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.
Using parallel banded linear system solvers in generalized eigenvalue problems
NASA Technical Reports Server (NTRS)
Zhang, Hong; Moss, William F.
1993-01-01
Subspace iteration is a reliable and cost effective method for solving positive definite banded symmetric generalized eigenproblems, especially in the case of large scale problems. This paper discusses an algorithm that makes use of two parallel banded solvers in subspace iteration. A shift is introduced to decompose the banded linear systems into relatively independent subsystems and to accelerate the iterations. With this shift, an eigenproblem is mapped efficiently into the memories of a multiprocessor and a high speed-up is obtained for parallel implementations. An optimal shift is a shift that balances total computation and communication costs. Under certain conditions, we show how to estimate an optimal shift analytically using the decay rate for the inverse of a banded matrix, and how to improve this estimate. Computational results on iPSC/2 and iPSC/860 multiprocessors are presented.
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
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.
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.
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. PMID:27491195
General complex polynomial root solver
NASA Astrophysics Data System (ADS)
Skowron, J.; Gould, A.
2012-12-01
This general complex polynomial root solver, implemented in Fortran and further optimized for binary microlenses, uses a new algorithm to solve polynomial equations and is 1.6-3 times faster than the ZROOTS subroutine that is commercially available from Numerical Recipes, depending on application. The largest improvement, when compared to naive solvers, comes from a fail-safe procedure that permits skipping the majority of the calculations in the great majority of cases, without risking catastrophic failure in the few cases that these are actually required.
A generalized gyrokinetic Poisson solver
Lin, Z.; Lee, W.W.
1995-03-01
A generalized gyrokinetic Poisson solver has been developed, which employs local operations in the configuration space to compute the polarization density response. The new technique is based on the actual physical process of gyrophase-averaging. It is useful for nonlocal simulations using general geometry equilibrium. Since it utilizes local operations rather than the global ones such as FFT, the new method is most amenable to massively parallel algorithms.
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 mod- eling 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 challeng- ing problems important to Sandia's mission that Aleph was specifically designed to address.
DPS--a computerised diagnostic problem solver.
Bartos, P; Gyárfas, F; Popper, M
1982-01-01
The paper contains a short description of the DPS system which is a computerized diagnostic problem solver. The system is under development of the Research Institute of Medical Bionics in Bratislava, Czechoslovakia. Its underlying philosophy yields from viewing the diagnostic process as process of cognitive problem solving. The implementation of the system is based on the methods of Artificial Intelligence and utilisation of production systems and frame theory should be noted in this context. Finally a list of program modules and their characterisation is presented. PMID:6811229
Scalable Adaptive Multilevel Solvers for Multiphysics Problems
Xu, Jinchao
2014-12-01
In this project, we investigated adaptive, parallel, and multilevel methods for numerical modeling of various real-world applications, including Magnetohydrodynamics (MHD), complex fluids, Electromagnetism, Navier-Stokes equations, and reservoir simulation. First, we have designed improved mathematical models and numerical discretizaitons for viscoelastic fluids and MHD. Second, we have derived new a posteriori error estimators and extended the applicability of adaptivity to various problems. Third, we have developed multilevel solvers for solving scalar partial differential equations (PDEs) as well as coupled systems of PDEs, especially on unstructured grids. Moreover, we have integrated the study between adaptive method and multilevel methods, and made significant efforts and advances in adaptive multilevel methods of the multi-physics problems.
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. (MP)
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.
General purpose nonlinear system solver based on Newton-Krylov method.
Energy Science and Technology Software Center (ESTSC)
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].
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.
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…
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…
General Equation Set Solver for Compressible and Incompressible Turbomachinery Flows
NASA Technical Reports Server (NTRS)
Sondak, Douglas L.; Dorney, Daniel J.
2002-01-01
Turbomachines for propulsion applications operate with many different working fluids and flow conditions. The flow may be incompressible, such as in the liquid hydrogen pump in a rocket engine, or supersonic, such as in the turbine which may drive the hydrogen pump. Separate codes have traditionally been used for incompressible and compressible flow solvers. The General Equation Set (GES) method can be used to solve both incompressible and compressible flows, and it is not restricted to perfect gases, as are many compressible-flow turbomachinery solvers. An unsteady GES turbomachinery flow solver has been developed and applied to both air and water flows through turbines. It has been shown to be an excellent alternative to maintaining two separate codes.
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…
A generalized Poisson solver for first-principles device simulations
NASA Astrophysics Data System (ADS)
Bani-Hashemian, Mohammad Hossein; Brück, Sascha; Luisier, Mathieu; VandeVondele, Joost
2016-01-01
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.
A generalized Poisson solver for first-principles device simulations.
Bani-Hashemian, Mohammad Hossein; Brück, Sascha; Luisier, Mathieu; VandeVondele, Joost
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. PMID:26827208
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.
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
2016-01-01
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. PMID:26747797
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…
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…
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--Area beyond the Formula
ERIC Educational Resources Information Center
Dean, Chrystal
2014-01-01
In this article, associate professor Chrystal Dean describes how teachers can challenge their upper elementary students' understanding of area beyond a memorized formula. Herein she describes an activity that will show students the "why" behind using A = l × w to solve rectangular area problems. The activity will help deepen…
Organization of Classical Genetics Problems by Faculty Problem Solvers.
ERIC Educational Resources Information Center
Smith, Mike U.
This paper is a progress report of the first phase of a project which essentially seeks to replicate previous studies using the successful/unsuccessful design in an attempt to: (1) corroborate the surface/deep structure conclusion which has become an essential component of an understanding of problem-solving; (2) examine more closely the nature of…
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
2013-09-01
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. PMID:23893938
Multiply scaled constrained nonlinear equation solvers. [for nonlinear heat conduction problems
NASA Technical Reports Server (NTRS)
Padovan, Joe; Krishna, Lala
1986-01-01
To improve the numerical stability of nonlinear equation solvers, a partitioned multiply scaled constraint scheme is developed. This scheme enables hierarchical levels of control for nonlinear equation solvers. To complement the procedure, partitioned convergence checks are established along with self-adaptive partitioning schemes. Overall, such procedures greatly enhance the numerical stability of the original solvers. To demonstrate and motivate the development of the scheme, the problem of nonlinear heat conduction is considered. In this context the main emphasis is given to successive substitution-type schemes. To verify the improved numerical characteristics associated with partitioned multiply scaled solvers, results are presented for several benchmark examples.
Generalized methods and solvers for noise removal from piecewise constant signals. II. New methods
Little, Max A.; Jones, Nick S.
2011-01-01
Removing noise from signals which are piecewise constant (PWC) is a challenging signal processing problem that arises in many practical scientific and engineering contexts. In the first paper (part I) of this series of two, we presented background theory building on results from the image processing community to show that the majority of these algorithms, and more proposed in the wider literature, are each associated with a special case of a generalized functional, that, when minimized, solves the PWC denoising problem. It shows how the minimizer can be obtained by a range of computational solver algorithms. In this second paper (part II), using this understanding developed in part I, we introduce several novel PWC denoising methods, which, for example, combine the global behaviour of mean shift clustering with the local smoothing of total variation diffusion, and show example solver algorithms for these new methods. Comparisons between these methods are performed on synthetic and real signals, revealing that our new methods have a useful role to play. Finally, overlaps between the generalized methods of these two papers and others such as wavelet shrinkage, hidden Markov models, and piecewise smooth filtering are touched on. PMID:22003313
PDRK: A General Kinetic Dispersion Relation Solver for Magnetized Plasma
NASA Astrophysics Data System (ADS)
Xie, Huasheng; Xiao, Yong
2016-02-01
A general, fast, and effective approach is developed for numerical calculation of kinetic plasma linear dispersion relations. The plasma dispersion function is approximated by J-pole expansion. Subsequently, the dispersion relation is transformed to a standard matrix eigenvalue problem of an equivalent linear system. Numerical solutions for the least damped or fastest growing modes using an 8-pole expansion are generally accurate; more strongly damped modes are less accurate, but are less likely to be of physical interest. In contrast to conventional approaches, such as Newton's iterative method, this approach can give either all the solutions in the system or a few solutions around the initial guess. It is also free from convergence problems. The approach is demonstrated for electrostatic dispersion equations with one-dimensional and two-dimensional wavevectors, and for electromagnetic kinetic magnetized plasma dispersion relation for bi-Maxwellian distribution with relative parallel velocity flows between species. supported by the National Magnetic Confinement Fusion Science Program of China (Nos. 2015GB110003, 2011GB105001, 2013GB111000), National Natural Science Foundation of China (No. 91130031), the Recruitment Program of Global Youth Experts
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.
Fast solver for large scale eddy current non-destructive evaluation problems
NASA Astrophysics Data System (ADS)
Lei, Naiguang
Eddy current testing plays a very important role in non-destructive evaluations of conducting test samples. Based on Faraday's law, an alternating magnetic field source generates induced currents, called eddy currents, in an electrically conducting test specimen. The eddy currents generate induced magnetic fields that oppose the direction of the inducing magnetic field in accordance with Lenz's law. In the presence of discontinuities in material property or defects in the test specimen, the induced eddy current paths are perturbed and the associated magnetic fields can be detected by coils or magnetic field sensors, such as Hall elements or magneto-resistance sensors. Due to the complexity of the test specimen and the inspection environments, the availability of theoretical simulation models is extremely valuable for studying the basic field/flaw interactions in order to obtain a fuller understanding of non-destructive testing phenomena. Theoretical models of the forward problem are also useful for training and validation of automated defect detection systems. Theoretical models generate defect signatures that are expensive to replicate experimentally. In general, modelling methods can be classified into two categories: analytical and numerical. Although analytical approaches offer closed form solution, it is generally not possible to obtain largely due to the complex sample and defect geometries, especially in three-dimensional space. Numerical modelling has become popular with advances in computer technology and computational methods. However, due to the huge time consumption in the case of large scale problems, accelerations/fast solvers are needed to enhance numerical models. This dissertation describes a numerical simulation model for eddy current problems using finite element analysis. Validation of the accuracy of this model is demonstrated via comparison with experimental measurements of steam generator tube wall defects. These simulations generating two
NASA Astrophysics Data System (ADS)
Mocek, Lukas; Kozubek, Tomas
2011-09-01
The paper deals with the numerical solution of elliptic boundary value problems for 2D linear elasticity using the fictitious domain method in combination with the discrete Fourier transform and the FETI domain decomposition. We briefly mention the theoretical background of these methods, introduce resulting solvers, and demonstrate their efficiency on model benchmarks.
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 indicate…
Generalized emissivity inverse problem.
Ming, DengMing; Wen, Tao; Dai, XianXi; Dai, JiXin; Evenson, William E
2002-04-01
Inverse problems have recently drawn considerable attention from the physics community due to of potential widespread applications [K. Chadan and P. C. Sabatier, Inverse Problems in Quantum Scattering Theory, 2nd ed. (Springer Verlag, Berlin, 1989)]. An inverse emissivity problem that determines the emissivity g(nu) from measurements of only the total radiated power J(T) has recently been studied [Tao Wen, DengMing Ming, Xianxi Dai, Jixin Dai, and William E. Evenson, Phys. Rev. E 63, 045601(R) (2001)]. In this paper, a new type of generalized emissivity and transmissivity inverse (GETI) problem is proposed. The present problem differs from our previous work on inverse problems by allowing the unknown (emissivity) function g(nu) to be temperature dependent as well as frequency dependent. Based on published experimental information, we have developed an exact solution formula for this GETI problem. A universal function set suggested for numerical calculation is shown to be robust, making this inversion method practical and convenient for realistic calculations. PMID:12005916
Implicit solvers for large-scale nonlinear problems
Keyes, D E; Reynolds, D; Woodward, C S
2006-07-13
Computational scientists are grappling with increasingly complex, multi-rate applications that couple such physical phenomena as fluid dynamics, electromagnetics, radiation transport, chemical and nuclear reactions, and wave and material propagation in inhomogeneous media. Parallel computers with large storage capacities are paving the way for high-resolution simulations of coupled problems; however, hardware improvements alone will not prove enough to enable simulations based on brute-force algorithmic approaches. To accurately capture nonlinear couplings between dynamically relevant phenomena, often while stepping over rapid adjustments to quasi-equilibria, simulation scientists are increasingly turning to implicit formulations that require a discrete nonlinear system to be solved for each time step or steady state solution. Recent advances in iterative methods have made fully implicit formulations a viable option for solution of these large-scale problems. In this paper, we overview one of the most effective iterative methods, Newton-Krylov, for nonlinear systems and point to software packages with its implementation. We illustrate the method with an example from magnetically confined plasma fusion and briefly survey other areas in which implicit methods have bestowed important advantages, such as allowing high-order temporal integration and providing a pathway to sensitivity analyses and optimization. Lastly, we overview algorithm extensions under development motivated by current SciDAC applications.
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
A monolithic FEM-multigrid solver for non-isothermal incompressible flow on general meshes
NASA Astrophysics Data System (ADS)
Damanik, H.; Hron, J.; Ouazzi, A.; Turek, S.
2009-06-01
We present special numerical simulation methods for non-isothermal incompressible viscous fluids which are based on LBB-stable FEM discretization techniques together with monolithic multigrid solvers. For time discretization, we apply the fully implicit Crank-Nicolson scheme of 2nd order accuracy while we utilize the high order Q2P1 finite element pair for discretization in space which can be applied on general meshes together with local grid refinement strategies including hanging nodes. To treat the nonlinearities in each time step as well as for direct steady approaches, the resulting discrete systems are solved via a Newton method based on divided differences to calculate explicitly the Jacobian matrices. In each nonlinear step, the coupled linear subproblems are solved simultaneously for all quantities by means of a monolithic multigrid method with local multilevel pressure Schur complement smoothers of Vanka type. For validation and evaluation of the presented methodology, we perform the MIT benchmark 2001 [M.A. Christon, P.M. Gresho, S.B. Sutton, Computational predictability of natural convection flows in enclosures, in: First MIT Conference on Computational Fluid and Solid Mechanics, vol. 40, Elsevier, 2001, pp. 1465-1468] of natural convection flow in enclosures to compare our results with respect to accuracy and efficiency. Additionally, we simulate problems with temperature and shear dependent viscosity and analyze the effect of an additional dissipation term inside the energy equation. Moreover, we discuss how these FEM-multigrid techniques can be extended to monolithic approaches for viscoelastic flow problems.
Stability analysis of a general toeplitz systems solver
NASA Astrophysics Data System (ADS)
Bojanczyk, Adam; Brent, Richard; Hoog, Frank
1995-09-01
We show that a fast algorithm for theQR factorization of a Toeplitz or Hankel matrixA is weakly stable in the sense thatRTR is close toATA. Thus, when the algorithm is used to solve the semi-normal equationsRTRxDATb, we obtain a weakly stable method for the solution of a nonsingular Toeplitz or Hankel linear systemAxDb. The algorithm also applies to the solution of the full-rank Toeplitz or Hankel least squares problem min ||Ax-b||2.
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
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. PMID:21930936
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.
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'.
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.
IDSOLVER: A general purpose solver for nth-order integro-differential equations
NASA Astrophysics Data System (ADS)
Gelmi, Claudio A.; Jorquera, Héctor
2014-01-01
Many mathematical models of complex processes may be posed as integro-differential equations (IDE). Many numerical methods have been proposed for solving those equations, but most of them are ad hoc thus new equations have to be solved from scratch for translating the IDE into the framework of the specific method chosen. Furthermore, there is a paucity of general-purpose numerical solvers that free the user from additional tasks.
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.
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.
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
NASA Astrophysics Data System (ADS)
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.
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.
ERIC Educational Resources Information Center
Kiehl, Ermalynn M.; Wink, Diane M.
2000-01-01
A nursing school operates nine community nursing centers in which students practice community-based learning and act as problem solvers and change agents. Examples include effecting systemwide change in school health services, coordinating multiple agencies to meet a health need, and solving a patient's complex problems involving multiple…
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
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
2014-08-01
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
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
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)
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.
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.
ERIC Educational Resources Information Center
Seeley, Cathy L.
2016-01-01
In "Making Sense of Math," Cathy L. Seeley, former president of the National Council of Teachers of Mathematics, shares her insight into how to turn your students into flexible mathematical thinkers and problem solvers. This practical volume concentrates on the following areas: (1) Making sense of math by fostering habits of mind that…
Application of the program package TURBO problem solver for some fluid dynamics problems
NASA Astrophysics Data System (ADS)
Belotserkovskaya, M. S.; Pronina, A. P.; Fortova, S. V.; Shepelev, V. V.
2016-06-01
A technology for building parallel applications for numerical simulation based on hyperbolic partial differential equations is described. A formalization of problems and methods that makes it possible to describe new problems and methods for their solution by configuring the universal technology for specific cases is proposed. Results of numerical simulation of spatial flows in shear layers of a compressible inviscid perfect medium and of the Rayleigh-Taylor instability are presented.
Veijola, Timo; Råback, Peter
2007-01-01
We present a straightforward method to solve gas damping problems for perforated structures in two dimensions (2D) utilising a Perforation Profile Reynolds (PPR) solver. The PPR equation is an extended Reynolds equation that includes additional terms modelling the leakage flow through the perforations, and variable diffusivity and compressibility profiles. The solution method consists of two phases: 1) determination of the specific admittance profile and relative diffusivity (and relative compressibility) profiles due to the perforation, and 2) solution of the PPR equation with a FEM solver in 2D. Rarefied gas corrections in the slip-flow region are also included. Analytic profiles for circular and square holes with slip conditions are presented in the paper. To verify the method, square perforated dampers with 16–64 holes were simulated with a three-dimensional (3D) Navier-Stokes solver, a homogenised extended Reynolds solver, and a 2D PPR solver. Cases for both translational (in normal to the surfaces) and torsional motion were simulated. The presented method extends the region of accurate simulation of perforated structures to cases where the homogenisation method is inaccurate and the full 3D Navier-Stokes simulation is too time-consuming.
NASA Astrophysics Data System (ADS)
Debreu, Laurent; Neveu, Emilie; Simon, Ehouarn; Le Dimet, Francois Xavier; Vidard, Arthur
2014-05-01
In order to lower the computational cost of the variational data assimilation process, we investigate the use of multigrid methods to solve the associated optimal control system. On a linear advection equation, we study the impact of the regularization term on the optimal control and the impact of discretization errors on the efficiency of the coarse grid correction step. We show that even if the optimal control problem leads to the solution of an elliptic system, numerical errors introduced by the discretization can alter the success of the multigrid methods. The view of the multigrid iteration as a preconditioner for a Krylov optimization method leads to a more robust algorithm. A scale dependent weighting of the multigrid preconditioner and the usual background error covariance matrix based preconditioner is proposed and brings significant improvements. [1] Laurent Debreu, Emilie Neveu, Ehouarn Simon, François-Xavier Le Dimet and Arthur Vidard, 2014: Multigrid solvers and multigrid preconditioners for the solution of variational data assimilation problems, submitted to QJRMS, http://hal.inria.fr/hal-00874643 [2] Emilie Neveu, Laurent Debreu and François-Xavier Le Dimet, 2011: Multigrid methods and data assimilation - Convergence study and first experiments on non-linear equations, ARIMA, 14, 63-80, http://intranet.inria.fr/international/arima/014/014005.html
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…
North Dakota's Centennial Quilt and Problem Solvers: Solutions: The Library Problem
ERIC Educational Resources Information Center
Small, Marian
2010-01-01
Quilt investigations, such as the Barn quilt problem in the December 2008/January 2009 issue of "Teaching Children Mathematics" and its solutions in last month's issue, can spark interdisciplinary pursuits for teachers and exciting connections for the full range of elementary school students. This month, North Dakota's centennial quilt problem…
Training tomorrow's environmental problem-solvers: an integrative approach to graduate education
Technology Transfer Automated Retrieval System (TEKTRAN)
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 independe...
A scalable 2-D parallel sparse solver
Kothari, S.C.; Mitra, S.
1995-12-01
Scalability beyond a small number of processors, typically 32 or less, is known to be a problem for existing parallel general sparse (PGS) direct solvers. This paper presents a parallel general sparse PGS direct solver for general sparse linear systems on distributed memory machines. The algorithm is based on the well-known sequential sparse algorithm Y12M. To achieve efficient parallelization, a 2-D scattered decomposition of the sparse matrix is used. The proposed algorithm is more scalable than existing parallel sparse direct solvers. Its scalability is evaluated on a 256 processor nCUBE2s machine using Boeing/Harwell benchmark matrices.
MILAMIN: MATLAB-based finite element method solver for large problems
NASA Astrophysics Data System (ADS)
Dabrowski, M.; Krotkiewski, M.; Schmid, D. W.
2008-04-01
The finite element method (FEM) combined with unstructured meshes forms an elegant and versatile approach capable of dealing with the complexities of problems in Earth science. Practical applications often require high-resolution models that necessitate advanced computational strategies. We therefore developed "Million a Minute" (MILAMIN), an efficient MATLAB implementation of FEM that is capable of setting up, solving, and postprocessing two-dimensional problems with one million unknowns in one minute on a modern desktop computer. MILAMIN allows the user to achieve numerical resolutions that are necessary to resolve the heterogeneous nature of geological materials. In this paper we provide the technical knowledge required to develop such models without the need to buy a commercial FEM package, programming compiler-language code, or hiring a computer specialist. It has been our special aim that all the components of MILAMIN perform efficiently, individually and as a package. While some of the components rely on readily available routines, we develop others from scratch and make sure that all of them work together efficiently. One of the main technical focuses of this paper is the optimization of the global matrix computations. The performance bottlenecks of the standard FEM algorithm are analyzed. An alternative approach is developed that sustains high performance for any system size. Applied optimizations eliminate Basic Linear Algebra Subprograms (BLAS) drawbacks when multiplying small matrices, reduce operation count and memory requirements when dealing with symmetric matrices, and increase data transfer efficiency by maximizing cache reuse. Applying loop interchange allows us to use BLAS on large matrices. In order to avoid unnecessary data transfers between RAM and CPU cache we introduce loop blocking. The optimization techniques are useful in many areas as demonstrated with our MILAMIN applications for thermal and incompressible flow (Stokes) problems. We use
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. PMID:25069109
A HLL-Rankine-Hugoniot Riemann solver for complex non-linear hyperbolic problems
NASA Astrophysics Data System (ADS)
Guy, Capdeville
2013-10-01
We present a new HLL-type approximate Riemann solver that aims at capturing any isolated discontinuity without necessitating extensive characteristic analysis of governing partial differential equations. This property is especially attractive for complex hyperbolic systems with more than two equations. Following Linde's (2002) approach [6], we introduce a generic middle wave into the classical two-state HLL solver. The property of this third wave is typified by the way of a "strength indicator" that is derived from polynomial considerations. The polynomial that constitutes the basis of the procedure is made non-oscillatory by an adapted fourth-order WENO algorithm (CWENO4). This algorithm makes it possible to derive an expression for the strength indicator. According to the size of this latter parameter, the resulting solver (HLL-RH), either computes the multi-dimensional Rankine-Hugoniot equations if an isolated discontinuity appears in the Riemann fan, or asymptotically tends towards the two-state HLL solver if the solution is locally smooth. The asymptotic version of the HLL-RH solver is demonstrated to be positively conservative and entropy satisfying in its first-order multi-dimensional form provided that a relevant and not too restrictive CFL condition is considered; specific limitations of the conservative increments of the numerical solution and a suited entropy condition enable to maintain these properties in its high-order version. With a monotonicity-preserving algorithm for the time integration, the numerical method so generated, is third order in time and fourth-order accurate in space for the smooth part of the solution; moreover, the scheme is stable and accurate when capturing a shock wave, whatever the complexity of the underlying differential system. Extensive numerical tests for the one- and two-dimensional Euler equation of gas dynamics and comparisons with classical Godunov-type methods help to point out the potentialities and insufficiencies
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…
Approximate Riemann solvers for the Godunov SPH (GSPH)
NASA Astrophysics Data System (ADS)
Puri, Kunal; Ramachandran, Prabhu
2014-08-01
The Godunov Smoothed Particle Hydrodynamics (GSPH) method is coupled with non-iterative, approximate Riemann solvers for solutions to the compressible Euler equations. The use of approximate solvers avoids the expensive solution of the non-linear Riemann problem for every interacting particle pair, as required by GSPH. In addition, we establish an equivalence between the dissipative terms of GSPH and the signal based SPH artificial viscosity, under the restriction of a class of approximate Riemann solvers. This equivalence is used to explain the anomalous “wall heating” experienced by GSPH and we provide some suggestions to overcome it. Numerical tests in one and two dimensions are used to validate the proposed Riemann solvers. A general SPH pairing instability is observed for two-dimensional problems when using unequal mass particles. In general, Ducowicz Roe's and HLLC approximate Riemann solvers are found to be suitable replacements for the iterative Riemann solver in the original GSPH scheme.
NASA Astrophysics Data System (ADS)
Vollebregt, E. A. H.
2014-01-01
This paper presents our new solver BCCG+FAI for solving elastic normal contact problems. This is a comprehensible approach that is based on the Conjugate Gradients (CG) algorithm and that uses FFTs. A first novel aspect is the definition of the “FFT-based Approximate Inverse” preconditioner. The underlying idea is that the inverse matrix can be approximated well using a Toeplitz or block-Toeplitz form, which can be computed using the FFT of the original matrix elements. This preconditioner makes the total number of CG iterations effectively constant in 2D and very slowly increasing in 3D problems. A second novelty is how we deal with a prescribed total force. This uses a deflation technique in such a way that CGs convergence and finite termination properties are maintained. Numerical results show that this solver is more effective than existing CG-based strategies, such that it can compete with Multi-Grid strategies over a much larger problem range. In our opinion it could be the new method of choice because of its simple structure and elegant theory, and because robust performance is achieved independently of any problem specific parameters.
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
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)
Li, Gang; Zhang, Lili; Hao, Tianyao
2016-02-01
An effective solver for the large complex system of linear equations is critical for improving the accuracy of numerical solutions in three-dimensional (3D) magnetotelluric (MT) modeling using the staggered finite-difference (SFD) method. In electromagnetic modeling, the formed system of linear equations is commonly solved using preconditioned iterative relaxation methods. We present 3D MT modeling using the SFD method, based on former work. The multigrid solver and three solvers preconditioned by incomplete Cholesky decomposition—the minimum residual method, the generalized product bi-conjugate gradient method and the bi-conjugate gradient stabilized method—are used to solve the formed system of linear equations. Divergence correction for the magnetic field is applied. We also present a comparison of the stability and convergence of these iterative solvers if divergence correction is used. Model tests show that divergence correction improves the convergence of iterative solvers and the accuracy of numerical results. Divergence correction can also decrease the number of iterations for fast convergence without changing the stability of linear solvers. For consideration of the computation time and memory requirements, the multigrid solver combined with divergence correction is preferred for 3D MT field simulation.
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.
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 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.
Dionne-Odom, J Nicholas; Lyons, Kathleen D; Akyar, Imatullah; Bakitas, Marie A
2016-01-01
Family caregivers of persons with advanced cancer often take on responsibilities that present daunting and complex problems. Serious problems that go unresolved may be burdensome and result in negative outcomes for caregivers' psychological and physical health and affect the quality of care delivered to the care recipients with cancer, especially at the end of life. Formal problem-solving training approaches have been developed over the past several decades to assist individuals with managing problems faced in daily life. Several of these problem-solving principles and techniques were incorporated into ENABLE (Educate, Nurture, Advise, Before Life End), an "early" palliative care telehealth intervention for individuals diagnosed with advanced cancer and their family caregivers. A hypothetical case resembling the situations of actual caregiver participants in ENABLE that exemplifies the complex problems that caregivers face is presented, followed by presentation of an overview of ENABLE's problem-solving key principles, techniques, and steps in problem-solving support. Though more research is needed to formally test the use of problem-solving support in social work practice, social workers can easily incorporate these techniques into everyday practice. PMID:27143574
ERIC Educational Resources Information Center
Ohio State Univ., Columbus. Vocational Instructional Materials Lab.
This curriculum guide provides resources that teachers and trainers can use to help learners improve their ability to apply mathematical problem-solving skills in the workplace. The instructional strategies and practice problems in the guide are patterned after those of the American College Testing (ACT) Work Keys System. Gains in skill levels can…
Applied Technology: Targets for Learning. Preparing Successful Problem Solvers in the Workplace.
ERIC Educational Resources Information Center
Ohio State Univ., Columbus. Vocational Instructional Materials Lab.
This curriculum guide provides resources that teachers and trainers can use to help learners improve their ability to apply technology problem-solving skills in the workplace. The instructional strategies and practice problems in the guide are patterned after those of the American College Testing (ACT) Work Keys System. Gains in skill levels can…
NASA Astrophysics Data System (ADS)
Sanan, P.; Schnepp, S. M.; May, D.; Schenk, O.
2014-12-01
Geophysical applications require efficient forward models for non-linear Stokes flow on high resolution spatio-temporal domains. The bottleneck in applying the forward model is solving the linearized, discretized Stokes problem which takes the form of a large, indefinite (saddle point) linear system. Due to the heterogeniety of the effective viscosity in the elliptic operator, devising effective preconditioners for saddle point problems has proven challenging and highly problem-dependent. Nevertheless, at least three approaches show promise for preconditioning these difficult systems in an algorithmically scalable way using multigrid and/or domain decomposition techniques. The first is to work with a hierarchy of coarser or smaller saddle point problems. The second is to use the Schur complement method to decouple and sequentially solve for the pressure and velocity. The third is to use the Schur decomposition to devise preconditioners for the full operator. These involve sub-solves resembling inexact versions of the sequential solve. The choice of approach and sub-methods depends crucially on the motivating physics, the discretization, and available computational resources. Here we examine the performance trade-offs for preconditioning strategies applied to idealized models of mantle convection and lithospheric dynamics, characterized by large viscosity gradients. Due to the arbitrary topological structure of the viscosity field in geodynamical simulations, we utilize low order, inf-sup stable mixed finite element spatial discretizations which are suitable when sharp viscosity variations occur in element interiors. Particular attention is paid to possibilities within the decoupled and approximate Schur complement factorization-based monolithic approaches to leverage recently-developed flexible, communication-avoiding, and communication-hiding Krylov subspace methods in combination with `heavy' smoothers, which require solutions of large per-node sub-problems, well
Bridging the Problem-Solver Communication Gap: Toward an Art of Professional Case Design.
ERIC Educational Resources Information Center
Johnson, Robert; Simpson, Mark
1990-01-01
Evaluates well-designed cases involving students in situations which simulate those outside the classroom environment. Offers additional features based on problem solving and rhetorical theory to help make cases more adaptable to the field of professional communications. Describes examples of two types of cases which put the theory into practice.…
Motivation in Adult Education: A Problem Solver or a Euphemism for Direction and Control?
ERIC Educational Resources Information Center
Ahl, Helene
2006-01-01
Adults' motivation to participate in continued education is of immediate interest, as lifelong learning is now considered as the solution to the pressing problems of increased levels of unemployment, not least among unskilled workers. Many theories concerning motivation and adult education maintain that individuals are innately motivated to learn,…
A fast nested dissection solver for Cartesian 3D elliptic problems using hierarchical matrices
NASA Astrophysics Data System (ADS)
Schmitz, Phillip G.; Ying, Lexing
2014-02-01
We present a fast algorithm for solutions to linear systems arising from three dimensional elliptic problems on a regular Cartesian mesh. We follow the approach of Schmitz and Ying (2012) on combining the nested dissection matrix factorization method with hierarchical matrices in two dimensions and extend it to the three dimensional case. A theoretical linear time complexity is derived and a more practical variant with slightly worse scaling is demonstrated.
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.
A multigrid fluid pressure solver handling separating solid boundary conditions.
Chentanez, Nuttapong; Müller-Fischer, Matthias
2012-08-01
We present a multigrid method for solving the linear complementarity problem (LCP) resulting from discretizing the Poisson equation subject to separating solid boundary conditions in an Eulerian liquid simulation’s pressure projection step. The method requires only a few small changes to a multigrid solver for linear systems. Our generalized solver is fast enough to handle 3D liquid simulations with separating boundary conditions in practical domain sizes. Previous methods could only handle relatively small 2D domains in reasonable time, because they used expensive quadratic programming (QP) solvers. We demonstrate our technique in several practical scenarios, including nonaxis-aligned containers and moving solids in which the omission of separating boundary conditions results in disturbing artifacts of liquid sticking to solids. Our measurements show, that the convergence rate of our LCP solver is close to that of a standard multigrid solver. PMID:22411885
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
2009-11-01
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
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
Parallel Multigrid Equation Solver
Energy Science and Technology Software Center (ESTSC)
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.
Generalized spectral decomposition for stochastic nonlinear problems
Nouy, Anthony Le Maitre, Olivier P.
2009-01-10
We present an extension of the generalized spectral decomposition method for the resolution of nonlinear stochastic problems. The method consists in the construction of a reduced basis approximation of the Galerkin solution and is independent of the stochastic discretization selected (polynomial chaos, stochastic multi-element or multi-wavelets). Two algorithms are proposed for the sequential construction of the successive generalized spectral modes. They involve decoupled resolutions of a series of deterministic and low-dimensional stochastic problems. Compared to the classical Galerkin method, the algorithms allow for significant computational savings and require minor adaptations of the deterministic codes. The methodology is detailed and tested on two model problems, the one-dimensional steady viscous Burgers equation and a two-dimensional nonlinear diffusion problem. These examples demonstrate the effectiveness of the proposed algorithms which exhibit convergence rates with the number of modes essentially dependent on the spectrum of the stochastic solution but independent of the dimension of the stochastic approximation space.
Predicting mental health problems in general practitioners.
Chambers, R; Belcher, J
1994-09-01
A total of 704 general practitioners completed questionnaires enquiring about mental health problems (response rate = 82.0%). Excessive anxiety was reported by 31.1%, troublesome depression by 13.4%, exhaustion or stress (on three or more weekdays) by 60.7%, and sleep difficulties by 47.6%. General practitioners aged 40-49 years old were most likely to report anxiety, exhaustion or stress, sexual and sleep difficulties. Retired doctors reported mental health problems markedly less often. Predictive factors for anxiety were depression, one or more nights on-call per week, and exhaustion or stress; predictive factors for depression were anxiety, and exhaustion or stress; predictive factors for exhaustion or stress were anxiety, depression, no hobbies, paperwork on three or more evenings per week, and sleep difficulties. Gender, country of origin, being single-handed, excessive alcohol consumption, and having no coping methods were not predictive factors for mental health problems. PMID:7949065
A general heuristic for genome rearrangement problems.
Dias, Ulisses; Galvão, Gustavo Rodrigues; Lintzmayer, Carla Négri; Dias, Zanoni
2014-06-01
In this paper, we present a general heuristic for several problems in the genome rearrangement field. Our heuristic does not solve any problem directly, it is rather used to improve the solutions provided by any non-optimal algorithm that solve them. Therefore, we have implemented several algorithms described in the literature and several algorithms developed by ourselves. As a whole, we implemented 23 algorithms for 9 well known problems in the genome rearrangement field. A total of 13 algorithms were implemented for problems that use the notions of prefix and suffix operations. In addition, we worked on 5 algorithms for the classic problem of sorting by transposition and we conclude the experiments by presenting results for 3 approximation algorithms for the sorting by reversals and transpositions problem and 2 approximation algorithms for the sorting by reversals problem. Another algorithm with better approximation ratio can be found for the last genome rearrangement problem, but it is purely theoretical with no practical implementation. The algorithms we implemented in addition to our heuristic lead to the best practical results in each case. In particular, we were able to improve results on the sorting by transpositions problem, which is a very special case because many efforts have been made to generate algorithms with good results in practice and some of these algorithms provide results that equal the optimum solutions in many cases. Our source codes and benchmarks are freely available upon request from the authors so that it will be easier to compare new approaches against our results. PMID:24969750
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…
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.
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.
NASA Astrophysics Data System (ADS)
Acebrón, Juan A.; Rodríguez-Rozas, Ángel
2011-09-01
A probabilistic representation for initial value semilinear parabolic problems based on generalized random trees has been derived. Two different strategies have been proposed, both requiring generating suitable random trees combined with a Pade approximant for approximating accurately a given divergent series. Such series are obtained by summing the partial contribution to the solution coming from trees with arbitrary number of branches. The new representation greatly expands the class of problems amenable to be solved probabilistically, and was used successfully to develop a generalized probabilistic domain decomposition method. Such a method has been shown to be suited for massively parallel computers, enjoying full scalability and fault tolerance. Finally, a few numerical examples are given to illustrate the remarkable performance of the algorithm, comparing the results with those obtained with a classical method.
Kotulski, Joseph D.; Womble, David E.; Greenberg, David; Driessen, Brian
2004-03-01
PLIRIS is an object-oriented solver built on top of a previous matrix solver used in a number of application codes. Puns solves a linear system directly via LU factorization with partial pivoting. The user provides the linear system in terms of Epetra Objects including a matrix and right-hand-sides. The user can then factor the matrix and perform the forward and back solve at a later time or solve for multiple right-hand-sides at once. This package is used when dense matrices are obtained in the problem formulation. These dense matrices occur whenever boundary element techniques are chosen for the solution procedure. This has been used in electromagnetics for both static and frequency domain problems.
Energy Science and Technology Software Center (ESTSC)
2004-03-01
PLIRIS is an object-oriented solver built on top of a previous matrix solver used in a number of application codes. Puns solves a linear system directly via LU factorization with partial pivoting. The user provides the linear system in terms of Epetra Objects including a matrix and right-hand-sides. The user can then factor the matrix and perform the forward and back solve at a later time or solve for multiple right-hand-sides at once. This packagemore » is used when dense matrices are obtained in the problem formulation. These dense matrices occur whenever boundary element techniques are chosen for the solution procedure. This has been used in electromagnetics for both static and frequency domain problems.« less
Fast computation of general forward gravitation problems
NASA Astrophysics Data System (ADS)
Casenave, Fabien; Métivier, Laurent; Pajot-Métivier, Gwendoline; Panet, Isabelle
2016-07-01
We consider the well-known problem of the forward computation of the gradient of the gravitational potential generated by a mass density distribution of general 3D geometry. Many methods have been developed for given geometries, and the computation time often appears as a limiting practical issue for considering large or complex problems. In this work, we develop a fast method to carry out this computation, where a tetrahedral mesh is used to model the mass density distribution. Depending on the close- or long-range nature of the involved interactions, the algorithm automatically switches between analytic integration formulae and numerical quadratic formulae, and relies on the Fast Multipole Method to drastically increase the computation speed of the long-range interactions. The parameters of the algorithm are empirically chosen for the computations to be the fastest possible while guarantying a given relative accuracy of the result. Computations that would load many-core clusters for days can now be carried out on a desk computer in minutes. The computation of the contribution of topographical masses to the Earth's gravitational field at the altitude of the GOCE satellite and over France are proposed as numerical illustrations of the method.
Fast computation of general forward gravitation problems
NASA Astrophysics Data System (ADS)
Casenave, Fabien; Métivier, Laurent; Pajot-Métivier, Gwendoline; Panet, Isabelle
2016-04-01
We consider the well-known problem of the forward computation of the gradient of the gravitational potential generated by a mass density distribution of general 3D geometry. Many methods have been developed for given geometries, and the computation time often appears as a limiting practical issue for considering large or complex problems. In this work, we develop a fast method to carry out this computation, where a tetrahedral mesh is used to model the mass density distribution. Depending on the close- or long-range nature of the involved interactions, the algorithm automatically switches between analytic integration formulae and numerical quadratic formulae, and relies on the Fast Multipole Method to drastically increase the computation speed of the long-range interactions. The parameters of the algorithm are empirically chosen for the computations to be the fastest possible while guarantying a given relative accuracy of the result. Computations that would load many-core clusters for days can now be carried out on a desk computer in minutes. The computation of the contribution of topographical masses to the Earth's gravitational field at the altitude of the GOCE satellite and over France are proposed as numerical illustrations of the method.
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.
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 Astrophysics Data System (ADS)
Kovalevsky, Louis; Gosselet, Pierre
2016-09-01
The Variational Theory of Complex Rays (VTCR) is an indirect Trefftz method designed to study systems governed by Helmholtz-like equations. It uses wave functions to represent the solution inside elements, which reduces the dispersion error compared to classical polynomial approaches but the resulting system is prone to be ill conditioned. This paper gives a simple and original presentation of the VTCR using the discontinuous Galerkin framework and it traces back the ill-conditioning to the accumulation of eigenvalues near zero for the formulation written in terms of wave amplitude. The core of this paper presents an efficient solving strategy that overcomes this issue. The key element is the construction of a search subspace where the condition number is controlled at the cost of a limited decrease of attainable precision. An augmented LSQR solver is then proposed to solve efficiently and accurately the complete system. The approach is successfully applied to different examples.
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
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.
Problem Solving in the General Mathematics Classroom
ERIC Educational Resources Information Center
Troutman, Andria Price; Lichtenberg, Betty Plunkett
1974-01-01
Five steps common to different problem solving models are listed. Next, seven specific abilities related to solving problems are discussed and examples given. Sample activities, appropriate to help in developing these specific abilities, are suggested. (LS)
General Description of Human Problem Solving.
ERIC Educational Resources Information Center
Klein, Gary A.; Weitzenfeld, Julian
A theoretical model relating problem identification to problem solving is presented. The main purpose of the study is to increase understanding of decision making among Air Force educators. The problem-solving process is defined as the generation and evaluation of alternatives that will accomplish what is needed and the reidentification of what is…
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.
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.
Generalized Kepler problems. I. Without magnetic charges
NASA Astrophysics Data System (ADS)
Meng, Guowu
2013-01-01
For each simple euclidean Jordan algebra V of rank ρ and degree δ, 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 ν, is obtained. Here, ν in {W}(V):=[ k δ/2mid k=1, ldots, (ρ -1)] \\cup ((ρ -1)δ / 2, infty ) 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 ν, the bound state spectra is -1/2/ (I+ν frac{ρ { 2})^2}, I = 0, 1, … and its Hilbert space of bound states gives a new realization for the afore-mentioned representation labelled by ν. 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 Vert dot{x}Vert ^2+1/ r. Here, dot{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.
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.
PSPIKE: A Parallel Hybrid Sparse Linear System Solver
NASA Astrophysics Data System (ADS)
Manguoglu, Murat; Sameh, Ahmed H.; Schenk, Olaf
The availability of large-scale computing platforms comprised of tens of thousands of multicore processors motivates the need for the next generation of highly scalable sparse linear system solvers. These solvers must optimize parallel performance, processor (serial) performance, as well as memory requirements, while being robust across broad classes of applications and systems. In this paper, we present a new parallel solver that combines the desirable characteristics of direct methods (robustness) and effective iterative solvers (low computational cost), while alleviating their drawbacks (memory requirements, lack of robustness). Our proposed hybrid solver is based on the general sparse solver PARDISO, and the “Spike” family of hybrid solvers. The resulting algorithm, called PSPIKE, is as robust as direct solvers, more reliable than classical preconditioned Krylov subspace methods, and much more scalable than direct sparse solvers. We support our performance and parallel scalability claims using detailed experimental studies and comparison with direct solvers, as well as classical preconditioned Krylov methods.
Self-correcting Multigrid Solver
Jerome L.V. Lewandowski
2004-06-29
A new multigrid algorithm based on the method of self-correction for the solution of elliptic problems is described. The method exploits information contained in the residual to dynamically modify the source term (right-hand side) of the elliptic problem. It is shown that the self-correcting solver is more efficient at damping the short wavelength modes of the algebraic error than its standard equivalent. When used in conjunction with a multigrid method, the resulting solver displays an improved convergence rate with no additional computational work.
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…
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. PMID:25000309
Boggs, P.; Tolle, J.; Kearsley, A.
1994-12-31
We have developed a large scale sequential quadratic programming (SQP) code based on an interior-point method for solving general (convex or nonconvex) quadratic programs (QP). We often halt this QP solver prematurely by employing a trust-region strategy. This procedure typically reduces the overall cost of the code. In this talk we briefly review the algorithm and some of its theoretical justification and then discuss recent enhancements including automatic procedures for both increasing and decreasing the parameter in the merit function, a regularization procedure for dealing with linearly dependent active constraint gradients, and a method for modifying the linearized equality constraints. Some numerical results on a significant set of {open_quotes}real-world{close_quotes} problems will be presented.
ERIC Educational Resources Information Center
Thevenot, Catherine; Castel, Caroline; Fanget, Muriel; Fayol, Michel
2010-01-01
The authors used the operand-recognition paradigm (C. Thevenot, M. Fanget, & M. Fayol, 2007) in order to study the strategies used by adults to solve subtraction problems. This paradigm capitalizes on the fact that algorithmic procedures degrade the memory traces of the operands. Therefore, greater difficulty in recognizing them is expected when…
Generalized ruin problems and asynchronous random walks
NASA Astrophysics Data System (ADS)
Abad, E.
2005-07-01
We consider a gambling game with two different kinds of trials and compute the duration of the game (averaged over all possible initial capitals of the players) by a mapping of the problem to a 1D lattice walk of two particles reacting upon encounter. The relative frequency of the trials is governed by the synchronicity parameter p of the random walk. The duration of the game is given by the mean time to reaction, which turns out to display a different behavior for even and odd lattices, i.e. this quantity is monotonic in p for odd lattices and non-monotonic for even lattices. In the game picture, this implies that the players minimize the duration of the game by restricting themselves to one type of trial if their joint capital is odd, otherwise a non-symmetric mixture of both trials is needed.
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.
Energy Science and Technology Software Center (ESTSC)
2004-03-01
Amesos is the Direct Sparse Solver Package in Trilinos. The goal of Amesos is to make AX=S as easy as it sounds, at least for direct methods. Amesos provides interfaces to a number of third party sparse direct solvers, including SuperLU, SuperLU MPI, DSCPACK, UMFPACK and KLU. Amesos provides a common object oriented interface to the best sparse direct solvers in the world. A sparse direct solver solves for x in Ax = b. wheremore » A is a matrix and x and b are vectors (or multi-vectors). A sparse direct solver flrst factors A into trinagular matrices L and U such that A = LU via gaussian elimination and then solves LU x = b. Switching amongst solvers in Amesos roquires a change to a single parameter. Yet, no solver needs to be linked it, unless it is used. All conversions between the matrices provided by the user and the format required by the underlying solver is performed by Amesos. As new sparse direct solvers are created, they will be incorporated into Amesos, allowing the user to simpty link with the new solver, change a single parameter in the calling sequence, and use the new solver. Amesos allows users to specify whether the matrix has changed. Amesos can be used anywhere that any sparse direct solver is needed.« less
Stanley, Vendall S.; Heroux, Michael A.; Hoekstra, Robert J.; Sala, Marzio
2004-03-01
Amesos is the Direct Sparse Solver Package in Trilinos. The goal of Amesos is to make AX=S as easy as it sounds, at least for direct methods. Amesos provides interfaces to a number of third party sparse direct solvers, including SuperLU, SuperLU MPI, DSCPACK, UMFPACK and KLU. Amesos provides a common object oriented interface to the best sparse direct solvers in the world. A sparse direct solver solves for x in Ax = b. where A is a matrix and x and b are vectors (or multi-vectors). A sparse direct solver flrst factors A into trinagular matrices L and U such that A = LU via gaussian elimination and then solves LU x = b. Switching amongst solvers in Amesos roquires a change to a single parameter. Yet, no solver needs to be linked it, unless it is used. All conversions between the matrices provided by the user and the format required by the underlying solver is performed by Amesos. As new sparse direct solvers are created, they will be incorporated into Amesos, allowing the user to simpty link with the new solver, change a single parameter in the calling sequence, and use the new solver. Amesos allows users to specify whether the matrix has changed. Amesos can be used anywhere that any sparse direct solver is needed.
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
Application of the general problem of moments to some optimization problems in elasticity theory
NASA Astrophysics Data System (ADS)
Grigoliuk, E. I.; Fil'Shtinskii, V. A.; Fil'Shtinskii, L. A.
1992-04-01
Several optimization problems in elasticity theory are formulated which are relevant to geomechanics. Methods are then presented for reducing these problems to general moment problems in continuous-function space. By using polynomial approximations of nonstandard moment functions, the general moment problems are reduced to the classical power-law moment problem. This allows an a priori evaluation of the optimal control structure. Theoretical and computational examples are presented.
A General Problem Describer for Computer Assisted Instruction.
ERIC Educational Resources Information Center
Wools, Ronald Joe
Currently in computer-assisted instruction (CAI) systems a number of problems are presented to each student during a session, with each individual problem being specified by the author of the session. A better approach might be to provide the author with a language in which he can describe to the computer the general type of problem he wants his…
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.
NASA Astrophysics Data System (ADS)
Balsara, Dinshaw S.
2012-09-01
In this paper we present a genuinely two-dimensional HLLC Riemann solver. On logically rectangular meshes, it accepts four input states that come together at an edge and outputs the multi-dimensionally upwinded fluxes in both directions. This work builds on, and improves, our prior work on two-dimensional HLL Riemann solvers. The HLL Riemann solver presented here achieves its stabilization by introducing a constant state in the region of strong interaction, where four one-dimensional Riemann problems interact vigorously with one another. A robust version of the HLL Riemann solver is presented here along with a strategy for introducing sub-structure in the strongly-interacting state. Introducing sub-structure turns the two-dimensional HLL Riemann solver into a two-dimensional HLLC Riemann solver. The sub-structure that we introduce represents a contact discontinuity which can be oriented in any direction relative to the mesh. The Riemann solver presented here is general and can work with any system of conservation laws. We also present a second order accurate Godunov scheme that works in three dimensions and is entirely based on the present multidimensional HLLC Riemann solver technology. The methods presented are cost-competitive with traditional higher order Godunov schemes. The two-dimensional HLLC Riemann solver is shown to work robustly for Euler and Magnetohydrodynamic (MHD) flows. Several stringent test problems are presented to show that the inclusion of genuinely multidimensional effects into higher order Godunov schemes indeed produces some very compelling advantages. For two dimensional problems, we were routinely able to run simulations with CFL numbers of ˜0.7, with some two-dimensional simulations capable of reaching higher CFL numbers. For three dimensional problems, CFL numbers as high as ˜0.6 were found to be stable. We show that on resolution-starved meshes, the scheme presented here outperforms unsplit second order Godunov schemes that are based
New generalizations of the integrable problems in rigid body dynamics
NASA Astrophysics Data System (ADS)
Yehia, H. M.
1997-10-01
We consider the general problem of motion of a rigid body about a fixed point under the action of an axisymmetric combination of potential and gyroscopic forces. We introduce six cases of this problem which are completely integrable for arbitrary initial conditions. The new cases generalize by several parameters all, but one, of the known results in the subject of rigid body dynamics. Namely, we generalize all the results due to Euler, Lagrange, Clebsch, Kovalevskaya, Brun and Lyapunov and also their subsequent generalizations by Rubanovsky and the present author.
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
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…
A Heuristic Framework to Solve a General Delivery Problem
NASA Astrophysics Data System (ADS)
Lian, Lian; Castelain, Emmanuel
2010-06-01
This paper presents a new distribution and route planning problem, General Delivery Problem (GDP) which is more general than the well-known Vehicle Routing Problem. To solve a GDP, a three-phase framework heuristic approach based on decomposition techniques is introduced. The decomposition techniques are employed to divide an original problem into a set of sub-problems, which can reduce the problem size. A kind of decomposition technique, Capacity Clustering Algorithm (CCA), is embedded into the framework with Simulated Annealing (SA) to solve a special GDP. The proposed three-phase framework with the above two algorithms is compared with five other decomposition methods in a distribution instance of the Regional Fire and Emergency Center in the north of France.
Fast Poisson, Fast Helmholtz and fast linear elastostatic solvers on rectangular parallelepipeds
Wiegmann, A.
1999-06-01
FFT-based fast Poisson and fast Helmholtz solvers on rectangular parallelepipeds for periodic boundary conditions in one-, two and three space dimensions can also be used to solve Dirichlet and Neumann boundary value problems. For non-zero boundary conditions, this is the special, grid-aligned case of jump corrections used in the Explicit Jump Immersed Interface method. Fast elastostatic solvers for periodic boundary conditions in two and three dimensions can also be based on the FFT. From the periodic solvers we derive fast solvers for the new 'normal' boundary conditions and essential boundary conditions on rectangular parallelepipeds. The periodic case allows a simple proof of existence and uniqueness of the solutions to the discretization of normal boundary conditions. Numerical examples demonstrate the efficiency of the fast elastostatic solvers for non-periodic boundary conditions. More importantly, the fast solvers on rectangular parallelepipeds can be used together with the Immersed Interface Method to solve problems on non-rectangular domains with general boundary conditions. Details of this are reported in the preprint The Explicit Jump Immersed Interface Method for 2D Linear Elastostatics by the author.
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…
NASA Astrophysics Data System (ADS)
Kergrene, Kenan; Babuška, Ivo; Banerjee, Uday
2016-06-01
The Generalized Finite Element Method (GFEM) is an extension of the Finite Element Method (FEM), where the standard finite element space is augmented with a space of non-polynomial functions, called the enrichment space. The functions in the enrichment space mimic the local behavior of the unknown solution of the underlying variational problem. GFEM has been successfully applied to a wide range of problems. However, it often suffers from bad conditioning, i.e., its conditioning may not be robust with respect to the mesh and in fact, the conditioning could be much worse than that of the standard FEM. In this paper, we present a numerical study that shows that if the "angle" between the finite element space and the enrichment space is bounded away from 0, uniformly with respect to the mesh, then the GFEM is stable, i.e., the conditioning of GFEM is not worse than that of the standard FEM. A GFEM with this property is called a Stable GFEM (SGFEM). The last part of the paper is devoted to the derivation of a robust iterative solver exploiting this angle condition. It is shown that the required "wall-clock" time is greatly reduced compared to popular GFEMs used in the literature.
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.
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
The trace minimization method for the symmetric generalized eigenvalue problem
NASA Astrophysics Data System (ADS)
Sameh, Ahmed; Tong, Zhanye
2000-11-01
In this paper, the trace minimization method for the generalized symmetric eigenvalue problems proposed by Sameh and Wisniewski [35] is reviewed. Convergence of an inexact trace minimization algorithm is established and a variant of the algorithm that uses expanding subspaces is introduced and compared with the block Jacobi-Davidson algorithm.
Finite Element Interface to Linear Solvers
Energy Science and Technology Software Center (ESTSC)
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 themore » 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.« less
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.
The little hierarchy problem in a generalized NMSSM
Kolda, Christopher
2013-05-23
In this talk, I review recent work on using a generalization of the Next-to-Minimal Supersymmetric Standard Model (NMSSM), called the Singlet-extended Minimal Supersymmetric Standard Model (SMSSM), to raise the mass of the Standard Model-like Higgs boson without requiring extremely heavy top squarks or large stop mixing. In so doing, this model solves the little hierarchy problem of the minimal model (MSSM), at the expense of leaving the {mu}-problem of the MSSM unresolved. This talk is based on work published in Refs. [1, 2, 3].
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. PMID:19563427
Local search for the generalized tree alignment problem
2013-01-01
Background A phylogeny postulates shared ancestry relationships among organisms in the form of a binary tree. Phylogenies attempt to answer an important question posed in biology: what are the ancestor-descendent relationships between organisms? At the core of every biological problem lies a phylogenetic component. The patterns that can be observed in nature are the product of complex interactions, constrained by the template that our ancestors provide. The problem of simultaneous tree and alignment estimation under Maximum Parsimony is known in combinatorial optimization as the Generalized Tree Alignment Problem (GTAP). The GTAP is the Steiner Tree Problem for the sequence edit distance. Like many biologically interesting problems, the GTAP is NP-Hard. Typically the Steiner Tree is presented under the Manhattan or the Hamming distances. Results Experimentally, the accuracy of the GTAP has been subjected to evaluation. Results show that phylogenies selected using the GTAP from unaligned sequences are competitive with the best methods and algorithms available. Here, we implement and explore experimentally existing and new local search heuristics for the GTAP using simulated and real data. Conclusions The methods presented here improve by more than three orders of magnitude in execution time the best local search heuristics existing to date when applied to real data. PMID:23441880
A Generalized Cauchy Distribution Framework for Problems Requiring Robust Behavior
NASA Astrophysics Data System (ADS)
Carrillo, Rafael E.; Aysal, Tuncer C.; Barner, Kenneth E.
2010-12-01
Statistical modeling is at the heart of many engineering problems. The importance of statistical modeling emanates not only from the desire to accurately characterize stochastic events, but also from the fact that distributions are the central models utilized to derive sample processing theories and methods. The generalized Cauchy distribution (GCD) family has a closed-form pdf expression across the whole family as well as algebraic tails, which makes it suitable for modeling many real-life impulsive processes. This paper develops a GCD theory-based approach that allows challenging problems to be formulated in a robust fashion. Notably, the proposed framework subsumes generalized Gaussian distribution (GGD) family-based developments, thereby guaranteeing performance improvements over traditional GCD-based problem formulation techniques. This robust framework can be adapted to a variety of applications in signal processing. As examples, we formulate four practical applications under this framework: (1) filtering for power line communications, (2) estimation in sensor networks with noisy channels, (3) reconstruction methods for compressed sensing, and (4) fuzzy clustering.
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.
ERIC Educational Resources Information Center
ten Berge, Jos M. F.
1988-01-01
A summary and a unified treatment of fully general computational solutions for two criteria for transforming two or more matrices to maximal agreement are provided. The two criteria--Maxdiff and Maxbet--have applications in the rotation of factor loading or configuration matrices to maximal agreement and the canonical correlation problem. (SLD)
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.
A Monte Carlo study of the generalized Coulomb Milne problem
NASA Astrophysics Data System (ADS)
Barghouthi, I.; Barakat, A.
2003-04-01
Because of its relevance to the solar wind and terrestrial polar wind, we investigated the problem where a swarm of minor ions escaped through a background of non-uniform major ions. The Fokker-Planck expression was used to represent the Coulomb collisions between the minor and major ions. A change of variables was utilized in order to transform the problem into a simpler form where the background medium was uniform. This transformed problem described minor ions diffusing through a background of ions of a constant density in the semi-infinite region (z>0), and vacuum in the region (z<0), which resembles the standard Milne problem. A Monte Carlo model was used to investigate this "generalized Coulomb Milne" problem for three different minor-to-major ion mass ratios, namely; R = m/M = 1/16, 1 and 16, where m and M are the minor and major ion masses, respectively. The minor ions' velocity distribution function and velocity moments (i.e. density, drift velocity, parallel and perpendicular temperatures, and parallel and perpendicular heat fluxes) were computed. The following conclusions can be drawn: (1) In general, the minor ion species for the cases of (R=1,16) show very similar characteristics, while the third case (R=1/16) shows very different characteristics. (2) In the collision-dominated region (z>>1), the gradient of the normalized density profile approaches a constant value. This asymptotic value of the gradient increases when R decreases. (3) As the minor ion species drifts from the collision-dominated region (z>>) to the collisionless region (z<<1), its velocity distribution starts as Maxwellian, then it develops a tail in the (-z) direction, and finally reaches a form close to bi-Maxwellian. The case of (R=1/16) develops a relatively more pronounced tail, and displays a double-hump form, which is absent for the other two cases. (4) The heat flux profile for the case of (R=1/6) in the collision-dominated region exceeds the corresponding values from the other
The Energy-Momentum Problem in General Relativity
NASA Astrophysics Data System (ADS)
Xulu, S. S.
2003-08-01
Energy-momentum is an important conserved quantity whose definition has been a focus of many investigations in general relativity. Unfortunately, there is still no generally accepted definition of energy and momentum in general relativity. Attempts aimed at finding a quantity for describing distribution of energy-momentum due to matter, non-gravitational and gravitational fields resulted in various energy-momentum complexes whose physical meaning have been questioned. The problems associated with energy-momentum complexes resulted in some researchers even abandoning the concept of energy-momentum localization in favour of the alternative concept of quasi-localization. However, quasi-local masses have their inadequacies, while the remarkable work of Virbhadra and some others, and recent results of Cooperstock and Chang et al. have revived an interest in various energy-momentum complexes. Hence in this work we use energy-momentum complexes to obtain the energy distributions in various space-times. We elaborate on the problem of energy localization in general relativity and use energy-momentum prescriptions of Einstein, Landau and Lifshitz, Papapetrou, Weinberg, and Møller to investigate energy distributions in various space-times. It is shown that several of these energy-momentum complexes give the same and acceptable results for a given space-time. This shows the importance of these energy-momentum complexes. Our results agree with Virbhadra's conclusion that the Einstein's energy-momentum complex is still the best tool for obtaining energy distribution in a given space-time. The Cooperstock hypothesis for energy localization in GR is also supported.
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
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.
Extending substructure based iterative solvers to multiple load and repeated analyses
NASA Technical Reports Server (NTRS)
Farhat, Charbel
1993-01-01
Direct solvers currently dominate commercial finite element structural software, but do not scale well in the fine granularity regime targeted by emerging parallel processors. Substructure based iterative solvers--often called also domain decomposition algorithms--lend themselves better to parallel processing, but must overcome several obstacles before earning their place in general purpose structural analysis programs. One such obstacle is the solution of systems with many or repeated right hand sides. Such systems arise, for example, in multiple load static analyses and in implicit linear dynamics computations. Direct solvers are well-suited for these problems because after the system matrix has been factored, the multiple or repeated solutions can be obtained through relatively inexpensive forward and backward substitutions. On the other hand, iterative solvers in general are ill-suited for these problems because they often must restart from scratch for every different right hand side. In this paper, we present a methodology for extending the range of applications of domain decomposition methods to problems with multiple or repeated right hand sides. Basically, we formulate the overall problem as a series of minimization problems over K-orthogonal and supplementary subspaces, and tailor the preconditioned conjugate gradient algorithm to solve them efficiently. The resulting solution method is scalable, whereas direct factorization schemes and forward and backward substitution algorithms are not. We illustrate the proposed methodology with the solution of static and dynamic structural problems, and highlight its potential to outperform forward and backward substitutions on parallel computers. As an example, we show that for a linear structural dynamics problem with 11640 degrees of freedom, every time-step beyond time-step 15 is solved in a single iteration and consumes 1.0 second on a 32 processor iPSC-860 system; for the same problem and the same parallel
General solutions of optimum problems in nonstationary flight
NASA Technical Reports Server (NTRS)
Miele, Angelo
1955-01-01
A general method concerning optimum problems in nonstationary flight is developed and discussed. Best flight techniques are determined for the following conditions: climb with minimum time, climb with minimum fuel consumption, steepest climb, descending and gliding flight with maximum time or with maximum distance. Optimum distributions of speed with altitude are derived assuming constant airplane weight and neglecting curvatures and squares of path inclination in the projection of the equation of motion on the normal to the flight path. The results of this paper differ from the well-known results obtained by neglecting accelerations with one exception, namely the case of gliding with maximum range. The paper is concluded with criticisms and remarks concerning the physical nature of the solutions and their usefulness for practical applications.
A Monte Carlo study of the generalized Coulomb Milne problem
NASA Astrophysics Data System (ADS)
Barghouthi, I. A.; Barakat, A. R.
2005-11-01
Because of its relevance to space plasma problems (such as the terrestrial polar wind), we investigated the diffusion of a minor ion species through a non-uniform background major ion species. A Fokker Planck expression was used to represent the Coulomb collisions between the minor and the background ions. A change of variables was implemented in order to transform the problem into a simpler form where the background medium is uniform. This transformed problem described minor ions diffusing through a background of ions with constant density in the semi-infinite region z˜⩾0 and zero density in the region z˜<0. This problem was termed the generalized Coulomb Milne problem and was addressed by a Monte Carlo simulation. Three different minor-to-background mass ratios (γ) were considered, namely γ=16, 1, and 116, which were relevant to H and O ions, the two most dominant ions in the terrestrial ionosphere. The minor ion velocity distribution (f) and the velocity moments (density (n); drift velocity (u), parallel (T) and perpendicular (T) temperatures; and parallel (q˜s∥) and perpendicular (q˜s⊥) heat fluxes) were computed. For the cases when the minor species mass was comparable to, or larger than the background species mass (γ=16,1), the distribution was close to Maxwellian at low altitudes due to Coulomb collisions, gradually formed a weak upward tail in the transition region, and eventually assumed a half-Maxwellian shape at the collisionless region. This was reflected in the enhancement of the flow and random energies, and the energy fluxes for these cases. Deep into the collision-dominated region, n was found to be linearly dependent on the normalized distance z˜ with a gradient (m=dn˜/dz˜). As γ decreased from 16 to 1 to 116, m decreased from 2.0 to 1.7 to 0.75, respectively. For the case of a lighter minor ion species drifting through a heavier background ion species (e.g. γ=116), the ion outflow exhibited some interesting qualitatively
Management of general surgical problems after cardiac transplantation.
Jones, M T; Menkis, A H; Kostuk, W J; McKenzie, F N
1988-07-01
Over a 6-year period at the University Hospital in London, Ont., 101 patients underwent heart transplantation and 5 heart-lung transplantation. The authors review the general surgical problems identified from the charts of 13 of these patients. In the early postoperative period (within 30 days), laparotomy was required for pancreatitis (one), perforated peptic ulcer (two), cholecystectomy (one), pancreatic cyst (one) and appendicitis (one). In addition, a spontaneous colocutaneous fistula and spontaneous pneumoperitoneum occurred; both were managed conservatively. Later, three patients required cholecystectomy; one underwent a below-knee and a Symes amputation for dry gangrene and one surgical correction of a lymphocele. The incidence of surgical problems (13%) indicates an increased susceptibility in this group of patients. Four of the 13 patients died. Pancreatitis is a well-recognized complication of cardiac surgery; it is frequently associated with a normal or only slightly elevated serum amylase level, making a definitive diagnosis without laparotomy almost impossible. Persistence of abdominal signs should signal the need for exploratory surgery. During the early postoperative period and in the absence of multiorgan failure, immediate operation for an acute abdomen is usually successful. Despite the additional risk, cardiac transplantation does not preclude later surgery, but immunosuppression must be continued and carefully monitored. PMID:3292032
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.
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 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.
Belos Block Linear Solvers Package
Energy Science and Technology Software Center (ESTSC)
2004-03-01
Belos is an extensible and interoperable framework for large-scale, iterative methods for solving systems of linear equations with multiple right-hand sides. The motivation for this framework is to provide a generic interface to a collection of algorithms for solving large-scale linear systems. Belos is interoperable because both the matrix and vectors are considered to be opaque objects--only knowledge of the matrix and vectors via elementary operations is necessary. An implementation of Balos is accomplished viamore » the use of interfaces. One of the goals of Belos is to allow the user flexibility in specifying the data representation for the matrix and vectors and so leverage any existing software investment. The algorithms that will be included in package are Krylov-based linear solvers, like Block GMRES (Generalized Minimal RESidual) and Block CG (Conjugate-Gradient).« less
Energy Science and Technology Software Center (ESTSC)
2007-03-01
HPCCG is a simple PDE application and preconditioned conjugate gradient solver that solves a linear system on a beam-shaped domain. Although it does not address many performance issues present in real engineering applications, such as load imbalance and preconditioner scalability, it can serve as a first "sanity test" of new processor design choices, inter-connect network design choices and the scalability of a new computer system. Because it is self-contained, easy to compile and easily scaledmore » to 100s or 1000s of porcessors, it can be an attractive study code for computer system designers.« less
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. PMID:24527060
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. PMID:24527060
Problems in Communications with Patients in General Surgery Outpatient Practice
Yilmaz, Tonguc Utku; Gumus, Enes; Salman, Bulent
2015-01-01
Objective: Communication between the patient and physician is central to medical care. However communication skills in Turkey haven’t been gained so much concern. This situation effect the national quality of health care. Here, we tried to perform some basic communication skills and to find the problems with the possible solution suggestions. Materials and Methods: The study was conducted for a month in general surgery outpatient department located in the slum part of Ankara with low socio-economic population. Basic communication skills were performed. The age, sex, education levels of the patients were obtained. Total symptom expression and interview time were recorded. Previous medical histories were asked. Interruptions including telephone, door knocking were noted. The questions of the patients at the end of the interview classified as hospital setting, nutrition and treatment. Results: Total 410 interviews were analysed. Mean symptom expression and interview times were 22.9 sec and 7.05 min, respectively. Educated patients, males and young patients expressed symptoms longer than the others (p<0.05). There were 174 interruptions in which total interview time signifantly increased than the non interrupted ones (p<0.05). Final questions about hospital setting were signifantly higher in illiterate patients than the educated ones (p<0.05). Awareness of medical history is higher in educated and young patients. Conclusion: Basic communications skills can be performed whether in rural regions. Much more concern should be given to the education of communication skills. The obstacles in communication in medicine are low education levels, and unorganised health system. PMID:26644767
NASA Astrophysics Data System (ADS)
Kevlahan, N. N.; Vasilyev, O. V.; Yuen, D. A.
2003-12-01
An adaptive multilevel wavelet collocation method for solving multi-dimensional elliptic problems with localized structures is developed. The method is based on the general class of multi-dimensional second generation wavelets and is an extension of the dynamically adaptive second generation wavelet collocation method for evolution problems. Wavelet decomposition is used for grid adaptation and interpolation, while O(N) hierarchical finite difference scheme, which takes advantage of wavelet multilevel decomposition, is used for derivative calculations. The multilevel structure of the wavelet approximation provides a natural way to obtain the solution on a near optimal grid. In order to accelerate the convergence of the iterative solver, an iterative procedure analogous to the multigrid algorithm is developed. For the problems with slowly varying viscosity simple diagonal preconditioning works. For problems with large laterally varying viscosity contrasts either direct solver on shared-memory machines or multilevel iterative solver with incomplete LU preconditioner may be used. The method is demonstrated for the solution of a number of two-dimensional elliptic test problems with both constant and spatially varying viscosity with multiscale character.
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.
Comparison of open-source linear programming solvers.
Gearhart, Jared Lee; Adair, Kristin Lynn; Durfee, Justin D.; 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.
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.
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.
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.
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,…
Investigating the Problem of Skill Generalization: Literature Review III.
ERIC Educational Resources Information Center
Haring, Norris
The third in a series of literature reviews, this monograph presents three articles on skill generalization among individuals with severe disabilities. Kathleen A. Liberty analyzes the results of 15 studies to determine how teaching self-control affected students' performance in training and generalization, "Behavior-Control of Stimulus Events to…
Parallel tridiagonal equation solvers
NASA Technical Reports Server (NTRS)
Stone, H. S.
1974-01-01
Three parallel algorithms were compared for the direct solution of tridiagonal linear systems of equations. The algorithms are suitable for computers such as ILLIAC 4 and CDC STAR. For array computers similar to ILLIAC 4, cyclic odd-even reduction has the least operation count for highly structured sets of equations, and recursive doubling has the least count for relatively unstructured sets of equations. Since the difference in operation counts for these two algorithms is not substantial, their relative running times may be more related to overhead operations, which are not measured in this paper. The third algorithm, based on Buneman's Poisson solver, has more arithmetic operations than the others, and appears to be the least favorable. For pipeline computers similar to CDC STAR, cyclic odd-even reduction appears to be the most preferable algorithm for all cases.
Amesos2 Templated Direct Sparse Solver Package
Energy Science and Technology Software Center (ESTSC)
2011-05-24
Amesos2 is a templated direct sparse solver package. Amesos2 provides interfaces to direct sparse solvers, rather than providing native solver capabilities. Amesos2 is a derivative work of the Trilinos package Amesos.
Top Element Problem and Macneille Completions of Generalized Effect Algebras
NASA Astrophysics Data System (ADS)
RieČanová, Z.; Kalina, M.
2014-10-01
Effect algebras (EAs), introduced by D. J. Foulis and M. K. Bennett, as common generalizations of Boolean algebras, orthomodular lattices and MV-algebras, are nondistributive algebraic structures including unsharp elements. Their unbounded versions, called generalized effect algebras, are posets which may have or may have not an EA-MacNeille completion, or cannot be embedded into any complete effect algebra. We give a necessary and sufficient condition for a generalized effect algebra to have an EA-MacNeille completion. Some examples are provided.
NASA Astrophysics Data System (ADS)
Szeto, Alan Ka-Fai
This study explored how undergraduate students in a new problem-centered General Chemistry Laboratory curriculum achieved cognitive growth. The new curriculum had three instructional segments: the highly-structured, semi-structured, and open-ended segments. The pedagogical approaches adopted were expository, guided-inquiry, and open-inquiry styles, respectively. Sixty-seven first-year undergraduate students who enrolled in the course in Spring semester, 2000, at Columbia University and three Ph.D.-level chemistry experts were included in the study. A qualitative approach was used including data collection through "think-aloud" problem solving; however, quantitative data such as test scores were also used. The findings from this study confirmed that chemistry experts possessed sophisticated and domain-specific conceptual knowledge structures; they mobilized and applied conceptual knowledge in conjunction with use of heuristics, tacit knowledge, and experience in authentic problem solving. They validated the new curriculum design in preparing students for inquiry-type of problem solving. For novices, solving of semi-structured before ill-structured problems had a positive effect on the solvers' chance of success in solving the latter type of problems as their abilities to mobilize and apply conceptual knowledge and use effective strategies appeared to be critical for successful problem solving. Students in the new course curriculum had grown cognitively as evidenced by their performance on the Case Study projects and Final Examination. High academic achievers were found to perform well independently while the medium and relatively low academic achievers should benefit from sustained and intensive instruction. It is proposed that ill-structured problems should be used to assess and identify the best from the better students. Finally, it was found that no significant change in students' attitudes had resulted from their curriculum experience. Gender and cognitive style
On a problem of Berenstein-Gay and its generalizations
NASA Astrophysics Data System (ADS)
Volchkov, Valerii V.; Volchkov, Vitaly V.
2010-09-01
We obtain a solution of the Berenstein-Gay problem on the local analogue of spectral analysis on Riemannian symmetric spaces X of rank 1. The proof is based on constructing transmutation maps connected with eigenfunction expansions of the Laplace-Beltrami operator on X.
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. PMID:9726194
The Nonlinear Stokes Problem with General Potentials Having Superquadratic Growth
NASA Astrophysics Data System (ADS)
Breit, Dominic; Fuchs, Martin
2011-09-01
We discuss partial regularity results concerning local minimizers {u : mathbb{R}^3 supset Ω rightarrow mathbb{R}^3} of variational integrals of the form intlimits_{Ω}left\\{h(|\\varepsilon(w)|) - f \\cdot wright\\} dx defined on appropriate classes of solenoidal fields, where h is a N-function of rather general type. As a byproduct we obtain a theorem on partial C 1-regularity for weak solutions of certain non-uniformly elliptic Stokes-type systems modelling generalized Newtonian fluids.
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.
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.
General Systems Theory Approaches to Organizations: Some Problems in Application
ERIC Educational Resources Information Center
Peery, Newman S., Jr.
1975-01-01
Considers the limitations of General Systems Theory (GST) as a major paradigm within administrative theory and concludes that most systems formulations overemphasize growth and show little appreciation for intraorganizational conflict, diversity of values, and political action within organizations. Suggests that these limitations are mainly due to…
NASA Technical Reports Server (NTRS)
Rosen, Bruce S.
1991-01-01
An upwind three-dimensional volume Navier-Stokes code is modified to facilitate modeling of complex geometries and flow fields represented by proposed National Aerospace Plane concepts. Code enhancements include an equilibrium air model, a generalized equilibrium gas model and several schemes to simplify treatment of complex geometric configurations. The code is also restructured for inclusion of an arbitrary number of independent and dependent variables. This latter capability is intended for eventual use to incorporate nonequilibrium/chemistry gas models, more sophisticated turbulence and transition models, or other physical phenomena which will require inclusion of additional variables and/or governing equations. Comparisons of computed results with experimental data and results obtained using other methods are presented for code validation purposes. Good correlation is obtained for all of the test cases considered, indicating the success of the current effort.
Handling Vacuum Regions in a Hybrid Plasma Solver
NASA Astrophysics Data System (ADS)
Holmström, M.
2013-04-01
In a hybrid plasma solver (particle ions, fluid mass-less electrons) regions of vacuum, or very low charge density, can cause problems since the evaluation of the electric field involves division by charge density. This causes large electric fields in low density regions that can lead to numerical instabilities. Here we propose a self consistent handling of vacuum regions for hybrid solvers. Vacuum regions can be considered having infinite resistivity, and in this limit Faraday's law approaches a magnetic diffusion equation. We describe an algorithm that solves such a diffusion equation in regions with charge density below a threshold value. We also present an implementation of this algorithm in a hybrid plasma solver, and an application to the interaction between the Moon and the solar wind. We also discuss the implementation of hyperresistivity for smoothing the electric field in a PIC solver.
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.
Casimir problem of spherical dielectrics: numerical evaluation for general permittivities.
Brevik, I; Aarseth, J B; Høye, J S
2002-08-01
The Casimir mutual free energy F for a system of two dielectric concentric nonmagnetic spherical bodies is calculated, at arbitrary temperatures. The present paper is a continuation of an earlier investigation [Phys. Rev. E 63, 051101 (2001)], in which F was evaluated in full only for the case of ideal metals (refractive index n= infinity ). Here, analogous results are presented for dielectrics, for some chosen values of n. Our basic calculational method stems from quantum statistical mechanics. The Debye expansions for the Riccati-Bessel functions when carried out to a high order are found to be very useful in practice (thereby overflow/underflow problems are easily avoided), and also to give accurate results even for the lowest values of l down to l=1. Another virtue of the Debye expansions is that the limiting case of metals becomes quite amenable to an analytical treatment in spherical geometry. We first discuss the zero-frequency TE mode problem from a mathematical viewpoint and then, as a physical input, invoke the actual dispersion relations. The result of our analysis, based upon the adoption of the Drude dispersion relation at low frequencies, is that the zero-frequency TE mode does not contribute for a real metal. Accordingly, F turns out in this case to be only one-half of the conventional value at high temperatures. The applicability of the Drude model in this context has, however, been questioned recently, and we do not aim at a complete discussion of this issue here. Existing experiments are low-temperature experiments, and are so far not accurate enough to distinguish between the different predictions. We also calculate explicitly the contribution from the zero-frequency mode for a dielectric. For a dielectric, this zero-frequency problem is absent. PMID:12241249
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.
Euler solvers for transonic applications
NASA Technical Reports Server (NTRS)
Vanleer, Bram
1989-01-01
The 1980s may well be called the Euler era of applied aerodynamics. Computer codes based on discrete approximations of the Euler equations are now routinely used to obtain solutions of transonic flow problems in which the effects of entropy and vorticity production are significant. Such codes can even predict separation from a sharp edge, owing to the inclusion of artificial dissipation, intended to lend numerical stability to the calculation but at the same time enforcing the Kutta condition. One effect not correctly predictable by Euler codes is the separation from a smooth surface, and neither is viscous drag; for these some form of the Navier-Stokes equation is needed. It, therefore, comes as no surprise to observe that the Navier-Stokes has already begun before Euler solutions were fully exploited. Moreover, most numerical developments for the Euler equations are now constrained by the requirement that the techniques introduced, notably artificial dissipation, must not interfere with the new physics added when going from an Euler to a full Navier-Stokes approximation. In order to appreciate the contributions of Euler solvers to the understanding of transonic aerodynamics, it is useful to review the components of these computational tools. Space discretization, time- or pseudo-time marching and boundary procedures, the essential constituents are discussed. The subject of grid generation and grid adaptation to the solution are touched upon only where relevant. A list of unanswered questions and an outlook for the future are covered.
NASA Astrophysics Data System (ADS)
Gasymov, E. A.; Guseinova, A. O.; Gasanova, U. N.
2016-07-01
One of the methods for solving mixed problems is the classical separation of variables (the Fourier method). If the boundary conditions of the mixed problem are irregular, this method, generally speaking, is not applicable. In the present paper, a generalized separation of variables and a way of application of this method to solving some mixed problems with irregular boundary conditions are proposed. Analytical representation of the solution to this irregular mixed problem is obtained.
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.
General approach to the problem of disruption forces in tokamaks
NASA Astrophysics Data System (ADS)
Pustovitov, V. D.
2015-09-01
An approach for calculating the force on the vessel wall during plasma disruptions in tokamaks is proposed. It is mainly based on the Maxwell equations and, therefore, is general. Another essential element is the integral force balance on the plasma that strongly constrains the possible solutions. The derived expressions are valid at any disruption scenario and finally give the net forces in terms of the magnetic perturbations behind the wall. The result can be used with magnetic measurements alone. It shows that the geometrical inhomogeneity of the wall and its resistivity are the key factors determining the direction and amplitude of the force.
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.
MILAMIN 2 - Fast MATLAB FEM solver
NASA Astrophysics Data System (ADS)
Dabrowski, Marcin; Krotkiewski, Marcin; Schmid, Daniel W.
2013-04-01
MILAMIN is a free and efficient MATLAB-based two-dimensional FEM solver utilizing unstructured meshes [Dabrowski et al., G-cubed (2008)]. The code consists of steady-state thermal diffusion and incompressible Stokes flow solvers implemented in approximately 200 lines of native MATLAB code. The brevity makes the code easily customizable. An important quality of MILAMIN is speed - it can handle millions of nodes within minutes on one CPU core of a standard desktop computer, and is faster than many commercial solutions. The new MILAMIN 2 allows three-dimensional modeling. It is designed as a set of functional modules that can be used as building blocks for efficient FEM simulations using MATLAB. The utilities are largely implemented as native MATLAB functions. For performance critical parts we use MUTILS - a suite of compiled MEX functions optimized for shared memory multi-core computers. The most important features of MILAMIN 2 are: 1. Modular approach to defining, tracking, and discretizing the geometry of the model 2. Interfaces to external mesh generators (e.g., Triangle, Fade2d, T3D) and mesh utilities (e.g., element type conversion, fast point location, boundary extraction) 3. Efficient computation of the stiffness matrix for a wide range of element types, anisotropic materials and three-dimensional problems 4. Fast global matrix assembly using a dedicated MEX function 5. Automatic integration rules 6. Flexible prescription (spatial, temporal, and field functions) and efficient application of Dirichlet, Neuman, and periodic boundary conditions 7. Treatment of transient and non-linear problems 8. Various iterative and multi-level solution strategies 9. Post-processing tools (e.g., numerical integration) 10. Visualization primitives using MATLAB, and VTK export functions We provide a large number of examples that show how to implement a custom FEM solver using the MILAMIN 2 framework. The examples are MATLAB scripts of increasing complexity that address a given
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
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.
[Intestinal helminthiasis--general practice problem of the gastroenterologist].
Volkheimer, G
1996-09-01
In case of nonspecific, not constantly occurring abdominal symptoms the investigator should be aware of invermination, especially when immigrants or tourists returning from far regions complain about diarrheal tendency, stomach ache, nausea or hepatic and biliary symptoms. Intestinal helminthism is spread all over the world. Some of these diseases are limited to warm regions, but they are more and more often seen in our gastroenterological outpatient departments. Nematodes are found most frequently, with a predominance of Ascaris, Trichuris, and Enterobius. But Ancylostoma and Strongyloides are not seldom, too. Concerning Cestodes, Taenia and Vampirolepis are predominant. Trematodes = Fasciola, Echinostoma, Schistosoma are less frequent. Larva migrans, Acanthocephala and Dipylidium sometimes cause considerable diagnostive problems. Classification of macroscopic and microscopic findings is decisive for the therapeutic strategy. For nematodiasis Mebendazole (Vermox, Surfont), Pyrantelembonate (Helmex), Pyrviniumembonate (Molevac, Pyrcon) are effective. Albendazole (Eskazole) is approved for strongyloidiasis. For cestodiasis Niclosamid (Yomesan) and Praziquantel (Cesol) are suited. Higher doses of Praziquantel (Biltricide) are recommended for trematodiasis. During pregnancy and lactation period absorbable anthelmintics have to be avoided. PMID:8975489
Using native plants as problem-solvers
Harper-Lore, B.L.
1996-11-01
The Federal Highway administration encourages state highway agencies to use native plants in erosion control, revegetation, and landscaping solutions. This paper explains both policy reasons and technical reasons for the use of native plants. How native species can be used is shown through a roadside case study. Other applications of native plant use will be explained through a plant community approach. 5 refs., 2 figs.
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…
The Social Problem Solver for Designing Change.
ERIC Educational Resources Information Center
Slawski, Carl
The aim of this paper is to summarize and tentatively synthesize a number of theories, typologies, and statements about systems and procedures for planned change in small groups, large organizations, and whole societies. Concepts are brought together from psychology, applied sociology, and business management, as well as diplomatic negotiation at…
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…
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.
Metcalfe, D. H. H.
1978-01-01
A short feasibility study to investigate the recognition rate and precision of family problems by general practitioners is described. The need for such work in preparing a taxonomy of family and social problems, and the difficulties involved are discussed. Further support by general practitioners is invited. PMID:553169
NASA Technical Reports Server (NTRS)
Ward, R. C.
1974-01-01
Backward error analyses of the application of Householder transformations to both the standard and the generalized eigenvalue problems are presented. The analysis for the standard eigenvalue problem determines the error from the application of an exact similarity transformation, and the analysis for the generalized eigenvalue problem determines the error from the application of an exact equivalence transformation. Bounds for the norms of the resulting perturbation matrices are presented and compared with existing bounds when known.
An amoeboid algorithm for solving linear transportation problem
NASA Astrophysics Data System (ADS)
Gao, Cai; Yan, Chao; Zhang, Zili; Hu, Yong; Mahadevan, Sankaran; Deng, Yong
2014-03-01
Transportation Problem (TP) is one of the basic operational research problems, which plays an important role in many practical applications. In this paper, a bio-inspired mathematical model is proposed to handle the Linear Transportation Problem (LTP) in directed networks by modifying the original amoeba model Physarum Solver. Several examples are used to prove that the provided model can effectively solve Balanced Transportation Problem (BTP), Unbalanced Transportation Problem (UTP), especially the Generalized Transportation Problem (GTP), in a nondiscrete way.
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.
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
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…
User documentation for PVODE, an ODE solver for parallel computers
Hindmarsh, A.C., LLNL
1998-05-01
PVODE is a general purpose ordinary differential equation (ODE) solver for stiff and nonstiff ODES It is based on CVODE [5] [6], which is written in ANSI- standard C PVODE uses MPI (Message-Passing Interface) [8] and a revised version of the vector module in CVODE to achieve parallelism and portability PVODE is intended for the SPMD (Single Program Multiple Data) environment with distributed memory, in which all vectors are identically distributed across processors In particular, the vector module is designed to help the user assign a contiguous segment of a given vector to each of the processors for parallel computation The idea is for each processor to solve a certain fixed subset of the ODES To better understand PVODE, we first need to understand CVODE and its historical background The ODE solver CVODE, which was written by Cohen and Hindmarsh, combines features of two earlier Fortran codes, VODE [l] and VODPK [3] Those two codes were written by Brown, Byrne, and Hindmarsh. Both use variable-coefficient multi-step integration methods, and address both stiff and nonstiff systems (Stiffness is defined as the presence of one or more very small damping time constants ) VODE uses direct linear algebraic techniques to solve the underlying banded or dense linear systems of equations in conjunction with a modified Newton method in the stiff ODE case On the other hand, VODPK uses a preconditioned Krylov iterative method [2] to solve the underlying linear system User-supplied preconditioners directly address the dominant source of stiffness Consequently, CVODE implements both the direct and iterative methods Currently, with regard to the nonlinear and linear system solution, PVODE has three method options available. functional iteration, Newton iteration with a diagonal approximate Jacobian, and Newton iteration with the iterative method SPGMR (Scaled Preconditioned Generalized Minimal Residual method) Both CVODE and PVODE are written in such a way that other linear
Sivertsen, Børge; Nordhus, Inger H; Bjorvatn, Bjørn; Pallesen, Ståle
2010-03-01
The aim of the current national survey of all general practitioners (GPs) practising in Norway was to explore assessment, treatment practice and perceived efficacy of treatment of sleep problems in general practice. A short questionnaire, including self-report measures of the frequency and routines of treatment and assessment of sleep problems, was sent to all 4049 GPs in Norway, of whom 1465 (36.7%) provided valid responses. The prevalence of sleep problems among patients in general practice was estimated to be 11.2%, of which almost two-thirds were believed to be caused by a medical condition. Anamnestic information and blood tests were the most common assessment of sleep problems, whereas GPs rarely referred patients to all-night polysomnographic recording. Sleep hygiene advices were the most commonly used treatment strategy, whereas hypnotics were believed to have the best short-term efficacy. Antidepressives were considered to be the best option for long-term management of sleep problems. About one-third of the patients were prescribed benzodiazepines or 'Z-drugs' for more than 6 months. This study demonstrates that sleep problems are recognized by GPs, but despite evidence that non-pharmacological treatment is superior in the long-term management of insomnia, the current study shows that hypnotics are still considered by GPs to be the most successful treatment. PMID:19732316
A multiple right hand side iterative solver for history matching
Killough, J.E.; Sharma, Y.; Dupuy, A.; Bissell, R.; Wallis, J.
1995-12-31
History matching of oil and gas reservoirs can be accelerated by directly calculating the gradients of observed quantities (e.g., well pressure) with respect to the adjustable reserve parameters (e.g., permeability). This leads to a set of linear equations which add a significant overhead to the full simulation run without gradients. Direct Gauss elimination solvers can be used to address this problem by performing the factorization of the matrix only once and then reusing the factor matrix for the solution of the multiple right hand sides. This is a limited technique, however. Experience has shown that problems with greater than few thousand cells may not be practical for direct solvers because of computation time and memory limitations. This paper discusses the implementation of a multiple right hand side iterative linear equation solver (MRHS) for a system of adjoint equations to significantly enhance the performance of a gradient simulator.
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
Barlow, D H; Brockie, J A; Rees, C M
1991-01-01
OBJECTIVE--To investigate the nature of work related to the menopause in general practice. DESIGN--Questionnaire study over six months among general practitioners after each consultation with a woman aged 40-69 at which issues related to the climacteric had been discussed. SETTING--9 General practices in the Oxford area. SUBJECTS--416 Women who had 572 consultations. MAIN OUTCOME MEASURES--Age, menopausal state, and first or subsequent consultation. Symptoms were classified together with the treatment and the outcome of the consultation. RESULTS--The consultation rate varied greatly between practices, the overall rate being 4.4%. There were many premenopausal women and women in their 60s presenting; women with hysterectomies presented more often--36% (37/103) of women with hysterectomies had more than one consultation compared with 26% (38/144) for premenopausal women and 24% (38/155) for postmenopausal women. 409 women had symptoms and 218 were prescribed oestrogen treatment. 156 of the consultations involved discussion and advice only. Only four women were referred to a local specialist clinic. CONCLUSION--There is a low overall use of hormone replacement therapy in the general postmenopausal population despite the recent media coverage of its benefits in the prevention of osteoporosis and subsequent fractures. PMID:1998795
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.
A GPU-accelerated flow solver for incompressible two-phase fluid flows
NASA Astrophysics Data System (ADS)
Codyer, Stephen; Raessi, Mehdi; Khanna, Gaurav
2011-11-01
We present a numerical solver for incompressible, immiscible, two-phase fluid flows that is accelerated by using Graphics Processing Units (GPUs). The Navier-Stokes equations are solved by the projection method, which involves solving a pressure Poisson problem at each time step. A second-order discretization of the Poisson problem leads to a sparse matrix with five and seven diagonals for two- and three-dimensional simulations, respectively. Running a serial linear algebra solver on a single CPU can take 50-99.9% of the total simulation time to solve the above system for pressure. To remove this bottleneck, we utilized the large parallelization capabilities of GPUs; we developed a linear algebra solver based on the conjugate gradient iterative method (CGIM) by using CUDA 4.0 libraries and compared its performance with CUSP, an open-source, GPU library for linear algebra. Compared to running the CGIM solver on a single CPU core, for a 2D case, our GPU solver yields speedups of up to 88x in solver time and 81x overall time on a single GPU card. In 3D cases, the speedups are up to 81x (solver) and 15x (overall). Speedup is faster at higher grid resolutions and our GPU solver outperforms CUSP. Current work examines the acceleration versus a parallel CGIM CPU solver.
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.
A block iterative LU solver for weakly coupled linear systems. [in fluid dynamics equations
NASA Technical Reports Server (NTRS)
Cooke, C. H.
1977-01-01
A hybrid technique, called the block iterative LU solver, is proposed for solving the linear equations resulting from a finite element numerical analysis of certain fluid dynamics problems where the equations are weakly coupled between distinct sets of variables. Either the block Jacobi iterative method or the block Gauss-Seidel iterative solver is combined with LU decomposition.
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.
Cederlöf, Martin; Pettersson, Erik; Sariaslan, Amir; Larsson, Henrik; Östberg, Per; Kelleher, Ian; Långström, Niklas; Gumpert, Clara Hellner; Lundström, Sebastian; Lichtenstein, Paul
2016-03-01
Studies suggest associations between childhood autistic traits and adolescent psychotic experiences. However, recent research suggests that a general neuropsychiatric problems factor predicts adverse outcomes better than specific diagnostic entities. To examine if the alleged association between autistic traits and psychotic experiences could rather be explained by a general neuropsychiatric problems factor comprising symptoms of ADHD, tic disorder, developmental coordination disorder, and learning disorder, we conducted a prospective cohort study based on the Child and Adolescent Twin Study in Sweden. In addition, we examined the genetic and environmental influences on the associations. A total of 9,282 twins with data on childhood autistic traits and other neuropsychiatric problems, and follow-up data on psychotic experiences at ages 15 and/or 18 years were included. First, psychotic experiences were regressed on autistic traits and second, the general neuropsychiatric problems factor was added to the model. Auditory hallucinations were analyzed separately from the other psychotic experiences. Finally, twin analyses were employed to disentangle genetic from environmental influences in the observed associations. Replicating prior research, significant associations were found between autistic traits in childhood and auditory hallucinations at ages 15 and 18. However, after controlling for the general neuropsychiatric problems factor, the associations between autistic traits and auditory hallucinations disappeared, whereas the association between the general neuropsychiatric problems factor and auditory hallucinations persisted after controlling for autistic traits. Twin analyses revealed that the association between the general neuropsychiatric problems factor and auditory hallucinations was driven by shared genetic influences. © 2015 Wiley Periodicals, Inc. PMID:26464122
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.
Shanahan, Lilly; Copeland, William E.; Angold, Adrian; Bondy, Carmen L.; Costello, E. Jane
2014-01-01
Objective We tested whether sleep problems co-occur with, precede, and/or follow common psychiatric disorders during childhood and adolescence. We also clarified the role of comorbidity, and tested for specificity of associations among sleep problems and psychiatric disorders. Method Data came from the Great Smoky Mountains Study, a representative population sample of 1,420 children, assessed 4 to 7 times per person between ages 9 and 16 for major DSM-IV disorders and sleep problems. Sleep-related symptoms were removed from diagnostic criteria when applicable. Results Sleep problems during childhood and adolescence were common, with restless sleep and difficulty falling asleep being the most common symptoms. Cross-sectional analyses showed that sleep problems co-occurred with many psychiatric disorders. Longitudinal analyses revealed that sleep problems predicted increases in the prevalence of later generalized anxiety disorder and high generalized anxiety disorder/depression symptoms, and oppositional defiant disorder. In turn, generalized anxiety disorder and/or depression and oppositional defiant disorder predicted increases in sleep problems over time. Conclusions Sleep problems both predict and are predicted by a diagnostic cluster that includes oppositional defiant disorder, generalized anxiety disorder and depression. Screening children for sleep problems could offer promising opportunities for reducing the burden from mental illness during the early life course. PMID:24745954
van den Brink-Muinen, A; de Bakker, D H; Bensing, J M
1994-01-01
AIM. This study set out to examine the degree to which women choose to visit a woman doctor for women's health problems and the determinants of this choice. The differences between women and men doctors with regard to treating women's health problems were also studied. METHOD. Data from the Dutch national survey of general practice were used. All group practices with both women and men general practitioners were selected. Analyses were restricted to consultations among women aged 15-65 years about menstruation, the menopause, vaginal discharge, breast examination and cervical smear tests. RESULts. Given the size of their female practice population, women doctors saw considerably more women with women's health problems than did their male colleagues. Women were more likely to consult a woman general practitioner if she was more available (that is, working longer hours), and younger women were more likely than older women to choose women general practitioners. Sex differences in the treatment of women's health problems were small and mainly related to the verbal part of the consultation: counselling and providing information. The doctors' availability and their certainty about the working diagnosis explained differences in the verbal aspects of consultations. Women general practitioners had longer consultations than their male colleagues mainly because more health problems were presented per consultation. CONCLUSION. In order to increase the possibility of patients choosing women general practitioners, policy should be directed towards the education of more women general practitioners and women general practitioners should be encouraged to work more days a week. PMID:8204333
Some properties of eigenvalues and generalized eigenvectors of one boundary-value problem
NASA Astrophysics Data System (ADS)
Olgar, Hayati; Mukhtarov, Oktay; Aydemir, Kadriye
2016-08-01
We investigate a discontinuous boundary value problem which consists of a Sturm-Liouville equation with piece-wise continuous potential together with eigenparameter-dependent boundary conditions and supplementary transmission conditions. We establish some spectral properties of the considered problem. In particular it is shown that the generalized eigen-functions form a Riesz basis of the adequate Hilbert space.
ERIC Educational Resources Information Center
Merriweather, Michelle; Tharp, Marcia L.
1999-01-01
Focuses on changes in attitude toward mathematics and calculator use and changes in how general mathematics students naturalistically solve algebraic problems. Uses a survey to determine whether a student is rule-based. Concludes that the rule-based students used an equation to solve the algebraic word problem whereas the non-rule-based students…
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.
An Exact Riemann Solver for a Granular Mixture Model with Multiple Solid Components
NASA Astrophysics Data System (ADS)
Crochet, Michael; Gonthier, Keith
2013-06-01
The solution of the two-phase Riemann problem is an essential component of finite-volume numerical methods applied to hyperbolic systems of multiphase model equations. These are typically used to study deflagration-to-detonation transition in energetic materials, and predict flow field structures associated with the dynamic compaction of gas-granular solid mixtures. A widely-used two-phase model has been extended recently to include an arbitrary number of solid components, which can be used to analyze the thermomechanical behavior of metallized explosives and mixtures containing multiple solid grain sizes. Although a solution to the two-phase Riemann problem has been formulated for gamma-law equations of state, there is currently no available solution for the N-phase analogue in the literature. Here, an extension of the exact two-phase solution to systems containing multiple solid phases is developed, where each phase is governed by general, convex equations of state. The resulting Riemann solver can be used in the verification of existing numerical schemes, and also serve as a framework for the future construction of upwind, Godunov-based numerical methods. A general overview of the solver methodology is given, and three-phase example problems are considered. This work was supported by NSF-IGERT on Computational Fluid Dynamics at Louisiana State University, grant number DGE-0504507.
Laser engine simulation using pressure based Navier-Stokes solver
NASA Astrophysics Data System (ADS)
Youssef, Hazim Saad
1994-03-01
Analysis of the flow field in a laser engine represents a difficult computational problem involving combinations of complex physical and gas-dynamical processes. Following a brief discussion of these processes a calculation procedure using primitive variables formulation on a nonstaggered grid system is introduced. Based on this procedure, a pressure based Navier-Stokes solver (PBNS) is developed using a generalized curvilinear coordinate system. The solver is first tested in application to a subsonic compressible flow over an insulated flat plate and to a flow in an axisymmetric converging-diverging nozzle. Next, the PBNS code is used to analyze the flowfield and performance of a laser thruster. The physical/numerical model includes the geometric ray tracing for the laser beam, beam power absorption, plasma radiation losses, and plasma thermophysical and optical properties. Equilibrium hydrogen is used as a flowing gas and its properties are calculated using the Hydrogen Properties Calculation (HPC) based on the methods of statistical thermodynamics. Two thrustor configurations, two laser types (CO2 and iodide), various laser power levels, and various injection conditions are tested. The results of these tests include the temperature, pressure, velocity, and Mach number contours, as well as tables of the laser beam power absorbed, radiation losses to the thrustor walls, thrust level, and specific impulse. The maximum specific impulse obtained in these tests is 1537 sec for a CO2 laser thruster and 827 sec for an iodide laser thruster. Up to 100% power absorption can be achieved; however, radiation losses from the hot plasma are quite high disallowing a full conversion of the absorbed power into the thermal energy of the propellant. The PBNS code can be used to study the effects of various design parameters on the performance of a laser thruster and provide guidelines for the preliminary design of a laser engine.
Fast Euler solver for transonic airfoils. I - Theory. II - Applications
NASA Technical Reports Server (NTRS)
Dadone, Andrea; Moretti, Gino
1988-01-01
Equations written in terms of generalized Riemann variables are presently integrated by inverting six bidiagonal matrices and two tridiagonal matrices, using an implicit Euler solver that is based on the lambda-formulation. The solution is found on a C-grid whose boundaries are very close to the airfoil. The fast solver is then applied to the computation of several flowfields on a NACA 0012 airfoil at various Mach number and alpha values, yielding results that are primarily concerned with transonic flows. The effects of grid fineness and boundary distances are analyzed; the code is found to be robust and accurate, as well as fast.
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.
Management of minor medical problems and trauma: general practice or hospital?
Myers, P
1982-01-01
An assessment of the problems for which 1000 consecutive patients attended an accident and emergency department of a district general hospital showed that 54.2% could have been treated by general practitioner. Amongst 150 patients attending hospital for minor problems between the hours of 09:00 and 19:00 on weekdays, the main reason given for not going to a GP was their impression that only in hospital could the required treatment be provided. A postal survey of 50 GPs found that they tended to avoid regularly handling certain specified minor problems which often present to hospital. The current trend away from the community management of such problems is discussed. It is suggested that improving patient education and GPs' incentives, while decreasing list sizes and expanding the primary care team, may encourage the management by GPs of trivial trauma and minor medical problems. PMID:7143339
Time-domain Raman analytical forward solvers.
Martelli, Fabrizio; Binzoni, Tiziano; Sekar, Sanathana Konugolu Venkata; Farina, Andrea; Cavalieri, Stefano; Pifferi, Antonio
2016-09-01
A set of time-domain analytical forward solvers for Raman signals detected from homogeneous diffusive media is presented. The time-domain solvers have been developed for two geometries: the parallelepiped and the finite cylinder. The potential presence of a background fluorescence emission, contaminating the Raman signal, has also been taken into account. All the solvers have been obtained as solutions of the time dependent diffusion equation. The validation of the solvers has been performed by means of comparisons with the results of "gold standard" Monte Carlo simulations. These forward solvers provide an accurate tool to explore the information content encoded in the time-resolved Raman measurements. PMID:27607645
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. PMID:27547676
On code verification of RANS solvers
NASA Astrophysics Data System (ADS)
Eça, L.; Klaij, C. M.; Vaz, G.; Hoekstra, M.; Pereira, F. S.
2016-04-01
This article discusses Code Verification of Reynolds-Averaged Navier Stokes (RANS) solvers that rely on face based finite volume discretizations for volumes of arbitrary shape. The study includes test cases with known analytical solutions (generated with the method of manufactured solutions) corresponding to laminar and turbulent flow, with the latter using eddy-viscosity turbulence models. The procedure to perform Code Verification based on grid refinement studies is discussed and the requirements for its correct application are illustrated in a simple one-dimensional problem. It is shown that geometrically similar grids are recommended for proper Code Verification and so the data should not have scatter making the use of least square fits unnecessary. Results show that it may be advantageous to determine the extrapolated error to cell size/time step zero instead of assuming that it is zero, especially when it is hard to determine the asymptotic order of grid convergence. In the RANS examples, several of the features of the ReFRESCO solver are checked including the effects of the available turbulence models in the convergence properties of the code. It is shown that it is required to account for non-orthogonality effects in the discretization of the diffusion terms and that the turbulence quantities transport equations can deteriorate the order of grid convergence of mean flow quantities.
Using the scalable nonlinear equations solvers package
Gropp, W.D.; McInnes, L.C.; Smith, B.F.
1995-02-01
SNES (Scalable Nonlinear Equations Solvers) is a software package for the numerical solution of large-scale systems of nonlinear equations on both uniprocessors and parallel architectures. SNES also contains a component for the solution of unconstrained minimization problems, called SUMS (Scalable Unconstrained Minimization Solvers). Newton-like methods, which are known for their efficiency and robustness, constitute the core of the package. As part of the multilevel PETSc library, SNES incorporates many features and options from other parts of PETSc. In keeping with the spirit of the PETSc library, the nonlinear solution routines are data-structure-neutral, making them flexible and easily extensible. This users guide contains a detailed description of uniprocessor usage of SNES, with some added comments regarding multiprocessor usage. At this time the parallel version is undergoing refinement and extension, as we work toward a common interface for the uniprocessor and parallel cases. Thus, forthcoming versions of the software will contain additional features, and changes to parallel interface may result at any time. The new parallel version will employ the MPI (Message Passing Interface) standard for interprocessor communication. Since most of these details will be hidden, users will need to perform only minimal message-passing programming.
Performance Models for the Spike Banded Linear System Solver
Manguoglu, Murat; Saied, Faisal; Sameh, Ahmed; Grama, Ananth
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
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
On unstructured grids and solvers
NASA Technical Reports Server (NTRS)
Barth, T. J.
1990-01-01
The fundamentals and the state-of-the-art technology for unstructured grids and solvers are highlighted. Algorithms and techniques pertinent to mesh generation are discussed. It is shown that grid generation and grid manipulation schemes rely on fast multidimensional searching. Flow solution techniques for the Euler equations, which can be derived from the integral form of the equations are discussed. Sample calculations are also provided.
Gulbrandsen, P.; Hjortdahl, P.; Fugelli, P.
1997-01-01
OBJECTIVES: To evaluate general practitioners' knowledge of a range of psychosocial problems among their patients and to explore whether doctors' recognition of psychosocial problems depends on previous general knowledge about the patient or the type of problem or on certain characteristics of the doctor or the patient. DESIGN: Multipractice survey of consecutive adult patients consulting general practitioners. Doctors and patients answered written questions. SETTING: Buskerud county, Norway. SUBJECTS: 1401 adults attending 89 general practitioners during one regular working day in March 1995. MAIN OUTCOME MEASURES: Doctors' knowledge of nine predefined psychosocial problems in patients; these problems were assessed by the patients as affecting their health on the day of consultation; odds ratios for the doctor's recognition of each problem, adjusted for characteristics of patients, doctors, and practices; and the doctor's assessment of previous general knowledge about the patient. RESULTS: Doctors' knowledge of the problems ranged from 53% (108/203) of "stressful working conditions" to 19% (12/63) of a history of "violence or threats." Good previous knowledge of the patient increased the odds for the doctor's recognition of "sorrow," "violence or threats," "substance misuse in close friend or relative," and "difficult conflict with close friend or relative." Age and sex of doctor and patient, patient's educational level and living situation, and location of practice influenced the doctor's awareness. CONCLUSIONS: Variation in the patients' communication abilities, the need for confidence in the doctor-patient relationship before revealing intimate problems, and a tendency for the doctors to be entrapped by their expectations may explain these findings. PMID:9112847
A general optimality criteria algorithm for a class of engineering optimization problems
NASA Astrophysics Data System (ADS)
Belegundu, Ashok D.
2015-05-01
An optimality criteria (OC)-based algorithm for optimization of a general class of nonlinear programming (NLP) problems is presented. The algorithm is only applicable to problems where the objective and constraint functions satisfy certain monotonicity properties. For multiply constrained problems which satisfy these assumptions, the algorithm is attractive compared with existing NLP methods as well as prevalent OC methods, as the latter involve computationally expensive active set and step-size control strategies. The fixed point algorithm presented here is applicable not only to structural optimization problems but also to certain problems as occur in resource allocation and inventory models. Convergence aspects are discussed. The fixed point update or resizing formula is given physical significance, which brings out a strength and trim feature. The number of function evaluations remains independent of the number of variables, allowing the efficient solution of problems with large number of variables.
An automatic ordering method for incomplete factorization iterative solvers
Forsyth, P.A.; Tang, W.P. . Dept. of Computer Science); D'Azevedo, E.F.D. )
1991-01-01
The minimum discarded fill (MDF) ordering strategy for incomplete factorization iterative solvers is developed. MDF ordering is demonstrated for several model son-symmetric problems, as well as a water-flooding simulation which uses an unstructured grid. The model problems show a three to five fold decrease in the number of iterations compared to natural orderings. Greater than twofold improvement was observed for the waterflooding simulation. 26 refs., 7 figs., 3 tabs.
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.
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…
Learning generalization in problem solving by a blue-fronted parrot (Amazona aestiva).
de Mendonça-Furtado, Olívia; Ottoni, Eduardo B
2008-10-01
Pepperberg (The Alex studies: cognitive and communicative abilities of gray parrots. Harvard University Press, Cambridge;1999) showed that some of the complex cognitive capabilities found in primates are also present in psittacine birds. Through the replication of an experiment performed with cotton-top tamarins (Saguinus oedipus oedipus) by Hauser et al. (Anim Behav 57:565-582; 1999), we examined a blue-fronted parrot's (Amazona aestiva) ability to generalize the solution of a particular problem in new but similar cases. Our results show that, at least when it comes to solving this particular problem, our parrot subject exhibited learning generalization capabilities resembling the tamarins'. PMID:18575906
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.
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
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.
Schulze-Halberg, Axel
2010-05-15
We study Green's functions of the generalized Sturm-Liouville problems that are related to each other by Darboux -equivalently, supersymmetrical - transformations. We establish an explicit relation between the corresponding Green's functions and derive a simple formula for their trace. The class of equations considered here includes the conventional Schroedinger equation and generalizations, such as for position-dependent mass and with linearly energy-dependent potential, as well as the stationary Fokker-Planck equation.
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.
[The Dutch College of General Practitioners practice guideline on 'Sexual problems'].
de Jong, Jip; Leusink, Peter; Wiersma, Tjerk
2016-01-01
The Dutch College of General Practitioners practice guideline on 'Sexual problems' describes the diagnostics and management of common sexual problems. An adequate sexual anamnesis is essential in order to obtain a good picture of the patient's symptoms and of any underlying causes. Additional physical or other medical examination is of limited value. The provision of information and advice are central to the treatment of sexual problems. Attention should be paid to the different aspects of sexual functioning: physical, psychological, relational and sociocultural, and to gender differences. In many cases, management is determined by the causal factor, for instance comorbidity, sexual trauma or relational problems. In other cases, a more specific problem is diagnosed, and management is based on this. PMID:27122071
Problem Youths or Problem Solvers? Building Resilience through Peer Helping.
ERIC Educational Resources Information Center
Wasmund, William; Copas, Randy
1994-01-01
Briefly reviews Positive Peer Culture (PPC) program employed in residential treatment centers, group homes, and schools, that focuses explicitly on peer group to create therapeutic community with unified staff and student goals. Presents question-and-answer session with six adolescent male participants in PPC program. (NB)
Linear solvers on multiprocessor machines
Kalogerakis, M.A.
1986-01-01
Two new methods are introduced for the parallel solution of banded linear systems on multiprocessor machines. Moreover, some new techniques are obtained as variations of the two methods that are applicable to special instances of the problem. Comparisons with the best known methods are performed, from which it is concluded that the two methods are superior, while their variations for special instances are, in general, competitive and in some cases best. In the process, some new results on the parallel prefix problem are obtained and a new design for this problem is presented that is suitable for VLSI implementation. Furthermore, a general model is introduced for the analysis and classification of methods that are based on row transformations of matrices. It is seen that most known methods are included in this model. It is demonstrated that this model may be used as a basis for the analysis as well as the generation of important aspects of those methods, such as their arithmetic complexity and interprocessor communication requirements.
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.
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.
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…
NASA Astrophysics Data System (ADS)
Iyer, Bala R.
2016-05-01
Over the last two decades, the search for gravitational waves from coalescing compact binaries by detectors like LIGO and Virgo has crucially required and consequently spurred tremendous progress in the two body problem in general relativity. A broad brush overview of these major developments and the current status of these significant results is presented.
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…
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.
La Pegna, Giovanni Battista; Brighina, Filippo; Saporito, Vincenzo; Aloisio, Antonina; Morreale, Calgero; D'Agati, Alfio
2005-09-01
The continuous care of headache patients, from headache centres to general practice, is a managerial problem that is still unsolved in Italy. In fact, if on the one hand patients do not usually go to headache centres because of poor information, on the other hand, if they do, they do not find their general practitioner (GP) sufficiently prepared to continue the management. In Sicily we have formed a dense network of headache centres that we will try to link on the Internet to deal with the problem of poor patients information and poor specialist consultation. We also have faced the problem of the continuous care, trying to overcome "the difficulties of communication between specialists, GPs and patients" and "the difficulties of GPs in diagnostic work", by simple instruments like the Italian version of ID-Migraine, a simple three-item questionnaire. PMID:16362696
Hybrid General Pattern Search and Simulated Annealing for Industrail Production Planning Problems
NASA Astrophysics Data System (ADS)
Vasant, P.; Barsoum, N.
2010-06-01
In this paper, the hybridization of GPS (General Pattern Search) method and SA (Simulated Annealing) incorporated in the optimization process in order to look for the global optimal solution for the fitness function and decision variables as well as minimum computational CPU time. The real strength of SA approach been tested in this case study problem of industrial production planning. This is due to the great advantage of SA for being easily escaping from trapped in local minima by accepting up-hill move through a probabilistic procedure in the final stages of optimization process. Vasant [1] in his Ph. D thesis has provided 16 different techniques of heuristic and meta-heuristic in solving industrial production problems with non-linear cubic objective functions, eight decision variables and 29 constraints. In this paper, fuzzy technological problems have been solved using hybrid techniques of general pattern search and simulated annealing. The simulated and computational results are compared to other various evolutionary techniques.
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. PMID:26058226
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.
Advances in computational fluid dynamics solvers for modern computing environments
NASA Astrophysics Data System (ADS)
Hertenstein, Daniel; Humphrey, John R.; Paolini, Aaron L.; Kelmelis, Eric J.
2013-05-01
EM Photonics has been investigating the application of massively multicore processors to a key problem area: Computational Fluid Dynamics (CFD). While the capabilities of CFD solvers have continually increased and improved to support features such as moving bodies and adjoint-based mesh adaptation, the software architecture has often lagged behind. This has led to poor scaling as core counts reach the tens of thousands. In the modern High Performance Computing (HPC) world, clusters with hundreds of thousands of cores are becoming the standard. In addition, accelerator devices such as NVIDIA GPUs and Intel Xeon Phi are being installed in many new systems. It is important for CFD solvers to take advantage of the new hardware as the computations involved are well suited for the massively multicore architecture. In our work, we demonstrate that new features in NVIDIA GPUs are able to empower existing CFD solvers by example using AVUS, a CFD solver developed by the Air Force Research Labratory (AFRL) and the Volcanic Ash Advisory Center (VAAC). The effort has resulted in increased performance and scalability without sacrificing accuracy. There are many well-known codes in the CFD space that can benefit from this work, such as FUN3D, OVERFLOW, and TetrUSS. Such codes are widely used in the commercial, government, and defense sectors.
Young, Susan E; Rhee, Soo Hyun; Stallings, Michael C; Corley, Robin P; Hewitt, John K
2006-07-01
Are genetic and environmental risks for adolescent substance use specific to individual substances or general across substance classes? We examined this question in 645 monozygotic twin pairs, 702 dizygotic twin pairs, 429 biological sibling pairs, and 96 adoptive (biologically unrelated) sibling pairs ascertained from community-based samples, and ranging in age from 12 to 18 years. Substance use patterns and symptoms were assessed using structured psychiatric interviews. Biometrical model fitting was carried out using age- and sex-specific thresholds for (a) repeated use and (b) problem use, defined as one or more DSM-IV symptoms of abuse or dependence. We hypothesized that problem use would be more heritable than use in adolescence, and that both genetic and environmental risks underlying tobacco, alcohol, and marijuana use and problem use would be significantly correlated. Results of univariate analyses suggested significant heritable factors for use and problem use for all substances with the exception of alcohol use. Shared environmental factors were important in all cases and special twin environmental factors were significant for tobacco use, tobacco problem use, and alcohol use. Multivariate analyses yielded significant genetic correlations between each of the substances (for both levels studied), and significant shared environmental correlations among use variables only. Our results suggest that tobacco, alcohol, and marijuana problem use are mediated by common genetic influences, but shared environmental influences may be more substance-specific for problem use. PMID:16619135
NASA Astrophysics Data System (ADS)
Pelanti, Marica; Bouchut, François; 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 Gallouët and Masella [T. Gallouët, J.-M. Masella, Un schéma de Godunov approché C.R. Acad. Sci. Paris, Série I, 323 (1996) 77-84]. The relaxation interpretation allows establishing positivity conditions for this VFRoe method.
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.
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.
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.
A General Approach to Time Periodic Incompressible Viscous Fluid Flow Problems
NASA Astrophysics Data System (ADS)
Geissert, Matthias; Hieber, Matthias; Nguyen, Thieu Huy
2016-06-01
This article develops a general approach to time periodic incompressible fluid flow problems and semilinear evolution equations. It yields, on the one hand, a unified approach to various classical problems in incompressible fluid flow and, on the other hand, gives new results for periodic solutions to the Navier-Stokes-Oseen flow, the Navier-Stokes flow past rotating obstacles, and, in the geophysical setting, for Ornstein-Uhlenbeck and various diffusion equations with rough coefficients. The method is based on a combination of interpolation and topological arguments, as well as on the smoothing properties of the linearized equation.
A Thermo-mechanical Shock Problem for Generalized Theory of Thermoviscoelasticity
NASA Astrophysics Data System (ADS)
Elhagary, M. A.
2013-01-01
A one-dimensional problem for a viscoelastic half space is considered in the context of the generalized theory of thermoviscoelasticity with one relaxation time. The bounding plane is acted upon by a combination of thermal and mechanical shock acting for short times. The Laplace transform technique is used to solve the problem. The solution in the transformed domain is obtained by a direct approach. The inverse transforms are obtained in an approximate analytical manner using asymptotic expansions valid for small values of time. The temperature, displacement, and stress are computed and represented graphically.
Koyanagi, Ai; Stickley, Andrew
2015-01-01
Study Objectives: To assess the prevalence of sleep problems and their association with psychotic symptoms using a global database. Design: Community-based cross-sectional study. Setting: Data were analyzed from the World Health Organization's World Health Survey (WHS), a population-based survey conducted in 70 countries between 2002 and 2004. Patients or Participants: 261,547 individuals aged ≥ 18 years from 56 countries. Interventions: N/A. Measurements and Results: The presence of psychotic symptoms in the past 12 months was established using 4 questions pertaining to positive symptoms from the psychosis screening module of the Composite International Diagnostic Interview. Sleep problems referred to severe or extreme sleep problems in the past 30 days. Multivariable logistic regression was used to estimate the associations. The overall prevalence of sleep problems was 7.6% and ranged from 1.6% (China) to 18.6% (Morocco). Sleep problems were associated with significantly higher odds for at least one psychotic symptom in the vast majority of countries. In the pooled sample, after adjusting for demographic factors, alcohol consumption, smoking, and chronic medical conditions, having sleep problems resulted in an odds ratio (OR) for at least one psychotic symptom of 2.41 (95% confidence interval [CI] 2.18–2.65). This OR was 1.59 (1.40–1.81) when further adjusted for anxiety and depression. Conclusions: A strong association between sleep problems and psychotic symptoms was observed globally. These results have clinical implications and serve as a basis for future studies to elucidate the causal association between psychotic symptoms and sleep problems. Citation: Koyanagi A, Stickley A. The association between sleep problems and psychotic symptoms in the general population: a global perspective. SLEEP 2015;38(12):1875–1885. PMID:26085291
NASA Astrophysics Data System (ADS)
Piero, Gianpietro Del
2016-03-01
The existence theorem of Fichera for the minimum problem of semicoercive quadratic functions in a Hilbert space is extended to a more general class of convex and lower semicontinuous functions. For unbounded domains, the behavior at infinity is controlled by a lemma which states that every unbounded sequence with bounded energy has a subsequence whose directions converge to a direction of recession of the function. Thanks to this result, semicoerciveness plus the assumption that the effective domain is boundedly generated, that is, admits a Motzkin decomposition, become sufficient conditions for existence. In particular, for functions with a smooth quadratic part, a generalization of the existence condition given by Fichera's theorem is proved.
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.
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.
KLU2 Direct Linear Solver Package
Energy Science and Technology Software Center (ESTSC)
2012-01-04
KLU2 is a direct sparse solver for solving unsymmetric linear systems. It is related to the existing KLU solver, (in Amesos package and also as a stand-alone package from University of Florida) but provides template support for scalar and ordinal types. It uses a left looking LU factorization method.
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
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).
On relative periodic solutions of the planar general three-body problem
NASA Technical Reports Server (NTRS)
Broucke, R.
1975-01-01
We describe two relatively simple reductions to order 6 for the planar general three-body problem. We also show that this reduction leads to the distinction between two types of periodic solutions: absolute or relative periodic solutions. An algorithm for obtaining relative periodic solutions using heliocentric coordinates is then described. It is concluded from the periodicity conditions that relative periodic solutions must form families with a single parameter. Finally, two such families have been obtained numerically and are described in some detail.
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.
Detwiler, Russell L; Mehl, Steffen; Rajaram, Harihar; Cheung, Wendy 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. PMID:12019641
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.
Performance issues for iterative solvers in device simulation
NASA Technical Reports Server (NTRS)
Fan, Qing; Forsyth, P. A.; Mcmacken, J. R. F.; Tang, Wei-Pai
1994-01-01
Due to memory limitations, iterative methods have become the method of choice for large scale semiconductor device simulation. However, it is well known that these methods still suffer from reliability problems. The linear systems which appear in numerical simulation of semiconductor devices are notoriously ill-conditioned. In order to produce robust algorithms for practical problems, careful attention must be given to many implementation issues. This paper concentrates on strategies for developing robust preconditioners. In addition, effective data structures and convergence check issues are also discussed. These algorithms are compared with a standard direct sparse matrix solver on a variety of problems.
Kim, Hyoun S; Salmon, Melissa; Wohl, Michael J A; Young, Matthew
2016-04-01
The current research examined whether alcohol consumption exacerbates suicidal ideations among gamblers in the general population. While prior research suggests problem gambling severity and excessive alcohol consumption are unique predictors of suicidal behaviors, the extant literature as almost exclusively focused on gamblers in treatment. This represents a significant gap in the literature as less than 10% of gamblers seek treatment. Furthermore, gamblers in treatment are not representative of gamblers in the general population, precluding a simple generalization of research findings. We address this gap using data obtained from the Canadian Community Health Survey (Cycle 4.1)--a cross-sectional national survey that assesses health-related information among the Canadian population. To this end, we conducted a moderation analysis with problem gambling severity as the independent variable, weekly alcohol consumption as the moderator variable and suicidal ideations (in the past 12 months) as the dependent variable. The results found that alcohol consumption alone did not reliably predict suicidal ideation among gamblers who did not gamble problematically. However, as predicted, the odds of suicidal ideation were greatest among problem gamblers who frequently consumed alcohol. Thus, it may behoove policy makers to re-visit the availability of alcohol in gambling venues. Moreover, responsible gambling-oriented education initiatives may be advanced by informing gamblers about the increased risk of suicidal ideations when problematic gambling is combined with frequent alcohol consumption. PMID:26790140
NASA Astrophysics Data System (ADS)
Wang, S.; De Hoop, M. V.; Xia, J.; Li, X.
2011-12-01
We consider the modeling of elastic seismic wave propagation on a rectangular domain via the discretization and solution of the inhomogeneous coupled Helmholtz equation in 3D, by exploiting a parallel multifrontal sparse direct solver equipped with Hierarchically Semi-Separable (HSS) structure to reduce the computational complexity and storage. In particular, we are concerned with solving this equation on a large domain, for a large number of different forcing terms in the context of seismic problems in general, and modeling in particular. We resort to a parsimonious mixed grid finite differences scheme for discretizing the Helmholtz operator and Perfect Matched Layer boundaries, resulting in a non-Hermitian matrix. We make use of a nested dissection based domain decomposition, and introduce an approximate direct solver by developing a parallel HSS matrix compression, factorization, and solution approach. We cast our massive parallelization in the framework of the multifrontal method. The assembly tree is partitioned into local trees and a global tree. The local trees are eliminated independently in each processor, while the global tree is eliminated through massive communication. The solver for the inhomogeneous equation is a parallel hybrid between multifrontal and HSS structure. The computational complexity associated with the factorization is almost linear with the size of the Helmholtz matrix. Our numerical approach can be compared with the spectral element method in 3D seismic applications.
Improving Resource-Unaware SAT Solvers
NASA Astrophysics Data System (ADS)
Hölldobler, Steffen; Manthey, Norbert; Saptawijaya, Ari
The paper discusses cache utilization in state-of-the-art SAT solvers. The aim of the study is to show how a resource-unaware SAT solver can be improved by utilizing the cache sensibly. The analysis is performed on a CDCL-based SAT solver using a subset of the industrial SAT Competition 2009 benchmark. For the analysis, the total cycles, the resource stall cycles, the L2 cache hits and the L2 cache misses are traced using sample based profiling. Based on the analysis, several techniques - some of which have not been used in SAT solvers so far - are proposed resulting in a combined speedup up to 83% without affecting the search path of the solver. The average speedup on the benchmark is 60%. The new techniques are also applied to MiniSAT2.0 improving its runtime by 20% on average.
Implicit solvers for unstructured meshes
NASA Technical Reports Server (NTRS)
Venkatakrishnan, V.; Mavriplis, Dimitri J.
1991-01-01
Implicit methods were developed and tested for unstructured mesh computations. The approximate system which arises from the Newton linearization of the nonlinear evolution operator is solved by using the preconditioned GMRES (Generalized Minimum Residual) technique. Three different preconditioners were studied, namely, the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over relaxation (SSOR). The preconditioners were optimized to have good vectorization properties. SSOR and ILU were also studied as iterative schemes. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also studied. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.
Artificial equilibrium points for a generalized sail in the elliptic restricted three-body problem
NASA Astrophysics Data System (ADS)
Aliasi, Generoso; Mengali, Giovanni; Quarta, Alessandro A.
2012-10-01
Different types of propulsion systems with continuous and purely radial thrust, whose modulus depends on the distance from a massive body, may be conveniently described within a single mathematical model by means of the concept of generalized sail. This paper discusses the existence and stability of artificial equilibrium points maintained by a generalized sail within an elliptic restricted three-body problem. Similar to the classical case in the absence of thrust, a generalized sail guarantees the existence of equilibrium points belonging only to the orbital plane of the two primaries. The geometrical loci of existing artificial equilibrium points are shown to coincide with those obtained for the circular three body problem when a non-uniformly rotating and pulsating coordinate system is chosen to describe the spacecraft motion. However, the generalized sail has to provide a periodically variable acceleration to maintain a given artificial equilibrium point. A linear stability analysis of the artificial equilibrium points is provided by means of the Floquet theory.
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
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.
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.
Domain decomposition solvers for PDEs : some basics, practical tools, and new developments.
Dohrmann, Clark R.
2010-11-01
The first part of this talk provides a basic introduction to the building blocks of domain decomposition solvers. Specific details are given for both the classical overlapping Schwarz (OS) algorithm and a recent iterative substructuring (IS) approach called balancing domain decomposition by constraints (BDDC). A more recent hybrid OS-IS approach is also described. The success of domain decomposition solvers depends critically on the coarse space. Similarities and differences between the coarse spaces for OS and BDDC approaches are discussed, along with how they can be obtained from discrete harmonic extensions. Connections are also made between coarse spaces and multiscale modeling approaches from computational mechanics. As a specific example, details are provided on constructing coarse spaces for incompressible fluid problems. The next part of the talk deals with a variety of implementation details for domain decomposition solvers. These include mesh partitioning options, local and global solver options, reducing the coarse space dimension, dealing with constraint equations, residual weighting to accelerate the convergence of OS methods, and recycling of Krylov spaces to efficiently solve problems with multiple right hand sides. Some potential bottlenecks and remedies for domain decomposition solvers are also discussed. The final part of the talk concerns some recent theoretical advances, new algorithms, and open questions in the analysis of domain decomposition solvers. The focus will be primarily on the work of the speaker and his colleagues on elasticity, fluid mechanics, problems in H(curl), and the analysis of subdomains with irregular boundaries.
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.
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.
A comparison of solver performance for complex gastric electrophysiology models.
Sathar, Shameer; Cheng, Leo K; Trew, Mark L
2015-08-01
Computational techniques for solving systems of equations arising in gastric electrophysiology have not been studied for efficient solution process. We present a computationally challenging problem of simulating gastric electrophysiology in anatomically realistic stomach geometries with multiple intracellular and extracellular domains. The multiscale nature of the problem and mesh resolution required to capture geometric and functional features necessitates efficient solution methods if the problem is to be tractable. In this study, we investigated and compared several parallel preconditioners for the linear systems arising from tetrahedral discretisation of electrically isotropic and anisotropic problems, with and without stimuli. The results showed that the isotropic problem was computationally less challenging than the anisotropic problem and that the application of extracellular stimuli increased workload considerably. Preconditioning based on block Jacobi and algebraic multigrid solvers were found to have the best overall solution times and least iteration counts, respectively. The algebraic multigrid preconditioner would be expected to perform better on large problems. PMID:26736543
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.
Analytical solutions to general anti-plane shear problems in finite elasticity
NASA Astrophysics Data System (ADS)
Gao, David Yang
2016-03-01
This paper presents a pure complementary energy variational method for solving a general anti-plane shear problem in finite elasticity. Based on the canonical duality-triality theory developed by the author, the nonlinear/nonconvex partial differential equations for the large deformation problem are converted into an algebraic equation in dual space, which can, in principle, be solved to obtain a complete set of stress solutions. Therefore, a general analytical solution form of the deformation is obtained subjected to a compatibility condition. Applications are illustrated by examples with both convex and nonconvex stored strain energies governed by quadratic-exponential and power-law material models, respectively. Results show that the nonconvex variational problem could have multiple solutions at each material point, the complementary gap function and the triality theory can be used to identify both global and local extremal solutions, while the popular convexity conditions (including rank-one condition) provide mainly local minimal criteria and the Legendre-Hadamard condition (i.e., the so-called strong ellipticity condition) does not guarantee uniqueness of solutions. This paper demonstrates again that the pure complementary energy principle and the triality theory play important roles in finite deformation theory and nonconvex analysis.
The Effective-One-Body Approach to the General Relativistic Two Body Problem
NASA Astrophysics Data System (ADS)
Damour, Thibault; Nagar, Alessandro
The two-body problem in General Relativity has been the subject of many analytical investigations. After reviewing some of the methods used to tackle this problem (and, more generally, the N-body problem), we focus on a new, recently introduced approach to the motion and radiation of (comparable mass) binary systems: the Effective One Body (EOB) formalism. We review the basic elements of this formalism, and discuss some of its recent developments. Several recent comparisons between EOB predictions and Numerical Relativity (NR) simulations have shown the aptitude of the EOB formalism to provide accurate descriptions of the dynamics and radiation of various binary systems (comprising black holes or neutron stars) in regimes that are inaccessible to other analytical approaches (such as the last orbits and the merger of comparable mass black holes). In synergy with NR simulations, post-Newtonian (PN) theory and Gravitational Self-Force (GSF) computations, the EOB formalism is likely to provide an efficient way of computing the very many accurate template waveforms that are needed for Gravitational Wave (GW) data analysis purposes.
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.
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.
A general analytical solution to the geometrical problem of field matching in radiotherapy
Hernandez, V.; Arenas, M.; Pons, F.; Sempau, J.
2009-09-15
Purpose: Several authors studied the problem of geometrical matching of fields produced by medical linear accelerators. However, a general solution has yet to be published. Currently available solutions are based on parallelism arguments. This study provides a general solution, considering not only parallelism but also field sizes. Methods: A fixed field with arbitrary field size, gantry, collimator, and couch angle is considered, and another field with a fixed gantry angle is matched to it. A single reference system attached to the treatment couch is used, and two approaches are followed. In the first approach, fixed field sizes are assumed and parallelism of the adjacent field-side planes is imposed. In the second approach, fixed isocenter positions are considered and both parallelism and coincidence between field-side planes are required. Results: When fixed field sizes are assumed, rotation angles are obtained; however, the isocenters may need to be shifted to make side planes coincident and therefore achieve a proper match. When fixed isocenter positions are considered, solutions for all parameters, including the field size, are obtained and an exact geometrical match is achieved. Conclusions: General expressions to the field-matching problem are found for the two approaches followed, fixed field sizes, and fixed isocenter positions. These results can be applied to any treatment technique and can easily be implemented in modern treatment planning systems.
Association of Problem Gambling with Type of Gambling Among Italian General Population.
Scalese, Marco; Bastiani, Luca; Salvadori, Stefano; Gori, Mercedes; Lewis, Isabella; Jarre, Paolo; Molinaro, Sabrina
2016-09-01
The origin of gambling disorders is uncertain; however, research has shown a tendency to focus on specific types of games as a potential important risk factor. The principal aim of this study is to examine the relationships between types of gambling practices and gambling disorder. The data were extracted from IPSAD-Italia(®) 2010-2011 (Italian Population Survey on Alcohol and other Drugs), a survey among the Italian general population which collects socio-cultural information, information about the use of drugs, legal substances and gambling habits. In order to identify the "problem gambler" we used the Problem Gambling Severity Index. Three groups are considered in this analysis: no-risk gamblers, low-risk gamblers, moderate-risk/problem gamblers. Type of gambling practice was considered among two types of gambler: one-game players and multi-games players. 1.9 % of multi-game players were considered problem gamblers, only 0.6 % of one-game players were problem gamblers (p < 0.001). The percentage of players who were low and moderate-risk gamblers was approximately double among multi-game players, with 14.4 % low-risk and 5.8 % moderate-risk; compared with 7.7 % low-risk and 2.5 % moderate risk among one-game players. Results of ordinal logistic regression analysis confirmed that higher level of gambling severity was associated with multi-game players (OR = 2.23, p < 0.0001). Video-poker/slot-machines show the highest association with gambling severity among both one-game players and multi-game players, with scores of OR equal to 4.3 and 4.5 respectively. These findings suggest a popular perception of risk associated with this type of gambling for the development of gambling problems. PMID:26475172
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.
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.
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.
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.
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.
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.
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.
The use of inexact ODE solver in waveform relaxation methods on a massively parallel computer
Luk, W.S.; Wing, O.
1995-12-01
This paper presents the use of inexact ordinary differential equation (ODE) solver in waveform relaxation methods for solving initial value problems: Since the conventional ODE solvers are inherently sequential, the inexact ODE solver is used by taking time points from only previous waveform iteration for time integration. As a result, this method is truly massively parallel, as the equation is completely unfolded both in system and in time. Convergence analysis shows that the spectral radius of the iteration equation resulting from the {open_quotes}inexact{close_quotes} solver is the same as that from the standard method, and hence the new method is robust. The parallel implementation issues on the DECmpp 12000/Sx computer will also be discussed. Numerical results illustrate that though the number of iterations in the inexact method is increased over the exact method, as expected, the computation time is much reduced because of the large-scale parallelism.
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.
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.
NASA Astrophysics Data System (ADS)
Willemsen, Bram; Malcolm, Alison; Lewis, Winston
2016-03-01
In a set of problems ranging from 4-D seismic to salt boundary estimation, updates to the velocity model often have a highly localized nature. Numerical techniques for these applications such as full-waveform inversion (FWI) require an estimate of the wavefield to compute the model updates. When dealing with localized problems, it is wasteful to compute these updates in the global domain, when we only need them in our region of interest. This paper introduces a local solver that generates forward and adjoint wavefields which are, to machine precision, identical to those generated by a full-domain solver evaluated within the region of interest. This means that the local solver computes all interactions between model updates within the region of interest and the inhomogeneities in the background model outside. Because no approximations are made in the calculation of the forward and adjoint wavefields, the local solver can compute the identical gradient in the region of interest as would be computed by the more expensive full-domain solver. In this paper, the local solver is used to efficiently generate the FWI gradient at the boundary of a salt body. This gradient is then used in a level set method to automatically update the salt boundary.
An advanced implicit solver for MHD
NASA Astrophysics Data System (ADS)
Udrea, Bogdan
A new implicit algorithm has been developed for the solution of the time-dependent, viscous and resistive single fluid magnetohydrodynamic (MHD) equations. The algorithm is based on an approximate Riemann solver for the hyperbolic fluxes and central differencing applied on a staggered grid for the parabolic fluxes. The algorithm employs a locally aligned coordinate system that allows the solution to the Riemann problems to be solved in a natural direction, normal to cell interfaces. The result is an original scheme that is robust and reduces the complexity of the flux formulas. The evaluation of the parabolic fluxes is also implemented using a locally aligned coordinate system, this time on the staggered grid. The implicit formulation employed by WARP3 is a two level scheme that was applied for the first time to the single fluid MHD model. The flux Jacobians that appear in the implicit scheme are evaluated numerically. The linear system that results from the implicit discretization is solved using a robust symmetric Gauss-Seidel method. The code has an explicit mode capability so that implementation and test of new algorithms or new physics can be performed in this simpler mode. Last but not least the code was designed and written to run on parallel computers so that complex, high resolution runs can be per formed in hours rather than days. The code has been benchmarked against analytical and experimental gas dynamics and MHD results. The benchmarks consisted of one-dimensional Riemann problems and diffusion dominated problems, two-dimensional supersonic flow over a wedge, axisymmetric magnetoplasmadynamic (MPD) thruster simulation and three-dimensional supersonic flow over intersecting wedges and spheromak stability simulation. The code has been proven to be robust and the results of the simulations showed excellent agreement with analytical and experimental results. Parallel performance studies showed that the code performs as expected when run on parallel
NASA Astrophysics Data System (ADS)
McCoy, B.
2011-12-01
General studies science classes at many universities, such as physical science, Earth science, or astronomy, stress memorization and repetition of concepts. This approach leaves students with little appreciation for how science is used to explain phenomena from general principles. We present a novel instructional technique for an Earth science class in which the students are instructed in the use of a general problem solving strategy, adapted from a quantitative problem solving strategy developed by physics education research, in order to train the students in how to apply general principles. Using the Epistemological Beliefs Assessment for Physical Science, we have found that explicit training in problem solving significantly improves students' epistemology.
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…
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…
Minesaki, Yukitaka
2013-08-01
For the restricted three-body problem, we propose an accurate orbital integration scheme that retains all conserved quantities of the two-body problem with two primaries and approximately preserves the Jacobi integral. The scheme is obtained by taking the limit as mass approaches zero in the discrete-time general three-body problem. For a long time interval, the proposed scheme precisely reproduces various periodic orbits that cannot be accurately computed by other generic integrators.
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...
TOPICAL REVIEW: On local and global aspects of the Cauchy problem in general relativity
NASA Astrophysics Data System (ADS)
Klainerman, Sergiu; Nicolò, Francesco
1999-08-01
In this paper we review some of the recent mathematical progress concerning the initial value problem formulation of general relativity. It is not our intention, however, to give an exhaustive presentation of all recent results on this topic, but rather to discuss some of the most promising mathematical techniques, which have been advanced in connection with the general Cauchy problem, in the absence of any special symmetries. Moreover, for the sake of simplicity and coherence, we restrict ourselves to the Einstein vacuum equations in the asymptotically flat regime. Our main goal is to discuss the main mathematical methods behind the various local existence and uniqueness results, as well as those used in the proof of global nonlinear stability of the Minkowski space. We also present an outline of a somewhat different and more transparent approach obtained by the authors in collaboration with Christodoulou. This relies, instead of the maximal foliation used by Christodoulou and Klainerman, on a double-null foliation. The new approach is fully adapted to domains of dependence and thus allows one to provide, directly, without having to rely on interior estimates, a proof of stability of `null infinity' for large asymptotically flat initial data sets.
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.
Optimization of solver for gas flow modeling
NASA Astrophysics Data System (ADS)
Savichkin, D.; Dodulad, O.; Kloss, Yu
2014-05-01
The main purpose of the work is optimization of the solver for rarefied gas flow modeling based on the Boltzmann equation. Optimization method is based on SIMD extensions for ×86 processors. Computational code is profiled and manually optimized with SSE instructions. Heat flow, shock waves and Knudsen pump are modeled with optimized solver. Dependencies of computational time from mesh sizes and CPU capabilities are provided.
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.
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.
Transition regions between stable periodic solutions of the general three-body problem
NASA Astrophysics Data System (ADS)
Iasko, P. P.; Orlov, V. V.
2014-11-01
The behavior of triple systems in the transition zones located between regions of stability is studied in the framework of the general three-body problem with equal masses and zero angular momentum. It is well known that there are exist three stable periodic orbits, namely, the Schubart orbit for the rectilinear problem, the Broucke orbit for the isosceles problem, and the Moore eight-figure orbit. In the space of the initial conditions, these orbits are surrounded by sets of points where bounded motions are observed over substantial time intervals. The transition zones between the Schubart and Moore orbits and the Moore and Broucke orbits are studied. It is shown that the boundaries of the regions of stability can be either smooth and sharp or diffuse. Beyond these boundary regions, the dynamical evolution of triple systems results in a distant ejection of one of the components, or the decay of the system. The distribution of the times when the stability is lost is constructed, and obeys a power law for long time intervals. Three stages in the evolution of an unstable triple system are identified.
Vieland, V J; Hodge, S E
1995-01-01
The problem of ascertainment in segregation analysis arises when families are selected for study through ascertainment of affected individuals. In this case, ascertainment must be corrected for in data analysis. However, methods for ascertainment correction are not available for many common sampling schemes, e.g., sequential sampling of extended pedigrees (except in the case of "single" selection). Concerns about whether ascertainment correction is even required for large pedigrees, about whether and how multiple probands in the same pedigree can be taken into account properly, and about how to apply sequential sampling strategies have occupied many investigators in recent years. We address these concerns by reconsidering a central issue, namely, how to handle pedigree structure (including size). We introduce a new distinction, between sampling in such a way that observed pedigree structure does not depend on which pedigree members are probands (proband-independent [PI] sampling) and sampling in such a way that observed pedigree structure does depend on who are the probands (proband-dependent [PD] sampling). This distinction corresponds roughly (but not exactly) to the distinction between fixed-structure and sequential sampling. We show that conditioning on observed pedigree structure in ascertained data sets obtained under PD sampling is not in general correct (with the exception of "single" selection), while PI sampling of pedigree structures larger than simple sibships is generally not possible. Yet, in practice one has little choice but to condition on observed pedigree structure. We conclude that the problem of genetic modeling in ascertained data sets is, in most situations, literally intractable. We recommend that future efforts focus on the development of robust approximate approaches to the problem. PMID:7825595
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.
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.
Analysis of optimal and near-optimal continuous-thrust transfer problems in general circular orbit
NASA Astrophysics Data System (ADS)
Kéchichian, Jean A.
2009-09-01
A pair of practical problems in optimal continuous-thrust transfer in general circular orbit is analyzed within the context of analytic averaging for rapid computations leading to near-optimal solutions. The first problem addresses the minimum-time transfer between inclined circular orbits by proposing an analytic solution based on a split-sequence strategy in which the equatorial inclination and node controls are done separately by optimally selecting the intermediate orbit size at the sequence switch point that results in the minimum-time transfer. The consideration of the equatorial inclination and node state variables besides the orbital velocity variable is needed to further account for the important J2 perturbation that precesses the orbit plane during the transfer, unlike the thrust-only case in which it is sufficient to consider the relative inclination and velocity variables thus reducing the dimensionality of the system equations. Further extensions of the split-sequence strategy with analytic J2 effect are thus possible for equal computational ease. The second problem addresses the maximization of the equatorial inclination in fixed time by adopting a particular thrust-averaging scheme that controls only the inclination and velocity variables, leaving the node at the mercy of the J2 precession, providing robust fast-converging codes that lead to efficient near-optimal solutions. Example transfers for both sets of problems are solved showing near-optimal features as far as transfer time is concerned, by directly comparing the solutions to "exact" purely numerical counterparts that rely on precision integration of the raw unaveraged system dynamics with continuously varying thrust vector orientation in three-dimensional space.
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.
An Optimal Order Nonnested Mixed Multigrid Method for Generalized Stokes Problems
NASA Technical Reports Server (NTRS)
Deng, Qingping
1996-01-01
A multigrid algorithm is developed and analyzed for generalized Stokes problems discretized by various nonnested mixed finite elements within a unified framework. It is abstractly proved by an element-independent analysis that the multigrid algorithm converges with an optimal order if there exists a 'good' prolongation operator. A technique to construct a 'good' prolongation operator for nonnested multilevel finite element spaces is proposed. Its basic idea is to introduce a sequence of auxiliary nested multilevel finite element spaces and define a prolongation operator as a composite operator of two single grid level operators. This makes not only the construction of a prolongation operator much easier (the final explicit forms of such prolongation operators are fairly simple), but the verification of the approximate properties for prolongation operators is also simplified. Finally, as an application, the framework and technique is applied to seven typical nonnested mixed finite elements.
Parallel computing study for the large-scale generalized eigenvalue problems in modal analysis
NASA Astrophysics Data System (ADS)
Fan, XuanHua; Chen, Pu; Wu, RuiAn; Xiao, ShiFu
2014-03-01
In this paper we study the algorithms and their parallel implementation for solving large-scale generalized eigenvalue problems in modal analysis. Three predominant subspace algorithms, i.e., Krylov-Schur method, implicitly restarted Arnoldi method and Jacobi-Davidson method, are modified with some complementary techniques to make them suitable for modal analysis. Detailed descriptions of the three algorithms are given. Based on these algorithms, a parallel solution procedure is established via the PANDA framework and its associated eigensolvers. Using the solution procedure on a machine equipped with up to 4800 processors, the parallel performance of the three predominant methods is evaluated via numerical experiments with typical engineering structures, where the maximum testing scale attains twenty million degrees of freedom. The speedup curves for different cases are obtained and compared. The results show that the three methods are good for modal analysis in the scale of ten million degrees of freedom with a favorable parallel scalability.
Psychological and social problems in HIV infection: interviews with general practitioners in London.
King, M B
1989-09-16
A random sample of 270 general practitioners in London was interviewed to assess current practice and opinions about managing psychological and social problems related to HIV infection. Physicians caring for patients with HIV infection were asked about numbers of patients in their pratice with HIV or AIDS; consultation with third parties such as sexual partners or family; reports to employers and other third parties; terminal care; contact with HIV clinics; testing for HIV infection without consent; and the impact of patients with HIV infection on their practice. All physicians were asked about patients concerned with HIV infection; awareness of other health resources for patients with HIV infection; terminal care; "safer sex" education; confidentiality; interest in AIDS; intravenous drug users as patients; managing homosexual patients; and ethical considerations. King discusses the findings and draws conclusions about primary care of HIV-infected patients in London. PMID:2508884
Prescribing benzodiazepines in general practice: a new view of an old problem.
Rogers, Anne; Pilgrim, David; Brennan, Susie; Sulaiman, Ilyas; Watson, Gareth; Chew-Graham, Carolyn
2007-04-01
General practitioner (GP) prescribing has been identified as an arena that has broad social and political implications, which stretch beyond individual outcomes for patients. This article revisits aspects of the controversy about prescribing benzodiazepines (or 'minor tranquillizers') through an exploration of contemporary views of GPs. In the 1980s the prescribing of these drugs was considered to be both a clinical and social problem, which brought medical decision making under public scrutiny. The legacy of this controversy for recent GPs remains a relatively under-explored topic. This article describes a qualitative study of GPs practising in the north-west of England about their views of prescribing benzodiazepines. The accounts of the respondents highlight a number of points about: blame allocation, past and present; clinical challenges about risk management; and deserving and undeserving patients. These GP views are then discussed in the wider context of psychotropic drug use. It is concluded that, while there has been a recent consensus that the benzodiazepines have been problematic, when they are placed in a longer historical context, a different picture is apparent because other psychotropic drugs have raised similar problems. PMID:17344271
NASA Astrophysics Data System (ADS)
Yamamoto, Satoru
2005-07-01
A preconditioned flux-vector splitting (PFVS) scheme in general curvilinear coordinates which can be applied to condensate fluid and solid coupling problems is presented and some typical calculated results are shown to prove the availability of the present method. This method is based on the preconditioning method applied to compressible Navier-Stokes (NS) equations with additional equations and source terms for condensate flows. Since the present PFVS terms composed of the convective and pressure terms of the NS equations are completely reduced to only the pressure terms when the velocities are set to zero, the present scheme can further applied to the calculation not only for a dynamic field but also for a static field including a transitional field from the dynamic region to the static region. In this paper, as a first stage of the present study, coupling problems between a condensate flow in a flow field and heat conduction in a solid structure are simultaneously calculated by using the present method. As numerical examples, transonic and low speed flows around the NACA0012 airfoil, nonequilibrium condensate flows in a nozzle, and natural convection with condensation around a pipe at 1g and zero gravity are simulated with heat conduction in the solid structure.
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.
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.
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.
Finite Element Interface to Linear Solvers (FEI) version 2.9 : users guide and reference manual.
Williams, Alan B.
2005-02-01
The Finite Element Interface to Linear Solvers (FEI) is a linear system assembly library. Sparse systems of linear equations arise in many computational engineering applications, and 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 package capable of solving all of the linear systems that arise. This motivates the need to switch an application from one solver library to another, depending on the problem being solved. The interfaces provided by various solver libraries for data assembly and problem solution 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 that puts a 'common face' on various solver libraries. The FEI has seen significant use by finite element applications at Sandia National Laboratories and Lawrence Livermore National Laboratory. The original FEI offered several advantages over using linear algebra libraries directly, but also imposed significant limitations and disadvantages. A new set of interfaces has been added with the goal of removing the limitations of the original FEI while maintaining and extending its strengths.
Trends in the treatment of alcohol problems in the US general population, 1979 through 1990.
Weisner, C; Greenfield, T; Room, R
1995-01-01
OBJECTIVES. The purpose of this study was to conduct a comprehensive analysis of alcohol-treatment service utilization trends in the general population during the 1980s. METHODS. Three national surveys of the US household population (1979, 1984, and 1990) were used for trend analysis of treatment utilization. Trends in demographic characteristics of persons with lifetime treatment rates and particular types of treatment were examined by means of logistic regression analysis, controlling for alcohol problem severity and other variables. RESULTS. Substantial increases in the numbers reporting treatment were found. In all surveys, Alcoholics Anonymous was the treatment used most frequently and its use increased most, especially for women. Men were more likely than women (odds ratio [OR] = 2.01, 95% confidence interval [CI] = 1.20, 5.39) and unmarried persons were twice as likely as married persons to have been treated [corrected]. Social consequences carried more predictive power than dependence symptoms. CONCLUSIONS. From a general population perspective, while overall treatment capacity has increased, the structural changes in the public/private balance of services have not positively affected the representation of women or other characteristics of the treatment population. PMID:7832262
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.
Generation of Minimum-Consistent DFA Using SAT Solver
NASA Astrophysics Data System (ADS)
Inui, Nobuo; Aizawa, Akiko
The purpose of this study is to develop efficient methods for the minimum-consistent DFA (deterministic finite state automaton) problem. The graph-coloring based SAT (satisfiability) approach proposed by Heule is a state of the art method for this problem. It specially achieves high performance computing in dense problems such as in a popular benchmark problem where rich information about labels is included. In contrast, to solve sparse problems is a challenge for the minimum-consistent DFA problem. To solve sparse problems, we propose three approaches to the SAT formulation: a) the binary color representation, b) the dynamic symmetry breaking and c) the hyper-graph coloring constraint. We organized an experiment using the existing benchmark problems and sparse problems made from them. We observed that our symmetry breaking constraints made the speed up the running time of SAT solver. In addition with this, our other proposed methods were showing the possibility to improve the performance. Then we simulated the perfomance of our methods under the condition that we executed the several program set-ups in parallel. Compared with the previous research results, we finally could reduce the average relative time by 66.5% and the total relative time by 7.6% for sparse problems and by 79.7% and 38.5% for dense problems, respectively. These results showed that our proposed methods were effective for difficult problems.
A fast solver for the Ornstein-Zernike equations
NASA Astrophysics Data System (ADS)
Kelley, C. T.; Pettitt, B. Montgomery
2004-07-01
In this paper, we report on the design and analysis of a multilevel method for the solution of the Ornstein-Zernike Equations and related systems of integro-algebraic equations. Our approach is based on an extension of the Atkinson-Brakhage method, with Newton-GMRES used as the coarse mesh solver. We report on several numerical experiments to illustrate the effectiveness of the method. The problems chosen are related to simple short ranged fluids with continuous potentials. Speedups over traditional methods for a given accuracy are reported. The new multilevel method is roughly six times faster than Newton-GMRES and 40 times faster than Picard.
Evaluating point-based POMDP solvers on multicore machines.
Shani, Guy
2010-08-01
Recent scaling up of partially observable Markov decision process solvers toward realistic applications is largely due to point-based methods which quickly provide approximate solutions for midsized problems. New multicore machines offer an opportunity to scale up to larger domains. These machines support parallel execution and can speed up existing algorithms considerably. In this paper, we evaluate several ways in which point-based algorithms can be adapted to parallel computing. We overview the challenges and opportunities and present experimental results, providing evidence to the usability of our suggestions. PMID:19914897
A Minds-On Approach to Active Learning in General Music
ERIC Educational Resources Information Center
Scott, Sheila
2010-01-01
Minds-on engagement in active learning is explored through the experiences of Margaret Sanders, a general music teacher. Minds-on learners think about their experiences. They are actively involved as questioners and problem solvers while they complete musical tasks and reflect on their work after it is completed. Minds-off learners focus on their…
NASA Astrophysics Data System (ADS)
Balsara, Dinshaw S.
2014-11-01
up to quartic variation in the self-similar variables. While linear variations are sufficient for numerical work, the higher order terms in the series solution could prove useful for analytical studies of the multidimensional Riemann problem. The formulation presented here is general enough to accommodate any hyperbolic conservation law. It can also accommodate any one-dimensional Riemann solver and yields a multidimensional version of the same. It has been incorporated in the author's RIEMANN code. As examples of the different types of hyperbolic conservation laws, we use Euler flow, Magnetohydrodynamics (MHD) and relativistic MHD. As examples of different types of Riemann solvers, we show multidimensional formulations of HLL, HLLC and HLLD Riemann solvers for MHD all working fluently within this formulation. Several stringent test problems are presented.
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.
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.
High order methods for elliptic problems in plasma physics
NASA Astrophysics Data System (ADS)
Pataki, Andras
In this dissertation, we develop fast high order solvers for two elliptic problems in plasma physics. The first is the Grad-Shafranov equation, a nonlinear elliptic PDE that describes the magnetohydrodynamic equilibrium of three dimensional, axisymmetric plasmas. A high order solver is desirable to ensure the accurate evaluation of derivatives, required both for the computation of physical quantities and for studying perturbations near equilibrium. Using suitable scaling, we transform the problem from cylindrical coordinates to a nonlinear Poisson problem in Cartesian coordinates. We compute the conformal map from the original domain to the unit circle where we build a separation of variables based solver to obtain a high order, accurate solution. A fixed point or eigenvalue outer iteration is used to solve the nonlinear equation. Our second problem is the computation of the Coulomb collision operator that arises in kinetic models of plasmas. The collision operator can be written in terms of two Rosenbluth potentials obtained by solving a Poisson and a biharmonic problem in the velocity variables. For these PDEs we describe a new class of fast solvers in cylindrical coordinates with free-space radiation conditions. By combining integral equation methods in the radial variable with Fourier methods in the angular and z directions, we show that high-order accuracy can be achieved in both the solution and its derivatives. A weak singularity arises in the Fourier transform with respect to z that is handled with special purpose quadratures. Such solvers are ideally suited to the Rosenbluth potentials, since the collision operator is expressed in terms of up to fourth derivatives of the potentials, placing stringent demands on the computational order. Also, since axisymmetry is generally assumed in the velocity variables, the use of cylindrical coordinates reduces the three dimensional problem to a two dimensional computation.
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
NASA Astrophysics Data System (ADS)
Giudici, M.; Baratelli, F.; Comunian, A.; Vassena, C.; Cattaneo, L.
2014-10-01
Numerical modelling of the dynamic evolution of ice sheets and glaciers requires the solution of discrete equations which are based on physical principles (e.g. conservation of mass, linear momentum and energy) and phenomenological constitutive laws (e.g. Glen's and Fourier's laws). These equations must be accompanied by information on the forcing term and by initial and boundary conditions (IBCs) on ice velocity, stress and temperature; on the other hand the constitutive laws involve many physical parameters, some of which depend on the ice thermodynamical state. The proper forecast of the dynamics of ice sheets and glaciers requires a precise knowledge of several quantities which appear in the IBCs, in the forcing terms and in the phenomenological laws. As these quantities cannot be easily measured at the study scale in the field, they are often obtained through model calibration by solving an inverse problem (IP). The objective of this paper is to provide a thorough and rigorous conceptual framework for IPs in cryospheric studies and in particular: to clarify the role of experimental and monitoring data to determine the calibration targets and the values of the parameters that can be considered to be fixed; to define and characterise identifiability, a property related to the solution to the forward problem; to study well-posedness in a correct way, without confusing instability with ill-conditioning or with the properties of the method applied to compute a solution; to cast sensitivity analysis in a general framework and to differentiate between the computation of local sensitivity indicators with a one-at-a-time approach and first-order sensitivity indicators that consider the whole possible variability of the model parameters. The conceptual framework and the relevant properties are illustrated by means of a simple numerical example of isothermal ice flow, based on the shallow-ice approximation.
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)…
NASA Astrophysics Data System (ADS)
Johnson, David T.
Quantum mechanics is an extremely successful and accurate physical theory, yet since its inception, it has been afflicted with numerous conceptual difficulties. The primary subject of this thesis is the theory of entropic quantum dynamics (EQD), which seeks to avoid these conceptual problems by interpreting quantum theory from an informational perspective. We begin by reviewing Cox's work in describing probability theory as a means of rationally and consistently quantifying uncertainties. We then discuss how probabilities can be updated according to either Bayes' theorem or the extended method of maximum entropy (ME). After that discussion, we review the work of Caticha and Giffin that shows that Bayes' theorem is a special case of ME. This important result demonstrates that the ME method is the general method for updating probabilities. We then review some motivating difficulties in quantum mechanics before discussing Caticha's work in deriving quantum theory from the approach of entropic dynamics, which concludes our review. After entropic dynamics is introduced, we develop the concepts of symmetries and transformations from an informational perspective. The primary result is the formulation of a symmetry condition that any transformation must satisfy in order to qualify as a symmetry in EQD. We then proceed to apply this condition to the extended Galilean transformation. This transformation is of interest as it exhibits features of both special and general relativity. The transformation yields a gravitational potential that arises from an equivalence of information. We conclude the thesis with a discussion of the measurement problem in quantum mechanics. We discuss the difficulties that arise in the standard quantum mechanical approach to measurement before developing our theory of entropic measurement. In entropic dynamics, position is the only observable. We show how a theory built on this one observable can account for the multitude of measurements present in
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.
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…
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
Steady potential solver for unsteady aerodynamic analyses
NASA Technical Reports Server (NTRS)
Hoyniak, Dan
1994-01-01
Development of a steady flow solver for use with LINFLO was the objective of this report. The solver must be compatible with LINFLO, be composed of composite mesh, and have transonic capability. The approaches used were: (1) steady flow potential equations written in nonconservative form; (2) Newton's Method; (3) implicit, least-squares, interpolation method to obtain finite difference equations; and (4) matrix inversion routines from LINFLO. This report was given during the NASA LeRC Workshop on Forced Response in Turbomachinery in August of 1993.
Multigrid in energy preconditioner for Krylov solvers
Slaybaugh, R.N.; Evans, T.M.; Davidson, G.G.; Wilson, P.P.H.
2013-06-01
We have added a new multigrid in energy (MGE) preconditioner to the Denovo discrete-ordinates radiation transport code. This preconditioner takes advantage of a new multilevel parallel decomposition. A multigroup Krylov subspace iterative solver that is decomposed in energy as well as space-angle forms the backbone of the transport solves in Denovo. The space-angle-energy decomposition facilitates scaling to hundreds of thousands of cores. The multigrid in energy preconditioner scales well in the energy dimension and significantly reduces the number of Krylov iterations required for convergence. This preconditioner is well-suited for use with advanced eigenvalue solvers such as Rayleigh Quotient Iteration and Arnoldi.
ODE System Solver W. Krylov Iteration & Rootfinding
Hindmarsh, Alan C.
1991-09-09
LSODKR is a new initial value ODE solver for stiff and nonstiff systems. It is a variant of the LSODPK and LSODE solvers, intended mainly for large stiff systems. The main differences between LSODKR and LSODE are the following: (a) for stiff systems, LSODKR uses a corrector iteration composed of Newton iteration and one of four preconditioned Krylov subspace iteration methods. The user must supply routines for the preconditioning operations, (b) Within the corrector iteration, LSODKR does automatic switching between functional (fixpoint) iteration and modified Newton iteration, (c) LSODKR includes the ability to find roots of given functions of the solution during the integration.
ODE System Solver W. Krylov Iteration & Rootfinding
Energy Science and Technology Software Center (ESTSC)
1991-09-09
LSODKR is a new initial value ODE solver for stiff and nonstiff systems. It is a variant of the LSODPK and LSODE solvers, intended mainly for large stiff systems. The main differences between LSODKR and LSODE are the following: (a) for stiff systems, LSODKR uses a corrector iteration composed of Newton iteration and one of four preconditioned Krylov subspace iteration methods. The user must supply routines for the preconditioning operations, (b) Within the corrector iteration,more » LSODKR does automatic switching between functional (fixpoint) iteration and modified Newton iteration, (c) LSODKR includes the ability to find roots of given functions of the solution during the integration.« less
Wave Speeds, Riemann Solvers and Artificial Viscosity
Rider, W.J.
1999-07-18
A common perspective on the numerical solution of the equation Euler equations for shock physics is examined. The common viewpoint is based upon the selection of nonlinear wavespeeds upon which the dissipation (implicit or explicit) is founded. This perspective shows commonality between Riemann solver based method (i.e. Godunov-type) and artificial viscosity (i.e. von Neumann-Richtmyer). As an example we derive an improved nonlinear viscous stabilization of a Richtmyer-Lax-Wendroff method. Additionally, we will define a form of classical artificial viscosity based upon the HLL Riemann solver.
NASA Astrophysics Data System (ADS)
Balsara, Dinshaw S.
2015-08-01
In this paper we build on our prior work on multidimensional Riemann solvers by detailing the construction of a three-dimensional HLL Riemann solver. As with the two-dimensional Riemann solver, this is accomplished by introducing a constant resolved state between the states being considered, which introduces sufficient dissipation for systems of conservation laws. Closed form expressions for the resolved fluxes are provided to facilitate numerical implementation. This is accomplished by introducing a novel derivation of the multidimensional Riemann solver. The novelty consists of integrating Lagrangian fluxes across moving surfaces. This makes the problem easier to visualize in three dimensions. (A video introduction to multidimensional Riemann solvers is available on http://www.nd.edu/~dbalsara/Numerical-PDE-Course A robust and efficient second order accurate numerical scheme for three dimensional Euler and MHD flows is presented. The scheme is built on the current three-dimensional Riemann solver and has been implemented in the author's RIEMANN code. We demonstrate that schemes that are based on the three-dimensional Riemann solver permit multidimensional discontinuities to propagate more isotropically on resolution-starved meshes. The number of zones updated per second by this scheme on a modern processor is shown to be cost competitive with schemes that are based on a one-dimensional Riemann solver. However, the present scheme permits larger timesteps in three dimensions because of its inclusion of genuinely three-dimensional effects in the flow. For MHD problems it is not necessary to double the dissipation when evaluating the edge-centered electric fields. Accuracy analysis for three-dimensional Euler and MHD problems shows that the scheme meets its design accuracy. Several stringent test problems involving Euler and MHD flows are also presented and the scheme is shown to perform robustly on all of them. For the very first time, we present the formulation and
Patterns of Verbal Mediation during Problem Solving: A Sequential Analysis of Self-Explanation.
ERIC Educational Resources Information Center
Neuman, Yair; Leibowitz, Liat; Schwarz, Baruch
2000-01-01
Studied patterns of self-explanation that distinguish between good and poor problem solvers. Results with 32 ninth graders identify self-explanation patterns that show that poor problem solvers are more likely to produce clarifications after inferences and good problem solvers are more likely to produce justifications after regulations. (SLD)
A general approximate method for the groundwater response problem caused by water level variation
NASA Astrophysics Data System (ADS)
Jiang, Qinghui; Tang, Yuehao
2015-10-01
The Boussinesq equation (BEQ) can be used to describe groundwater flow through an unconfined aquifer. Based on 1D BEQ, we present a general approximate method to predict the water table response in a semi-infinite aquifer system with a vertical or sloping boundary. A decomposition method is adopted by separating the original problem into a linear diffusion equation (DE) and two correction functions. The linear DE satisfies all the initial and boundary conditions, reflecting the basic characteristics of groundwater movement. The correction functions quantitatively measure the errors due to the degeneration from the original BEQ to a linear DE. As the correction functions must be linearized to obtain analytical solution forms, the proposed method is an approximate approach. In the case studies, we apply this method to four different situations of water level variation (i.e., constant, sudden, linear and periodic change) resting on vertical or sloping boundaries. The results are compared against numerical results, field data and other analytical solutions, which demonstrate that the proposed method has a good accuracy and versatility over a wide range of applications.
On the stability of the solutions of the general problem of three bodies
NASA Technical Reports Server (NTRS)
Standish, E. M., Jr.
1976-01-01
The extent through which the initial conditions of a given three-body system may be varied without completely changing the qualitative nature of the subsequent system evolution is investigated. It is assumed that the three masses are equal, all initial velocities are zero, the first two bodies initially lie on the x-axis, and the position of the third body is confined to a specific region of space. Analysis of the system evolution for different initial positions of the third body shows that there is a whole area or 'island' in the x-y plane throughout which the initial position of the third body may be moved in a continuous fashion to produce an evolution which also changes in a continuous manner. A Monte Carlo approach is adopted to determine the full extent of this island in the general problem. It is concluded that the stability of a full solution may be directly related to the size of its island in phase space.
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.
Ordinary Differential Equation System Solver
Energy Science and Technology Software Center (ESTSC)
1992-03-05
LSODE is a package of subroutines for the numerical solution of the initial value problem for systems of first order ordinary differential equations. The package is suitable for either stiff or nonstiff systems. For stiff systems the Jacobian matrix may be treated in either full or banded form. LSODE can also be used when the Jacobian can be approximated by a band matrix.
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.
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
NASA Astrophysics Data System (ADS)
Kinugawa, Tohru
2014-02-01
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^2X}/{dt^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/sqrt{π })int 0E {dU}/sqrt{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 = TA(E) + TN(E) where τ is a constant period, TA(E) is the transit-time in the Abel type [A-type] region spanning X > 0 and TN(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 XA(U) is determined from TA(E) via the Abel-transform relation XA(U) ∝ A[TA(E)]. In contrast, the N-type region in X < 0 does not ensure this linear relation: the region is covered with a predetermined potential UN(X) of some arbitrary choice, not necessarily obeying the Abel-transform relation. In discussing the isochronicity problem, there has been no attempt of N-type regions that are
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.…
Allan, Nicholas P.; Albanese, Brian J.; Norr, Aaron M.; Zvolensky, Michael J.; Schmidt, Norman B.
2014-01-01
Aims To test whether the relations between anxiety sensitivity (AS), a transdiagnostic risk factor, and alcohol problems are explained by chained mediation models, from AS through anxiety or depressive symptoms then drinking motives in an at-risk sample. It was hypothesized that AS would influence alcohol problems through generalized anxiety or depression symptoms and then through negatively-reinforced drinking motives (i.e., drinking to cope with negative affect and drinking to conform). Design Cross-sectional single- and chained-mediation models were tested. Setting Self-report measures were completed in clinics at Florida State University and the University of Vermont, USA. Participants Participants consisted of 523 adult daily cigarette smokers (M age = 37.23, SD = 13.53; 48.6% female). Measurements As part of a larger battery of self-report measures, participants completed self-report measures of AS, generalized anxiety, depression, drinking motives, and alcohol problems. Findings Chained mediation was found from AS to alcohol problems through generalized anxiety then through drinking to cope with negative affect (B = .04, 90% confidence interval [CI; .004, .10]). Chained mediation was also found from AS to alcohol problems through depression then through drinking to cope with negative affect (B = .11, 90% CI [.05, .21]) and, separately, through socially motivated drinking (B = .05, 90% CI [.003, .11]). Conclusions Anxiety sensitivity and alcohol problems are indirectly related through several intervening variables, such as through generalized anxiety or depression and then through drinking to cope with negative affect. PMID:25220033
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…
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.
Variable transfer methods for fluid-structure interaction computations with staggered solvers
NASA Astrophysics Data System (ADS)
Vaassen, J. M.; Klapka, I.; Leonard, B.; Hirsch, C.
2009-09-01
This paper intends to study methods that have been tested to transfer variables from one skin mesh to another (the two meshes being nonconform) in order to compute fluid-structure interaction (FSI) problems with staggered solvers. The methods are a contact elements method developed by Stam, and different radial basis functions methods. The structure code is OOFELIE® developed at Open-Engineering (Belgium) and the fluid code is FINETM/Hexa developed at Numeca International (Belgium). The paper presents the performances of the methods on a simple variable transfer, and testcases that have been performed with the solver developed by the two companies.
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.
User documentation for KINSOL, a nonlinear solver for sequential and parallel computers
Taylor, A. G., LLNL
1998-07-01
KINSOL is a general purpose nonlinear system solver callable from either C or Fortran programs It is based on NKSOL [3], but is written in ANSI-standard C rather than Fortran77 Its most notable feature is that it uses Krylov Inexact Newton techniques in the system`s approximate solution, thus sharing significant modules previously written within CASC at LLNL to support CVODE[6, 7]/PVODE[9, 5] It also requires almost no matrix storage for solving the Newton equations as compared to direct methods The name KINSOL is derived from those techniques Krylov Inexact Newton SOLver The package was arranged so that selecting one of two forms of a single module in the compilation process will allow the entire package to be created in either sequential (serial) or parallel form The parallel version of KINSOL uses MPI (Message-Passing Interface) [8] and an appropriately revised version of the vector module NVECTOR, as mentioned above, to achieve parallelism and portability KINSOL in parallel form is intended for the SPMD (Single Program Multiple Data) model with distributed memory, in which all vectors are identically distributed across processors In particular, the vector module NVECTOR is designed to help the user assign a contiguous segment of a given vector to each of the processors for parallel computation Several primitives were added to NVECTOR as originally written for PVODE to implement KINSOL KINSOL has been run on a Cray-T3D, an eight- processor DEC ALPHA and a cluster of workstations It is currently being used in a simulation of tokamak edge plasmas and in groundwater two-phase flow studies at LLNL The remainder of this paper is organized as follows Section 2 sets the mathematical notation and summarizes the basic methods Section 3 summarizes the organization of the KINSOL solver, while Section 4 summarizes its usage Section 5 describes a preconditioner module, Section 6 describes a set of Fortran/C interfaces, Section 7 describes an example problem, and Section 8
A Fast and Robust Poisson-Boltzmann Solver Based on Adaptive Cartesian Grids.
Boschitsch, Alexander H; Fenley, Marcia O
2011-05-10
An adaptive Cartesian grid (ACG) concept is presented for the fast and robust numerical solution of the 3D Poisson-Boltzmann Equation (PBE) governing the electrostatic interactions of large-scale biomolecules and highly charged multi-biomolecular assemblies such as ribosomes and viruses. The ACG offers numerous advantages over competing grid topologies such as regular 3D lattices and unstructured grids. For very large biological molecules and multi-biomolecule assemblies, the total number of grid-points is several orders of magnitude less than that required in a conventional lattice grid used in the current PBE solvers thus allowing the end user to obtain accurate and stable nonlinear PBE solutions on a desktop computer. Compared to tetrahedral-based unstructured grids, ACG offers a simpler hierarchical grid structure, which is naturally suited to multigrid, relieves indirect addressing requirements and uses fewer neighboring nodes in the finite difference stencils. Construction of the ACG and determination of the dielectric/ionic maps are straightforward, fast and require minimal user intervention. Charge singularities are eliminated by reformulating the problem to produce the reaction field potential in the molecular interior and the total electrostatic potential in the exterior ionic solvent region. This approach minimizes grid-dependency and alleviates the need for fine grid spacing near atomic charge sites. The technical portion of this paper contains three parts. First, the ACG and its construction for general biomolecular geometries are described. Next, a discrete approximation to the PBE upon this mesh is derived. Finally, the overall solution procedure and multigrid implementation are summarized. Results obtained with the ACG-based PBE solver are presented for: (i) a low dielectric spherical cavity, containing interior point charges, embedded in a high dielectric ionic solvent - analytical solutions are available for this case, thus allowing rigorous
The Effect of a Problem-Solving Teaching Method on Student Problem-Solving Processes.
ERIC Educational Resources Information Center
Frank, David V.; Herron, J. Dudley
A problem-solving method of teaching was used in the recitation sections of a freshmen chemistry course for science and engineering majors at Purdue University. The method was based on prior research which revealed that good problem solvers formed better representations and used heuristics more often than poor problem solvers. Consequently, the…
NASA Astrophysics Data System (ADS)
Cerroni, D.; Fancellu, L.; Manservisi, S.; Menghini, F.
2016-06-01
In this work we propose to study the behavior of a solid elastic object that interacts with a multiphase flow. Fluid structure interaction and multiphase problems are of great interest in engineering and science because of many potential applications. The study of this interaction by coupling a fluid structure interaction (FSI) solver with a multiphase problem could open a large range of possibilities in the investigation of realistic problems. We use a FSI solver based on a monolithic approach, while the two-phase interface advection and reconstruction is computed in the framework of a Volume of Fluid method which is one of the more popular algorithms for two-phase flow problems. The coupling between the FSI and VOF algorithm is efficiently handled with the use of MEDMEM libraries implemented in the computational platform Salome. The numerical results of a dam break problem over a deformable solid are reported in order to show the robustness and stability of this numerical approach.
NASA Astrophysics Data System (ADS)
Calogero, Francesco
2004-06-01
A simple approach is discussed which associates to (solvable) matrix equations (solvable) dynamical systems, generally interpretable as (interesting) many-body problems, possibly involving auxiliary dependent variables in addition to those identifying the positions of the moving particles. We then focus on cases in which the auxiliary variables can be altogether eliminated, reobtaining thereby (via this unified approach) well-known solvable many-body problems, and moreover a (solvable) extension of the "goldfish" model.
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.
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.
Diffusion of Zonal Variables Using Node-Centered Diffusion Solver
Yang, T B
2007-08-06
Tom Kaiser [1] has done some preliminary work to use the node-centered diffusion solver (originally developed by T. Palmer [2]) in Kull for diffusion of zonal variables such as electron temperature. To avoid numerical diffusion, Tom used a scheme developed by Shestakov et al. [3] and found their scheme could, in the vicinity of steep gradients, decouple nearest-neighbor zonal sub-meshes leading to 'alternating-zone' (red-black mode) errors. Tom extended their scheme to couple the sub-meshes with appropriate chosen artificial diffusion and thereby solved the 'alternating-zone' problem. Because the choice of the artificial diffusion coefficient could be very delicate, it is desirable to use a scheme that does not require the artificial diffusion but still able to avoid both numerical diffusion and the 'alternating-zone' problem. In this document we present such a scheme.
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
Progress in developing Poisson-Boltzmann equation solvers.
Li, Chuan; Li, Lin; Petukh, Marharyta; Alexov, Emil
2013-03-01
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
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
General solution of the inverse problem of the calculus of variations
Tonti, E.
1982-06-01
Using the operator notation, we show that for every nonlinera problem there exists a variational formulation and, much more an infinity of them. The corresponding functionals are easily obtained. It follows that the requirement of the existence of a variational formulation for a given problem as a heuristic criterion to select admissible field equations, or equations of motion, or interactions, is to be abandoned.
ERIC Educational Resources Information Center
Burns, Nicholas R.; Lee, Michael D.; Vickers, Douglas
2006-01-01
Studies of human problem solving have traditionally used deterministic tasks that require the execution of a systematic series of steps to reach a rational and optimal solution. Most real-world problems, however, are characterized by uncertainty, the need to consider an enormous number of variables and possible courses of action at each stage in…
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)
Fu, X.; Waters, T.; Gary, S. P.
2014-12-01
Collisionless space plasmas often deviate from Maxwellian-like velocity distributions. To study kinetic waves and instabilities in such plasmas, the dispersion relation, which depends on the velocity distribution, needs to be solved numerically. Most current dispersion solvers (e.g. WHAMP) take advantage of mathematical properties of the Gaussian (or generalized Lorentzian) function, and assume that the velocity distributions can be modeled by a combination of several drift-Maxwellian (or drift-Lorentzian) components. In this study we are developing a kinetic dispersion solver that admits nearly arbitrary non-relativistic parallel velocity distributions. A key part of any dispersion solver is the evaluation of a Hilbert transform of the velocity distribution function and its derivative along Landau contours. Our new solver builds upon a recent method to compute the Hilbert transform accurately and efficiently using the fast Fourier transform, while simultaneously treating the singularities arising from resonances analytically. We have benchmarked our new solver against other codes dealing with Maxwellian distributions. As an example usage of our code, we will show results for several instabilities that occur for electron velocity distributions observed in the solar wind.
Alcohol problems and the differentiation of partner, stranger, and general violence.
Cogan, Rosemary; Ballinger, Bud C
2006-07-01
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 women had high alcohol problems scores. Men with alcohol problems were more likely than other men to commit violence toward strangers or to partners and strangers. However, men with alcohol problems were not more likely than other men to commit violence toward partners only. Among women, alcohol problems had little relationship to committing violence or being the victim of violence. PMID:16731992
Van Bavel, Eric; Van Den Driessen Mareeuw, Francine; Macfarlane, Anne; Van Weel-Baumgarten, Evelyn; Van Den Muijsenbergh, Maria; Van Weel, Chris
2015-01-01
Objective. To explore the views and experiences of general practitioners (GPs) in relation to recognition, recording, and treatment of mental health problems of undocumented migrants (UMs), and to gain insight in the reasons for under-registration of mental health problems in the electronic medical records. Design. Qualitative study design with semi-structured interviews using a topic guide. Subjects and setting. Sixteen GPs in the Netherlands with clinical expertise in the care of UMs. Results. GPs recognized many mental health problems in UMs. Barriers that prevented them from recording these problems and from delivering appropriate care were their low consultation rates, physical presentation of mental health problems, high number of other problems, the UM’s lack of trust towards health care professionals, and cultural differences in health beliefs and language barriers. Referrals to mental health care organizations were often seen as problematic by GPs. To overcome these barriers, GPs provided personalized care as far as possible, referred to other primary care professionals such as social workers or mental health care nurses in their practice, and were a little less restrictive in prescribing psychotropics than guidelines recommended. Conclusions. GPs experienced a variety of barriers in engaging with UMs when identifying or suspecting mental health problems. This explains why there is a gap between the high recognition of mental health problems and the low recording of these problems in general practice files. It is recommended that GPs address mental health problems more actively, strive for continuity of care in order to gain trust of the UMs, and look for opportunities to provide mental care that is accessible and acceptable for UMs. PMID:25961462
Using computer algebra and SMT solvers in algebraic biology
NASA Astrophysics Data System (ADS)
Pineda Osorio, Mateo
2014-05-01
Biologic processes are represented as Boolean networks, in a discrete time. The dynamics within these networks are approached with the help of SMT Solvers and the use of computer algebra. Software such as Maple and Z3 was used in this case. The number of stationary states for each network was calculated. The network studied here corresponds to the immune system under the effects of drastic mood changes. Mood is considered as a Boolean variable that affects the entire dynamics of the immune system, changing the Boolean satisfiability and the number of stationary states of the immune network. Results obtained show Z3's great potential as a SMT Solver. Some of these results were verified in Maple, even though it showed not to be as suitable for the problem approach. The solving code was constructed using Z3-Python and Z3-SMT-LiB. Results obtained are important in biology systems and are expected to help in the design of immune therapies. As a future line of research, more complex Boolean network representations of the immune system as well as the whole psychological apparatus are suggested.
Matrix decomposition graphics processing unit solver for Poisson image editing
NASA Astrophysics Data System (ADS)
Lei, Zhao; Wei, Li
2012-10-01
In recent years, gradient-domain methods have been widely discussed in the image processing field, including seamless cloning and image stitching. These algorithms are commonly carried out by solving a large sparse linear system: the Poisson equation. However, solving the Poisson equation is a computational and memory intensive task which makes it not suitable for real-time image editing. A new matrix decomposition graphics processing unit (GPU) solver (MDGS) is proposed to settle the problem. A matrix decomposition method is used to distribute the work among GPU threads, so that MDGS will take full advantage of the computing power of current GPUs. Additionally, MDGS is a hybrid solver (combines both the direct and iterative techniques) and has two-level architecture. These enable MDGS to generate identical solutions with those of the common Poisson methods and achieve high convergence rate in most cases. This approach is advantageous in terms of parallelizability, enabling real-time image processing, low memory-taken and extensive applications.
Assessent of elliptic solvers for the pressure Poisson equation
NASA Astrophysics Data System (ADS)
Strodtbeck, J. P.; Polly, J. B.; McDonough, J. M.
2008-11-01
It is well known that as much as 80% of the total arithmetic needed for a solution of the incompressible Navier--Stokes equations can be expended for solving the pressure Poisson equation, and this has long been one of the prime motivations for study of elliptic solvers. In recent years various Krylov-subspace methods have begun to receive wide use because of their rapid convergence rates and automatic generation of iteration parameters. However, it is actually total floating-point arithmetic operations that must be of concern when selecting a solver for CFD, and not simply required number of iterations. In the present study we recast speed of convergence for typical CFD pressure Poisson problems in terms of CPU time spent on floating-point arithmetic and demonstrate that in many cases simple successive-overrelaxation (SOR) methods are as effective as some of the popular Krylov-subspace techniques such as BiCGStab(l) provided optimal SOR iteration parameters are employed; furthermore, SOR procedures require significantly less memory. We then describe some techniques for automatically predicting optimal SOR parameters.
Verifying a Local Generic Solver in Coq
NASA Astrophysics Data System (ADS)
Hofmann, Martin; Karbyshev, Aleksandr; Seidl, Helmut
Fixpoint engines are the core components of program analysis tools and compilers. If these tools are to be trusted, special attention should be paid also to the correctness of such solvers. In this paper we consider the local generic fixpoint solver RLD which can be applied to constraint systems {x}sqsupseteq fx,{x}in V, over some lattice {D} where the right-hand sides f x are given as arbitrary functions implemented in some specification language. The verification of this algorithm is challenging, because it uses higher-order functions and relies on side effects to track variable dependences as they are encountered dynamically during fixpoint iterations. Here, we present a correctness proof of this algorithm which has been formalized by means of the interactive proof assistant Coq.
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. PMID:25053122
ERIC Educational Resources Information Center
Ertör, Eren; Akan, Durdagi
2016-01-01
In this study, it was aimed to analyze the problems that the nursery school teachers, who worked in primary schools of Ministry of National Education in Agri city center in 2014-2015 academic years, experience in personnel services and general services according to the views of the teachers. In the direction of this purpose, phenomenology design,…
ERIC Educational Resources Information Center
Gauthier, N.
2008-01-01
A general method is presented for evaluating the sums of "m"th powers of the integers that can, and that cannot, be represented in the two-element Frobenius problem. Generating functions are introduced and used for that purpose. Explicit formulas for the desired sums are obtained and specific examples are discussed.
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…
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
Madison, James H.
1984-01-01
In 1923 John D. Rockefeller's General Education Board (GED) undertook a project to reform the public schools in two rural Indiana counties. The GED demonstration project developed from more than two decades of concern about America's rural problems. The attempt by cosmopolitan outside experts to change the rural schools is described. (RM)
Divergence of Faculty Perceptions of General Chemistry and Problem Solving Skills.
ERIC Educational Resources Information Center
Holme, Thomas
2001-01-01
Describes differences in modes of thinking between natural sciences and engineering practitioners and presents a study investigating the differences in how engineering and chemistry faculty approach problem solving. (YDS)
NASA Technical Reports Server (NTRS)
Salmon, R. F.; Imbrogno, S.
1976-01-01
The importance of measuring accurate air and fuel flows as well as the importance of obtaining accurate exhaust pollutant measurements were emphasized. Some of the problems and the corrective actions taken to incorporate fixes and/or modifications were identified.
NASA Astrophysics Data System (ADS)
Caruthers, Heather Anne
Analysis of the effect of course structure, including motivational tools, laboratory and how problem solving was presented in lecture on students' exam performance, attitudes toward the subject of chemistry, and problem solving strategy use. Exam performance indicates that the use of ressurection points on the final exam benefits students' learning, especially for the Middle Bottom quartile of students. Laboratory improves students' understanding when the exams correspond to laboratory content. Attitude differences, as measured by the Attitude toward the subject of chemistry inventory version 2, show some differences and the influence of the level of expertise in graduate student teaching assistants. The use of dimensional analysis to solve stoichiometry problems in lecture leads students to use that process to solve novel tasks in a similiar way, even if it is not efficient or effective. The students' familiarity with the content, as well as the problem solving process, influence how they solve tasks.
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)
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.
Petri Net Modeling and Decomposition Method for Solving Production Scheduling Problems
NASA Astrophysics Data System (ADS)
Nishi, Tatsushi; Maeno, Ryota
Considering the need to develop general scheduling problem solver, the recent integration of Petri Nets as modeling tools into effective optimization methods for scheduling problems is very promising. The paper addresses a Petri Net modeling and decomposition method for solving a wide variety of scheduling problems. The scheduling problems are represented as the optimal transition firing sequence problems for timed Petri Nets. The Petri Net is decomposed into several subnets in which each subproblem can be easily solved by Dijkstra' algorithm. The approach is applied to a flowshop scheduling problem. The performance of the proposed algorithm is compared with that of a simulated annealing method.
Toward robust scalable algebraic multigrid solvers.
Waisman, Haim; Schroder, Jacob; Olson, Luke; Hiriyur, Badri; Gaidamour, Jeremie; Siefert, Christopher; Hu, Jonathan Joseph; Tuminaro, Raymond Stephen
2010-10-01
This talk highlights some multigrid challenges that arise from several application areas including structural dynamics, fluid flow, and electromagnetics. A general framework is presented to help introduce and understand algebraic multigrid methods based on energy minimization concepts. Connections between algebraic multigrid prolongators and finite element basis functions are made to explored. It is shown how the general algebraic multigrid framework allows one to adapt multigrid ideas to a number of different situations. Examples are given corresponding to linear elasticity and specifically in the solution of linear systems associated with extended finite elements for fracture problems.
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…
The case for case studies in nursing research: the problem of generalization.
Sharp, K
1998-04-01
This paper examines the logic of generalizing from case studies and other nonrepresentative samples. It is argued that the generalizability of such research is often underestimated, because of a fundamental confusion about two quite distinct logical bases upon which generalizations can be made: empirical and theoretical. It is suggested that once it is accepted that theoretical generalizations do not depend upon representativeness for their validity, the full value of case study, and other small-scale qualitative research to nursing and other health care disciplines, can be appreciated. PMID:9578209
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.
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.
Frequency Domain Modelling by a Direct-Iterative Solver: A Space and Wavelet Approach
NASA Astrophysics Data System (ADS)
Hustedt, B.; Operto, S.; Virieux, J.
2002-12-01
Seismic forward modelling of wave propagation phenomena in complex rheologic media using a frequency domain finite-difference (FDFD) technique is of special interest for multisource experiments and waveform inversion schemes, because the complete wavefield solution can be computed in a fast and efficient way. FDFD modelling requires the inversion of an extremely large matrix-equation A x x = b, by either a direct or an iterative solver. The direct solver computes an effective inverse of A, called LU factorization. The main handicap is additional computer memory required for storing matrix fill-in coefficients, that are created during the factorization process. Iterative solvers are not limited by memory constraints (additional coefficients), but the convergence depends on a good initial solution difficult to guess before hand. For both solvers, available computer resources has limited wide-spread FDFD modelling applications to mainly two-dimensional (2D) and rarely three-dimensional (3D) problems. In order to overcome these limits, we propose the combination of a direct solver and an iterative solver, called Direct-Iterative Solver (DIS). The direct solver is used to compute an exact wavefield solution on a coarse discretized grid. We use a multifrontal decomposition technique. The coarse-grid size is determined preliminary by limits of the available computer resources, rather than by the wave simulation problem. We project the exact coarse-grid solution on a fine-grid, and use it as an initial solution for an iterative solver, which convergences to an acceptable approximation of the desired fine-grid solution. Two different DIS schemes have been implemented and tested for numerical accuracy and computational performance. The first approach, called the Direct-Iterative-Space Solver (DISS), projects the coarse-grid solution on the fine-grid by a bilinear interpolation. Though the interpolated solution nicely approximates the desired fine-grid solution, still for
Lee, S. L.; Hovland, P. D.
2000-11-01
PVODE is a high-performance ordinary differential equation solver for the types of initial value problems (IVPs) that arise in large-scale computational simulations. Often, one wants to compute sensitivities with respect to certain parameters in the IVP. We discuss the use of automatic differentiation (AD) to compute these sensitivities in the context of PVODE. Results on a simple test problem indicate that the use of AD-generated derivative code can reduce the time to solution over finite difference approximations.
Lee, S L; Hovland, P D
2000-09-15
PVODE is a high-performance ordinary differential equation solver for the types of initial value problems (IVPs) that arise in large-scale computational simulations. often, one wants to compute sensitivities with respect to certain parameters in the IVP. They discuss the use of automatic differentiation (AD) to compute these sensitivities in the context of PVODE. Results on a simple test problem indicate that the use of AD-generated derivative code can reduce the time to solution over finite difference approximations.
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).
Tarber, Christel; Frostholm, Lisbeth
2014-01-01
Common mental disorders often go undetected in primary care. Sharpening general practitioners' (GPs') attention to potential signs thereof is therefore crucial. This conversation-analytic study arises from the observation that the consideration of psychological problems in new-concern visits can be achieved by way of 'gradual topic emergence'. This entails that the problem is not presented directly, but adjunct to somatic symptoms, and is hinted at by way of generic, ambiguous complaints, and furthermore by expressions of frustration and uncertainty and talk about lifeworld problems. It is argued that these materials are 'trouble-premonitory, alerting the GP to the presence of an underlying problem that can then be addressed throughfurther inquiry. The patient logic behind this approach is to assure the GP's recipiency and thus ratification of the problem's medical legitimacy. It allows the patient to introduce a potentially delicate problem 'off the record, thus guarding the patient against the loss of face that could resultfrom no uptake by the GP. The results of the study point to the importance of GPs being receptive to such interactional clues to psychological problems provided by patients. PMID:26596126
Children's Use of Domain-Specific Knowledge and Domain-General Strategies in Novel Problem Solving.
ERIC Educational Resources Information Center
English, Lyn D.
Seventy-two Australian children aged from 4 years 6 months to 9 years 10 months were individually administered a set of six combinatorial problems involving the dressing of toy bears in all possible combinations of clothing items. Six age groups were represented: eight children were in each of the 4, 5, and 6 year categories; and 16 children were…
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…
General case of contact problems for a regular polygon weakened with full-strength hole
NASA Astrophysics Data System (ADS)
Odishelidze, Nana; Criado-Aldeanueva, Francisco; Criado, Francisco; Sanchez, Jose Maria
2015-06-01
The paper addresses a problem of plane elasticity theory for a doubly connected body whose external boundary is a regular polygon and the internal boundary is the required full-strength hole including the origin of coordinates. The full-strength hole is cycle symmetric. It is assumed that to every link of the broken line conforming the outer boundary of the given body are applied absolutely smooth rigid punches with rectilinear bases, which are under the action of the force P that applies to their middle points. There is no friction between the surface of the given elastic body and the punches. The uniformly distributed normal stress Q is applied to the hole boundary. Using the methods of complex analysis, the analytical image of Kolosov-Muskhelishvili's complex potentials (characterizing an elastic equilibrium of the body) and the shape of the hole's contour are determined under the condition that the tangential normal stress arising at it takes a constant value. A similar problem is considered for a square and an equilateral triangle, which are weakened with full-strength holes. Using the method developed here, the partially unknown boundary value problems under consideration is reduced to known boundary value problems of the theory of analytic functions. The solutions are presented in quadratures, and full-strength contours are constructed.
General and Specific Predictors of Behavioral and Emotional Problems Among Adolescents
ERIC Educational Resources Information Center
Windle, M.; Mason, W. A.
2004-01-01
Based on a sample of 1,218 students in the 10th and 11th grades, 14 variables measuring behavioral and emotional problems were modeled as four factors via confirmatory factor analysis. The factors were labeled Polydrug Use, Delinquency, Negative Affect, and Academic Orientation. A similar four-factor structure was supported 1 year later, and a…
The Effect of General Versus Specific Heuristics in Mathematical Problem-Solving Tasks.
ERIC Educational Resources Information Center
Smith, James Philip
This study investigated differences in problem-solving performance following instruction varying in the type of heuristic advice given. The subjects, 176 college students with two years of high school mathematics experience, were provided programed instruction over a three-week period in three topic areas: finite geometry, Boolean algebra, and…
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
Periodic Density Functional Theory Solver using Multiresolution Analysis with MADNESS
NASA Astrophysics Data System (ADS)
Harrison, Robert; Thornton, William
2011-03-01
We describe the first implementation of the all-electron Kohn-Sham density functional periodic solver (DFT) using multi-wavelets and fast integral equations using MADNESS (multiresolution adaptive numerical environment for scientific simulation; http://code.google.com/p/m-a-d-n-e-s-s). The multiresolution nature of a multi-wavelet basis allows for fast computation with guaranteed precision. By reformulating the Kohn-Sham eigenvalue equation into the Lippmann-Schwinger equation, we can avoid using the derivative operator which allows better control of overall precision for the all-electron problem. Other highlights include the development of periodic integral operators with low-rank separation, an adaptable model potential for nuclear potential, and an implementation for Hartree Fock exchange. This work was supported by NSF project OCI-0904972 and made use of resources at the Center for Computational Sciences at Oak Ridge National Laboratory under contract DE-AC05-00OR22725.
Status Of The UPS Space-Marching Flow Solver
NASA Technical Reports Server (NTRS)
Lawerence, Scott L.; VanDalsem, William (Technical Monitor)
1995-01-01
The status of the three-dimensional parabolized Navier-Stokes solver UPS is described. The UPS code, initiated at NASA Ames Research Center in 1986, continues to develop and evolve through application to supersonic and hypersonic flow fields. Hypersonic applications have motivated enhancement of the physical modeling capabilities of the code, specifically real gas modeling, boundary conditions, and turbulence and transition modeling. The UPS code has also been modified to enhance robustness and efficiency in order to be practically used in concert with an optimization code for supersonic transport design. These developments are briefly described along with some relevant results for generic test problems obtained during verification of the enhancements. Included developments and results have previously been published and widely disseminated domestically.
Sartorius, N; Ustün, T B; Costa e Silva, J A; Goldberg, D; Lecrubier, Y; Ormel, J; Von Korff, M; Wittchen, H U
1993-10-01
This article describes a large longitudinal multicenter collaborative study that investigated the form, frequency, course, and outcome of psychological problems that were seen in primary health care settings in 15 different sites around the world. The research employed a two-stage sampling design in which the 12-item General Health Questionnaire was administered to 26,422 persons aged 18 to 65 years who were consulting health care services. Of these persons, 5604 were selected for detailed examinations using standardized instruments and were followed up at 3 months and 1 year to provide information on course and outcome. All assessment instruments have been translated into 13 different languages. The project has produced a database that allows for the exploration of the nature of psychological disorders experienced by patients in general medical care and their association with physical illness, illness behavior, and disability over time. PMID:8215805
NASA Astrophysics Data System (ADS)
Kishor, Ram
2016-07-01
We consider a generalized photogravitational Chermnykh-like problem and determine orbits in the basin of collinear equilibrium points. We suppose that bigger primary is radiating body; smaller primary is an oblate spheroid and a disk with power law density profile is rotating around the common center of mass of the system. We compute three types of orbits namely, periodic, hyperbolic and asymptotic orbit, of the infinitesimal body. Also, we analyse, effect of radiation pressure and oblateness and it is noticed that time period of the periodic orbits depends on these parameters. KEYWORDS: Chermnykh-like problem; Orbits; Radiation pressure; Oblateness; Disk; Collinear equilibrium points.
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.
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…
The generalized divisor problem with natural numbers of a special form
NASA Astrophysics Data System (ADS)
Eminyan, K. M.
2015-07-01
An asymptotic formula with a uniform bound for the remainder term is obtained for the sum of the values of the generalized divisor function over those positive integers whose prime divisor have binary representations of a special form. Bibliography: 12 titles.
The general solution to the classical problem of the finite Euler-Bernoulli beam
NASA Technical Reports Server (NTRS)
Hussaini, M. Y.; Amba-Rao, C. L.
1978-01-01
An analytical solution is obtained for the problem of free and forced vibrations of a finite Euler-Bernoulli beam with arbitrary (partially fixed) boundary conditions. The effects of linear viscous damping, Winkler foundation, constant axial tension, a concentrated mass, and an arbitrary forcing function are included in the analysis. No restriction is placed on the values of the parameters involved, and the solution presented here contains all cited previous solutions as special cases.
The general solution to the classical problem of finite Euler Bernoulli beam
NASA Technical Reports Server (NTRS)
Hussaini, M. Y.; Amba-Rao, C. L.
1977-01-01
An analytical solution is obtained for the problem of free and forced vibrations of a finite Euler Bernoulli beam with arbitrary (partially fixed) boundary conditions. The effects of linear viscous damping, Winkler foundation, constant axial tension, a concentrated mass, and an arbitrary forcing function are included in the analysis. No restriction is placed on the values of the parameters involved, and the solution presented here contains all cited previous solutions as special cases.
An algorithm for a general class of routing problems derived from Huygens' principle
NASA Technical Reports Server (NTRS)
Avis, L. M.; Young, G. R.
1974-01-01
If a set of N points or nodes with a nonnegative cost associated with each ordered pair is known, it is desired to find a path from one given node to another given node which minimizes the cost sum. An algorithm is presented which yields a global minimum solution after at most N - 1 iterations or on a typical large third-generation computer, after 1 hour of computation time for a 10,000-node problem. The rapid-access data storage capacity demanded by the algorithm is approximately 3N words for costs read in from slow-access storage or 2N words for calculable costs. The time-storage requirements of the algorithm known to the authors. When the problem is viewed as a discretized optimal control problem, after N-1 iterations, an optimal control or node transition is established for each of the N nodes or states; thus, the algorithm can be applied to situations were there may be errors in the control that necessitate a closed loop control that necessitate a closed loop control philosophy.
Population problems: A constituent of general culture in the 21st century
NASA Astrophysics Data System (ADS)
Rath, Ferdinand J. C. M.
1993-03-01
Present world population growth is unprecedented. In Third World countries, the mere satisfaction of basic human needs is jeopardized; in the industrialized countries population pressure is felt differently, and to varying degrees; and some problems are common to rich and poor countries — for example, a galloping urbanization exacerbating the already critical social, economic and environmental problems of cities. Contrary to Malthus' time, the population debate is no longer confined to an elite. Moreover, demographic events in one part of the world are increasingly affecting other parts. Increased political awareness and maturity will encourage more and more people to participate in discussions on the factual and moral aspects of the problem. The question arises as to how society will prepare its citizens to take part in these discussions and the ensuing decision-making. "Population" must become an integral part of the socialization process, of which education is an essential element. In a time when the involvement of the average citizen in the national and international affairs of States and societies will be greater than ever before, adequate information and education will help to avoid the debate's being dominated by prejudice and sentiment instead of by insight.
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
AQUASOL: An efficient solver for the dipolar Poisson-Boltzmann-Langevin equation.
Koehl, Patrice; Delarue, Marc
2010-02-14
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 the PBE
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
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.
NASA Astrophysics Data System (ADS)
Kalainoff, Melinda Zapata
Studio classrooms, designed such that laboratory and lecture functions can occur in the same physical space, have been recognized as a promising contributing factor in promoting collaborative learning in the sciences (NRC, 2011). Moreover, in designing for instruction, a critical goal, especially in the sciences and engineering, is to foster an environment where students have opportunities for learning problem solving practices (NRC, 2012a). However, few studies show how this type of innovative learning environment shapes opportunities for learning in the sciences, which is critical to informing future curricular and instructional designs for these environments. Even fewer studies show how studio environments shape opportunities to develop problem solving practices specifically. In order to make visible how the learning environment promotes problem solving practices, this study explores problem solving phenomena in the daily life of an undergraduate General Chemistry studio class using an ethnographic perspective. By exploring problem solving as a sociocultural process, this study shows how the instructor and students co-construct opportunities for learning in whole class and small group interactional spaces afforded in this studio environment and how the differential demands on students in doing problems requires re-conceptualizing what it means to "apply a concept".
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.
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
Global stability of steady states in the classical Stefan problem for general boundary shapes
Hadžić, Mahir; Shkoller, Steve
2015-01-01
The classical one-phase Stefan problem (without surface tension) allows for a continuum of steady-state solutions, given by an arbitrary (but sufficiently smooth) domain together with zero temperature. We prove global-in-time stability of such steady states, assuming a sufficient degree of smoothness on the initial domain, but without any a priori restriction on the convexity properties of the initial shape. This is an extension of our previous result (Hadžić & Shkoller 2014 Commun. Pure Appl. Math. 68, 689–757 (doi:10.1002/cpa.21522)) in which we studied nearly spherical shapes. PMID:26261359
New Multigrid Solver Advances in TOPS
Falgout, R D; Brannick, J; Brezina, M; Manteuffel, T; McCormick, S
2005-06-27
In this paper, we highlight new multigrid solver advances in the Terascale Optimal PDE Simulations (TOPS) project in the Scientific Discovery Through Advanced Computing (SciDAC) program. We discuss two new algebraic multigrid (AMG) developments in TOPS: the adaptive smoothed aggregation method ({alpha}SA) and a coarse-grid selection algorithm based on compatible relaxation (CR). The {alpha}SA method is showing promising results in initial studies for Quantum Chromodynamics (QCD) applications. The CR method has the potential to greatly improve the applicability of AMG.
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.
Input-output-controlled nonlinear equation solvers
NASA Technical Reports Server (NTRS)
Padovan, Joseph
1988-01-01
To upgrade the efficiency and stability of the successive substitution (SS) and Newton-Raphson (NR) schemes, the concept of input-output-controlled solvers (IOCS) is introduced. By employing the formal properties of the constrained version of the SS and NR schemes, the IOCS algorithm can handle indefiniteness of the system Jacobian, can maintain iterate monotonicity, and provide for separate control of load incrementation and iterate excursions, as well as having other features. To illustrate the algorithmic properties, the results for several benchmark examples are presented. These define the associated numerical efficiency and stability of the IOCS.
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. PMID:23418367
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.
Jenny, Patrick Tchelepi, Hamdi A.; Lee, Seong H.
2009-11-01
This paper addresses the convergence properties of implicit numerical solution algorithms for nonlinear hyperbolic transport problems. It is shown that the Newton-Raphson (NR) method converges for any time step size, if the flux function is convex, concave, or linear, which is, in general, the case for CFD problems. In some problems, e.g., multiphase flow in porous media, the nonlinear flux function is S-shaped (not uniformly convex or concave); as a result, a standard NR iteration can diverge for large time steps, even if an implicit discretization scheme is used to solve the nonlinear system of equations. In practice, when such convergence difficulties are encountered, the current time step is cut, previous iterations are discarded, a smaller time step size is tried, and the NR process is repeated. The criteria for time step cutting and selection are usually based on heuristics that limit the allowable change in the solution over a time step and/or NR iteration. Here, we propose a simple modification to the NR iteration scheme for conservation laws with S-shaped flux functions that converges for any time step size. The new scheme allows one to choose the time step size based on accuracy consideration only without worrying about the convergence behavior of the nonlinear solver. The proposed method can be implemented in an existing simulator, e.g., for CO{sub 2} sequestration or reservoir flow modeling, quite easily. The numerical analysis is confirmed with simulation studies using various test cases of nonlinear multiphase transport in porous media. The analysis and numerical experiments demonstrate that the modified scheme allows for the use of arbitrarily large time steps for this class of problems.
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
NASA Astrophysics Data System (ADS)
Verleye, B.; Croce, R.; Griebel, M.; Klitz, M.; Lomov, S. V.; Verpoest, I.; Roose, D.
2007-04-01
For the simulation of the impregnation process of Resin Transfer Moulding, the permeability of the textile is a key input parameter. Using Darcy's law, the permeability can be derived from a numerical simulation of the fluid flow for a unit cell problem. In this paper we present the results of simulations with a Stokes solver, implemented in the permeability predicting software FlowTex. The results are compared with those of a Navier-Stokes solver and validated using theoretical results for model problems and with experimental data for real textiles.
NASA Astrophysics Data System (ADS)
Sterken, C.; Freyhammer, L. M.; Arentoft, T.; van Genderen, A. M.
2001-06-01
We review the particular problems of ground-based photometry of the composite object eta Carinae for which high-precision long-term photometric monitoring is so hard to accomplish. eta Car, by its appearance as an ultrabright extended object, by its anomalous spectral nature, and by its most outspoken variability, is the single most difficult stellar object to measure photometrically and to monitor over a long time interval. The problems belong to several levels: very limited availability of an astrophysically appropriate photometric system, the presence of strong (and variable) emission lines, the need for a telescope with a suitable f-ratio, and the steadily diminishing possibilities to collect data over a long period of time. We demonstrate that the transformation from our y measurements to V is valid for many stars, but not for eta Car nor for some less peculiar objects. Even pure Johnson V data can not be guaranteed to be accurately tied to the E-region standard stars. The'underestimated' V-magnitude of eta Car based on y-filter photometry is not to be considered a suspicious characteristic of our intermediate-band photometry, but is an inherent element of the photometric approach of discussing V magnitudes on the basis of data obtained with a Stromgren y filter. Aperture corrections of a single isolated measurement remain prone to random errors of the order of 0.005-0.015 mag.
A fast Euler solver for steady flows
NASA Technical Reports Server (NTRS)
Moretti, G.
1983-01-01
A numerical technique to solve the Euler equations for steady, two-dimensional flows is presented. The technique extends to two-dimensional problems a formulation which was found to be extremely efficient for one-dimensional flows. Generalized Riemann variables are defined along two families of orthogonal coordinates, and integrated separately, sweeping back and forth alternatively along coordinate lines. The technique is second-order accurate and converges very rapidly. In addition, each step requires a minimal number of operations. Preliminary results for subsonic and transonic shockless flows are presented and discussed.
Comparison of electromagnetic solvers for antennas mounted on vehicles
NASA Astrophysics Data System (ADS)
Mocker, M. S. L.; Hipp, S.; Spinnler, F.; Tazi, H.; Eibert, T. F.
2015-11-01
An electromagnetic solver comparison for various use cases of antennas mounted on vehicles is presented. For this purpose, several modeling approaches, called transient, frequency and integral solver, including the features fast resonant method and autoregressive filter, offered by CST MWS, are investigated. The solvers and methods are compared for a roof antenna itself, a simplified vehicle, a roof including a panorama window and a combination of antenna and vehicle. With these examples, the influence of different materials, data formats and parameters such as size and complexity are investigated. Also, the necessary configurations for the mesh and the solvers are described.
ERIC Educational Resources Information Center
Martinez, Michael E.
1998-01-01
Many important human activities involve accomplishing goals without a script. There is no formula for true problem-solving. Heuristic, cognitive "rules of thumb" are the problem-solver's best guide. Learners should understand heuristic tools such as means-end analysis, working backwards, successive approximation, and external representation. Since…
[Medical Problems in Air Travel from a General Practitioner’s Perspective].
Stutz, Andreas; Ensslin, Angela
2016-07-01
As travel by air increases, so does the number of passengers with chronic or acute medical issues. To evaluate fitness for air travel, it is necessary to consider the impact of the altered atmospheric surroundings in an airplane on the current illness to avoid a worsening of health conditions or even an emergency. As first medical contact person, the general practitioner will define supportive measures together with the patient and discuss these with the Medical Service of the airline for implementation. After a thorough evaluation, most patients will be classified fit to fly. Furthermore, a pre-travel consultation should address necessary vaccinations and information on infectious diseases. PMID:27381306
NASA Astrophysics Data System (ADS)
Singh, R.; Kumar, V.
2016-02-01
In this study an eigen value approach has been employed to examine the mechanical force applied along with a transverse magnetic field in a two dimensional generalized magneto micropolar thermoelastic infinite space. Results have been obtained by treating rotational velocity to be invariant. Integral transforms have been applied to solve the system of partial differential equations. Components of displacement, normal stress, tangential couple stress, temperature distribution, electric field and magnetic field have been obtained in the transformed domain. Finally numerical inversion technique has been used to invert the result in the physical domain. Graphical analysis has been done to described the study.
Investigating the early Earth faint young Sun problem with a general circulation model
NASA Astrophysics Data System (ADS)
Kunze, M.; Godolt, M.; Langematz, U.; Grenfell, J. L.; Hamann-Reinus, A.; Rauer, H.
2014-08-01
The faint young Sun problem, i.e. the contradiction of a reduced solar luminosity by 15-25% during the Archaean and the geological evidence for relatively high surface temperatures that allowed the presence of liquid water, is still mostly open. It is suggested that the cooling induced by a fainter Sun was e.g. offset by higher levels of greenhouse gases (GHGs) during the Archaean, but achieving the amounts of carbon dioxide (CO2) that are necessary to solve the problem can not be supported by proxy data and the estimates of other additional GHGs diverge. In our study we investigate this problem by using the climate model EMAC with a spectrally resolved irradiance dataset valid for the Archaean epoch of the Earth. Our experimental setup contains a series of model runs which allow the investigation of the role of the continents, the ozone and oxygen content of the atmosphere, the solar luminosity, and the CO2 concentration on the climate of the Archaean. Replacing the present day continents with a global ocean lead to a warming at the surface by ~3 K and an intensified hydrological cycle. The generation of planetary waves and their propagation to the middle atmosphere is reduced, which intensifies the polar night jet and decelerates the Brewer-Dobson circulation. Slightly lower global annual mean temperatures can be found for an anoxic atmosphere. The absent ozone heating in the middle atmosphere leads to very low temperatures in the middle atmosphere and a vanishing polar night jet, whereas the subtropical jets and the Hadley circulation are intensified. The reduction of the solar luminosity to 82% of the present value leads to a globally ice-covered planet and very dry conditions. Prescribing 10 times the present atmospheric level of CO2 with the same solar luminosity leads to a broad belt of liquid surface water throughout the year, although the global annual mean temperature is below the freezing point of water. On reducing the solar luminosity to 77% of the
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.
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.
Webster, Clayton G; Gunzburger, Max D
2013-01-01
We present a scalable, parallel mechanism for stochastic identification/control for problems constrained by partial differential equations with random input data. Several identification objectives will be discussed that either minimize the expectation of a tracking cost functional or minimize the difference of desired statistical quantities in the appropriate $L^p$ norm, and the distributed parameters/control can both deterministic or stochastic. Given an objective we prove the existence of an optimal solution, establish the validity of the Lagrange multiplier rule and obtain a stochastic optimality system of equations. The modeling process may describe the solution in terms of high dimensional spaces, particularly in the case when the input data (coefficients, forcing terms, boundary conditions, geometry, etc) are affected by a large amount of uncertainty. For higher accuracy, the computer simulation must increase the number of random variables (dimensions), and expend more effort approximating the quantity of interest in each individual dimension. Hence, we introduce a novel stochastic parameter identification algorithm that integrates an adjoint-based deterministic algorithm with the sparse grid stochastic collocation FEM approach. This allows for decoupled, moderately high dimensional, parameterized computations of the stochastic optimality system, where at each collocation point, deterministic analysis and techniques can be utilized. The advantage of our approach is that it allows for the optimal identification of statistical moments (mean value, variance, covariance, etc.) or even the whole probability distribution of the input random fields, given the probability distribution of some responses of the system (quantities of physical interest). Our rigorously derived error estimates, for the fully discrete problems, will be described and used to compare the efficiency of the method with several other techniques. Numerical examples illustrate the theoretical
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 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)
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.
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.
Elhai, Jon D; Don Richardson, J; Pedlar, David J
2007-01-01
We investigated general medical and psychological treatment use predictors among peacekeeping veterans with health problems, aiming to find those characteristics most associated with treatment use intensity (i.e., visit counts). One thousand one hundred and thirty-two male Canadian Forces peacekeeping veterans registered with Veterans Affairs for health problems were randomly recruited for a prospective national survey. Regression analyses for treatment use intensity controlled for age, total time deployed and health problems (covariates), and examined the incremental contribution of depression and post-traumatic stress disorder (PTSD) severity on health service use intensity. Results revealed that after controlling for covariates, the depression and PTSD model was associated with increased medical and psychological treatment use intensity. Medical use intensity was significantly predicted by married status, greater depression and health problems; psychological treatment use intensity was predicted by younger age, greater PTSD severity and health problems. This study highlights the importance of an integrated primary care-mental health service delivery model for veterans. PMID:16965892
Tzvetkova, G.V.; Resconi, G.
1999-10-01
The paper deals with the forward dynamics problem in robotics. The solution of the problem is found on the basis of a new theory, called general system logical theory. It uses operators and transformation of operators extensively to study objects and their relations in the real world. The basis notions and operator equations are given. The forward dynamics problem is presented as a diagram, called elementary logical system. The diagram unities a set of variables, a set of operators, and a set of relations between the operators. A generic form of a recursive process using the operators and the Lie product is described. The convergence of the process is discussed. Original operator procedures dedicated to the links of the robot are proposed. The wanted solution is found at the limit of the recursive process. An example is given, as well. The result obtained illustrates the ability of the theory to study robotics problems. The forward dynamics problem is solved in a new way and without inversion of the mass matrix of the robot.
Piserchia, Andrea; Barone, Vincenzo
2016-08-01
A generalization to arbitrary large amplitude motions of a recent approach to the evaluation of diffusion tensors [ J. Comput. Chem. , 2009 , 30 , 2 - 13 ] is presented and implemented in a widely available package for electronic structure computations. A fully black-box tool is obtained, which, starting from the generation of geometric structures along different kinds of paths, proceeds toward the evaluation of an effective diffusion tensor and to the solution of one-dimensional Smoluchowski equations by a robust numerical approach rooted in the discrete variable representation (DVR). Application to a number of case studies shows that the results issuing from our approach are identical to those delivered by previous software (in particular DiTe) for rigid scans along a dihedral angle, but can be improved by employing relaxed scans (i.e., constrained geometry optimizations) or even more general large amplitude paths. The theoretical and numerical background is robust and general enough to allow quite straightforward extensions in several directions (e.g., inclusion of reactive paths, solution of Fokker-Planck or stochastic Liouville equations, multidimensional problems, free-energy rather than electronic-energy driven processes). PMID:27403666
Algebraic Multiscale Solver for Elastic Geomechanical Deformation
NASA Astrophysics Data System (ADS)
Castelletto, N.; Hajibeygi, H.; Tchelepi, H.
2015-12-01
Predicting the geomechanical response of geological formations to thermal, pressure, and mechanical loading is important in many engineering applications. The mathematical formulation that describes deformation of a reservoir coupled with flow and transport entails heterogeneous coefficients with a wide range of length scales. Such detailed heterogeneous descriptions of reservoir properties impose severe computational challenges for the study of realistic-scale (km) reservoirs. To deal with these challenges, we developed an Algebraic Multiscale Solver for ELastic geomechanical deformation (EL-AMS). Constructed on finite element fine-scale system, EL-AMS imposes a coarse-scale grid, which is a non-overlapping decomposition of the domain. Then, local (coarse) basis functions for the displacement vector are introduced. These basis functions honor the elastic properties of the local domains subject to the imposed local boundary conditions. The basis form the Restriction and Prolongation operators. These operators allow for the construction of accurate coarse-scale systems for the displacement. While the multiscale system is efficient for resolving low-frequency errors, coupling it with a fine-scale smoother, e.g., ILU(0), leads to an efficient iterative solver. Numerical results for several test cases illustrate that EL-AMS is quite efficient and applicable to simulate elastic deformation of large-scale heterogeneous reservoirs.
Progress in Application of Generalized Wigner Distribution to Growth and Other Problems
NASA Astrophysics Data System (ADS)
Einstein, T. L.; Morales-Cifuentes, Josue; Pimpinelli, Alberto; Gonzalez, Diego Luis
We recap the use of the (single-parameter) Generalized Wigner Distribution (GWD) to analyze capture-zone distributions associated with submonolayer epitaxial growth. We discuss recent applications to physical systems, as well as key simulations. We pay particular attention to how this method compares with other methods to assess the critical nucleus size characterizing growth. The following talk discusses a particular case when special insight is needed to reconcile the various methods. We discuss improvements that can be achieved by going to a 2-parameter fragmentation approach. At a much larger scale we have applied this approach to various distributions in socio-political phenomena (areas of secondary administrative units [e.g., counties] and distributions of subway stations). Work at UMD supported by NSF CHE 13-05892.
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.
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.
NASA Astrophysics Data System (ADS)
Pereira, J. P.; Duarte, C. A.; Jiao, X.; Guoy, D.
2009-06-01
This paper presents a study of generalized enrichment functions for 3D curved crack fronts. Two coordinate systems used in the definition of singular curved crack front enrichment functions are analyzed. In the first one, a set of Cartesian coordinate systems defined along the crack front is used. In the second case, the geometry of the crack front is approximated by a set of curvilinear coordinate systems. A description of the computation of derivatives of enrichment functions and curvilinear base vectors is presented. The coordinate systems are automatically defined using geometrical information provided by an explicit representation of the crack surface. A detailed procedure to accurately evaluate the surface normal, conormal and tangent vectors along curvilinear crack fronts in explicit crack surface representations is also presented. An accurate and robust definition of orthonormal vectors along crack fronts is crucial for the proper definition of enrichment functions. Numerical experiments illustrate the accuracy and robustness of the proposed approaches.
NASA Technical Reports Server (NTRS)
Mon, G. R.
1985-01-01
A general research approach was outlined toward understanding water-module interactions and the influence of temperature involving the need to: quantify module performance loss versus level of accumulated degradation, establish the dependence of the degradation reaction rate on module moisture and temperature levels, and determine module moisture and temperature levels in field environments. These elements were illustrated with examples drawn from studies of the now relatively well understood module electrochemical degradation process. Research data presented include temperature and humidity-dependent equilibrium leakage current values for multiparameter module material and design configurations. The contributions of surface, volume, and interfacial conductivities was demonstrated. Research directions were suggested to more fully understand the contributions to overall module conductivity of surface, volume, and interfacial conductivities over ranges of temperature and relative humidity characteristic of field environments.
2013-01-01
Background Refugees are a particularly vulnerable group in relation to the development of mental illness and many may have been subjected to torture or other traumatic experiences. General practitioners are gatekeepers for access to several parts of the psychiatric system and knowledge of their patients’ refugee background is crucial to secure adequate care. The aim of this study is to investigate how general practitioners experience providing care to refugees with mental health problems. Methods The study was conducted as part of an EU project on European Best Practices in Access, Quality and Appropriateness of Health Services for Immigrants in Europe (EUGATE). Semi-structured interviews were carried out with nine general practitioners in the vicinity of Copenhagen purposively selected from areas with a high proportion of immigrants. The analysis of the interviews is inspired by qualitative content analysis. Results One of the main themes identified in the analysis is communication. This includes the use of professional interpreters and that communication entails more than sharing a common language. Quality of care is another theme that emerges and includes awareness of possible trauma history, limited possibilities for refugees to participate in certain treatments due to language barriers and feelings of hopelessness in the general practitioners. The general practitioners may also choose different referral pathways for refugees and they report that their patients lack understanding regarding the differences between psychological problems and physical symptoms. Conclusion General practitioners experience that providing care to refugees differs from providing care for patients from the majority population. The different strategies employed by the general practitioners in the health care treatment of refugees may be the result of the great diversity in the organisation of general practice in Denmark and the lack of a national strategy in the health care management
Stable large-scale solver for Ginzburg-Landau equations for superconductors
NASA Astrophysics Data System (ADS)
Sadovskyy, I. A.; Koshelev, A. E.; Phillips, C. L.; Karpeyev, D. A.; Glatz, A.
2015-08-01
Understanding the interaction of vortices with inclusions in type-II superconductors is a major outstanding challenge both for fundamental science and energy applications. At application-relevant scales, the long-range interactions between a dense configuration of vortices and the dependence of their behavior on external parameters, such as temperature and an applied magnetic field, are all important to the net response of the superconductor. Capturing these features, in general, precludes analytical description of vortex dynamics and has also made numerical simulation prohibitively expensive. Here we report on a highly optimized iterative implicit solver for the time-dependent Ginzburg-Landau equations suitable for investigations of type-II superconductors on massively parallel architectures. Its main purpose is to study vortex dynamics in disordered or geometrically confined mesoscopic systems. In this work, we present the discretization and time integration scheme in detail for two types of boundary conditions. We describe the necessary conditions for a stable and physically accurate integration of the equations of motion. Using an inclusion pattern generator, we can simulate complex pinning landscapes and the effect of geometric confinement. We show that our algorithm, implemented on a GPU, can provide static and dynamic solutions of the Ginzburg-Landau equations for mesoscopically large systems over thousands of time steps in a matter of hours. Using our formulation, studying scientifically-relevant problems is a computationally reasonable task.
General Features of Supersymmetric Signals at the ILC: Solving the LHC Inverse Problem
Berger, Carola F.; Gainer, James S.; Hewett, JoAnne L.; Lillie, Ben; Rizzo, Thomas G.
2007-12-19
We examine whether the {radical}s = 500 GeV International Linear Collider with 80% electron beam polarization can be used to solve the LHC Inverse Problem within the framework of the MSSM. We investigate 242 points in the MSSM parameter space, which we term models, that correspond to the 162 pairs of models found by Arkani-Hamed et al. to give indistinguishable signatures at the LHC. We first determine whether the production of the various SUSY particles is visible above the Standard Model background for each of these parameter space points, and then make a detailed comparison of their various signatures. Assuming an integrated luminosity of 500 fb{sup -1}, we find that only 82 out of 242 models lead to visible signatures of some kind with a significance {ge} 5 and that only 57(63) out of the 162 model pairs are distinguishable at 5(3){sigma}. Our analysis includes PYTHIA and CompHEP SUSY signal generation, full matrix element SM backgrounds for all 2 {yields} 2, 2 {yields} 4, and 2 {yields} 6 processes, ISR and beamstrahlung generated via WHIZARD/GuineaPig, and employs the fast SiD detector simulation org.lcsim.
Merwa, Robert; Hollaus, Karl; Brandstätter, Bernhard; Scharfetter, Hermann
2003-05-01
Magnetic induction tomography (MIT) is used for reconstructing the changes of the conductivity in a target object using alternating magnetic fields. Applications include, for example, the non-invasive monitoring of oedema in the human brain. A powerful software package has been developed which makes it possible to generate a finite element (FE) model of complex structures and to calculate the eddy currents in the object under investigation. To validate our software a model of a previously published experimental arrangement was generated. The model consists of a coaxial coil system and a conducting sphere which is moved perpendicular to the coil axis (a) in an empty space and (b) in a saline-filled cylindrical tank. The agreement of the measured and simulated data is very good when taking into consideration the systematic measurement errors in case (b). Thus the applicability of the simulation algorithm for two-compartment systems has been demonstrated even in the case of low conductivities and weak contrast. This can be considered an important step towards the solution of the inverse problem of MIT. PMID:12812437
Developing Discontinuous Galerkin Methods for Solving Multiphysics Problems in General Relativity
NASA Astrophysics Data System (ADS)
Kidder, Lawrence; Field, Scott; Teukolsky, Saul; Foucart, Francois; SXS Collaboration
2016-03-01
Multi-messenger observations of the merger of black hole-neutron star and neutron star-neutron star binaries, and of supernova explosions will probe fundamental physics inaccessible to terrestrial experiments. Modeling these systems requires a relativistic treatment of hydrodynamics, including magnetic fields, as well as neutrino transport and nuclear reactions. The accuracy, efficiency, and robustness of current codes that treat all of these problems is not sufficient to keep up with the observational needs. We are building a new numerical code that uses the Discontinuous Galerkin method with a task-based parallelization strategy, a promising combination that will allow multiphysics applications to be treated both accurately and efficiently on petascale and exascale machines. The code will scale to more than 100,000 cores for efficient exploration of the parameter space of potential sources and allowed physics, and the high-fidelity predictions needed to realize the promise of multi-messenger astronomy. I will discuss the current status of the development of this new code.
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.
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.