results, this algorithm should be preferred over existing algorithms which attempt to solve the class of generalized eigenproblems where both matrices are singular or nearly singular.
NASA Astrophysics Data System (ADS)
Balsara, Dinshaw S.; Vides, Jeaniffer; Gurski, Katharine; Nkonga, Boniface; Dumbser, Michael; Garain, Sudip; Audit, Edouard
2016-01-01
Just as the quality of a one-dimensional approximate Riemann solver is improved by the inclusion of internal sub-structure, the quality of a multidimensional Riemann solver is also similarly improved. Such multidimensional Riemann problems arise when multiple states come together at the vertex of a mesh. The interaction of the resulting one-dimensional Riemann problems gives rise to a strongly-interacting state. We wish to endow this strongly-interacting state with physically-motivated sub-structure. The self-similar formulation of Balsara [16] proves especially useful for this purpose. While that work is based on a Galerkin projection, in this paper we present an analogous self-similar formulation that is based on a different interpretation. In the present formulation, we interpret the shock jumps at the boundary of the strongly-interacting state quite literally. The enforcement of the shock jump conditions is done with a least squares projection (Vides, Nkonga and Audit [67]). With that interpretation, we again show that the multidimensional Riemann solver can be endowed with sub-structure. However, we find that the most efficient implementation arises when we use a flux vector splitting and a least squares projection. An alternative formulation that is based on the full characteristic matrices is also presented. The multidimensional Riemann solvers that are demonstrated here use one-dimensional HLLC Riemann solvers as building blocks. Several stringent test problems drawn from hydrodynamics and MHD are presented to show that the method works. Results from structured and unstructured meshes demonstrate the versatility of our method. The reader is also invited to watch a video introduction to multidimensional Riemann solvers on http://www.nd.edu/ dbalsara/Numerical-PDE-Course.
New numerical solver for flows at various Mach numbers
NASA Astrophysics Data System (ADS)
Miczek, F.; Röpke, F. K.; Edelmann, P. V. F.
2015-04-01
Context. Many problems in stellar astrophysics feature flows at low Mach numbers. Conventional compressible hydrodynamics schemes frequently used in the field have been developed for the transonic regime and exhibit excessive numerical dissipation for these flows. Aims: While schemes were proposed that solve hydrodynamics strictly in the low Mach regime and thus restrict their applicability, we aim at developing a scheme that correctly operates in a wide range of Mach numbers. Methods: Based on an analysis of the asymptotic behavior of the Euler equations in the low Mach limit we propose a novel scheme that is able to maintain a low Mach number flow setup while retaining all effects of compressibility. This is achieved by a suitable modification of the well-known Roe solver. Results: Numerical tests demonstrate the capability of this new scheme to reproduce slow flow structures even in moderate numerical resolution. Conclusions: Our scheme provides a promising approach to a consistent multidimensional hydrodynamical treatment of astrophysical low Mach number problems such as convection, instabilities, and mixing in stellar evolution.
Children with Generalized Anxiety Disorder Do Not Have Peer Problems, Just Fewer Friends
ERIC Educational Resources Information Center
Scharfstein, Lindsay; Alfano, Candice; Beidel, Deborah; Wong, Nina
2011-01-01
A common assumption is that all youth with anxiety disorders (AD) experience impaired peer relationships relative to healthy control children. Social impairments have been identified among youth with certain AD (e.g., social anxiety disorder; SAD), but less is known about the peer relationships of children with generalized anxiety disorder (GAD).…
Thin-Layer Chromatography Experiments That Illustrate General Problems in Chromatography.
ERIC Educational Resources Information Center
Lederer, M.; Leipzig-Pagani, E.
1996-01-01
Describes experiments that illustrate a number of general principles such as pattern identification, displacement chromatography, and salting-out adsorption, plus an experiment that demonstrates that identification by chromatography alone is impossible. Illustrates that chromatography is still possible with quite simple means, notwithstanding the…
Unified formalism for the generalized kth-order Hamilton-Jacobi problem
NASA Astrophysics Data System (ADS)
Colombo, Leonardo; de Léon, Manuel; Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso
2014-08-01
The geometric formulation of the Hamilton-Jacobi theory enables us to generalize it to systems of higher-order ordinary differential equations. In this work we introduce the unified Lagrangian-Hamiltonian formalism for the geometric Hamilton-Jacobi theory on higher-order autonomous dynamical systems described by regular Lagrangian functions.
Navajo Community College Funding Problems. Report by the Comptroller General of the United States.
ERIC Educational Resources Information Center
Comptroller General of the U.S., Washington, DC.
Funding for the Navajo Community College was reviewed by the Comptroller General of the United States to determine if the Bureau of Indian Affairs' (BIA) regulations and method of computing full-time equivalent enrollments were consistent with the Tribally Controlled Community College Assistance Act of 1978 (P.L. 95-471). The investigation…
Safran, D; Bauwens, C
1988-01-01
General anaesthesia in pregnancy is still responsible for a significant morbidity and mortality. The most common and most serious complications are respiratory secondary to changes induced by pregnancy. These are dominated by hypoxia during difficult intubation and inhalation of gastric contents. Their incidence could be largely reduced by the extensive use of regional local anaesthesia.
2002-01-01
texture mapping; and general geometric mapping between high dimensional surfaces. Instituto de Ingenieria Electrica, Universidad de la Republica...Minnesota. This work was partially supported by a grant from the Office of Naval Research ONR-N00014-97-1-0509, the Office of Naval Research Young
NASA Technical Reports Server (NTRS)
Cunningham, A. M., Jr.
1973-01-01
A study was conducted to investigate the feasibility of using combined subsonic and supersonic linear theory as a means for solving unsteady transonic flow problems in an economical and yet realistic manner. With some modification, existing linear theory methods are combined into a single program and a simple algorithm is derived for determining interference between lifting surface elements of different Mach number. The method is applied to a wide variety of problems for which measured unsteady pressure distributions and Mach number distributions are available. By comparing theory and experiment, the transonic method solutions show a significant improvement over uniform flow solutions. It is concluded that with these refinements the method will provide a means for performing realistic transonic flutter and dynamic response analyses at costs which are compatible with current linear theory based solutions.
Existence and uniqueness of solutions in general multisolute renal flow problems.
Garner, J B; Kellogg, R B
1988-01-01
This paper considers systems of differential equations that describe flows in renal networks. The flow geometry is of the type that occurs in modelling the renal medulla. The unknowns in the system include the flow rate, the hydrostatic pressure, and the concentrations of the various solutes. Existence and uniqueness of solutions of the appropriate boundary value problems are established, in the case of small permeability coefficients and transport rates, or large diffusion coefficients and small resistance to flow constants.
NASA Astrophysics Data System (ADS)
Vincenti, H.; Vay, J.-L.
2016-03-01
Very high order or pseudo-spectral Maxwell solvers are the method of choice to reduce discretization effects (e.g. numerical dispersion) that are inherent to low order Finite-Difference Time-Domain (FDTD) schemes. However, due to their large stencils, these solvers are often subject to truncation errors in many electromagnetic simulations. These truncation errors come from non-physical modifications of Maxwell's equations in space that may generate spurious signals affecting the overall accuracy of the simulation results. Such modifications for instance occur when Perfectly Matched Layers (PMLs) are used at simulation domain boundaries to simulate open media. Another example is the use of arbitrary order Maxwell solver with domain decomposition technique that may under some condition involve stencil truncations at subdomain boundaries, resulting in small spurious errors that do eventually build up. In each case, a careful evaluation of the characteristics and magnitude of the errors resulting from these approximations, and their impact at any frequency and angle, requires detailed analytical and numerical studies. To this end, we present a general analytical approach that enables the evaluation of numerical errors of fully three-dimensional arbitrary order finite-difference Maxwell solver, with arbitrary modification of the local stencil in the simulation domain. The analytical model is validated against simulations of domain decomposition technique and PMLs, when these are used with very high-order Maxwell solver, as well as in the infinite order limit of pseudo-spectral solvers. Results confirm that the new analytical approach enables exact predictions in each case. It also confirms that the domain decomposition technique can be used with very high-order Maxwell solvers and a reasonably low number of guard cells with negligible effects on the whole accuracy of the simulation.
NASA Astrophysics Data System (ADS)
Prayudhatama, D.; Waris, A.; Kurniasih, N.; Kurniadi, R.
2010-06-01
In-core fuel management study is a crucial activity in nuclear power plant design and operation. Its common problem is to find an optimum arrangement of fuel assemblies inside the reactor core. Main objective for this activity is to reduce the cost of generating electricity, which can be done by altering several physical properties of the nuclear reactor without violating any of the constraints imposed by operational and safety considerations. This research try to address the problem of nuclear fuel arrangement problem, which is, leads to the multi-objective optimization problem. However, the calculation of the reactor core physical properties itself is a heavy computation, which became obstacle in solving the optimization problem by using genetic algorithm optimization. This research tends to address that problem by using the emerging General Purpose Computation on Graphics Processing Units (GPGPU) techniques implemented by C language for CUDA (Compute Unified Device Architecture) parallel programming. By using this parallel programming technique, we develop parallelized nuclear reactor fitness calculation, which is involving numerical finite difference computation. This paper describes current prototype of the parallel algorithm code we have developed on CUDA, that performs one hundreds finite difference calculation for nuclear reactor fitness evaluation in parallel by using GPU G9 Hardware Series developed by NVIDIA.
Prayudhatama, D.; Waris, A.; Kurniasih, N.; Kurniadi, R.
2010-06-22
In-core fuel management study is a crucial activity in nuclear power plant design and operation. Its common problem is to find an optimum arrangement of fuel assemblies inside the reactor core. Main objective for this activity is to reduce the cost of generating electricity, which can be done by altering several physical properties of the nuclear reactor without violating any of the constraints imposed by operational and safety considerations. This research try to address the problem of nuclear fuel arrangement problem, which is, leads to the multi-objective optimization problem. However, the calculation of the reactor core physical properties itself is a heavy computation, which became obstacle in solving the optimization problem by using genetic algorithm optimization.This research tends to address that problem by using the emerging General Purpose Computation on Graphics Processing Units (GPGPU) techniques implemented by C language for CUDA (Compute Unified Device Architecture) parallel programming. By using this parallel programming technique, we develop parallelized nuclear reactor fitness calculation, which is involving numerical finite difference computation. This paper describes current prototype of the parallel algorithm code we have developed on CUDA, that performs one hundreds finite difference calculation for nuclear reactor fitness evaluation in parallel by using GPU G9 Hardware Series developed by NVIDIA.
Population problems: a constituent of general culture in the 21st century.
Rath, F J
1993-03-01
World population doubled in less than two centuries after 1650 reaching 1 billion. Between 1830 and 1930 the population doubled again. By 1975, the world population was 4 billion. Population is currently increasing at the rate of 250,000 people per day. The population problems is one of an intertwining of population, poverty, and environmental damage. Both developing and developed countries have population problems, which vary in intensity and nature. The consequences of high growth rates are reflected in population and development problems and pose a threat to long term survival of the human species. Quality of life is threatened. In 1948, UNESCO reported that using technology to provide sufficiently for food, shelter, and basic amenities only postponed the point at which problems would become acute; demographic growth cannot continue in a finite world. For example, by 2025 Nigeria could have more inhabitants than the US, and a population density of 327 people per sq kilometer. The demographic characteristics of population vary by country. There is growing awareness, however, that there is an interdependence between people and regions, and inter-relationships between demographic, economic, social, cultural, environmental, and political factors. Examples of the implications of demographic growth are given for school enrollments, landless farmers in Honduras, development strategies, and urbanization and migration. Population pressure in one country will lead to migration of the excess population to another country. Rural-urban migration already is motivated by economic gain; the economic recession in urban areas means competition for jobs, housing, welfare benefits. Political conditions can contribute to migration in the case of war or civil unrest or can halt migration because of fear of multi-ethnicity. The Malthusian checks were increased mortality; today population stabilization can be achieved through control of reproduction. The prospects for the immediate
Wen, Dao-Jun
2013-01-01
In this paper, a Meir-Keeler contraction is introduced to propose a viscosity-projection approximation method for finding a common element of the set of solutions of a family of general equilibrium problems and the set of fixed points of asymptotically strict pseudocontractions in the intermediate sense. Strong convergence of the viscosity iterative sequences is obtained under some suitable conditions. Results presented in this paper extend and unify the previously known results announced by many other authors. PMID:24285937
Fernandes, L.; Friedlander, A.; Guedes, M.; Judice, J.
2001-07-01
This paper addresses a General Linear Complementarity Problem (GLCP) that has found applications in global optimization. It is shown that a solution of the GLCP can be computed by finding a stationary point of a differentiable function over a set defined by simple bounds on the variables. The application of this result to the solution of bilinear programs and LCPs is discussed. Some computational evidence of its usefulness is included in the last part of the paper.
NASA Astrophysics Data System (ADS)
Chen, Miawjane; Yan, Shangyao; Wang, Sin-Siang; Liu, Chiu-Lan
2015-02-01
An effective project schedule is essential for enterprises to increase their efficiency of project execution, to maximize profit, and to minimize wastage of resources. Heuristic algorithms have been developed to efficiently solve the complicated multi-mode resource-constrained project scheduling problem with discounted cash flows (MRCPSPDCF) that characterize real problems. However, the solutions obtained in past studies have been approximate and are difficult to evaluate in terms of optimality. In this study, a generalized network flow model, embedded in a time-precedence network, is proposed to formulate the MRCPSPDCF with the payment at activity completion times. Mathematically, the model is formulated as an integer network flow problem with side constraints, which can be efficiently solved for optimality, using existing mathematical programming software. To evaluate the model performance, numerical tests are performed. The test results indicate that the model could be a useful planning tool for project scheduling in the real world.
Cape, J; Barker, C; Buszewicz, M; Pistrang, N
2000-01-01
The majority of patients with common emotional or psychological problems are treated solely by general practitioners (GPs). Such treatment frequently includes some form of psychological management within the consultation, whether limited to listening and discussion or involving more specific techniques. This paper sets out a research agenda for the development of effective approaches to GP psychological management. Evidence is reviewed on three core components of all psychological treatments: establishing a positive therapeutic relationship, developing a shared understanding of the problem, and promoting change in behaviour, thoughts or emotions. The application of these components in GP psychological management is outlined and methodological issues in the development and evaluation of GP management approaches are discussed. Since the number of patients with emotional problems seen by each GP is so large, the population effects of even small improvements in psychological management would be sizeable. PMID:10897540
van Meel, D; de Vrij, J H; Kunst, A E; Mackenbach, J P
1992-08-08
The aim of this study was to determine whether the austerely living Trappist and Benedictine monks have a lower prevalence of a number of risk factors and health problems than the general Dutch population. A written questionnaire was submitted to monks of 7 monasteries. The response was 67 per cent (134 monks). The data were compared with data from the national Health Interview Survey of 1989, which used an almost identical questionnaire. Adjustment was made for differences in age and education. Monks consume less alcohol and tobacco and have a more austere diet. Their average Quetelet index is lower. The prevalence of cardiovascular disease is lower. On the other hand, monks more often report a number of other chronic diseases, physical complaints, and problems with activities of daily life. They more often have contact with general practitioners and with consultants. The lower prevalence of a number of risk factors among monks reflects their austere way of life. It is not certain whether the lower prevalence of cardiovascular diseases can be attributed to this way of life. The fact that, in general, health problems are more prevalent among monks suggests that changes in lifestyle do not necessarily lead to compression of morbidity.
Relative equilibria for general gravity fields in the sphere-restricted full two-body problem.
Scheeres, D J
2005-12-01
Equilibrium conditions for a mutually attracting general mass distribution and point mass are stated. The equilibrium conditions can be reduced to six equations in six unknowns, plus the existence of integrals of motion consisting of the total angular momentum and energy of the system. The equilibrium conditions are further reduced to two independent equations, and their theoretical properties are studied. We state a set of necessary and sufficient conditions for an equilibrium that is well suited to the computation of certain classes of equilibria. These equations are solved for nonsymmetric gravity fields of interest, using a real asteroid shape model for the general gravity fields. The stability of the resulting equilibria are also noted.
NASA Astrophysics Data System (ADS)
Wagenhoffer, Nathan; Moored, Keith; Jaworski, Justin
2016-11-01
The design of quiet and efficient bio-inspired propulsive concepts requires a rapid, unified computational framework that integrates the coupled fluid dynamics with the noise generation. Such a framework is developed where the fluid motion is modeled with a two-dimensional unsteady boundary element method that includes a vortex-particle wake. The unsteady surface forces from the potential flow solver are then passed to an acoustic boundary element solver to predict the radiated sound in low-Mach-number flows. The use of the boundary element method for both the hydrodynamic and acoustic solvers permits dramatic computational acceleration by application of the fast multiple method. The reduced order of calculations due to the fast multipole method allows for greater spatial resolution of the vortical wake per unit of computational time. The coupled flow-acoustic solver is validated against canonical vortex-sound problems. The capability of the coupled solver is demonstrated by analyzing the performance and noise production of an isolated bio-inspired swimmer and of tandem swimmers.
Hintermair, Manfred
2013-01-01
In this study, behavioral problems of deaf and hard-of-hearing (D/HH) school-aged children are discussed in the context of executive functioning and communicative competence. Teachers assessed the executive functions of a sample of 214 D/HH students from general schools and schools for the deaf, using a German version of the Behavior Rating Inventory of Executive Functions (BRIEF-D). This was complemented by a questionnaire that measured communicative competence and behavioral problems (German version of the Strengths and Difficulties Questionnaire; SDQ-D). The results in nearly all the scales show a significantly higher problem rate for executive functions in the group of D/HH students compared with a normative sample of hearing children. In the D/HH group, students at general schools had better scores on most scales than students at schools for the deaf. Regression analysis reveals the importance of executive functions and communicative competence for behavioral problems. The relevance of the findings for pedagogical work is discussed. A specific focus on competencies such as self-efficacy or self-control in educational concepts for D/HH students seems to be necessary in addition to extending language competencies.
NASA Astrophysics Data System (ADS)
Sherer, Scott Eric
Various high-order and optimized interpolation procedures have been developed for use in a high-order overset grid computational fluid dynamics solver. Because of the high spatial order of accuracy of the solver, second-order accurate trilinear interpolation typically used in low-order overset grid flow solvers is insufficient to maintain overall order of accuracy, and thus high-order interpolation methods must be employed. Candidate interpolation methods, including a generalized Lagrangian method and a method based on the use of B-splines, were formulated. The coefficients for the generalized Lagrangian method may be found strictly from constraints on the formal order of accuracy of the method, in which case the method is non-optimized, or through constraints arising from the minimization of a one-dimensional integrated error, in which case the method is considered optimized. The interpolation methods were investigated using a one-dimensional Fourier error analysis, and their spectral behavior studied. They also were examined in multiple dimensions for the problem of grid-to-grid interpolation of various two- and three-dimensional analytical test functions. The high-order non-optimized explicit Lagrangian method was found to be the most robust and accurate of the interpolation methods considered. The fourth-order B-spline method was very competitive when the interpolation points were located in the middle of the stencil, but was shown to be weak when the interpolation points were located near the boundary of the stencil. The complete high-order overset grid method was validated for several fluid flow problems including flat-plate boundary-layer flow, an inviscid convecting vortex, and the unsteady flow past a circular cylinder at a low Reynolds number. Results indicate that second-order interpolation was insufficient to maintain a high-order rate of grid convergence, and that explicit high-order interpolation methods are superior to optimized, implicit or B
Investigating the Faint young Sun problem with a general circulation model
NASA Astrophysics Data System (ADS)
Kunze, M.; Godolt, M.; Langematz, U.; Rauer, H.
2012-04-01
The faint young sun problem, the contradiction of a reduced solar luminosity by 15-25% during the Archean and the geologic evidence for relatively high surface temperatures that allowed the presence of liquid water, is still unresolved. It is suggested that the cooling induced by a fainter sun was e.g. offset by higher levels of greenhouse gases (GHGs) during the Archean, but the amounts of GHGs that are necessary to solve the problem can not be supported by proxy data. We present a study in which we investigate this problem by using the Chemistry Climate model EMAC (ECHAM/MESSy Atmospheric Chemistry) with a, spectrally resolved irradiance dataset valid for the Archean. As proxy for the irradiance of the young Sun at 2.5 Ga before today we use the G0V-dwarf star beta Com, which is scaled to have a total solar irradiance of 82% the present value. The EMAC model is used in a configuration with the highly resolving short-wave radiative transfer parametrization FUBRad, coupled to a mixed layer ocean, where the sea surface temperatures and the sea ice are derived from the thermodynamics of an ocean layer. We analyse the climatic impact of the spectrally resolved irradiances and other parameters representing the late Archean Earth, such as the composition of the atmosphere and the land/ocean distribution. We can show that an increase of the CO2 concentration by a factor of 10 is sufficient to obtain liquid oceans in the tropics. Further analysis concentrates on the thermal and dynamical state of the atmosphere with emphasis on the middle atmosphere.
Govender, Indiran; Hugo, Jannie
2015-01-01
Abstract Background Sexual problems are common. Many patients with sexual health dysfunction use self-help literature or are often managed in general practice. However, many general practitioners (GPs) find it difficult to discuss sexual health issues because they feel uncomfortable with this and lack training in these matters. These GPs are now referring patients with sexual dysfunction to specialists. Aim We sought to explore how GPs working in the Mabopane and Ga-Rankuwa areas of handle sexual problems of their patients. Setting The setting was the Mabopane and Ga-Rankuwa areas of North-West Tshwane, in Gauteng Province. Methods A qualitative study comprising eight free attitude interviews with purposefully selected four male and four female GPs. All interviews were conducted in English and tape-recorded. Field notes in the form of a detailed diary was kept. The tapes were transcribed verbatim, and the transcriptions were checked against the tapes for omissions and inaccuracies. Results Six themes emerged from the interviews: causes of sexual problems; presentation of sexual problems to the doctor; management of sexual health problems; sex is a taboo topic; society's need for sexual health discussions, and these discussions have already begun; previous limited exposure and training, and a need for more sexual health training. Conclusion This study confirms earlier findings that patients could be either reluctant to discuss their problems or are open about them when presenting to doctors with sexual dysfunction. GPs were not exposed to sexual health training at medical school and, because of this shortcoming, felt that training in sexual medicine should be part of the curriculum. PMID:26842520
Development of a new 3D OpenFOAM¯ solver to model the cooling stage in profile extrusion
NASA Astrophysics Data System (ADS)
Fernandes, C.; Habla, F.; Carneiro, O. S.; Hinrichsen, O.; Nóbrega, J. M.
2016-03-01
In this work a new solver is developed in OpenFOAM® computational library, to model the cooling state in profile extrusion. The solver is able to calculate the temperature distribution in a two domain system, comprising the profile and calibrator, considering the temperature discontinuity at the interface. The derivation of the model is based on the local instantaneous energy conservation equation, in conjunction with the conditional volume averaging technique, which yields a single governing equation valid in both domains. Aiming the solution of automatic optimization/parameterization problems, the developed solver was coupled with the DAKOTA toolkit. The application of the novel calculation system is illustrated in a study of a complex geometry extruded profile cooling stage.
1987-11-27
Teenage Pregnancy : 500,000 PEMD-86-16BR 07/21/86 Births a Year but Few Tested Programs An Evaluation of the 1981 AFDC PEMD-85-4 07/02/85 Changes: Final...At that time, we will send copies to S other interested parties and make copies available to others who request them. Should you need further...as by coapplication and coeligibility determination for services. S (GAO/HRD-87-11OFS, p. 30; GAO/HRD-87-51BR, p. 19) 4 V6 lot . .. .. Problems Quest
Cortner, H.J.; Shannon, M.A.; Wallace, M.G.; Burke, S.; Moote, M.A.
1996-02-01
This report identifies five problem areas where social science research can improve the authors` understanding of how ecosystem management can best be implemented. These include (1) the extent to which existing laws, policies, and programs may constrain or aid the implementation of ecosystem management; (2) institutional mechanisms for managing across jurisdictions; (3) internal organizational changes and new arrangements among resource agencies and the public; (4) theoretical principles underlying natural resource management; and (5) methodological approaches for researching instutional questions. Strategies to begin researching these questions are also suggested.
AQUAgpusph, a new free 3D SPH solver accelerated with OpenCL
NASA Astrophysics Data System (ADS)
Cercos-Pita, J. L.
2015-07-01
In this paper, AQUAgpusph, a new free Smoothed Particle Hydrodynamics (SPH) software accelerated with OpenCL, is described. The main differences and progress with respect to other existing alternatives are considered. These are the use of the Open Computing Language (OpenCL) framework instead of the Compute Unified Device Architecture (CUDA), the implementation of the most popular boundary conditions, the easy customization of the code to different problems, the extensibility with regard to Python scripts, and the runtime output which allows the tracking of simulations in real time, or a higher frequency in saving some results without a significant performance lost. These modifications are shown to improve the solver speed, the results quality, and allow for a wider areas of application. AQUAgpusph has been designed trying to provide researchers and engineers with a valuable tool to test and apply the SPH method. Three practical applications are discussed in detail. The evolution of a dam break is used to quantify and compare the computational performance and modeling accuracy with the most popular SPH Graphics Processing Unit (GPU) accelerated alternatives. The dynamics of a coupled system, a Tuned Liquid Damper (TLD), is discussed in order to show the integration capabilities of the solver with external dynamics. Finally, the sloshing flow inside a nuclear reactor is simulated in order to show the capabilities of the solver to treat 3-D problems with complex geometries and of industrial interest.
Amesos2 and Belos: Direct and Iterative Solvers for Large Sparse Linear Systems
Bavier, Eric; Hoemmen, Mark; Rajamanickam, Sivasankaran; ...
2012-01-01
Solvers for large sparse linear systems come in two categories: direct and iterative. Amesos2, a package in the Trilinos software project, provides direct methods, and Belos, another Trilinos package, provides iterative methods. Amesos2 offers a common interface to many different sparse matrix factorization codes, and can handle any implementation of sparse matrices and vectors, via an easy-to-extend C++ traits interface. It can also factor matrices whose entries have arbitrary “Scalar” type, enabling extended-precision and mixed-precision algorithms. Belos includes many different iterative methods for solving large sparse linear systems and least-squares problems. Unlike competing iterative solver libraries, Belos completely decouples themore » algorithms from the implementations of the underlying linear algebra objects. This lets Belos exploit the latest hardware without changes to the code. Belos favors algorithms that solve higher-level problems, such as multiple simultaneous linear systems and sequences of related linear systems, faster than standard algorithms. The package also supports extended-precision and mixed-precision algorithms. Together, Amesos2 and Belos form a complete suite of sparse linear solvers.« less
NASA Astrophysics Data System (ADS)
Xiao, Cheng-Nian; Denner, Fabian; van Wachem, Berend
2015-11-01
A pressure-based Navier-Stokes solver which is applicable to fluid flow problems of a wide range of speeds is presented. The novel solver is based on collocated variable arrangement and uses a modified Rhie-Chow interpolation method to assure implicit pressure-velocity coupling. A Mach number biased modification to the continuity equation as well as coupling of flow and thermodynamic variables via an energy equation and equation of state enable the simulation of compressible flows belonging to transonic or supersonic Mach number regimes. The flow equation systems are all solved simultaneously, thus guaranteeing strong coupling between pressure and velocity at each iteration step. Shock-capturing is accomplished via nonlinear spatial discretisation schemes which adaptively apply an appropriate blending of first-order upwind and second-order central schemes depending on the local smoothness of the flow field. A selection of standard test problems will be presented to demonstrate the solver's capability of handling incompressible as well as compressible flow fields of vastly different speed regimes on structured as well as unstructured meshes. The authors are grateful for the financial support of Shell.
Barnes, Derek N; George, John S; Ng, Kwong T
2008-09-01
Currently the resolution of the head models used in electroencephalography (EEG) studies is limited by the speed of the forward solver. Here, we present a parallel finite difference technique that can reduce the solution time of the governing Poisson equation for a head model. Multiple processors are used to work on the problem simultaneously in order to speed up the solution and provide the memory for solving large problems. The original computational domain is divided into multiple rectangular partitions. Each partition is then assigned to a processor, which is responsible for all the computations and inter-processor communication associated with the nodes in that particular partition. Since the forward solution time is mainly spent on solving the associated matrix equation, it is desirable to find the optimum matrix solver. A detailed comparison of various iterative solvers was performed for both isotropic and anisotropic realistic head models constructed from MRI images. The conjugate gradient (CG) method preconditioned with an advanced geometric multigrid technique was found to provide the best overall performance. For an anisotropic model with 256 x 128 x 256 cells, this technique provides a speedup of 508 on 32 processors over the serial CG solution, with a speedup of 20.1 and 25.3 through multigrid preconditioning and parallelization, respectively.
Extending Clause Learning of SAT Solvers with Boolean Gröbner Bases
NASA Astrophysics Data System (ADS)
Zengler, Christoph; Küchlin, Wolfgang
We extend clause learning as performed by most modern SAT Solvers by integrating the computation of Boolean Gröbner bases into the conflict learning process. Instead of learning only one clause per conflict, we compute and learn additional binary clauses from a Gröbner basis of the current conflict. We used the Gröbner basis engine of the logic package Redlog contained in the computer algebra system Reduce to extend the SAT solver MiniSAT with Gröbner basis learning. Our approach shows a significant reduction of conflicts and a reduction of restarts and computation time on many hard problems from the SAT 2009 competition.
A Massively Parallel Solver for the Mechanical Harmonic Analysis of Accelerator Cavities
O. Kononenko
2015-02-17
ACE3P is a 3D massively parallel simulation suite that developed at SLAC National Accelerator Laboratory that can perform coupled electromagnetic, thermal and mechanical study. Effectively utilizing supercomputer resources, ACE3P has become a key simulation tool for particle accelerator R and D. A new frequency domain solver to perform mechanical harmonic response analysis of accelerator components is developed within the existing parallel framework. This solver is designed to determine the frequency response of the mechanical system to external harmonic excitations for time-efficient accurate analysis of the large-scale problems. Coupled with the ACE3P electromagnetic modules, this capability complements a set of multi-physics tools for a comprehensive study of microphonics in superconducting accelerating cavities in order to understand the RF response and feedback requirements for the operational reliability of a particle accelerator. (auth)
ERIC Educational Resources Information Center
Math Forum @ Drexel, 2009
2009-01-01
Different techniques for understanding a problem can lead to ideas for never-used-before solutions. Good problem-solvers use a problem-solving strategy and may come back to it frequently while they are working on the problem to refine their strategy, see if they can find better solutions, or find other questions. Writing is an integral part of…
A non-conforming 3D spherical harmonic transport solver
Van Criekingen, S.
2006-07-01
A new 3D transport solver for the time-independent Boltzmann transport equation has been developed. This solver is based on the second-order even-parity form of the transport equation. The angular discretization is performed through the expansion of the angular neutron flux in spherical harmonics (PN method). The novelty of this solver is the use of non-conforming finite elements for the spatial discretization. Such elements lead to a discontinuous flux approximation. This interface continuity requirement relaxation property is shared with mixed-dual formulations such as the ones based on Raviart-Thomas finite elements. Encouraging numerical results are presented. (authors)
GPU accelerated kinetic solvers for rarefied gas dynamics
NASA Astrophysics Data System (ADS)
Zabelok, Sergey A.; Kolobov, Vladimir I.; Arslanbekov, Robert R.
2012-11-01
GPU-acceleration is applied to the Boltzmann solver with adaptive Cartesian mesh in the Unified Flow Solver framework. NVIDIA CUDA technology is used with threads being grouped in thread blocks by points of Korobov sequences in each cell for computing the collision integral and by points in coordinate space for the free-molecular flow stage. GPU-accelerated Boltzmann solver with octree Cartesian mesh has been tested on several computer systems. Speedup of several times for GPU-based code compared to single-core CPU computations on the same machines has been observed.
Review and analysis of dense linear system solver package for distributed memory machines
NASA Technical Reports Server (NTRS)
Narang, H. N.
1993-01-01
A dense linear system solver package recently developed at the University of Texas at Austin for distributed memory machine (e.g. Intel Paragon) has been reviewed and analyzed. The package contains about 45 software routines, some written in FORTRAN, and some in C-language, and forms the basis for parallel/distributed solutions of systems of linear equations encountered in many problems of scientific and engineering nature. The package, being studied by the Computer Applications Branch of the Analysis and Computation Division, may provide a significant computational resource for NASA scientists and engineers in parallel/distributed computing. Since the package is new and not well tested or documented, many of its underlying concepts and implementations were unclear; our task was to review, analyze, and critique the package as a step in the process that will enable scientists and engineers to apply it to the solution of their problems. All routines in the package were reviewed and analyzed. Underlying theory or concepts which exist in the form of published papers or technical reports, or memos, were either obtained from the author, or from the scientific literature; and general algorithms, explanations, examples, and critiques have been provided to explain the workings of these programs. Wherever the things were still unclear, communications were made with the developer (author), either by telephone or by electronic mail, to understand the workings of the routines. Whenever possible, tests were made to verify the concepts and logic employed in their implementations. A detailed report is being separately documented to explain the workings of these routines.
[A case of datura stramonium poisoning--general problems of differential diagnosis].
Osváth, P; Nagy, A; Fekete, S; Tényi, T; Trixler, M; Radnai, I
2000-01-16
In past year drug abuse becomes more and more general in Hungary. In addition to consume traditional drugs, other substances are used frequently too. One of them is the Datura stramonium, which contains alkaloids (mostly atropine), and can result in hallucinations. Therefore Datura stramonium is seemingly becoming popular as a hallucinogenic drug. The consumption of any part of the plant causes atropine intoxication, thus anticholinergic delirium. Differential diagnosis of Datura intoxication can be difficult in the everyday medical practise. In our paper the symptomatology, diagnosis, differential diagnosis, and therapy of Datura intoxication are discussed and we report one of our cases.
NASA Astrophysics Data System (ADS)
Acker, A.
We give an analytical proof of the existence of convex classical solutions for the (convex) Prandtl-Batchelor free boundary problem in fluid dynamics. In this problem, a convex vortex core of constant vorticity μ >0 is embedded in a closed irrotational flow inside a closed, convex vessel in ℜ 2. The unknown boundary of the vortex core is a closed curve Γ along which (v+)^2-(v^-)^2=Λ , where v+ and v- denote, respectively, the exterior and interior flow-speeds along Γ and Λ is a given constant. Our existence results all apply to the natural multidimensional mathematical generalization of the above problem. The present existence theorems are the only ones available for the Prandtl-Batchelor problem for Λ >0, because (a) the author's prior existence treatment was restricted to the case where Λ <0, and because (b) there is no analytical existence theory available for this problem in the non-convex case, regardless of the sign of Λ .
libmpdata++ 0.1: a library of parallel MPDATA solvers for systems of generalised transport equations
NASA Astrophysics Data System (ADS)
Jaruga, A.; Arabas, S.; Jarecka, D.; Pawlowska, H.; Smolarkiewicz, P. K.; Waruszewski, M.
2014-11-01
This paper accompanies first release of libmpdata++, a C++ library implementing the Multidimensional Positive-Definite Advection Transport Algorithm (MPDATA). The library offers basic numerical solvers for systems of generalised transport equations. The solvers are forward-in-time, conservative and non-linearly stable. The libmpdata++ library covers the basic second-order-accurate formulation of MPDATA, its third-order variant, the infinite-gauge option for variable-sign fields and a flux-corrected transport extension to guarantee non-oscillatory solutions. The library is equipped with a non-symmetric variational elliptic solver for implicit evaluation of pressure gradient terms. All solvers offer parallelisation through domain decomposition using shared-memory parallelisation. The paper describes the library programming interface, and serves as a user guide. Supported options are illustrated with benchmarks discussed in the MPDATA literature. Benchmark descriptions include code snippets as well as quantitative representations of simulation results. Examples of applications include: homogeneous transport in one, two and three dimensions in Cartesian and spherical domains; shallow-water system compared with analytical solution (originally derived for a 2-D case); and a buoyant convection problem in an incompressible Boussinesq fluid with interfacial instability. All the examples are implemented out of the library tree. Regardless of the differences in the problem dimensionality, right-hand-side terms, boundary conditions and parallelisation approach, all the examples use the same unmodified library, which is a key goal of libmpdata++ design. The design, based on the principle of separation of concerns, prioritises the user and developer productivity. The libmpdata++ library is implemented in C++, making use of the Blitz++ multi-dimensional array containers, and is released as free/libre and open-source software.
libmpdata++ 1.0: a library of parallel MPDATA solvers for systems of generalised transport equations
NASA Astrophysics Data System (ADS)
Jaruga, A.; Arabas, S.; Jarecka, D.; Pawlowska, H.; Smolarkiewicz, P. K.; Waruszewski, M.
2015-04-01
This paper accompanies the first release of libmpdata++, a C++ library implementing the multi-dimensional positive-definite advection transport algorithm (MPDATA) on regular structured grid. The library offers basic numerical solvers for systems of generalised transport equations. The solvers are forward-in-time, conservative and non-linearly stable. The libmpdata++ library covers the basic second-order-accurate formulation of MPDATA, its third-order variant, the infinite-gauge option for variable-sign fields and a flux-corrected transport extension to guarantee non-oscillatory solutions. The library is equipped with a non-symmetric variational elliptic solver for implicit evaluation of pressure gradient terms. All solvers offer parallelisation through domain decomposition using shared-memory parallelisation. The paper describes the library programming interface, and serves as a user guide. Supported options are illustrated with benchmarks discussed in the MPDATA literature. Benchmark descriptions include code snippets as well as quantitative representations of simulation results. Examples of applications include homogeneous transport in one, two and three dimensions in Cartesian and spherical domains; a shallow-water system compared with analytical solution (originally derived for a 2-D case); and a buoyant convection problem in an incompressible Boussinesq fluid with interfacial instability. All the examples are implemented out of the library tree. Regardless of the differences in the problem dimensionality, right-hand-side terms, boundary conditions and parallelisation approach, all the examples use the same unmodified library, which is a key goal of libmpdata++ design. The design, based on the principle of separation of concerns, prioritises the user and developer productivity. The libmpdata++ library is implemented in C++, making use of the Blitz++ multi-dimensional array containers, and is released as free/libre and open-source software.
NASA Technical Reports Server (NTRS)
Bortolussi, Michael R.
1997-01-01
The General Aviation (GA) industry has suffered a ten-year decline in the number of airplanes sold. This decline is due mainly to the increase cost associated with purchasing, insuring, maintaining, operating, and pilot training a GA airplane. In response to this decline the Federal Aviation Administration (FAA) and the National Aeronautics and Space Administration (NASA) developed a program (Advanced General Aviation Transport Experiments - AGATE) to address these issues. The purpose of AGATE focused within this report is to reduce the costs to acquire and maintain instrument-flight-proficiency. The AGATE program defined four elements necessary to accomplish these goals: (1) new and intuitive cockpit displays and controls, (2) situation technologies for weather, traffic, and navigation, (3) expert systems for system monitoring, and (4) reduced cost training methods. One recognized need for the GA pilot and airplane is to provide cockpit displays and systems already available to transport category airplane. These displays such as Electronic Flight and Instrument System (EFIS), graphic weather and traffic displays, and flight management systems. The goal of this grant was to develop the AGATE GA Display Evaluation Workstation as a tool to test these existing and emerging technologies in the GA environment.
Periodic solutions about the collinear Lagrangian solution in the general problem of three bodies
NASA Technical Reports Server (NTRS)
Broucke, R.; Davoust, E.; Anderson, J. D.; Lass, H.; Blitzer, L.
1981-01-01
The article describes the solutions near Lagrange's circular collinear configuration in the planar problem of three bodies with three finite masses. The article begins with a detailed review of the properties of Lagrange's collinear solution. Lagrange's quintic equation is derived and several expressions are given for the angular velocity of the rotating frame. The equations of motion are then linearized near the circular collinear solution, and the characteristic equation is also derived in detail. The different types of roots and their corresponding solutions are discussed. The special case of two equal outer masses receives special attention, as well as the special case of two small outer masses. Finally, the fundamental family of periodic solutions is extended by numerical integration all the way up to and past a binary collision orbit. The stability and the bifurcations of this family are briefly enumerated.
Modularization and Validation of FUN3D as a CREATE-AV Helios Near-Body Solver
NASA Technical Reports Server (NTRS)
Jain, Rohit; Biedron, Robert T.; Jones, William T.; Lee-Rausch, Elizabeth M.
2016-01-01
Under a recent collaborative effort between the US Army Aeroflightdynamics Directorate (AFDD) and NASA Langley, NASA's general unstructured CFD solver, FUN3D, was modularized as a CREATE-AV Helios near-body unstructured grid solver. The strategies adopted in Helios/FUN3D integration effort are described. A validation study of the new capability is performed for rotorcraft cases spanning hover prediction, airloads prediction, coupling with computational structural dynamics, counter-rotating dual-rotor configurations, and free-flight trim. The integration of FUN3D, along with the previously integrated NASA OVERFLOW solver, lays the ground for future interaction opportunities where capabilities of one component could be leveraged with those of others in a relatively seamless fashion within CREATE-AV Helios.
NASA Astrophysics Data System (ADS)
Losch, Martin; Danilov, Sergey
Experiments with idealized geometry are used to compare model solutions of implicit VP- and explicit EVP-solvers in two very different ice-ocean codes: the regular-grid, finite-volume Massachusetts Institute of Technology general circulation model (MITgcm) and the Alfred Wegener Institute Finite Element Ocean Model (FEOM). It is demonstrated that for both codes the obtained solutions of implicit VP-and EVP-solvers can differ significantly, because the EVP solutions tend to have smaller ice viscosities ("weaker" ice). EVP solutions tend to converge only slowly to implicit VP solutions for very small sub-cycling time steps. Variable resolution in the unstructured-grid model FEOM also affects the solution as smaller grid cell size leads to smaller viscosity in EVP solutions. Models with implicit VP-solvers can block narrow straits under certain conditions, while EVP-models are found to always allow flow as a consequence of lower viscosities.
Progress Toward Overset-Grid Moving Body Capability for USM3D Unstructured Flow Solver
NASA Technical Reports Server (NTRS)
Pandyna, Mohagna J.; Frink, Neal T.; Noack, Ralph W.
2005-01-01
A static and dynamic Chimera overset-grid capability is added to an established NASA tetrahedral unstructured parallel Navier-Stokes flow solver, USM3D. Modifications to the solver primarily consist of a few strategic calls to the Donor interpolation Receptor Transaction library (DiRTlib) to facilitate communication of solution information between various grids. The assembly of multiple overlapping grids into a single-zone composite grid is performed by the Structured, Unstructured and Generalized Grid AssembleR (SUGGAR) code. Several test cases are presented to verify the implementation, assess overset-grid solution accuracy and convergence relative to single-grid solutions, and demonstrate the prescribed relative grid motion capability.
Inverse backscattering problem for the generalized nonlinear Schrödinger operator in two dimensions
NASA Astrophysics Data System (ADS)
Serov, V.; Sandhu, J.
2010-08-01
The inverse Born approximation is studied for the generalized nonlinear two-dimensional Schrödinger equation - \\Delta u + \\sum _ {l = 0} ^ m \\alpha _ l |u| ^ l u = k ^ 2 u, where the real-valued unknown potentials αl belong to L ^ {p} _ {\\mathrm{comp}} (\\mathbb {R} ^ 2) for some 2 <= p <= ∞ and their Fourier transforms belong to the space L ^ {s} (\\mathbb {R} ^ 2) for some 1 < s < 2. We prove that the leading-order singularities of the sum of the unknown potentials can be recovered from the inverse Born approximation. We also prove that the approximation is equal to the true function up to sum of two functions: one of them from the Sobolev space Ht while the other being a continuous function.
corr3p_tr: A particle approach for the general three-body problem
NASA Astrophysics Data System (ADS)
Edvardsson, S.; Karlsson, K.; Olin, H.
2016-03-01
This work presents a convenient way to solve the non-relativistic Schrödinger equation numerically for a general three-particle system including full correlation and mass polarization. Both Coulombic and non-Coulombic interactions can be studied. The eigensolver is based on a second order dynamical system treatment (particle method). The Hamiltonian matrix never needs to be realized. The wavefunction evolves towards the steady state solution for which the Schrödinger equation is fulfilled. Subsequent Richardson extrapolations for several meshes are then made symbolically in matlab to obtain the continuum solution. The computer C code is tested under Linux 64 bit and both double and extended precision versions are provided. Test runs are exemplified and, when possible, compared with corresponding values in the literature. The computer code is small and self contained making it unusually simple to compile and run on any system. Both serial and parallel computer runs are straight forward.
Retrieving the Balanced Winds on the Globe as a Generalized Inverse Problem
NASA Technical Reports Server (NTRS)
Lu, Huei-Iin; Robertson, Franklin R.; Arnold, James E. (Technical Monitor)
2000-01-01
A generalized inverse technique is applied to retrieve two types of balanced winds that characterize the large-scale dynamics of the atmosphere: rotational winds based upon the linear balance equation, and divergent winds based upon the vorticity budget equation. Both balance equations are singular at or near the equator. The balance equations are transformed in spherical harmonic function space to an under-determined system, for which the scale-weighed least-squares solution consists of a sum of principal and singular components. The principal components represent the response to the source function for the regular eigenmodes, while the singular components are determined by the projection of an independent measurement on the singular eigenmodes. The method was tested with the NCEP/NCAR reanalysis data in which a quasi-balance condition exists. A realistic balanced wind field is retrievable when the singular components are computed based upon the reanalyzed wind data.
The problem of exact interior solutions for rotating rigid bodies in general relativity
NASA Technical Reports Server (NTRS)
Wahlquist, H. D.
1993-01-01
The (3 + 1) dyadic formalism for timelike congruences is applied to derive interior solutions for stationary, axisymmetric, rigidly rotating bodies. In this approach the mathematics is formulated in terms of three-space-covariant, first-order, vector-dyadic, differential equations for a and Omega, the acceleration and angular velocity three-vectors of the rigid body; for T, the stress dyadic of the matter; and for A and B, the 'electric' and 'magnetic' Weyl curvature dyadics which describe the gravitational field. It is shown how an appropriate ansatz for the forms of these dyadics can be used to discover exact rotating interior solutions such as the perfect fluid solution first published in 1968. By incorporating anisotropic stresses, a generalization is found of that previous solution and, in addition, a very simple new solution that can only exist in toroidal configurations.
Children with Generalized Anxiety Disorder Do Not Have Peer Problems, Just Fewer Friends
Alfano, Candice; Beidel, Deborah; Wong, Nina
2011-01-01
A common assumption is that all youth with anxiety disorders (AD) experience impaired peer relationships relative to healthy control children. Social impairments have been identified among youth with certain AD (e.g., social anxiety disorder; SAD), but less is known about the peer relationships of children with generalized anxiety disorder (GAD). We therefore compared the interpersonal functioning of youth with GAD, SAD, and controls (6 to 13 years). Despite having relatively fewer friends overall, children with GAD did not differ from controls in terms of the likelihood of having a best friend, participation in groups/clubs, and parent ratings of social competence. In comparison, youth with SAD were less socially competent, had fewer friends and difficulty making new friends compared to controls. Findings suggest that peer difficulties are not a universal feature of all childhood AD and highlight a need to better understand the social experiences and functioning of children with GAD. PMID:21739298
Rahaman, Mijanur; Pang, Chin-Tzong; Ishtyak, Mohd; Ahmad, Rais
2017-01-01
In this article, we introduce a perturbed system of generalized mixed quasi-equilibrium-like problems involving multi-valued mappings in Hilbert spaces. To calculate the approximate solutions of the perturbed system of generalized multi-valued mixed quasi-equilibrium-like problems, firstly we develop a perturbed system of auxiliary generalized multi-valued mixed quasi-equilibrium-like problems, and then by using the celebrated Fan-KKM technique, we establish the existence and uniqueness of solutions of the perturbed system of auxiliary generalized multi-valued mixed quasi-equilibrium-like problems. By deploying an auxiliary principle technique and an existence result, we formulate an iterative algorithm for solving the perturbed system of generalized multi-valued mixed quasi-equilibrium-like problems. Lastly, we study the strong convergence analysis of the proposed iterative sequences under monotonicity and some mild conditions. These results are new and generalize some known results in this field.
Algorithmic Enhancements to the VULCAN Navier-Stokes Solver
NASA Technical Reports Server (NTRS)
Litton, D. K.; Edwards, J. R.; White, J. A.
2003-01-01
VULCAN (Viscous Upwind aLgorithm for Complex flow ANalysis) is a cell centered, finite volume code used to solve high speed flows related to hypersonic vehicles. Two algorithms are presented for expanding the range of applications of the current Navier-Stokes solver implemented in VULCAN. The first addition is a highly implicit approach that uses subiterations to enhance block to block connectivity between adjacent subdomains. The addition of this scheme allows more efficient solution of viscous flows on highly-stretched meshes. The second algorithm addresses the shortcomings associated with density-based schemes by the addition of a time-derivative preconditioning strategy. High speed, compressible flows are typically solved with density based schemes, which show a high level of degradation in accuracy and convergence at low Mach numbers (M less than or equal to 0.1). With the addition of preconditioning and associated modifications to the numerical discretization scheme, the eigenvalues will scale with the local velocity, and the above problems will be eliminated. With these additions, VULCAN now has improved convergence behavior for multi-block, highly-stretched meshes and also can solve the Navier-Stokes equations for very low Mach numbers.
Shared Memory Parallelism for 3D Cartesian Discrete Ordinates Solver
NASA Astrophysics Data System (ADS)
Moustafa, Salli; Dutka-Malen, Ivan; Plagne, Laurent; Ponçot, Angélique; Ramet, Pierre
2014-06-01
This paper describes the design and the performance of DOMINO, a 3D Cartesian SN solver that implements two nested levels of parallelism (multicore+SIMD) on shared memory computation nodes. DOMINO is written in C++, a multi-paradigm programming language that enables the use of powerful and generic parallel programming tools such as Intel TBB and Eigen. These two libraries allow us to combine multi-thread parallelism with vector operations in an efficient and yet portable way. As a result, DOMINO can exploit the full power of modern multi-core processors and is able to tackle very large simulations, that usually require large HPC clusters, using a single computing node. For example, DOMINO solves a 3D full core PWR eigenvalue problem involving 26 energy groups, 288 angular directions (S16), 46 × 106 spatial cells and 1 × 1012 DoFs within 11 hours on a single 32-core SMP node. This represents a sustained performance of 235 GFlops and 40:74% of the SMP node peak performance for the DOMINO sweep implementation. The very high Flops/Watt ratio of DOMINO makes it a very interesting building block for a future many-nodes nuclear simulation tool.
Parallelizable approximate solvers for recursions arising in preconditioning
Shapira, Y.
1996-12-31
For the recursions used in the Modified Incomplete LU (MILU) preconditioner, namely, the incomplete decomposition, forward elimination and back substitution processes, a parallelizable approximate solver is presented. The present analysis shows that the solutions of the recursions depend only weakly on their initial conditions and may be interpreted to indicate that the inexact solution is close, in some sense, to the exact one. The method is based on a domain decomposition approach, suitable for parallel implementations with message passing architectures. It requires a fixed number of communication steps per preconditioned iteration, independently of the number of subdomains or the size of the problem. The overlapping subdomains are either cubes (suitable for mesh-connected arrays of processors) or constructed by the data-flow rule of the recursions (suitable for line-connected arrays with possibly SIMD or vector processors). Numerical examples show that, in both cases, the overhead in the number of iterations required for convergence of the preconditioned iteration is small relatively to the speed-up gained.
Approximate Riemann solvers for the cosmic ray magnetohydrodynamical equations
NASA Astrophysics Data System (ADS)
Kudoh, Yuki; Hanawa, Tomoyuki
2016-11-01
We analyse the cosmic ray magnetohydrodynamic (CR MHD) equations to improve the numerical simulations. We propose to solve them in the fully conservation form, which is equivalent to the conventional CR MHD equations. In the fully conservation form, the CR energy equation is replaced with the CR `number' conservation, where the CR number density is defined as the three-fourths power of the CR energy density. The former contains an extra source term, while latter does not. An approximate Riemann solver is derived from the CR MHD equations in the fully conservation form. Based on the analysis, we propose a numerical scheme of which solutions satisfy the Rankine-Hugoniot relation at any shock. We demonstrate that it reproduces the Riemann solution derived by Pfrommer et al. for a 1D CR hydrodynamic shock tube problem. We compare the solution with those obtained by solving the CR energy equation. The latter solutions deviate from the Riemann solution seriously, when the CR pressure dominates over the gas pressure in the post-shocked gas. The former solutions converge to the Riemann solution and are of the second-order accuracy in space and time. Our numerical examples include an expansion of high-pressure sphere in a magnetized medium. Fast and slow shocks are sharply resolved in the example. We also discuss possible extension of the CR MHD equations to evaluate the average CR energy.
NASA Astrophysics Data System (ADS)
Balsara, Dinshaw S.; Amano, Takanobu; Garain, Sudip; Kim, Jinho
2016-08-01
collocation also ensures that electromagnetic radiation that is propagating in a vacuum has both electric and magnetic fields that are exactly divergence-free. Coupled relativistic fluid dynamic equations are solved for the positively and negatively charged fluids. The fluids' numerical fluxes also provide a self-consistent current density for the update of the electric field. Our reconstruction strategy ensures that fluid velocities always remain sub-luminal. Our third innovation consists of an efficient design for several popular IMEX schemes so that they provide strong coupling between the finite-volume-based fluid solver and the electromagnetic fields at high order. This innovation makes it possible to efficiently utilize high order IMEX time update methods for stiff source terms in the update of high order finite-volume methods for hyperbolic conservation laws. We also show that this very general innovation should extend seamlessly to Runge-Kutta discontinuous Galerkin methods. The IMEX schemes enable us to use large CFL numbers even in the presence of stiff source terms. Several accuracy analyses are presented showing that our method meets its design accuracy in the MHD limit as well as in the limit of electromagnetic wave propagation. Several stringent test problems are also presented. We also present a relativistic version of the GEM problem, which shows that our algorithm can successfully adapt to challenging problems in high energy astrophysics.
Balsara, Dinshaw S.; Amano, Takanobu; Garain, Sudip; Kim, Jinho
2016-08-01
collocation also ensures that electromagnetic radiation that is propagating in a vacuum has both electric and magnetic fields that are exactly divergence-free. Coupled relativistic fluid dynamic equations are solved for the positively and negatively charged fluids. The fluids' numerical fluxes also provide a self-consistent current density for the update of the electric field. Our reconstruction strategy ensures that fluid velocities always remain sub-luminal. Our third innovation consists of an efficient design for several popular IMEX schemes so that they provide strong coupling between the finite-volume-based fluid solver and the electromagnetic fields at high order. This innovation makes it possible to efficiently utilize high order IMEX time update methods for stiff source terms in the update of high order finite-volume methods for hyperbolic conservation laws. We also show that this very general innovation should extend seamlessly to Runge–Kutta discontinuous Galerkin methods. The IMEX schemes enable us to use large CFL numbers even in the presence of stiff source terms. Several accuracy analyses are presented showing that our method meets its design accuracy in the MHD limit as well as in the limit of electromagnetic wave propagation. Several stringent test problems are also presented. We also present a relativistic version of the GEM problem, which shows that our algorithm can successfully adapt to challenging problems in high energy astrophysics.
Towards Verification of Unstructured-Grid Solvers
NASA Technical Reports Server (NTRS)
Thomas, James L.; Diskin, Boris; Rumsey, Christopher L.
2008-01-01
New methodology for verification of finite-volume computational methods using unstructured grids is presented. The discretization order properties are studied in computational windows, easily constructed within a collection of grids or a single grid. Tests are performed within each window and address a combination of problem-, solution-, and discretization/grid-related features affecting discretization error convergence. The windows can be adjusted to isolate particular elements of the computational scheme, such as the interior discretization, the boundary discretization, or singularities. Studies can use traditional grid-refinement computations within a fixed window or downscaling, a recently-introduced technique in which computations are made within windows contracting toward a focal point of interest. Grids within the windows are constrained to be consistently refined, allowing a meaningful assessment of asymptotic error convergence on unstructured grids. Demonstrations of the method are shown, including a comparative accuracy assessment of commonly-used schemes on general mixed grids and the identification of local accuracy deterioration at boundary intersections. Recommendations to enable attainment of design-order discretization errors for large-scale computational simulations are given.
Performance of NASA Equation Solvers on Computational Mechanics Applications
NASA Technical Reports Server (NTRS)
Storaasli, Olaf O.
1996-01-01
This paper describes the performance of a new family of NASA-developed equation solvers used for large-scale (i.e. 551,705 equations) structural analysis. To minimize computer time and memory, the solvers are divided by application and matrix characteristics (sparse/dense, real/complex, symmetric/nonsymmetric, size: in-core/out of core) and exploit the hardware features of current and future computers. In this paper, the equation solvers, which are written in FORTRAN, and are therefore easily transportable, are shown to be faster than specialized computer library routines utilizing assembly code. Twenty NASA structural benchmark models with NASA solver timings reside on World Wide Web with a challenge to beat them.
Fan, Yurui; Huang, Guohe; Veawab, Amornvadee
2012-01-01
In this study, a generalized fuzzy linear programming (GFLP) method was developed to deal with uncertainties expressed as fuzzy sets that exist in the constraints and objective function. A stepwise interactive algorithm (SIA) was advanced to solve GFLP model and generate solutions expressed as fuzzy sets. To demonstrate its application, the developed GFLP method was applied to a regional sulfur dioxide (SO2) control planning model to identify effective SO2 mitigation polices with a minimized system performance cost under uncertainty. The results were obtained to represent the amount of SO2 allocated to different control measures from different sources. Compared with the conventional interval-parameter linear programming (ILP) approach, the solutions obtained through GFLP were expressed as fuzzy sets, which can provide intervals for the decision variables and objective function, as well as related possibilities. Therefore, the decision makers can make a tradeoff between model stability and the plausibility based on solutions obtained through GFLP and then identify desired policies for SO2-emission control under uncertainty.
Generalized thermoelastic problem of an infinite body with a spherical cavity under dual-phase-lags
NASA Astrophysics Data System (ADS)
Karmakar, R.; Sur, A.; Kanoria, M.
2016-07-01
The aim of the present contribution is the determination of the thermoelastic temperatures, stress, displacement, and strain in an infinite isotropic elastic body with a spherical cavity in the context of the mechanism of the two-temperature generalized thermoelasticity theory (2TT). The two-temperature Lord-Shulman (2TLS) model and two-temperature dual-phase-lag (2TDP) model of thermoelasticity are combined into a unified formulation with unified parameters. The medium is assumed to be initially quiescent. The basic equations are written in the form of a vector matrix differential equation in the Laplace transform domain, which is then solved by the state-space approach. The expressions for the conductive temperature and elongation are obtained at small times. The numerical inversion of the transformed solutions is carried out by using the Fourier-series expansion technique. A comparative study is performed for the thermoelastic stresses, conductive temperature, thermodynamic temperature, displacement, and elongation computed by using the Lord-Shulman and dual-phase-lag models.