Science.gov

Sample records for active problem solvers

  1. 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)

  2. Wicked Problem Solvers.

    PubMed

    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

  3. 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)

  4. Aleph Field Solver Challenge Problem Results Summary.

    SciTech Connect

    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.

  5. DPS--a computerised diagnostic problem solver.

    PubMed

    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

  6. Scalable Adaptive Multilevel Solvers for Multiphysics Problems

    SciTech Connect

    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.

  7. Experiences with linear solvers for oil reservoir simulation problems

    SciTech Connect

    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.

  8. 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…

  9. 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…

  10. 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.

  11. 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)

  12. 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.

  13. 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…

  14. 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).

  15. Navier-Stokes Solvers and Generalizations for Reacting Flow Problems

    SciTech Connect

    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).

  16. 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…

  17. 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.

  18. Parallel Auxiliary Space AMG Solver for $H(div)$ Problems

    SciTech Connect

    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.

  19. 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…

  20. 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.

  1. 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…

  2. 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.

  3. Polyurethanes: versatile materials and sustainable problem solvers for today's challenges.

    PubMed

    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

  4. An optimal iterative solver for the Stokes problem

    SciTech Connect

    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.

  5. GPU accelerated solver for nonlinear reaction-diffusion systems. Application to the electrophysiology problem

    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.

  6. 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.

  7. Black box multigrid solver for definite and indefinite problems

    SciTech Connect

    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.

  8. Efficient Solvers for Linear Elasticity Problems Based on the Discrete Fourier Transform and TFETI Decomposition

    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.

  9. 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…

  10. Implicit solvers for large-scale nonlinear problems

    SciTech Connect

    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.

  11. PowerPlay: Training an Increasingly General Problem Solver by Continually Searching for the Simplest Still Unsolvable Problem

    PubMed Central

    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

  12. PowerPlay: Training an Increasingly General Problem Solver by Continually Searching for the Simplest Still Unsolvable Problem.

    PubMed

    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

  13. Problem Solvers

    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,…

  14. Knowledge-based design of generate-and-patch problem solvers that solve global resource assignment 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'.

  15. 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.

  16. Robust parallel iterative solvers for linear and least-squares problems, Final Technical Report

    SciTech Connect

    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

  17. Nursing Students as Change Agents and Problem Solvers in the Community: Community-based Nursing Education in Practice.

    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…

  18. High-resolution coupled physics solvers for analysing fine-scale nuclear reactor design problems

    PubMed Central

    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

  19. High-resolution coupled physics solvers for analysing fine-scale nuclear reactor design problems.

    PubMed

    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

  20. 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

  1. Making Sense of Math: How to Help Every Student become a Mathematical Thinker and Problem Solver (ASCD Arias)

    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…

  2. 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.

  3. Methods for Solving Gas Damping Problems in Perforated Microstructures Using a 2D Finite-Element Solver

    PubMed Central

    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.

  4. Multigrid solvers and multigrid preconditioners for the solution of variational data assimilation problems

    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

  5. 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…

  6. 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…

  7. Larger groups of passerines are more efficient problem solvers in the wild.

    PubMed

    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

  8. 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

  9. A fast parallel solver for the forward problem in electrical impedance tomography.

    PubMed

    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

  10. 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

  11. A high-order integral solver for scalar problems of diffraction by screens and apertures in three-dimensional space

    SciTech Connect

    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.

  12. A new solver for the elastic normal contact problem using conjugate gradients, deflation, and an FFT-based preconditioner

    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.

  13. Algebraic multigrid preconditioning within parallel finite-element solvers for 3-D electromagnetic modelling problems in geophysics

    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

  14. An evaluation of parallel multigrid as a solver and a preconditioner for singular perturbed problems

    SciTech Connect

    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.

  15. Junction-Generalized Riemann Problem for stiff hyperbolic balance laws in networks: An implicit solver and ADER schemes

    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.

  16. A fast algorithm for parabolic PDE-based inverse problems based on Laplace transforms and flexible Krylov solvers

    SciTech Connect

    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.

  17. TRIQS/CTHYB: A continuous-time quantum Monte Carlo hybridisation expansion solver for quantum impurity problems

    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.

  18. Coaching Family Caregivers to Become Better Problem Solvers When Caring for Persons with Advanced Cancer.

    PubMed

    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

  19. [Problem Solving Activities.

    ERIC Educational Resources Information Center

    Wisconsin Univ. - Stout, Menomonie. Center for Vocational, Technical and Adult Education.

    The teacher directed problem solving activities package contains 17 units: Future Community Design, Let's Build an Elevator, Let's Construct a Catapult, Let's Design a Recreational Game, Let's Make a Hand Fishing Reel, Let's Make a Wall Hanging, Let's Make a Yo-Yo, Marooned in the Past, Metrication, Mousetrap Vehicles, The Multi System…

  20. Applied Mathematics: Targets for Learning. Strategies for 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 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…

  1. 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…

  2. 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...

  3. Understanding the Problem. Problem Solving and Communication Activity Series. The Math Forum: Problems of the Week

    ERIC Educational Resources Information Center

    Math Forum @ Drexel, 2009

    2009-01-01

    Different techniques for understanding a problem can lead to ideas for never-used-before solutions. Good problem-solvers use a problem-solving strategy and may come back to it frequently while they are working on the problem to refine their strategy, see if they can find better solutions, or find other questions. Writing is an integral part of…

  4. Composite solvers for linear saddle point problems arising from the incompressible Stokes equations with highly heterogeneous viscosity structure

    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

  5. 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.…

  6. 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,…

  7. 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…

  8. 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.

  9. 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.

  10. Analysis of a parallelized nonlinear elliptic boundary value problem solver with application to reacting flows

    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.

  11. Software-engineering challenges of building and deploying reusable problem solvers.

    PubMed

    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

  12. Software-engineering challenges of building and deploying reusable problem solvers

    PubMed Central

    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

  13. Parallel Multigrid Equation Solver

    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.

  14. Computing Ro in a population with heterogeneity in sexual activity and proportionate mixing using a STM-solver

    NASA Astrophysics Data System (ADS)

    Gutierrez A., Natalia A.

    2014-06-01

    A model to determinate the reproductive basic number, detonated Ro, for the case of population with heterogeneity in sexual activity and proportionate mixing is solved using computer algebra and SMT solvers. Specifically Maple and Z3 were used. The code for the solution of the model was written in Z3-Python, but it can also be played by Z3-SMT-Lib. Ro represents an algebraic synthesis of every epidemiological parameter. Numerical simulations were done to prove the effectiveness of the model and the code. The algebraic structure of Ro suggests the possible control measurements that should be implemented to avoid the propagation of the sexual transmitted diseases. The obtained results are important on the computational epidemiology field. As a future investigation, it is suggested to apply the STM solvers to analyze models for other kinds of epidemic diseases.

  15. Pliris Solver Package

    SciTech Connect

    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.

  16. Pliris Solver Package

    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

  17. A quasi-optimal coarse problem and an augmented Krylov solver for the variational theory of complex rays

    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.

  18. Noticing relevant problem features: activating prior knowledge affects problem solving by guiding encoding

    PubMed Central

    Crooks, Noelle M.; Alibali, Martha W.

    2013-01-01

    This study investigated whether activating elements of prior knowledge can influence how problem solvers encode and solve simple mathematical equivalence problems (e.g., 3 + 4 + 5 = 3 + __). Past work has shown that such problems are difficult for elementary school students (McNeil and Alibali, 2000). One possible reason is that children's experiences in math classes may encourage them to think about equations in ways that are ultimately detrimental. Specifically, children learn a set of patterns that are potentially problematic (McNeil and Alibali, 2005a): the perceptual pattern that all equations follow an “operations = answer” format, the conceptual pattern that the equal sign means “calculate the total”, and the procedural pattern that the correct way to solve an equation is to perform all of the given operations on all of the given numbers. Upon viewing an equivalence problem, knowledge of these patterns may be reactivated, leading to incorrect problem solving. We hypothesized that these patterns may negatively affect problem solving by influencing what people encode about a problem. To test this hypothesis in children would require strengthening their misconceptions, and this could be detrimental to their mathematical development. Therefore, we tested this hypothesis in undergraduate participants. Participants completed either control tasks or tasks that activated their knowledge of the three patterns, and were then asked to reconstruct and solve a set of equivalence problems. Participants in the knowledge activation condition encoded the problems less well than control participants. They also made more errors in solving the problems, and their errors resembled the errors children make when solving equivalence problems. Moreover, encoding performance mediated the effect of knowledge activation on equivalence problem solving. Thus, one way in which experience may affect equivalence problem solving is by influencing what students encode about the

  19. Three-dimensional neuronal brain activity estimation using shrinking smooth weighted-minimum-norm focal underdetermined-system solver methods

    NASA Astrophysics Data System (ADS)

    Zouch, Wassim; Slima, Mohamed Ben; Feki, Imed; Derambure, Philippe; Taleb-Ahmed, Abdelmalik; Hamida, Ahmed Ben

    2010-12-01

    A new nonparametric method, based on the smooth weighted-minimum-norm (WMN) focal underdetermined-system solver (FOCUSS), for electrical cerebral activity localization using electroencephalography measurements is proposed. This method iteratively adjusts the spatial sources by reducing the size of the lead-field and the weighting matrix. Thus, an enhancement of source localization is obtained, as well as a reduction of the computational complexity. The performance of the proposed method, in terms of localization errors, robustness, and computation time, is compared with the WMN-FOCUSS and nonshrinking smooth WMN-FOCUSS methods as well as with standard generalized inverse methods (unweighted minimum norm, WMN, and FOCUSS). Simulation results for single-source localization confirm the effectiveness and robustness of the proposed method with respect to the reconstruction accuracy of a simulated single dipole.

  20. 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.

  1. Finite Element Interface to Linear Solvers

    SciTech Connect

    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.

  2. Self-correcting Multigrid Solver

    SciTech Connect

    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.

  3. Class and Homework Problems: The Break-Even Radius of Insulation Computed Using Excel Solver and WolframAlpha

    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,…

  4. Training Interdisciplinary "Wicked Problem" Solvers: Applying Lessons from HERO in Community-Based Research Experiences for Undergraduates

    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…

  5. Mental Subtraction in High- and Lower Skilled Arithmetic Problem Solvers: Verbal Report versus Operand-Recognition Paradigms

    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…

  6. Performance of preconditioned iterative and multigrid solvers in solving the three-dimensional magnetotelluric modeling problem using the staggered finite-difference method: a comparative study

    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.

  7. Scalable Parallel Algebraic Multigrid Solvers

    SciTech Connect

    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.

  8. Amesos Solver Package

    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

  9. Amesos Solver Package

    SciTech Connect

    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.

  10. Every Unsuccessful Problem Solver Is Unsuccessful in His or Her Own Way: Affective and Cognitive Factors in Proving

    ERIC Educational Resources Information Center

    Furinghetti, Fulvia; Morselli, Francesca

    2009-01-01

    It is widely recognized that purely cognitive behavior is extremely rare in performing mathematical activity: other factors, such as the affective ones, play a crucial role. In light of this observation, we present a reflection on the presence of affective and cognitive factors in the process of proving. Proof is considered as a special case of…

  11. Neural Activity When People Solve Verbal Problems with Insight

    PubMed Central

    2004-01-01

    People sometimes solve problems with a unique process called insight, accompanied by an “Aha!” experience. It has long been unclear whether different cognitive and neural processes lead to insight versus noninsight solutions, or if solutions differ only in subsequent subjective feeling. Recent behavioral studies indicate distinct patterns of performance and suggest differential hemispheric involvement for insight and noninsight solutions. Subjects solved verbal problems, and after each correct solution indicated whether they solved with or without insight. We observed two objective neural correlates of insight. Functional magnetic resonance imaging (Experiment 1) revealed increased activity in the right hemisphere anterior superior temporal gyrus for insight relative to noninsight solutions. The same region was active during initial solving efforts. Scalp electroencephalogram recordings (Experiment 2) revealed a sudden burst of high-frequency (gamma-band) neural activity in the same area beginning 0.3 s prior to insight solutions. This right anterior temporal area is associated with making connections across distantly related information during comprehension. Although all problem solving relies on a largely shared cortical network, the sudden flash of insight occurs when solvers engage distinct neural and cognitive processes that allow them to see connections that previously eluded them. PMID:15094802

  12. 3-D magnetotelluric inversion including topography using deformed hexahedral edge finite elements and direct solvers parallelized on SMP computers - Part I: forward problem and parameter Jacobians

    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

  13. Problem Solvers to the Rescue

    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…

  14. A scalable 2-D parallel sparse solver

    SciTech Connect

    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.

  15. Finite Element Interface to Linear Solvers

    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

  16. Magnetic Field Solver

    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.

  17. 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.

  18. Simulation of Unsteady Flows Using an Unstructured Navier-Stokes Solver on Moving and Stationary Grids

    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.

  19. A parallel PCG solver for MODFLOW.

    PubMed

    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

  20. Code Verification of the HIGRAD Computational Fluid Dynamics Solver

    SciTech Connect

    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.

  1. A coupled 3D-1D numerical monodomain solver for cardiac electrical activation in the myocardium with detailed Purkinje network

    NASA Astrophysics Data System (ADS)

    Vergara, Christian; Lange, Matthias; Palamara, Simone; Lassila, Toni; Frangi, Alejandro F.; Quarteroni, Alfio

    2016-03-01

    We present a model for the electrophysiology in the heart to handle the electrical propagation through the Purkinje system and in the myocardium, with two-way coupling at the Purkinje-muscle junctions. In both the subproblems the monodomain model is considered, whereas at the junctions a resistor element is included that induces an orthodromic propagation delay from the Purkinje network towards the heart muscle. We prove a sufficient condition for convergence of a fixed-point iterative algorithm to the numerical solution of the coupled problem. Numerical comparison of activation patterns is made with two different combinations of models for the coupled Purkinje network/myocardium system, the eikonal/eikonal and the monodomain/monodomain models. Test cases are investigated for both physiological and pathological activation of a model left ventricle. Finally, we prove the reliability of the monodomain/monodomain coupling on a realistic scenario. Our results underlie the importance of using physiologically realistic Purkinje-trees with propagation solved using the monodomain model for simulating cardiac activation.

  2. What Is Problem Solving?

    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…

  3. BOOK REVIEW: Inverse Problems. Activities for Undergraduates

    NASA Astrophysics Data System (ADS)

    Yamamoto, Masahiro

    2003-06-01

    This book is a valuable introduction to inverse problems. In particular, from the educational point of view, the author addresses the questions of what constitutes an inverse problem and how and why we should study them. Such an approach has been eagerly awaited for a long time. Professor Groetsch, of the University of Cincinnati, is a world-renowned specialist in inverse problems, in particular the theory of regularization. Moreover, he has made a remarkable contribution to educational activities in the field of inverse problems, which was the subject of his previous book (Groetsch C W 1993 Inverse Problems in the Mathematical Sciences (Braunschweig: Vieweg)). For this reason, he is one of the most qualified to write an introductory book on inverse problems. Without question, inverse problems are important, necessary and appear in various aspects. So it is crucial to introduce students to exercises in inverse problems. However, there are not many introductory books which are directly accessible by students in the first two undergraduate years. As a consequence, students often encounter diverse concrete inverse problems before becoming aware of their general principles. The main purpose of this book is to present activities to allow first-year undergraduates to learn inverse theory. To my knowledge, this book is a rare attempt to do this and, in my opinion, a great success. The author emphasizes that it is very important to teach inverse theory in the early years. He writes; `If students consider only the direct problem, they are not looking at the problem from all sides .... The habit of always looking at problems from the direct point of view is intellectually limiting ...' (page 21). The book is very carefully organized so that teachers will be able to use it as a textbook. After an introduction in chapter 1, sucessive chapters deal with inverse problems in precalculus, calculus, differential equations and linear algebra. In order to let one gain some insight

  4. 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.

  5. ALPS: A Linear Program Solver

    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.

  6. 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.

  7. A multigrid fluid pressure solver handling separating solid boundary conditions.

    PubMed

    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

  8. HPCCG Solver Package

    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

  9. A 3D Finite-Difference BiCG Iterative Solver with the Fourier-Jacobi Preconditioner for the Anisotropic EIT/EEG Forward Problem

    PubMed Central

    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

  10. A 3D finite-difference BiCG iterative solver with the Fourier-Jacobi preconditioner for the anisotropic EIT/EEG forward problem.

    PubMed

    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

  11. Comparison of open-source linear programming solvers.

    SciTech Connect

    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.

  12. 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.

  13. 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.

  14. Amesos2 Templated Direct Sparse Solver Package

    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.

  15. 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.

  16. Analysis, tuning and comparison of two general sparse solvers for distributed memory computers

    SciTech Connect

    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.

  17. 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.

  18. Parallel iterative solvers and preconditioners using approximate hierarchical methods

    SciTech Connect

    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.

  19. 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.

  20. 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.

  1. 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

  2. Quantitative analysis of numerical solvers for oscillatory biomolecular system models

    PubMed Central

    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

  3. Using native plants as problem-solvers

    SciTech Connect

    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.

  4. 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…

  5. 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…

  6. 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…

  7. Verification of cardiac mechanics software: benchmark problems and solutions for testing active and passive material behaviour

    PubMed Central

    Gurev, Viatcheslav; Arens, Sander; Augustin, Christoph M.; Baron, Lukas; Blake, Robert; Bradley, Chris; Castro, Sebastian; Crozier, Andrew; Favino, Marco; Fastl, Thomas E.; Fritz, Thomas; Gao, Hao; Gizzi, Alessio; Griffith, Boyce E.; Hurtado, Daniel E.; Krause, Rolf; Luo, Xiaoyu; Nash, Martyn P.; Pezzuto, Simone; Plank, Gernot; Rossi, Simone; Ruprecht, Daniel; Seemann, Gunnar; Smith, Nicolas P.; Sundnes, Joakim; Rice, J. Jeremy; Trayanova, Natalia; Wang, Dafang; Jenny Wang, Zhinuo; Niederer, Steven A.

    2015-01-01

    Models of cardiac mechanics are increasingly used to investigate cardiac physiology. These models are characterized by a high level of complexity, including the particular anisotropic material properties of biological tissue and the actively contracting material. A large number of independent simulation codes have been developed, but a consistent way of verifying the accuracy and replicability of simulations is lacking. To aid in the verification of current and future cardiac mechanics solvers, this study provides three benchmark problems for cardiac mechanics. These benchmark problems test the ability to accurately simulate pressure-type forces that depend on the deformed objects geometry, anisotropic and spatially varying material properties similar to those seen in the left ventricle and active contractile forces. The benchmark was solved by 11 different groups to generate consensus solutions, with typical differences in higher-resolution solutions at approximately 0.5%, and consistent results between linear, quadratic and cubic finite elements as well as different approaches to simulating incompressible materials. Online tools and solutions are made available to allow these tests to be effectively used in verification of future cardiac mechanics software. PMID:26807042

  8. 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.

  9. T2CG1, a package of preconditioned conjugate gradient solvers for TOUGH2

    SciTech Connect

    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.

  10. A multiple right hand side iterative solver for history matching

    SciTech Connect

    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.

  11. 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.

  12. 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.

  13. 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.

  14. Optimising a parallel conjugate gradient solver

    SciTech Connect

    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.

  15. 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.

  16. The problem of active SETI: An overview

    NASA Astrophysics Data System (ADS)

    Musso, Paolo

    2012-09-01

    In the present paper (originally presented at the First IAA Symposium on Searching for Life Signatures hold at the UNESCO on 22-26 September 2008) I try to summarize the results of all my previous studies on active SETI and its possible dangers for us, also considering some new topics, in order to provide a possibly complete overview of the whole matter. First, I try to evaluate the possible risks of an indirect contact with aliens, from the social, cultural, and religious point of view; then, the possible risks related with receiving information about alien science and technology; finally, the risk that active SETI could increase the probability of a physical contact with hostile aliens. My conclusion is that active SETI is very unlikely to be dangerous for us, but, at present, such a possibility cannot be completely excluded. Surprisingly, it turns out that a very important point to be assessed in order to improve our evaluation of active SETI is the pace of our technological progress. Some suggestions about the policy that international community should adopt towards active SETI are also included.

  17. Transition Problems and Play as Transitory Activity

    ERIC Educational Resources Information Center

    Brostrom, Stig

    2005-01-01

    Because too many children experience the transition to school as a culture shock, during the past decade teachers have implemented so-called transition activities in order to bridge the gap between preschool and school. However, transition to school also calls for a development of higher mental functions, among others the development of children's…

  18. Constructive Metacognitive Activity Shift in Mathematical Problem Solving

    ERIC Educational Resources Information Center

    Hastuti, Intan Dwi; Nusantara, Toto; Subanji; Susanto, Hery

    2016-01-01

    This study aims to describe the constructive metacognitive activity shift of eleventh graders in solving a mathematical problem. Subjects in this study were 10 students in grade 11 of SMAN 1 Malang. They were divided into 4 groups. Three types of metacognitive activity undertaken by students when completing mathematical problem are awareness,…

  19. Problem-Based Group Activities for Teaching Sensation and Perception

    ERIC Educational Resources Information Center

    Kreiner, David S.

    2009-01-01

    This article describes 14 problem-based group activities for a sensation and perception course. The intent was to provide opportunities for students to practice applying their knowledge to real-world problems related to course content. Student ratings of how effectively the activities helped them learn were variable but relatively high. Students…

  20. 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.

  1. Time-domain Raman analytical forward solvers.

    PubMed

    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

  2. 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.

  3. Using the scalable nonlinear equations solvers package

    SciTech Connect

    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.

  4. Performance Models for the Spike Banded Linear System Solver

    DOE PAGESBeta

    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

  5. The Problem with Word Problems: Solving Word Problems in Math Requires a Complex Web of Skills. But There's No Reason Why it Can't Be Fun

    ERIC Educational Resources Information Center

    Forsten, Char

    2004-01-01

    Children need to combine reading, thinking, and computational skills to solve math word problems. The author provides some strategies that principals can share with their teachers to help students become proficient and advanced problem-solvers. They include creating a conducive classroom environment, providing daily mental math activities, making…

  6. A generalized gyrokinetic Poisson solver

    SciTech Connect

    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.

  7. 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.

  8. Monitoring Affect States during Effortful Problem Solving Activities

    ERIC Educational Resources Information Center

    D'Mello, Sidney K.; Lehman, Blair; Person, Natalie

    2010-01-01

    We explored the affective states that students experienced during effortful problem solving activities. We conducted a study where 41 students solved difficult analytical reasoning problems from the Law School Admission Test. Students viewed videos of their faces and screen captures and judged their emotions from a set of 14 states (basic…

  9. Problem-Centered and Experimental Mathematics Activities for Aboriginal Students.

    ERIC Educational Resources Information Center

    Seputro, Theresia Tirta

    1998-01-01

    Presents an activity carried out by aboriginal students that addresses solving a real-life problem that could be linked to number sequence, graph theory, and combinations. Contains 14 references. (ASK)

  10. The Intermediate Impossible: A Prewriting Activity for Creative Problem Solving.

    ERIC Educational Resources Information Center

    Karloff, Kenneth

    1985-01-01

    Adapts Edward de Bono's "Intermediate Impossible" strategy--for considering ideas that normally would be discarded as stepping-stones to new ideas--for use as a prewriting activity to enhance creative problem solving. (HTH)

  11. An automatic ordering method for incomplete factorization iterative solvers

    SciTech Connect

    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.

  12. 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…

  13. 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.

  14. Problem Posing Based on Investigation Activities by University Students

    ERIC Educational Resources Information Center

    da Ponte, Joao Pedro; Henriques, Ana

    2013-01-01

    This paper reports a classroom-based study involving investigation activities in a university numerical analysis course. The study aims to analyse students' mathematical processes and to understand how these activities provide opportunities for problem posing. The investigations were intended to stimulate students in asking questions, to trigger…

  15. Real Life Problem Solving: A Collaborative Learning Activity.

    ERIC Educational Resources Information Center

    Englander, Karen

    2002-01-01

    Suggests that classroom activities that emphasize interaction help students to use language. Interaction allows students to practice being effective speakers by developing two needed sets of skills: managing an interaction and negotiating meaning. Provides examples of problem solving activities for use in the language classroom. (Author/VWL)

  16. Activities: Make Your Own Problems--And Then Solve Them.

    ERIC Educational Resources Information Center

    Mathematics Teacher, 1991

    1991-01-01

    Presented is a teacher's guide for a hands-on activity challenging students to develop problem-solving behaviors by exploring the construction of a right-cylinder of maximum volume from an m x n sheet of metal. Reproducible worksheets leading students through the activity are provided. (MDH)

  17. 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)

  18. Students' Experiences in Problem-Based Learning: Three Blind Mice Episode or Educational Innovation?

    ERIC Educational Resources Information Center

    Tan, Oon Seng

    2004-01-01

    Problem-based learning architecture typically involves a shift in three loci of educational preoccupation, namely (1) content coverage to problem engagement; (2) role of lecturing to role of coaching; and (3) students as passive learners to that of active problem-solvers. The purpose of this paper is to examine the issues of students' experiences…

  19. Migration of vectorized iterative solvers to distributed memory architectures

    SciTech Connect

    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.

  20. 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.

  1. Private school activities and psychosomatic problems in Japanese children.

    PubMed

    Matsumoto, K; Kaku, R; Nakagawa, K; Kaneko, Z

    1975-01-01

    This paper investigates the relation between private school activities and psychosomatic problems in Japanese elementary school children. Of 1,073 children studied, 67.3 percent attended private schools to study such subjects as calligraphy, abacus, and music. Of these children, 25.3 percent attended three to four times per week, and 18.1 percent five times and more. Statistical analysis showed that frequently attending children exhibited symptoms of dizziness, sleep disturbance, and other psycholphsiological problems. The results may warn educators as well as parents of some of the unfavorable effects of these extracurricular activities. PMID:1139974

  2. Elliptic Solvers with Adaptive Mesh Refinement on Complex Geometries

    SciTech Connect

    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.

  3. 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

  4. Student Technological Creativity Using Online Problem-Solving Activities

    ERIC Educational Resources Information Center

    Chang, Yu-Shan

    2013-01-01

    The purpose of this study was to investigate the effects of online (web-based) creative problem-solving (CPS) activities on student technological creativity and to examine the characteristics of student creativity in the context of online CPS. A pretest-posttest quasi-experiment was conducted with 107 fourth-grade students in Taiwan. The…

  5. 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.

  6. KLU2 Direct Linear Solver Package

    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.

  7. Multiscale Universal Interface: A concurrent framework for coupling heterogeneous solvers

    SciTech Connect

    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)

  8. 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

  9. 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).

  10. 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.

  11. 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.

  12. Belos Block Linear Solvers Package

    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

  13. A two-dimensional HLLC Riemann solver for conservation laws: Application to Euler and magnetohydrodynamic flows

    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

  14. Quadratic Optimization in the Problems of Active Control of Sound

    NASA Technical Reports Server (NTRS)

    Loncaric, J.; Tsynkov, S. V.; Bushnell, Dennis M. (Technical Monitor)

    2002-01-01

    We analyze the problem of suppressing the unwanted component of a time-harmonic acoustic field (noise) on a predetermined region of interest. The suppression is rendered by active means, i.e., by introducing the additional acoustic sources called controls that generate the appropriate anti-sound. Previously, we have obtained general solutions for active controls in both continuous and discrete formulations of the problem. We have also obtained optimal solutions that minimize the overall absolute acoustic source strength of active control sources. These optimal solutions happen to be particular layers of monopoles on the perimeter of the protected region. Mathematically, minimization of acoustic source strength is equivalent to minimization in the sense of L(sub 1). By contrast. in the current paper we formulate and study optimization problems that involve quadratic functions of merit. Specifically, we minimize the L(sub 2) norm of the control sources, and we consider both the unconstrained and constrained minimization. The unconstrained L(sub 2) minimization is certainly the easiest problem to address numerically. On the other hand, the constrained approach allows one to analyze sophisticated geometries. In a special case, we call compare our finite-difference optimal solutions to the continuous optimal solutions obtained previously using a semi-analytic technique. We also show that the optima obtained in the sense of L(sub 2) differ drastically from those obtained in the sense of L(sub 1).

  15. Elliptic Solvers for Adaptive Mesh Refinement Grids

    SciTech Connect

    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.

  16. 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.

  17. The impact of improved sparse linear solvers on industrial engineering applications

    SciTech Connect

    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.

  18. Domain decomposition solvers for PDEs : some basics, practical tools, and new developments.

    SciTech Connect

    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.

  19. A comparison of solver performance for complex gastric electrophysiology models.

    PubMed

    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

  20. 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.

  1. On improving linear solver performance: a block variant of GMRES

    SciTech Connect

    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.

  2. SUDOKU A STORY & A SOLVER

    SciTech Connect

    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.

  3. SIERRA framework version 4 : solver services.

    SciTech Connect

    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.

  4. The use of inexact ODE solver in waveform relaxation methods on a massively parallel computer

    SciTech Connect

    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.

  5. Finite difference method accelerated with sparse solvers for structural analysis of the metal-organic complexes

    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.

  6. 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.

  7. A numerically exact local solver applied to salt boundary inversion in seismic full-waveform inversion

    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.

  8. Fast Poisson, Fast Helmholtz and fast linear elastostatic solvers on rectangular parallelepipeds

    SciTech Connect

    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.

  9. 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

  10. 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.

  11. Physical activity problem-solving inventory for adolescents: Development and initial validation

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Youth encounter physical activity barriers, often called problems. The purpose of problem-solving is to generate solutions to overcome the barriers. Enhancing problem-solving ability may enable youth to be more physically active. Therefore, a method for reliably assessing physical activity problem-s...

  12. 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...

  13. 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.

  14. High-performance parallel solver for 3D time-dependent Schrodinger equation for large-scale nanosystems

    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.

  15. NITSOL: A Newton iterative solver for nonlinear systems

    SciTech Connect

    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.

  16. Active Physics Problem Based Learning for High Schools

    NASA Astrophysics Data System (ADS)

    Eisenkraft, Arthur

    2006-12-01

    Active Physics bridges research and practice. This NSF supported curriculum project uses a 7E instructional model and a problem based learning approach. Students learn physics on a need to know basis as they construct solutions to challenges such as developing a sport that can be played on the moon, creating an appliance package for developing countries, designing a light and sound show, or building a museum exhibit. In addition to meeting the content requirements of an introductory physics course, there is also an emphasis on engineering design principles and on essential questions. The excitement and frustration of trying to bridge research and practice will be discussed.

  17. 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.

  18. Benchmarking ICRF Full-wave Solvers for ITER

    SciTech Connect

    R. V. Budny, L. Berry, R. Bilato, P. Bonoli, M. Brambilla, R. J. Dumont, A. Fukuyama, R. Harvey, E. F. Jaeger, K. Indireshkumar, E. Lerche, D. McCune, C. K. Phillips, V. Vdovin, J. Wright, and members of the ITPA-IOS

    2011-01-06

    Abstract Benchmarking of full-wave solvers for ICRF simulations is performed using plasma profiles and equilibria obtained from integrated self-consistent modeling predictions of four ITER plasmas. One is for a high performance baseline (5.3 T, 15 MA) DT H-mode. The others are for half-field, half-current plasmas of interest for the pre-activation phase with bulk plasma ion species being either hydrogen or He4. The predicted profiles are used by six full-wave solver groups to simulate the ICRF electromagnetic fields and heating, and by three of these groups to simulate the current-drive. Approximate agreement is achieved for the predicted heating power for the DT and He4 cases. Factor of two disagreements are found for the cases with second harmonic He3 heating in bulk H cases. Approximate agreement is achieved simulating the ICRF current drive.

  19. 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.

  20. Subliminal psychodynamic activation: methodological problems and questions in Silverman's experiments.

    PubMed

    Fudin, R

    1999-08-01

    Analyses of procedures in Lloyd H. Silverman's subliminal psychodynamic activation experiments identify problems and questions. Given the information provided, none of his experiments can be replicated, and none of his positive results were found under luminance conditions he reckoned in 1983 were typical of such outcomes. Furthermore, there is no evidence in any of his experiments that all stimuli were presented completely within the fovea, a condition critical to the production of positive findings (Silverman & Geisler, 1986). These considerations and the fact that no experiment using Silverman's procedures can yield unambiguous positive results (Fudin, 1986) underscore the need to start anew research in this area. Such research should be undertaken with a greater appreciation of methodological issues involved in exposing and encoding subliminal stimuli than that found in all but a few experiments on subliminal psychodynamic activation. PMID:10544424

  1. Domain decomposed preconditioners with Krylov subspace methods as subdomain solvers

    SciTech Connect

    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.

  2. Finite Element Interface to Linear Solvers (FEI) version 2.9 : users guide and reference manual.

    SciTech Connect

    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.

  3. Variants and extensions of a fast direct numerical cauchy-riemann solver, with illustrative applications

    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.

  4. 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.

  5. Areas of Unsolved Problems in Caribbean Active Tectonics

    NASA Astrophysics Data System (ADS)

    Mann, P.

    2015-12-01

    I review some unsolved problems in Caribbean active tectonics. At the regional and plate scale: 1) confirm the existence of intraplate deformation zones of the central Caribbean plate that are within the margin of error of ongoing GPS measurements; 2) carry out field studies to evaluate block models versus models for distributed fault shear on the densely populated islands of Jamaica, Hispaniola, Puerto Rico, and the Virgin Islands; 3) carry out paleoseismological research of key plate boundary faults that may have accumulated large strains but have not been previously studied in detail; 4) determine the age of onset and far-field effects of the Cocos ridge and the Central America forearc sliver; 4) investigate the origin and earthquake-potential of obliquely-sheared rift basins along the northern coast of Venezuela; 5) determine the age of onset and regional active, tectonic effects of the Panama-South America collision including the continued activation of the Maracaibo block; and 6) validate longterm rates on active subduction zones with improving, tomographic maps of subducted slabs. At the individual fault scale: 1) determine the mode of termination of large and active strike -slip faults and application of the STEP model (Septentrional, Polochic, El Pilar, Bocono, Santa Marta-Bucaramanaga); 2) improve the understanding of the earthquake potential on the Enriquillo-Plantain Garden fault zone given "off-fault" events such as the 2010 Haiti earthquake; how widespread is this behavior?; and 3) estimate size of future tsunamis from studies of historic or prehistoric slump scars and mass transport deposits; what potential runups can be predicted from this information?; and 4) devise ways to keep rapidly growing, circum-Caribbean urban populations better informed and safer in the face of inevitable and future, large earthquakes.

  6. 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.

  7. Evaluating point-based POMDP solvers on multicore machines.

    PubMed

    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

  8. New iterative solvers for the NAG Libraries

    SciTech Connect

    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.

  9. Using SPARK as a Solver for Modelica

    SciTech Connect

    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.

  10. 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…

  11. 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

  12. 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.

  13. Multigrid in energy preconditioner for Krylov solvers

    SciTech Connect

    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.

  14. ODE System Solver W. Krylov Iteration & Rootfinding

    SciTech Connect

    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.

  15. ODE System Solver W. Krylov Iteration & Rootfinding

    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

  16. Wave Speeds, Riemann Solvers and Artificial Viscosity

    SciTech Connect

    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.

  17. 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.

  18. Three dimensional HLL Riemann solver for conservation laws on structured meshes; Application to Euler and magnetohydrodynamic flows

    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

  19. 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)

  20. Ordinary Differential Equation System Solver

    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.

  1. MGLab3D: An interactive environment for iterative solvers for elliptic PDEs in two and three dimensions

    SciTech Connect

    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.

  2. A Computationally Efficient Multicomponent Equilibrium Solver for Aerosols (MESA)

    SciTech Connect

    Zaveri, Rahul A.; Easter, Richard C.; Peters, Len K.

    2005-12-23

    This paper describes the development and application of a new multicomponent equilibrium solver for aerosol-phase (MESA) to predict the complex solid-liquid partitioning in atmospheric particles containing H+, NH4+, Na+, Ca2+, SO4=, HSO4-, NO3-, and Cl- ions. The algorithm of MESA involves integrating the set of ordinary differential equations describing the transient precipitation and dissolution reactions for each salt until the system satisfies the equilibrium or mass convergence criteria. Arbitrary values are chosen for the dissolution and precipitation rate constants such that their ratio is equal to the equilibrium constant. Numerically, this approach is equivalent to iterating all the equilibrium reactions simultaneously with a single iteration loop. Because CaSO4 is sparingly soluble, it is assumed to exist as a solid over the entire RH range to simplify the algorithm for calcium containing particles. Temperature-dependent mutual deliquescence relative humidity polynomials (valid from 240 to 310 K) for all the possible salt mixtures were constructed using the comprehensive Pitzer-Simonson-Clegg (PSC) activity coefficient model at 298.15 K and temperature-dependent equilibrium constants in MESA. Performance of MESA is evaluated for 16 representative mixed-electrolyte systems commonly found in tropospheric aerosols using PSC and two other multicomponent activity coefficient methods – Multicomponent Taylor Expansion Method (MTEM) of Zaveri et al. [2004], and the widely-used Kusik and Meissner method (KM), and the results are compared against the predictions of the Web-based AIM Model III or available experimental data. Excellent agreement was found between AIM, MESA-PSC, and MESA-MTEM predictions of the multistage deliquescence growth as a function of RH. On the other hand, MESA-KM displayed up to 20% deviations in the mass growth factors for common salt mixtures in the sulfate-poor cases while significant discrepancies were found in the predicted multistage

  3. OREGANO_VE: a new parallelised 3D solver for the general (non-)linear Maxwell visco-elastic problem: validation and application to the calculation of surface deformation in the earthquake cycle

    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

  4. Stress, active coping, and problem behaviors among Chinese adolescents.

    PubMed

    Hsieh, Hsing-Fang; Zimmerman, Marc A; Xue, Yange; Bauermeister, Jose A; Caldwell, Cleopatra H; Wang, Zhenhong; Hou, Yubo

    2014-07-01

    Little is known about the stress and coping mechanisms on problem behaviors among Chinese adolescents, which might be quite different from their counterparts in Western cultures. We examined risk process of stress for internalizing outcomes (i.e., psychological distress, self-acceptance) and externalizing outcomes (i.e., substance use, delinquency, violent behavior) among Chinese adolescents. We also examined John Henryism Active Coping as a protective factor in a test of resilience from the negative effects of stress. A cross-sectional survey using self-reported questionnaires was conducted in 2 urban cities in China: Beijing and Xian. Participants included 1,356 students in Grades 7 to 12 (48% male, 52% female). Structural equation modeling analyses were conducted to test the conceptual model. The modifying (protective) effects of John Henryism were tested in multiple-group analysis. After controlling for demographics, we found that stress was associated with decreased self-acceptance and increased psychological distress among adolescents. Higher degree of psychological distress was then associated with increased delinquent behaviors and substance use. The results also indicated that individuals who scored higher in John Henryism reported more substance use as a result of psychological distress. Overall, our results support previous research with Western samples. Although John Henryism did not serve as a protective factor between stress and its negative outcomes, the findings underscore the relevance of addressing stress and possible coping strategies among Chinese adolescents. Further research that refines the active coping tailored for Chinese adolescents is necessary to more precisely test its protective effects. PMID:24999522

  5. 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

  6. The Human Mind As General Problem Solver, Is Observed To Find ``Best'' Solutions, That Correspond To Highest Mental Coherence: Will Discuss ``sing Glass Type Theory'' of Princeton Physicist J J Hopfield, Points To How Best Use Our Own Human Mind!!

    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.

  7. Linear solvers on multiprocessor machines

    SciTech Connect

    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.

  8. 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.

  9. 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…

  10. Fluid structure interaction solver coupled with volume of fluid method for two-phase flow simulations

    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.

  11. Wavelet-based Poisson Solver for use in Particle-In-CellSimulations

    SciTech Connect

    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.

  12. Plasma wave simulation based on versatile FEM solver on Alcator C-mod

    SciTech Connect

    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.

  13. Diffusion of Zonal Variables Using Node-Centered Diffusion Solver

    SciTech Connect

    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.

  14. Progress in developing Poisson-Boltzmann equation solvers

    PubMed Central

    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

  15. Progress in developing Poisson-Boltzmann equation solvers.

    PubMed

    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

  16. 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.

  17. 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

  18. A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments.

    PubMed

    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

  19. 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.

  20. 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.

  1. 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.

  2. Automatic activation of addition facts in arithmetic word problems.

    PubMed

    Orrantia, Josetxu; Rodriguez, Laura; Vicente, Santiago

    2010-02-01

    Studies of mental arithmetic have shown that adults solve simple arithmetic problems by retrieving an answer automatically from a network of stored associations. However, most studies have been limited to single-digit addition and multiplication problems. In this article, we examine whether retrieval is also automatic in the context of more complex arithmetic tasks, such as arithmetic word problems. To test this hypothesis, we used a priming procedure with a target-naming task, in which the primes were the numbers included in two sentences containing the numerical information of an arithmetic word problem (e.g., 3 and 2 in "Joe had 3 marbles. Then Tom gave him 2 marbles"), and the targets were either congruent (e.g., 5) or incongruent (e.g., 8) with the prime. A neutral prime was also used replacing the numbers of the problem by capital letters (e.g., X and Y). Manipulating the relationship between the prime and the target and the duration of time that separates these two events, the overall results revealed shorter times in naming the congruent target than in a neutral condition and longer times in naming the incongruent target, even though mental arithmetic was completely irrelevant to the task. These results support the notion that automaticity of arithmetic-fact retrieval is not limited to simple addition, but it is also possible in other tasks, such as arithmetic word problems, which demand more cognitive resources than single-digit addition. PMID:19440930

  3. 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.

  4. Domain decomposition for the SPN solver MINOS

    SciTech Connect

    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)

  5. 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…

  6. Help with Solving Technological Problems in Project Activities

    ERIC Educational Resources Information Center

    Herold, Jean-Francois; Ginestie, Jacques

    2011-01-01

    In France, project activities figure predominantly in technology education. The general idea behind learning based on project activity is to allow the pupil to get involved in the activity in question, with the pupil tackling real situations rather than ones of an abstract nature. But too often, we notice that the pedagogical strategies used by…

  7. Common Problems and Solutions for Being Physically Active

    MedlinePlus

    ... the road again… Take workout clothes when you travel. Use your hotel's health club or pool. If there isn't one, ... Concerns • What Can I Expect? Introduction Getting Physically Active - Introduction - Physical Activity & Health - What Type of Activity is Best? - Develop a ...

  8. 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

  9. 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

  10. Sensitivity analysis using parallel ODE solvers and automatic differentiation in C : SensPVODE and ADIC.

    SciTech Connect

    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.

  11. Sensitivity analysis using parallel ODE solvers and automatic differentiation in C: sensPVODE and ADIC

    SciTech Connect

    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.

  12. Group Problem Solving as a Zone of Proximal Development activity

    NASA Astrophysics Data System (ADS)

    Brewe, Eric

    2006-12-01

    Vygotsky described learning as a process, intertwined with development, which is strongly influenced by social interactions with others that are at differing developmental stages.i These interactions create a Zone of Proximal Development for each member of the interaction. Vygotsky’s notion of social constructivism is not only a theory of learning, but also of development. While teaching introductory physics in an interactive format, I have found manifestations of Vygotsky’s theory in my classroom. The source of evidence is a paired problem solution. A standard mechanics problem was solved by students in two classes as a homework assignment. Students handed in the homework and then solved the same problem in small groups. The solutions to both the group and individual problem were assessed by multiple reviewers. In many cases the group score was the same as the highest individual score in the group, but in some cases, the group score was higher than any individual score. For this poster, I will analyze the individual and group scores and focus on three groups solutions and video that provide evidence of learning through membership in a Zone of Proximal Development. Endnotes i L. Vygotsky -Mind and society: The development of higher mental processes. Cambridge, MA: Harvard University Press. (1978).

  13. Carbon Dioxide and the Greenhouse Effect: A Problem Evaluation Activity.

    ERIC Educational Resources Information Center

    Brewer, Carol A.; Beiswenger, Jane M.

    1993-01-01

    Describes exercises to examine the global carbon cycle. Students are asked to predict consequences of increased carbon dioxide emissions into the atmosphere and to suggest ways to mitigate problems associated with these higher levels of atmospheric carbon dioxide. A comparison modeling exercise examines some of the variables related to the success…

  14. Problems of Scientific Research Activity in Institutions of Higher Learning

    ERIC Educational Resources Information Center

    Solodnikov, V. V.

    2008-01-01

    Under current conditions, the role played by scientific knowledge in all spheres of public life is rising substantially, and more and more attention is being paid to problems of the development and modernization of the Academy of Sciences. Not long ago, for example, there was wide response to the findings of a special study by S. Belanovskii on…

  15. Age, Physical Activity, Physical Fitness, Body Composition, and Incidence of Orthopedic Problems.

    ERIC Educational Resources Information Center

    Research Quarterly for Exercise and Sport, 1989

    1989-01-01

    Effects of age, physical activity, physical fitness, and body mass index (BMI) on the occurrence of orthopedic problems were examined. For men, physical fitness, BMI, and physical activity were associated with orthopedic problems; for women, physical activity was the main predictor. Age was not a factor for either gender. (JD)

  16. 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).

  17. Multidimensional physical activity: An opportunity not a problem

    PubMed Central

    Thompson, Dylan; Peacock, Oliver; Western, Max; Batterham, Alan M.

    2015-01-01

    Our research shows that no single metric will adequately reflect an individual’s physical activity because multiple biologically-important dimensions are independent and unrelated. We propose that there is an opportunity to exploit this multidimensional characteristic of physical activity in order to improve personalised feedback and offer physical activity options and choices that are tailored to an individual’s needs and preferences. PMID:25607280

  18. 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.

  19. AN ADAPTIVE PARTICLE-MESH GRAVITY SOLVER FOR ENZO

    SciTech Connect

    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.

  20. 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.

  1. User documentation for PVODE, an ODE solver for parallel computers

    SciTech Connect

    Hindmarsh, A.C., LLNL

    1998-05-01

    algebraic techniques could be easily incorporated, since the code is written with a layer of linear system solver modules that is isolated, as far as possible, from the rest of the code Further, the code is structured so that it can readily be converted from double precision to single precision This precludes the maintenance of two versions of PVODE PVODE has been run on an IBM SP2, a Cray-T3D and Cray-T3E, and a cluster of workstations It is currently being used in a simulation of tokamak edge plasmas at LLNL (We are grateful to Dr Michael Minkoff at Argonne National Laboratory for assistance in the use of the IBM SP2 there ) Recently, the PVODE solver was incorporated into the PETSc package (Portable Extensible Toolkit for Scientific computation) [9] developed at Argonne 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 PVODE solver, while Section 4 summarizes its usage Section 5 describes a preconditioner module, and Section 6 describes a set of Fortran/C interfaces Section 7 describes two example problems, and Section 8 gives some test results.

  2. The Geography of Wind Energy: Problem Solving Activities.

    ERIC Educational Resources Information Center

    Lahart, David E.; Allen, Rodney F.

    1985-01-01

    Today there are many attempts to use wind machines to confront the increasing costs of electricity. Described are activities to help secondary students understand wind energy, its distribution, applications, and limitations. (RM)

  3. AQUASOL: An efficient solver for the dipolar Poisson–Boltzmann–Langevin equation

    PubMed Central

    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

  4. AQUASOL: An efficient solver for the dipolar Poisson-Boltzmann-Langevin equation.

    PubMed

    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

  5. 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.

  6. Adaptive Multilevel Second-Generation Wavelet Collocation Elliptic Solver: A Cure for High Viscosity Contrasts

    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.

  7. Problem Solving Skills of People Doing Sporty Recreation Activities in Karaman Province

    ERIC Educational Resources Information Center

    Birol, Sefa Sahan

    2015-01-01

    The aim of the study is to examine the problem solving skills of people who are doing sporty recreation activities in Karaman Province. A total of 143 people participated in this study (51 females and 92 males) Their age mean was 1.2168 ± 0.41350. Problem Solving Inventory, developed by Heppner and Peterson, was used to measure the problem solving…

  8. Some problems in coupling solar activity to meteorological phenomena

    NASA Technical Reports Server (NTRS)

    Dessler, A. J.

    1974-01-01

    The development of a theory of coupling of solar activity to meteorological phenomena has to date foundered on the two difficulties of (1) devising a mechanism that can modify the behavior of the troposphere while employing only a negligible amount of energy compared with the energy necessary to drive the normal meteorological system; and (2) determining how such a mechanism can effectively couple some relevant magnetospheric process into the troposphere in such a way as to influence the weather. A clue to the nature of the interaction between the weather and solar activity might be provided by the fact that most solar activity undergoes a definite 11-year cycle, while meteorological phenomena undergo either no closely correlated variation, or an 11-year variation, or a 22-year variation.

  9. Some problems in coupling solar activity to meteorological phenomena

    NASA Technical Reports Server (NTRS)

    Dessler, A. J.

    1975-01-01

    The development of a theory of coupling of solar activity to meteorological phenomena is hindered by the difficulties of devising a mechanism that can modify the behavior of the troposphere while employing only a negligible amount of energy compared with the energy necessary to drive the normal meteorological system, and determining how such a mechanism can effectively couple some relevant magnetospheric process into the troposphere in such a way as to influence the weather. A clue to the nature of the interaction between the weather and solar activity might be provided by the fact that most solar activity undergoes a definite 11-yr cycle, and meteorological phenomena undergo either no closely correlated variation, an 11-yr variation, or a 22-yr variation.

  10. New Multigrid Solver Advances in TOPS

    SciTech Connect

    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.

  11. 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.

  12. 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.

  13. A hierarchical Krylov-Bayes iterative inverse solver for MEG with physiological preconditioning

    NASA Astrophysics Data System (ADS)

    Calvetti, D.; Pascarella, A.; Pitolli, F.; Somersalo, E.; Vantaggi, B.

    2015-12-01

    The inverse problem of MEG aims at estimating electromagnetic cerebral activity from measurements of the magnetic fields outside the head. After formulating the problem within the Bayesian framework, a hierarchical conditionally Gaussian prior model is introduced, including a physiologically inspired prior model that takes into account the preferred directions of the source currents. The hyperparameter vector consists of prior variances of the dipole moments, assumed to follow a non-conjugate gamma distribution with variable scaling and shape parameters. A point estimate of both dipole moments and their variances can be computed using an iterative alternating sequential updating algorithm, which is shown to be globally convergent. The numerical solution is based on computing an approximation of the dipole moments using a Krylov subspace iterative linear solver equipped with statistically inspired preconditioning and a suitable termination rule. The shape parameters of the model are shown to control the focality, and furthermore, using an empirical Bayes argument, it is shown that the scaling parameters can be naturally adjusted to provide a statistically well justified depth sensitivity scaling. The validity of this interpretation is verified through computed numerical examples. Also, a computed example showing the applicability of the algorithm to analyze realistic time series data is presented.

  14. Finite difference computation of the permeability of textile reinforcements with a fast stokes solver and new validation examples

    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.

  15. Quantum Theory, Active Information and the Mind-Matter Problem

    NASA Astrophysics Data System (ADS)

    Pylkkänen, Paavo

    Bohm and Hiley suggest that a certain new type of active information plays a key objective role in quantum processes. This chapter discusses the implications of this suggestion to our understanding of the relation between the mental and the physical aspects of reality.

  16. Nursing problem-based learning activity: song writing and singing.

    PubMed

    Chan, Zenobia C Y

    2014-08-01

    The function of song is not only to deliver individual's messages, but also to serve as a learning approach to facilitate students' learning. To observe the effectiveness of songs in facilitating students' learning, a Problem-based Learning (PBL) class with twenty students was divided into four groups with five students per group. Each group was asked to write a song based on two given scenarios, to sing the song out loud, and to participate in a follow-up focus group interview afterwards. The four songs reflected the students' understanding of academic knowledge and their perspectives toward the protagonists in the presented scenarios. Two songs are presented in this paper to demonstrate how the approach was carried out in the nursing PBL class. This paper aims to show the implication of song writing and singing in PBL and shed some light on teaching and learning. PMID:24560491

  17. 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.

  18. Using Problem-Based Pre-Class Activities to Prepare Students for In-Class Learning

    ERIC Educational Resources Information Center

    Alayont, Feryal

    2014-01-01

    This article presents a problem-based approach that prepares students for future learning in the classroom. In this approach, students complete problem-based activities before coming to class to familiarize themselves with the topics to be covered. After the discussion on how the use of these activities relate to the learning and transfer…

  19. New preconditioning strategy for Jacobian-free solvers for variably saturated flows with Richards’ equation

    DOE PAGESBeta

    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

  20. Fast linear solver for radiative transport equation with multiple right hand sides in diffuse optical tomography

    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.

  1. New preconditioning strategy for Jacobian-free solvers for variably saturated flows with Richards' equation

    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.

  2. Activity restriction in mild COPD: a challenging clinical problem.

    PubMed

    O'Donnell, Denis E; Gebke, Kevin B

    2014-01-01

    Dyspnea, exercise intolerance, and activity restriction are already apparent in mild chronic obstructive pulmonary disease (COPD). However, patients may not seek medical help until their symptoms become troublesome and persistent and significant respiratory impairment is already present; as a consequence, further sustained physical inactivity may contribute to disease progression. Ventilatory and gas exchange impairment, cardiac dysfunction, and skeletal muscle dysfunction are present to a variable degree in patients with mild COPD, and collectively may contribute to exercise intolerance. As such, there is increasing interest in evaluating exercise tolerance and physical activity in symptomatic patients with COPD who have mild airway obstruction, as defined by spirometry. Simple questionnaires, eg, the modified British Medical Research Council dyspnea scale and the COPD Assessment Test, or exercise tests, eg, the 6-minute or incremental and endurance exercise tests can be used to assess exercise performance and functional status. Pedometers and accelerometers are used to evaluate physical activity, and endurance tests (cycle or treadmill) using constant work rate protocols are used to assess the effects of interventions such as pulmonary rehabilitation. In addition, alternative outcome measurements, such as tests of small airway dysfunction and laboratory-based exercise tests, are used to measure the extent of physiological impairment in individuals with persistent dyspnea. This review describes the mechanisms of exercise limitation in patients with mild COPD and the interventions that can potentially improve exercise tolerance. Also discussed are the benefits of pulmonary rehabilitation and the potential role of pharmacologic treatment in symptomatic patients with mild COPD. PMID:24940054

  3. Activity restriction in mild COPD: a challenging clinical problem

    PubMed Central

    O’Donnell, Denis E; Gebke, Kevin B

    2014-01-01

    Dyspnea, exercise intolerance, and activity restriction are already apparent in mild chronic obstructive pulmonary disease (COPD). However, patients may not seek medical help until their symptoms become troublesome and persistent and significant respiratory impairment is already present; as a consequence, further sustained physical inactivity may contribute to disease progression. Ventilatory and gas exchange impairment, cardiac dysfunction, and skeletal muscle dysfunction are present to a variable degree in patients with mild COPD, and collectively may contribute to exercise intolerance. As such, there is increasing interest in evaluating exercise tolerance and physical activity in symptomatic patients with COPD who have mild airway obstruction, as defined by spirometry. Simple questionnaires, eg, the modified British Medical Research Council dyspnea scale and the COPD Assessment Test, or exercise tests, eg, the 6-minute or incremental and endurance exercise tests can be used to assess exercise performance and functional status. Pedometers and accelerometers are used to evaluate physical activity, and endurance tests (cycle or treadmill) using constant work rate protocols are used to assess the effects of interventions such as pulmonary rehabilitation. In addition, alternative outcome measurements, such as tests of small airway dysfunction and laboratory-based exercise tests, are used to measure the extent of physiological impairment in individuals with persistent dyspnea. This review describes the mechanisms of exercise limitation in patients with mild COPD and the interventions that can potentially improve exercise tolerance. Also discussed are the benefits of pulmonary rehabilitation and the potential role of pharmacologic treatment in symptomatic patients with mild COPD. PMID:24940054

  4. 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.

  5. 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.

  6. 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.

  7. Parallel performance of a preconditioned CG solver for unstructured finite element applications

    SciTech Connect

    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.

  8. High Resolution Euler Solvers Based on the Space-Time Conservation Element and Solution Element Method

    NASA Technical Reports Server (NTRS)

    Wang, Xiao-Yen; Chow, Chuen-Yen; Chang, Sin-Chung

    1996-01-01

    The I-D, quasi I-D and 2-D Euler solvers based on the method of space-time conservation element and solution element are used to simulate various flow phenomena including shock waves, Mach stem, contact surface, expansion waves, and their intersections and reflections. Seven test problems are solved to demonstrate the capability of this method for handling unsteady compressible flows in various configurations. Numerical results so obtained are compared with exact solutions and/or numerical solutions obtained by schemes based on other established computational techniques. Comparisons show that the present Euler solvers can generate highly accurate numerical solutions to complex flow problems in a straightforward manner without using any ad hoc techniques in the scheme.

  9. [Safety problems of occupational activity during alcoholic intoxication].

    PubMed

    Ushakov, I B; Popov, V I

    1999-01-01

    It has been established that work efficiency of persons occupied by machine operating duties degrades markedly under the action of an acute alcoholic intoxication--less on real machines and more on simulators and when operating simple technical devices. Work efficiency degradation is manifested by the task execution time increase (to a lesser degree) and by erroneous action quantity increase after taking alcohol, i.e. by work reliability decease. Most heavily it is manifested during the first 0.7-1.5 hr. After taking alcohol. And direct work efficiency index is usually improved 12-16 hr. after taking alcohol. Increase of erroneous action quantity is caused probably by a series of physiological, psychophysiological and psychological changes in the condition of a man under the action of alcohol. Time of the day when the activity takes place after taking that dose of alcohol is practically non valid for changing work efficiency index. PMID:11965736

  10. A Newton-Krylov Solver for Implicit Solution of Hydrodynamics in Core Collapse Supernovae

    SciTech Connect

    Reynolds, D R; Swesty, F D; Woodward, C S

    2008-06-12

    This paper describes an implicit approach and nonlinear solver for solution of radiation-hydrodynamic problems in the context of supernovae and proto-neutron star cooling. The robust approach applies Newton-Krylov methods and overcomes the difficulties of discontinuous limiters in the discretized equations and scaling of the equations over wide ranges of physical behavior. We discuss these difficulties, our approach for overcoming them, and numerical results demonstrating accuracy and efficiency of the method.

  11. Hybrid MPI+OpenMP Programming of an Overset CFD Solver and Performance Investigations

    NASA Technical Reports Server (NTRS)

    Djomehri, M. Jahed; Jin, Haoqiang H.; Biegel, Bryan (Technical Monitor)

    2002-01-01

    This report describes a two level parallelization of a Computational Fluid Dynamic (CFD) solver with multi-zone overset structured grids. The approach is based on a hybrid MPI+OpenMP programming model suitable for shared memory and clusters of shared memory machines. The performance investigations of the hybrid application on an SGI Origin2000 (O2K) machine is reported using medium and large scale test problems.

  12. 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.

  13. A RADIATION TRANSFER SOLVER FOR ATHENA USING SHORT CHARACTERISTICS

    SciTech Connect

    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.

  14. jShyLU Scalable Hybrid Preconditioner and Solver

    2012-09-11

    ShyLU is numerical software to solve sparse linear systems of equations. ShyLU uses a hybrid direct-iterative Schur complement method, and may be used either as a preconditioner or as a solver. ShyLU is parallel and optimized for a single compute Solver node. ShyLU will be a package in the Trilinos software framework.

  15. Two-dimensional flux-corrected transport solver for convectively dominated flows

    SciTech Connect

    Baer, M.R.; Gross, R.J.

    1986-01-01

    A numerical technique designed to solve a wide class of convectively dominated flow problems is presented. An attractive feature of the technique is its ability to resolve the behavior of field quantities possessing large gradients and/or shocks. The method is a finite-difference technique known as flux-corrected transport (FCT) that maintains four important numerical considerations - stability, accuracy, monotonicity, and conservation. The theory and methodology of two-dimensional FCT is presented. The method is applied in demonstrative example calculations of a 2-D Riemann problem with known exact solutions and to the Euler equations in a study of classical Rayleigh-Taylor and Kelvin-Helmholtz instability problems. The FCT solver has been vectorized for execution on the Cray 1S - a typical call with a 50 by 50 mesh requires about 0.00428 cpu seconds of execution time per call to the routine. Additionally, we have maintained a modular structure for the solver that eases its implementation. Fortran listings of two versions of the 2-D FCT solvers are appended with a driver main program illustrating the call sequence for the modules. 59 refs., 49 figs.

  16. Unconditionally convergent nonlinear solver for immiscible two-phase flow dominated by buoyancy and capillary forces

    NASA Astrophysics Data System (ADS)

    Tchelepi, H. A.; Wang, X.

    2011-12-01

    We describe a Newton-based nonlinear solver for immiscible two-phase Darcy flow and transport in the presence of significant viscous, buoyancy, and capillary forces. The evolution of CO2 plumes in heterogeneous saline aquifers, especially during the post-injection period, is an important example of this class of problem. The total flux (fractional flow) function is split into two parts: one part accounts for the viscous and buoyancy forces, and the other part accounts for capillarity. These flux functions, which are strongly nonlinear functions of saturation, are divided into trust regions. The delineation of the regions is dictated by the inflection, sonic, and end points present in the two flux functions. Within each trust region, the standard Newton iterative scheme is guaranteed to converge. For problems where the dynamics are dominated by buoyancy and capillary forces, the proposed scheme allows for taking much larger time steps than existing Newton based solvers. The nonlinear solver is demonstrated using challenging CO2-brine problems in heterogeneous domains with emphasis on the post-injection period.

  17. Parallelization of Unsteady Adaptive Mesh Refinement for Unstructured Navier-Stokes Solvers

    NASA Technical Reports Server (NTRS)

    Schwing, Alan M.; Nompelis, Ioannis; Candler, Graham V.

    2014-01-01

    This paper explores the implementation of the MPI parallelization in a Navier-Stokes solver using adaptive mesh re nement. Viscous and inviscid test problems are considered for the purpose of benchmarking, as are implicit and explicit time advancement methods. The main test problem for comparison includes e ects from boundary layers and other viscous features and requires a large number of grid points for accurate computation. Ex- perimental validation against double cone experiments in hypersonic ow are shown. The adaptive mesh re nement shows promise for a staple test problem in the hypersonic com- munity. Extension to more advanced techniques for more complicated ows is described.

  18. Performance of the block-Krylov energy group solvers in Jaguar

    SciTech Connect

    Watson, A. M.; Kennedy, R. A.

    2012-07-01

    A new method of coupling the inner and outer iterations for deterministic transport problems is proposed. This method is termed the Multigroup Energy Blocking Method (MEBM) and has been implemented in the deterministic transport solver Jaguar, which is currently under development at KAPL. The method is derived for both fixed-source and eigenvalue problems. The method is then applied to a PWR pin cell model, both in fixed-source mode and eigenvalue mode. The results show that the MEBM improves the convergence of both types of problems when applied to the thermal (up-scattering) groups. (authors)

  19. Robust large-scale parallel nonlinear solvers for simulations.

    SciTech Connect

    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

  20. General purpose nonlinear system solver based on Newton-Krylov method.

    2013-12-01

    KINSOL is part of a software family called SUNDIALS: SUite of Nonlinear and Differential/Algebraic equation Solvers [1]. KINSOL is a general-purpose nonlinear system solver based on Newton-Krylov and fixed-point solver technologies [2].

  1. Conducting Automated Test Assembly Using the Premium Solver Platform Version 7.0 with Microsoft Excel and the Large-Scale LP/QP Solver Engine Add-In

    ERIC Educational Resources Information Center

    Cor, Ken; Alves, Cecilia; Gierl, Mark J.

    2008-01-01

    This review describes and evaluates a software add-in created by Frontline Systems, Inc., that can be used with Microsoft Excel 2007 to solve large, complex test assembly problems. The combination of Microsoft Excel 2007 with the Frontline Systems Premium Solver Platform is significant because Microsoft Excel is the most commonly used spreadsheet…

  2. Differences in EEG Alpha Activity between Gifted and Non-Identified Individuals: Insights into Problem Solving.

    ERIC Educational Resources Information Center

    Jausovec, Norbert

    1997-01-01

    This study examined differences in electroencephalography (EEG) alpha activity between gifted and nongifted Slovenian student-teachers (N=17 each). Gifted students showed greater left hemisphere activation than nongifted subjects in relaxed states, but lower activation during problem solving. The same pattern was observed in overall hemispheric…

  3. A two-dimensional Riemann solver with self-similar sub-structure - Alternative formulation based on least squares projection

    NASA Astrophysics Data System (ADS)

    Balsara, Dinshaw S.; Vides, Jeaniffer; Gurski, Katharine; Nkonga, Boniface; Dumbser, Michael; Garain, Sudip; Audit, Edouard

    2016-01-01

    Just as the quality of a one-dimensional approximate Riemann solver is improved by the inclusion of internal sub-structure, the quality of a multidimensional Riemann solver is also similarly improved. Such multidimensional Riemann problems arise when multiple states come together at the vertex of a mesh. The interaction of the resulting one-dimensional Riemann problems gives rise to a strongly-interacting state. We wish to endow this strongly-interacting state with physically-motivated sub-structure. The self-similar formulation of Balsara [16] proves especially useful for this purpose. While that work is based on a Galerkin projection, in this paper we present an analogous self-similar formulation that is based on a different interpretation. In the present formulation, we interpret the shock jumps at the boundary of the strongly-interacting state quite literally. The enforcement of the shock jump conditions is done with a least squares projection (Vides, Nkonga and Audit [67]). With that interpretation, we again show that the multidimensional Riemann solver can be endowed with sub-structure. However, we find that the most efficient implementation arises when we use a flux vector splitting and a least squares projection. An alternative formulation that is based on the full characteristic matrices is also presented. The multidimensional Riemann solvers that are demonstrated here use one-dimensional HLLC Riemann solvers as building blocks. Several stringent test problems drawn from hydrodynamics and MHD are presented to show that the method works. Results from structured and unstructured meshes demonstrate the versatility of our method. The reader is also invited to watch a video introduction to multidimensional Riemann solvers on http://www.nd.edu/~dbalsara/Numerical-PDE-Course.

  4. 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…

  5. Towards Batched Linear Solvers on Accelerated Hardware Platforms

    SciTech Connect

    Haidar, Azzam; Dong, Tingzing Tim; Tomov, Stanimire; Dongarra, Jack J

    2015-01-01

    As hardware evolves, an increasingly effective approach to develop energy efficient, high-performance solvers, is to design them to work on many small and independent problems. Indeed, many applications already need this functionality, especially for GPUs, which are known to be currently about four to five times more energy efficient than multicore CPUs for every floating-point operation. In this paper, we describe the development of the main one-sided factorizations: LU, QR, and Cholesky; that are needed for a set of small dense matrices to work in parallel. We refer to such algorithms as batched factorizations. Our approach is based on representing the algorithms as a sequence of batched BLAS routines for GPU-contained execution. Note that this is similar in functionality to the LAPACK and the hybrid MAGMA algorithms for large-matrix factorizations. But it is different from a straightforward approach, whereby each of GPU's symmetric multiprocessors factorizes a single problem at a time. We illustrate how our performance analysis together with the profiling and tracing tools guided the development of batched factorizations to achieve up to 2-fold speedup and 3-fold better energy efficiency compared to our highly optimized batched CPU implementations based on the MKL library on a two-sockets, Intel Sandy Bridge server. Compared to a batched LU factorization featured in the NVIDIA's CUBLAS library for GPUs, we achieves up to 2.5-fold speedup on the K40 GPU.

  6. New numerical solver for flows at various Mach numbers

    NASA Astrophysics Data System (ADS)

    Miczek, F.; Röpke, F. K.; Edelmann, P. V. F.

    2015-04-01

    Context. Many problems in stellar astrophysics feature flows at low Mach numbers. Conventional compressible hydrodynamics schemes frequently used in the field have been developed for the transonic regime and exhibit excessive numerical dissipation for these flows. Aims: While schemes were proposed that solve hydrodynamics strictly in the low Mach regime and thus restrict their applicability, we aim at developing a scheme that correctly operates in a wide range of Mach numbers. Methods: Based on an analysis of the asymptotic behavior of the Euler equations in the low Mach limit we propose a novel scheme that is able to maintain a low Mach number flow setup while retaining all effects of compressibility. This is achieved by a suitable modification of the well-known Roe solver. Results: Numerical tests demonstrate the capability of this new scheme to reproduce slow flow structures even in moderate numerical resolution. Conclusions: Our scheme provides a promising approach to a consistent multidimensional hydrodynamical treatment of astrophysical low Mach number problems such as convection, instabilities, and mixing in stellar evolution.

  7. Microsituations as an Active-Learning Tool To Teach Endocrine Pharmacology and Problem-Solving Skills.

    ERIC Educational Resources Information Center

    Brandt, Barbara F.; Lubawy, William C.

    1998-01-01

    Microsituations teaching is a case-based, active learning tool developed from cognitive learning theory to teach problem-solving skills to large classes while conserving faculty and other resources. Since implementing this method in an endocrine pharmacology course at the University of Kentucky, student performance on problem-solving examinations…

  8. A Case Study of an Induction Year Teacher's Problem-Solving Using the LIBRE Model Activity

    ERIC Educational Resources Information Center

    Guerra, Norma S.; Flores, Belinda Bustos; Claeys, Lorena

    2009-01-01

    Background: A federally-funded program at the University of Texas at San Antonio adopted a holistic problem solving mentoring approach for novice teachers participating in an accelerated teacher certification program. Aims/focus of discussion: To investigate a novice teacher's problem-solving activity through self-expression of challenges and…

  9. An Electronic Library-Based Learning Environment for Supporting Web-Based Problem-Solving Activities

    ERIC Educational Resources Information Center

    Tsai, Pei-Shan; Hwang, Gwo-Jen; Tsai, Chin-Chung; Hung, Chun-Ming; Huang, Iwen

    2012-01-01

    This study aims to develop an electronic library-based learning environment to support teachers in developing web-based problem-solving activities and analyzing the online problem-solving behaviors of students. Two experiments were performed in this study. In study 1, an experiment on 103 elementary and high school teachers (the learning activity…

  10. Studies of visual attention in physics problem solving

    NASA Astrophysics Data System (ADS)

    Madsen, Adrian M.

    The work described here represents an effort to understand and influence visual attention while solving physics problems containing a diagram. Our visual system is guided by two types of processes -- top-down and bottom-up. The top-down processes are internal and determined by ones prior knowledge and goals. The bottom-up processes are external and determined by features of the visual stimuli such as color, and luminance contrast. When solving physics problems both top-down and bottom-up processes are active, but to varying degrees. The existence of two types of processes opens several interesting questions for physics education. For example, how do bottom-up processes influence problem solvers in physics? Can we leverage these processes to draw attention to relevant diagram areas and improve problem-solving? In this dissertation we discuss three studies that investigate these open questions and rely on eye movements as a primary data source. We assume that eye movements reflect a person's moment-to-moment cognitive processes, providing a window into one's thinking. In our first study, we compared the way correct and incorrect solvers viewed relevant and novice-like elements in a physics problem diagram. We found correct solvers spent more time attending to relevant areas while incorrect solvers spent more time looking at novice-like areas. In our second study, we overlaid these problems with dynamic visual cues to help students' redirect their attention. We found that in some cases these visual cues improved problem-solving performance and influenced visual attention. To determine more precisely how the perceptual salience of diagram elements influenced solvers' attention, we conducted a third study where we manipulated the perceptual salience of the diagram elements via changes in luminance contrast. These changes did not influence participants' answers or visual attention. Instead, similar to our first study, the time spent looking in various areas of the

  11. Incubation Provides Relief from Artificial Fixation in Problem Solving

    ERIC Educational Resources Information Center

    Penaloza, Alan A.; Calvillo, Dustin P.

    2012-01-01

    An incubation effect occurs when taking a break from a problem helps solvers arrive at the correct solution more often than working on it continuously. The forgetting-fixation account, a popular explanation of how incubation works, posits that a break from a problem allows the solver to forget the incorrect path to the solution and finally access…

  12. The Problem-Solving Revolution.

    ERIC Educational Resources Information Center

    Bardige, Art

    1983-01-01

    Discusses the use of microcomputers and software as problem-solving tools, including comments on "TK! Solver," automatic problem-solving program (reviewed in detail on pp.84-86 in this same issue). Also discusses problem-solving approaches to bridge the disciplines, such as music/physics, junior high science/mathematics (genetics),…

  13. Development of a new 3D OpenFOAM¯ solver to model the cooling stage in profile extrusion

    NASA Astrophysics Data System (ADS)

    Fernandes, C.; Habla, F.; Carneiro, O. S.; Hinrichsen, O.; Nóbrega, J. M.

    2016-03-01

    In this work a new solver is developed in OpenFOAM® computational library, to model the cooling state in profile extrusion. The solver is able to calculate the temperature distribution in a two domain system, comprising the profile and calibrator, considering the temperature discontinuity at the interface. The derivation of the model is based on the local instantaneous energy conservation equation, in conjunction with the conditional volume averaging technique, which yields a single governing equation valid in both domains. Aiming the solution of automatic optimization/parameterization problems, the developed solver was coupled with the DAKOTA toolkit. The application of the novel calculation system is illustrated in a study of a complex geometry extruded profile cooling stage.

  14. AQUAgpusph, a new free 3D SPH solver accelerated with OpenCL

    NASA Astrophysics Data System (ADS)

    Cercos-Pita, J. L.

    2015-07-01

    In this paper, AQUAgpusph, a new free Smoothed Particle Hydrodynamics (SPH) software accelerated with OpenCL, is described. The main differences and progress with respect to other existing alternatives are considered. These are the use of the Open Computing Language (OpenCL) framework instead of the Compute Unified Device Architecture (CUDA), the implementation of the most popular boundary conditions, the easy customization of the code to different problems, the extensibility with regard to Python scripts, and the runtime output which allows the tracking of simulations in real time, or a higher frequency in saving some results without a significant performance lost. These modifications are shown to improve the solver speed, the results quality, and allow for a wider areas of application. AQUAgpusph has been designed trying to provide researchers and engineers with a valuable tool to test and apply the SPH method. Three practical applications are discussed in detail. The evolution of a dam break is used to quantify and compare the computational performance and modeling accuracy with the most popular SPH Graphics Processing Unit (GPU) accelerated alternatives. The dynamics of a coupled system, a Tuned Liquid Damper (TLD), is discussed in order to show the integration capabilities of the solver with external dynamics. Finally, the sloshing flow inside a nuclear reactor is simulated in order to show the capabilities of the solver to treat 3-D problems with complex geometries and of industrial interest.

  15. An implicit compact scheme solver with application to chemically reacting flows

    NASA Astrophysics Data System (ADS)

    Noskov, Mikhail; Smooke, Mitchell D.

    2005-03-01

    A novel, stable, implicit compact scheme solver that is higher order in space, suitable for modeling steady-state and time-dependent phenomena on nonuniform grids for one-dimensional configurations, is presented. Several properties of compact scheme discretizations are introduced to develop efficient algorithms for Jacobian matrix generation and Jacobian-vector multiplication using a new component form for Jacobian operations. Composite nonuniform grids are introduced that enable the implicit compact scheme solver to achieve sixth order accuracy. A robust Newton's method is employed with explicit generation of Jacobian matrices. Superior resolution characteristics of the implicit compact scheme solver are demonstrated with several steady-state and time-dependent problems for the Burgers equation. The example of the solution of stiff flame problem is given. An analysis of spectral properties of Jacobian matrices is presented, which shows that the condition number and the eigenvalue distributions behave similarly to those found in Jacobians associated with low-order discretizations. Two sparsification strategies are developed for the systematic approximation of a dense Jacobian aimed at the practical implementation of linear system preconditioning through partial Jacobians.

  16. Finite difference iterative solvers for electroencephalography: serial and parallel performance analysis.

    PubMed

    Barnes, Derek N; George, John S; Ng, Kwong T

    2008-09-01

    Currently the resolution of the head models used in electroencephalography (EEG) studies is limited by the speed of the forward solver. Here, we present a parallel finite difference technique that can reduce the solution time of the governing Poisson equation for a head model. Multiple processors are used to work on the problem simultaneously in order to speed up the solution and provide the memory for solving large problems. The original computational domain is divided into multiple rectangular partitions. Each partition is then assigned to a processor, which is responsible for all the computations and inter-processor communication associated with the nodes in that particular partition. Since the forward solution time is mainly spent on solving the associated matrix equation, it is desirable to find the optimum matrix solver. A detailed comparison of various iterative solvers was performed for both isotropic and anisotropic realistic head models constructed from MRI images. The conjugate gradient (CG) method preconditioned with an advanced geometric multigrid technique was found to provide the best overall performance. For an anisotropic model with 256 x 128 x 256 cells, this technique provides a speedup of 508 on 32 processors over the serial CG solution, with a speedup of 20.1 and 25.3 through multigrid preconditioning and parallelization, respectively. PMID:18478286

  17. Implementation of a fully-balanced periodic tridiagonal solver on a parallel distributed memory architecture

    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.

  18. Amesos2 and Belos: Direct and Iterative Solvers for Large Sparse Linear Systems

    DOE PAGESBeta

    Bavier, Eric; Hoemmen, Mark; Rajamanickam, Sivasankaran; Thornquist, Heidi

    2012-01-01

    Solvers for large sparse linear systems come in two categories: direct and iterative. Amesos2, a package in the Trilinos software project, provides direct methods, and Belos, another Trilinos package, provides iterative methods. Amesos2 offers a common interface to many different sparse matrix factorization codes, and can handle any implementation of sparse matrices and vectors, via an easy-to-extend C++ traits interface. It can also factor matrices whose entries have arbitrary “Scalar” type, enabling extended-precision and mixed-precision algorithms. Belos includes many different iterative methods for solving large sparse linear systems and least-squares problems. Unlike competing iterative solver libraries, Belos completely decouples themore » algorithms from the implementations of the underlying linear algebra objects. This lets Belos exploit the latest hardware without changes to the code. Belos favors algorithms that solve higher-level problems, such as multiple simultaneous linear systems and sequences of related linear systems, faster than standard algorithms. The package also supports extended-precision and mixed-precision algorithms. Together, Amesos2 and Belos form a complete suite of sparse linear solvers.« less

  19. A matrix-form GSM-CFD solver for incompressible fluids and its application to hemodynamics

    NASA Astrophysics Data System (ADS)

    Yao, Jianyao; Liu, G. R.

    2014-10-01

    A GSM-CFD solver for incompressible flows is developed based on the gradient smoothing method (GSM). A matrix-form algorithm and corresponding data structure for GSM are devised to efficiently approximate the spatial gradients of field variables using the gradient smoothing operation. The calculated gradient values on various test fields show that the proposed GSM is capable of exactly reproducing linear field and of second order accuracy on all kinds of meshes. It is found that the GSM is much more robust to mesh deformation and therefore more suitable for problems with complicated geometries. Integrated with the artificial compressibility approach, the GSM is extended to solve the incompressible flows. As an example, the flow simulation of carotid bifurcation is carried out to show the effectiveness of the proposed GSM-CFD solver. The blood is modeled as incompressible Newtonian fluid and the vessel is treated as rigid wall in this paper.

  20. Generating Combinatorial Test Cases by Efficient SAT Encodings Suitable for CDCL SAT Solvers

    NASA Astrophysics Data System (ADS)

    Banbara, Mutsunori; Matsunaka, Haruki; Tamura, Naoyuki; Inoue, Katsumi

    Generating test cases for combinatorial testing is to find a covering array in Combinatorial Designs. In this paper, we consider the problem of finding optimal covering arrays by SAT encoding. We present two encodings suitable for modern CDCL SAT solvers. One is based on the order encoding that is efficient in the sense that unit propagation achieves the bounds consistency in CSPs. Another one is based on a combination of the order encoding and Hnich's encoding. CDCL SAT solvers have an important role in the latest SAT technology. The effective use of them is essential for enhancing efficiency. In our experiments, we found solutions that can be competitive with the previously known results for the arrays of strength two to six with small to moderate size of components and symbols. Moreover, we succeeded either in proving the optimality of known bounds or in improving known lower bounds for some arrays.

  1. Extending Clause Learning of SAT Solvers with Boolean Gröbner Bases

    NASA Astrophysics Data System (ADS)

    Zengler, Christoph; Küchlin, Wolfgang

    We extend clause learning as performed by most modern SAT Solvers by integrating the computation of Boolean Gröbner bases into the conflict learning process. Instead of learning only one clause per conflict, we compute and learn additional binary clauses from a Gröbner basis of the current conflict. We used the Gröbner basis engine of the logic package Redlog contained in the computer algebra system Reduce to extend the SAT solver MiniSAT with Gröbner basis learning. Our approach shows a significant reduction of conflicts and a reduction of restarts and computation time on many hard problems from the SAT 2009 competition.

  2. Gauss-Seidel Accelerated: Implementing Flow Solvers on Field Programmable Gate Arrays

    SciTech Connect

    Chassin, David P.; Armstrong, Peter R.; Chavarría-Miranda, Daniel; Guttromson, Ross T.

    2006-06-01

    Non-linear steady-state power flow solvers have typically relied on the Newton-Raphson method to efficiently compute solutions on today's computer systems. Field Programmable Gate Array (FPGA) devices, which have recently been integrated into high-performance computers by major computer system vendors, offer an opportunity to significantly increase the performance of power flow solvers. However, only some algorithms are suitable for an FPGA implementation. The Gauss-Seidel method of solving the AC power flow problem is an excellent example of such an opportunity. In this paper we discuss algorithmic design considerations, optimization, implementation, and performance results of the implementation of the Gauss-Seidel method running on a Silicon Graphics Inc. Altix-350 computer equipped with a Xilinx Virtex II 6000 FPGA.

  3. A Massively Parallel Solver for the Mechanical Harmonic Analysis of Accelerator Cavities

    SciTech Connect

    O. Kononenko

    2015-02-17

    ACE3P is a 3D massively parallel simulation suite that developed at SLAC National Accelerator Laboratory that can perform coupled electromagnetic, thermal and mechanical study. Effectively utilizing supercomputer resources, ACE3P has become a key simulation tool for particle accelerator R and D. A new frequency domain solver to perform mechanical harmonic response analysis of accelerator components is developed within the existing parallel framework. This solver is designed to determine the frequency response of the mechanical system to external harmonic excitations for time-efficient accurate analysis of the large-scale problems. Coupled with the ACE3P electromagnetic modules, this capability complements a set of multi-physics tools for a comprehensive study of microphonics in superconducting accelerating cavities in order to understand the RF response and feedback requirements for the operational reliability of a particle accelerator. (auth)

  4. The NASA SCI Files[TM]: The Case of the Shaky Quake. A Lesson Guide with Activities in Mathematics, Science, and Technology.

    ERIC Educational Resources Information Center

    Ricles, Shannon

    The NASA SCI Files is a series of instructional programs consisting of broadcast, print, and online elements emphasizing standards-based instruction, problem-based learning, and science as inquiry. The series seeks to motivate students in grades 3-5 to become critical thinkers and active problem solvers. In this program, the tree house detectives…

  5. Active Solution Space and Search on Job-shop Scheduling Problem

    NASA Astrophysics Data System (ADS)

    Watanabe, Masato; Ida, Kenichi; Gen, Mitsuo

    In this paper we propose a new searching method of Genetic Algorithm for Job-shop scheduling problem (JSP). The coding method that represent job number in order to decide a priority to arrange a job to Gannt Chart (called the ordinal representation with a priority) in JSP, an active schedule is created by using left shift. We define an active solution at first. It is solution which can create an active schedule without using left shift, and set of its defined an active solution space. Next, we propose an algorithm named Genetic Algorithm with active solution space search (GA-asol) which can create an active solution while solution is evaluated, in order to search the active solution space effectively. We applied it for some benchmark problems to compare with other method. The experimental results show good performance.

  6. Multi-GPU kinetic solvers using MPI and CUDA

    NASA Astrophysics Data System (ADS)

    Zabelok, Sergey; Arslanbekov, Robert; Kolobov, Vladimir

    2014-12-01

    This paper describes recent progress towards porting a Unified Flow Solver (UFS) to heterogeneous parallel computing. The main challenge of porting UFS to graphics processing units (GPUs) comes from the dynamically adapted mesh, which causes irregular data access. We describe the implementation of CUDA kernels for three modules in UFS: the direct Boltzmann solver using discrete velocity method (DVM), the DSMC module, and the Lattice Boltzmann Method (LBM) solver, all using octree Cartesian mesh with adaptive Mesh Refinement (AMR). Double digit speedup on single GPU and good scaling for multi-GPU has been demonstrated.

  7. A non-conforming 3D spherical harmonic transport solver

    SciTech Connect

    Van Criekingen, S.

    2006-07-01

    A new 3D transport solver for the time-independent Boltzmann transport equation has been developed. This solver is based on the second-order even-parity form of the transport equation. The angular discretization is performed through the expansion of the angular neutron flux in spherical harmonics (PN method). The novelty of this solver is the use of non-conforming finite elements for the spatial discretization. Such elements lead to a discontinuous flux approximation. This interface continuity requirement relaxation property is shared with mixed-dual formulations such as the ones based on Raviart-Thomas finite elements. Encouraging numerical results are presented. (authors)

  8. libmpdata++ 0.1: a library of parallel MPDATA solvers for systems of generalised transport equations

    NASA Astrophysics Data System (ADS)

    Jaruga, A.; Arabas, S.; Jarecka, D.; Pawlowska, H.; Smolarkiewicz, P. K.; Waruszewski, M.

    2014-11-01

    This paper accompanies first release of libmpdata++, a C++ library implementing the Multidimensional Positive-Definite Advection Transport Algorithm (MPDATA). The library offers basic numerical solvers for systems of generalised transport equations. The solvers are forward-in-time, conservative and non-linearly stable. The libmpdata++ library covers the basic second-order-accurate formulation of MPDATA, its third-order variant, the infinite-gauge option for variable-sign fields and a flux-corrected transport extension to guarantee non-oscillatory solutions. The library is equipped with a non-symmetric variational elliptic solver for implicit evaluation of pressure gradient terms. All solvers offer parallelisation through domain decomposition using shared-memory parallelisation. The paper describes the library programming interface, and serves as a user guide. Supported options are illustrated with benchmarks discussed in the MPDATA literature. Benchmark descriptions include code snippets as well as quantitative representations of simulation results. Examples of applications include: homogeneous transport in one, two and three dimensions in Cartesian and spherical domains; shallow-water system compared with analytical solution (originally derived for a 2-D case); and a buoyant convection problem in an incompressible Boussinesq fluid with interfacial instability. All the examples are implemented out of the library tree. Regardless of the differences in the problem dimensionality, right-hand-side terms, boundary conditions and parallelisation approach, all the examples use the same unmodified library, which is a key goal of libmpdata++ design. The design, based on the principle of separation of concerns, prioritises the user and developer productivity. The libmpdata++ library is implemented in C++, making use of the Blitz++ multi-dimensional array containers, and is released as free/libre and open-source software.

  9. libmpdata++ 1.0: a library of parallel MPDATA solvers for systems of generalised transport equations

    NASA Astrophysics Data System (ADS)

    Jaruga, A.; Arabas, S.; Jarecka, D.; Pawlowska, H.; Smolarkiewicz, P. K.; Waruszewski, M.

    2015-04-01

    This paper accompanies the first release of libmpdata++, a C++ library implementing the multi-dimensional positive-definite advection transport algorithm (MPDATA) on regular structured grid. The library offers basic numerical solvers for systems of generalised transport equations. The solvers are forward-in-time, conservative and non-linearly stable. The libmpdata++ library covers the basic second-order-accurate formulation of MPDATA, its third-order variant, the infinite-gauge option for variable-sign fields and a flux-corrected transport extension to guarantee non-oscillatory solutions. The library is equipped with a non-symmetric variational elliptic solver for implicit evaluation of pressure gradient terms. All solvers offer parallelisation through domain decomposition using shared-memory parallelisation. The paper describes the library programming interface, and serves as a user guide. Supported options are illustrated with benchmarks discussed in the MPDATA literature. Benchmark descriptions include code snippets as well as quantitative representations of simulation results. Examples of applications include homogeneous transport in one, two and three dimensions in Cartesian and spherical domains; a shallow-water system compared with analytical solution (originally derived for a 2-D case); and a buoyant convection problem in an incompressible Boussinesq fluid with interfacial instability. All the examples are implemented out of the library tree. Regardless of the differences in the problem dimensionality, right-hand-side terms, boundary conditions and parallelisation approach, all the examples use the same unmodified library, which is a key goal of libmpdata++ design. The design, based on the principle of separation of concerns, prioritises the user and developer productivity. The libmpdata++ library is implemented in C++, making use of the Blitz++ multi-dimensional array containers, and is released as free/libre and open-source software.

  10. Advances in high-performance spectral-element solvers for seismic tomography

    NASA Astrophysics Data System (ADS)

    Peter, D. B.; Rietmann, M.; Komatitsch, D.; Tromp, J.

    2011-12-01

    In seismic tomography, waveform inversions require accurate simulations of seismic wave propagation in complex media. That is, seismic inverse problems benefit from accurate and fast forward solvers. This is the main motivation for further development of solvers based on the spectral-element method (SEM). All our open-source SEM codes have the ability to compute Fréchet derivatives with respect to isotropic and anisotropic model parameters as well as topographic boundary undulations, making use of adjoint methods. These adjoint sensitivity kernels can be used for gradient-based optimization, minimizing, e.g., traveltimes or full waveform misfits. We highlight our most recent efforts in SEM solvers, which mainly focus on two different aspects: flexibility and performance. For local- to regional-scale applications, the widely used SEM code SPECFEM3D has been further extended to simulate acoustic and (an)elastic wave propagation. This facilitates running SEM solvers on fully unstructured meshes, which readily honor topography of complex geological surfaces. By coupling acoustic and elastic wave propagation, this new SEM code can simulate seismic wave propagation for land and marine surveys to produce highly accurate seismograms and sensitivity kernels. Code performance often governs whether seismic inversions become feasible or remain elusive. The current versions of our SEM packages, the local-scale code SPECFEM3D and the global-scale code SPECFEM3D_GLOBE, are tackling this problem by optimizing matrix-vector multiplications, the most common operation in SEM codes. New code developments are porting our SEM codes to graphic processing units (GPUs) to further exploit massively parallel processors. Running simulations on such dedicated GPU clusters will further reduce computation times. This leads to simulations an order of magnitude faster as before, and pushes seismic inversions into a new, higher frequency realm.

  11. Examination of Pre-Service Science Teachers' Activities Using Problem Based Learning Method

    ERIC Educational Resources Information Center

    Ekici, Didem Inel

    2016-01-01

    In this study, both the activities prepared by pre-service science teachers regarding the Problem Based Learning method and the pre-service science teachers' views regarding the method were examined before and after applying their activities in a real class environment. 69 pre-service science teachers studying in the 4th grade of the science…

  12. Developing Clinical Competency in Crisis Event Management: An Integrated Simulation Problem-Based Learning Activity

    ERIC Educational Resources Information Center

    Liaw, S. Y.; Chen, F. G.; Klainin, P.; Brammer, J.; O'Brien, A.; Samarasekera, D. D.

    2010-01-01

    This study aimed to evaluate the integration of a simulation based learning activity on nursing students' clinical crisis management performance in a problem-based learning (PBL) curriculum. It was hypothesized that the clinical performance of first year nursing students who participated in a simulated learning activity during the PBL session…

  13. 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.

  14. LSPRAY: Lagrangian Spray Solver for Applications With Parallel Computing and Unstructured Gas-Phase Flow Solvers

    NASA Technical Reports Server (NTRS)

    Raju, Manthena S.

    1998-01-01

    Sprays occur in a wide variety of industrial and power applications and in the processing of materials. A liquid spray is a phase flow with a gas as the continuous phase and a liquid as the dispersed phase (in the form of droplets or ligaments). Interactions between the two phases, which are coupled through exchanges of mass, momentum, and energy, can occur in different ways at different times and locations involving various thermal, mass, and fluid dynamic factors. An understanding of the flow, combustion, and thermal properties of a rapidly vaporizing spray requires careful modeling of the rate-controlling processes associated with the spray's turbulent transport, mixing, chemical kinetics, evaporation, and spreading rates, as well as other phenomena. In an attempt to advance the state-of-the-art in multidimensional numerical methods, we at the NASA Lewis Research Center extended our previous work on sprays to unstructured grids and parallel computing. LSPRAY, which was developed by M.S. Raju of Nyma, Inc., is designed to be massively parallel and could easily be coupled with any existing gas-phase flow and/or Monte Carlo probability density function (PDF) solver. The LSPRAY solver accommodates the use of an unstructured mesh with mixed triangular, quadrilateral, and/or tetrahedral elements in the gas-phase solvers. It is used specifically for fuel sprays within gas turbine combustors, but it has many other uses. The spray model used in LSPRAY provided favorable results when applied to stratified-charge rotary combustion (Wankel) engines and several other confined and unconfined spray flames. The source code will be available with the National Combustion Code (NCC) as a complete package.

  15. Algorithmic Enhancements to the VULCAN Navier-Stokes Solver

    NASA Technical Reports Server (NTRS)

    Litton, D. K.; Edwards, J. R.; White, J. A.

    2003-01-01

    VULCAN (Viscous Upwind aLgorithm for Complex flow ANalysis) is a cell centered, finite volume code used to solve high speed flows related to hypersonic vehicles. Two algorithms are presented for expanding the range of applications of the current Navier-Stokes solver implemented in VULCAN. The first addition is a highly implicit approach that uses subiterations to enhance block to block connectivity between adjacent subdomains. The addition of this scheme allows more efficient solution of viscous flows on highly-stretched meshes. The second algorithm addresses the shortcomings associated with density-based schemes by the addition of a time-derivative preconditioning strategy. High speed, compressible flows are typically solved with density based schemes, which show a high level of degradation in accuracy and convergence at low Mach numbers (M less than or equal to 0.1). With the addition of preconditioning and associated modifications to the numerical discretization scheme, the eigenvalues will scale with the local velocity, and the above problems will be eliminated. With these additions, VULCAN now has improved convergence behavior for multi-block, highly-stretched meshes and also can solve the Navier-Stokes equations for very low Mach numbers.

  16. 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.

  17. A generalized Poisson solver for first-principles device simulations.

    PubMed

    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

  18. Parallelizable approximate solvers for recursions arising in preconditioning

    SciTech Connect

    Shapira, Y.

    1996-12-31

    For the recursions used in the Modified Incomplete LU (MILU) preconditioner, namely, the incomplete decomposition, forward elimination and back substitution processes, a parallelizable approximate solver is presented. The present analysis shows that the solutions of the recursions depend only weakly on their initial conditions and may be interpreted to indicate that the inexact solution is close, in some sense, to the exact one. The method is based on a domain decomposition approach, suitable for parallel implementations with message passing architectures. It requires a fixed number of communication steps per preconditioned iteration, independently of the number of subdomains or the size of the problem. The overlapping subdomains are either cubes (suitable for mesh-connected arrays of processors) or constructed by the data-flow rule of the recursions (suitable for line-connected arrays with possibly SIMD or vector processors). Numerical examples show that, in both cases, the overhead in the number of iterations required for convergence of the preconditioned iteration is small relatively to the speed-up gained.

  19. Approximate Riemann Solvers for the Cosmic Ray Magnetohydrodynamical Equations

    NASA Astrophysics Data System (ADS)

    Kudoh, Yuki; Hanawa, Tomoyuki

    2016-08-01

    We analyze the cosmic-ray magnetohydrodynamic (CR MHD) equations to improve the numerical simulations. We propose to solve them in the fully conservation form, which is equivalent to the conventional CR MHD equations. In the fully conservation form, the CR energy equation is replaced with the CR "number" conservation, where the CR number density is defined as the three fourths power of the CR energy density. The former contains an extra source term, while latter does not. An approximate Riemann solver is derived from the CR MHD equations in the fully conservation form. Based on the analysis, we propose a numerical scheme of which solutions satisfy the Rankine-Hugoniot relation at any shock. We demonstrate that it reproduces the Riemann solution derived by Pfrommer et al. (2006) for a 1D CR hydrodynamic shock tube problem. We compare the solution with those obtained by solving the CR energy equation. The latter solutions deviate from the Riemann solution seriously, when the CR pressure dominates over the gas pressure in the post-shocked gas. The former solutions converge to the Riemann solution and are of the second order accuracy in space and time. Our numerical examples include an expansion of high pressure sphere in an magnetized medium. Fast and slow shocks are sharply resolved in the example. We also discuss possible extension of the CR MHD equations to evaluate the average CR energy.

  20. Shared Memory Parallelism for 3D Cartesian Discrete Ordinates Solver

    NASA Astrophysics Data System (ADS)

    Moustafa, Salli; Dutka-Malen, Ivan; Plagne, Laurent; Ponçot, Angélique; Ramet, Pierre

    2014-06-01

    This paper describes the design and the performance of DOMINO, a 3D Cartesian SN solver that implements two nested levels of parallelism (multicore+SIMD) on shared memory computation nodes. DOMINO is written in C++, a multi-paradigm programming language that enables the use of powerful and generic parallel programming tools such as Intel TBB and Eigen. These two libraries allow us to combine multi-thread parallelism with vector operations in an efficient and yet portable way. As a result, DOMINO can exploit the full power of modern multi-core processors and is able to tackle very large simulations, that usually require large HPC clusters, using a single computing node. For example, DOMINO solves a 3D full core PWR eigenvalue problem involving 26 energy groups, 288 angular directions (S16), 46 × 106 spatial cells and 1 × 1012 DoFs within 11 hours on a single 32-core SMP node. This represents a sustained performance of 235 GFlops and 40:74% of the SMP node peak performance for the DOMINO sweep implementation. The very high Flops/Watt ratio of DOMINO makes it a very interesting building block for a future many-nodes nuclear simulation tool.

  1. Assessment of the 2D MOC solver in MPACT: Michigan parallel characteristics transport code

    SciTech Connect

    Collins, B.; Kochunas, B.; Downar, T.

    2013-07-01

    MPACT (Michigan Parallel Characteristics Transport Code) is a new reactor analysis tool being developed by researchers at the University of Michigan as an advanced pin-resolved transport capability within VERA (Virtual Environment for Reactor Analysis). VERA is the end-user reactor simulation tool being developed by the Consortium for the Advanced Simulation of Light Water Reactors (CASL). The MPACT development project is itself unique for the way it is changing how students perform research to achieve the instructional and research goals of an academic institution, while providing immediate value to the industry. One of the major computational pieces in MPACT is the 2D MOC solver. It is critical that the 2D MOC solver provide an efficient, accurate, and robust solution over a broad range of reactor operating conditions. The C5G7 benchmark is first used to test the accuracy of the method with a fixed set of cross-sections. The VERA Core Physics Progression Problems are then used to compare the accuracy of both the 2D transport solver and also the cross-section treatments. (authors)

  2. Activity performance problems of patients with cardiac diseases and their impact on quality of life

    PubMed Central

    Duruturk, Neslihan; Tonga, Eda; Karatas, Metin; Doganozu, Ersin

    2015-01-01

    [Purpose] To describe the functional consequences of patients with cardiac diseases and analyze associations between activity limitations and quality of life. [Subjects and Methods] Seventy subjects (mean age: 60.1±12.0 years) were being treated by Physical Medicine and Rehabilitation and Cardiology Departments were included in the study. Activity limitations and participation restrictions as perceived by the individual were measured by the Canadian Occupational Performance Measure (COPM). The Nottingham Extended Activities of Daily Living (NEADL) Scale was used to describe limitations in daily living activities. To detect the impact of activity limitations on quality of life the Nottingham Health Profile (NHP) was used. [Results] The subjects described 46 different types of problematic activities. The five most identified problems were walking (45.7%), climbing up the stairs (41.4%), bathing (30%), dressing (28.6%) and outings (27.1%). The associations between COPM performance score with all subgroups of NEADL and NHP; total, energy, physical abilities subgroups, were statistically significant. [Conclusion] Our results showed that patients with cardiac diseases reported problems with a wide range of activities, and that also quality of life may be affected by activities of daily living. COPM can be provided as a patient-focused outcome measure, and it may be a useful tool for identifying those problems. PMID:26311919

  3. Activity performance problems of patients with cardiac diseases and their impact on quality of life.

    PubMed

    Duruturk, Neslihan; Tonga, Eda; Karatas, Metin; Doganozu, Ersin

    2015-07-01

    [Purpose] To describe the functional consequences of patients with cardiac diseases and analyze associations between activity limitations and quality of life. [Subjects and Methods] Seventy subjects (mean age: 60.1±12.0 years) were being treated by Physical Medicine and Rehabilitation and Cardiology Departments were included in the study. Activity limitations and participation restrictions as perceived by the individual were measured by the Canadian Occupational Performance Measure (COPM). The Nottingham Extended Activities of Daily Living (NEADL) Scale was used to describe limitations in daily living activities. To detect the impact of activity limitations on quality of life the Nottingham Health Profile (NHP) was used. [Results] The subjects described 46 different types of problematic activities. The five most identified problems were walking (45.7%), climbing up the stairs (41.4%), bathing (30%), dressing (28.6%) and outings (27.1%). The associations between COPM performance score with all subgroups of NEADL and NHP; total, energy, physical abilities subgroups, were statistically significant. [Conclusion] Our results showed that patients with cardiac diseases reported problems with a wide range of activities, and that also quality of life may be affected by activities of daily living. COPM can be provided as a patient-focused outcome measure, and it may be a useful tool for identifying those problems. PMID:26311919

  4. Recent extensions to the OMNI language to allow nonlinear equation and an interface to a nonlinear solver

    SciTech Connect

    Golush, W.G.

    1994-12-31

    Nonlinear equations are expressed using a new OMNI statement FORM NLE. This allows OMNI Constructs, Classes, Tables, and New Variables to be used in nonlinear equations. The interface passes the nonlinear equations and symbolic derivatives to a general nonlinear solver. After optimization, the row and column activities of the solution are written to an OMNI Standard Solution File. Reports are written from this file using the OMNI FORM LINE report writer. The interface will be illustrated with an example of a nonlinear model written in OMNI and solved using the MINOS nonlinear solver.

  5. A Comparative Study of Randomized Constraint Solvers for Random-Symbolic Testing

    NASA Technical Reports Server (NTRS)

    Takaki, Mitsuo; Cavalcanti, Diego; Gheyi, Rohit; Iyoda, Juliano; dAmorim, Marcelo; Prudencio, Ricardo

    2009-01-01

    The complexity of constraints is a major obstacle for constraint-based software verification. Automatic constraint solvers are fundamentally incomplete: input constraints often build on some undecidable theory or some theory the solver does not support. This paper proposes and evaluates several randomized solvers to address this issue. We compare the effectiveness of a symbolic solver (CVC3), a random solver, three hybrid solvers (i.e., mix of random and symbolic), and two heuristic search solvers. We evaluate the solvers on two benchmarks: one consisting of manually generated constraints and another generated with a concolic execution of 8 subjects. In addition to fully decidable constraints, the benchmarks include constraints with non-linear integer arithmetic, integer modulo and division, bitwise arithmetic, and floating-point arithmetic. As expected symbolic solving (in particular, CVC3) subsumes the other solvers for the concolic execution of subjects that only generate decidable constraints. For the remaining subjects the solvers are complementary.

  6. Flow and transport simulations using T2CG1, a package of conjugate gradient solvers for the TOUGH2 family of codes

    SciTech Connect

    Moridis, G.; Pruess, K.

    1995-04-01

    This report discusses the details of modifications made to the TOUGH2 family of codes to complement its direct solver which significantly increases the size of problems solved by the TOUGH2 code. With this modification, the TOUGH2 system is being tested in multiphase, multicomponent fluid and heat flow problems related to vadose zone hydrology, nuclear waste disposal, and environmental remediation.

  7. How number line estimation skills relate to neural activations in single digit subtraction problems.

    PubMed

    Berteletti, I; Man, G; Booth, J R

    2015-02-15

    The Number Line (NL) task requires judging the relative numerical magnitude of a number and estimating its value spatially on a continuous line. Children's skill on this task has been shown to correlate with and predict future mathematical competence. Neurofunctionally, this task has been shown to rely on brain regions involved in numerical processing. However, there is no direct evidence that performance on the NL task is related to brain areas recruited during arithmetical processing and that these areas are domain-specific to numerical processing. In this study, we test whether 8- to 14-year-old's behavioral performance on the NL task is related to fMRI activation during small and large single-digit subtraction problems. Domain-specific areas for numerical processing were independently localized through a numerosity judgment task. Results show a direct relation between NL estimation performance and the amount of the activation in key areas for arithmetical processing. Better NL estimators showed a larger problem size effect than poorer NL estimators in numerical magnitude (i.e., intraparietal sulcus) and visuospatial areas (i.e., posterior superior parietal lobules), marked by less activation for small problems. In addition, the direction of the activation with problem size within the IPS was associated with differences in accuracies for small subtraction problems. This study is the first to show that performance in the NL task, i.e. estimating the spatial position of a number on an interval, correlates with brain activity observed during single-digit subtraction problem in regions thought to be involved in numerical magnitude and spatial processes. PMID:25497398

  8. Developing clinical competency in crisis event management: an integrated simulation problem-based learning activity.

    PubMed

    Liaw, S Y; Chen, F G; Klainin, P; Brammer, J; O'Brien, A; Samarasekera, D D

    2010-08-01

    This study aimed to evaluate the integration of a simulation based learning activity on nursing students' clinical crisis management performance in a problem-based learning (PBL) curriculum. It was hypothesized that the clinical performance of first year nursing students who participated in a simulated learning activity during the PBL session would be superior to those who completed the conventional problem-based session. The students were allocated into either simulation with problem-based discussion (SPBD) or problem-based discussion (PBD) for scenarios on respiratory and cardiac distress. Following completion of each scenario, students from both groups were invited to sit an optional individual test involving a systematic assessment and immediate management of a simulated patient facing a crisis event. A total of thirty students participated in the first post test related to a respiratory scenario and thirty-three participated in the second post test related to a cardiac scenario. Their clinical performances were scored using a checklist. Mean test scores for students completing the SPBD were significantly higher than those who completing the PBD for both the first post test (SPBD 20.08, PBD 18.19) and second post test (SPBD 27.56, PBD 23.07). Incorporation of simulation learning activities into problem-based discussion appeared to be an effective educational strategy for teaching nursing students to assess and manage crisis events. PMID:19916052

  9. Continuous-time quantum Monte Carlo impurity solvers

    NASA Astrophysics Data System (ADS)

    Gull, Emanuel; Werner, Philipp; Fuchs, Sebastian; Surer, Brigitte; Pruschke, Thomas; Troyer, Matthias

    2011-04-01

    Continuous-time quantum Monte Carlo impurity solvers are algorithms that sample the partition function of an impurity model using diagrammatic Monte Carlo techniques. The present paper describes codes that implement the interaction expansion algorithm originally developed by Rubtsov, Savkin, and Lichtenstein, as well as the hybridization expansion method developed by Werner, Millis, Troyer, et al. These impurity solvers are part of the ALPS-DMFT application package and are accompanied by an implementation of dynamical mean-field self-consistency equations for (single orbital single site) dynamical mean-field problems with arbitrary densities of states. Program summaryProgram title: dmft Catalogue identifier: AEIL_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIL_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: ALPS LIBRARY LICENSE version 1.1 No. of lines in distributed program, including test data, etc.: 899 806 No. of bytes in distributed program, including test data, etc.: 32 153 916 Distribution format: tar.gz Programming language: C++ Operating system: The ALPS libraries have been tested on the following platforms and compilers: Linux with GNU Compiler Collection (g++ version 3.1 and higher), and Intel C++ Compiler (icc version 7.0 and higher) MacOS X with GNU Compiler (g++ Apple-version 3.1, 3.3 and 4.0) IBM AIX with Visual Age C++ (xlC version 6.0) and GNU (g++ version 3.1 and higher) compilers Compaq Tru64 UNIX with Compq C++ Compiler (cxx) SGI IRIX with MIPSpro C++ Compiler (CC) HP-UX with HP C++ Compiler (aCC) Windows with Cygwin or coLinux platforms and GNU Compiler Collection (g++ version 3.1 and higher) RAM: 10 MB-1 GB Classification: 7.3 External routines: ALPS [1], BLAS/LAPACK, HDF5 Nature of problem: (See [2].) Quantum impurity models describe an atom or molecule embedded in a host material with which it can exchange electrons. They are basic to nanoscience as

  10. LP-DIT interchange tool for linear programming problems

    SciTech Connect

    Makowski, M.

    1994-12-31

    LP-DIT is a small library that provides an easy handling of LP problem data between a problem generator, solver and other modules (problem modification, generation of multi-criteria problem, report writers, etc). So far LP-DIT has been implemented with 4 LP (including one MIP) solvers and is being used as a module for model-based Decision Support System. LP-DIT will be released as a public domain soft-ware in the coming weeks.

  11. Riemann solvers and boundary conditions for two-dimensional shallow water simulations

    NASA Astrophysics Data System (ADS)

    Guinot, Vincent

    2003-04-01

    Most existing algorithms for two-dimensional shallow water simulations treat multi-dimensional waves using wave splitting or time splitting. This often results in anisotropy of the computed flow. Both wave splitting and time splitting are based on a local decomposition of the multi-dimensional problem into one-dimensional, orthogonal problems. Therefore, these algorithms handle boundary conditions in a very similar way to classical one-dimensional algorithms. This should be expected to trigger a dependence of the number of boundary conditions on the direction of the flow at the boundaries. However, most computational codes based on alternate directions do not exhibit such sensitivity, which seems to contradict the theory of existence and uniqueness of the solution. The present paper addresses these issues. A Riemann solver is presented that aims to convert two-dimensional Riemann problems into a one-dimensional equivalent Riemann problem (ERP) at the interfaces between the computational cells. The ERP is derived by applying the theory of bicharacteristics at each end of the interface and by performing a linear averaging along the interface. The proposed approach is tested against the traditional one-dimensional approach on the classical circular dambreak problem. The results show that the proposed solver allows the isotropy of the solution to be better preserved. Use of the two-dimensional solver with a first-order scheme may give better results than use of a second-order scheme with a one-dimensional solver. The theory of bicharacteristics is also used to discuss the issue of boundary conditions. It is shown that, when the flow is subcritical, the number of boundary conditions affects the accuracy of the solution, but not its existence and uniqueness. When only one boundary condition is to be prescribed, it should not be the velocity in the direction parallel to the boundary. When two boundary conditions are to be prescribed, at least one of them should involve

  12. 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

    Forced periodic flows arise in a broad range of aerodynamic applications such as rotorcraft, turbomachinery, and flapping wing configurations. Standard practice involves solving the unsteady flow equations forward in time until the initial transient exits the domain and a statistically stationary flow is achieved. It is often required to simulate through several periods to remove the initial transient making unsteady design optimization prohibitively expensive for most realistic problems. An effort to reduce the computational cost of these calculations led to the development of the Harmonic Balance method [1, 2] which capitalizes on the periodic nature of the solution. The approach exploits the fact that forced temporally periodic flow, while varying in the time domain, is invariant in the frequency domain. Expanding the temporal variation at each spatial node into a Fourier series transforms the unsteady governing equations into a steady set of equations in integer harmonics that can be tackled with the acceleration techniques afforded to steady-state flow solvers. Other similar approaches, such as the Nonlinear Frequency Domain [3,4,5], Reduced Frequency [6] and Time-Spectral [7, 8, 9] methods, were developed shortly thereafter. Additionally, adjoint-based optimization techniques can be applied [10, 11] as well as frequency-adaptive methods [12, 13, 14] to provide even more flexibility to the method. The Fourier temporal basis functions imply spectral convergence as the number of harmonic modes, and correspondingly number of time samples, N, is increased. Some elect to solve the equations in the frequency domain directly, while others choose to transform the equations back into the time domain to simplify the process of adding this capability to existing solvers, but each harnesses the underlying steady solution in the frequency domain. These temporal projection methods will herein be collectively referred to as Time-Spectral methods. Time-Spectral methods have

  13. Euler/Navier-Stokes Solvers Applied to Ducted Fan Configurations

    NASA Technical Reports Server (NTRS)

    Keith, Theo G., Jr.; Srivastava, Rakesh

    1997-01-01

    Due to noise considerations, ultra high bypass ducted fans have become a more viable design. These ducted fans typically consist of a rotor stage containing a wide chord fan and a stator stage. One of the concerns for this design is the classical flutter that keeps occurring in various unducted fan blade designs. These flutter are catastrophic and are to be avoided in the flight envelope of the engine. Some numerical investigations by Williams, Cho and Dalton, have suggested that a duct around a propeller makes it more unstable. This needs to be further investigated. 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 be available. Aerodynamic solvers based on unsteady three-dimensional analysis will provide accurate and fast solutions and are best suited for aeroelastic analysis. The Euler solvers capture significant physics of the flowfield and are reasonably fast. An aerodynamic solver Ref. based on Euler equations had been developed under a separate grant from NASA Lewis in the past. Under the current grant, this solver has been modified to calculate the aeroelastic characteristics of unducted and ducted rotors. Even though, the aeroelastic solver based on three-dimensional Euler equations is computationally efficient, it is still very expensive to investigate the effects of multiple stages on the aeroelastic characteristics. In order to investigate the effects of multiple stages, a two-dimensional multi stage aeroelastic solver was also developed under this task, in collaboration with Dr. T. S. R. Reddy of the University of Toledo. Both of these solvers were applied to several test cases and validated against experimental data, where available.

  14. Efficient IMRT inverse planning with a new L1-solver: template for first-order conic solver.

    PubMed

    Kim, Hojin; Suh, Tae-Suk; Lee, Rena; Xing, Lei; Li, Ruijiang

    2012-07-01

    Intensity modulated radiation therapy (IMRT) inverse planning using total-variation (TV) regularization has been proposed to reduce the complexity of fluence maps and facilitate dose delivery. Conventionally, the optimization problem with L-1 norm is solved with quadratic programming (QP), which is time consuming and memory expensive due to the second-order Newton update. This study proposes to use a new algorithm, template for first-order conic solver (TFOCS), for fast and memory-efficient optimization in IMRT inverse planning. The TFOCS utilizes dual-variable updates and first-order approaches for TV minimization without the need to compute and store the enlarged Hessian matrix required for Newton update in the QP technique. To evaluate the effectiveness and efficiency of the proposed method, two clinical cases were used for IMRT inverse planning: a head and neck case and a prostate case. For comparison, the conventional QP-based method for the TV form was adopted to solve the fluence map optimization problem in the above two cases. The convergence criteria and algorithm parameters were selected to achieve similar dose conformity for a fair comparison between the two methods. Compared with conventional QP-based approach, the proposed TFOCS-based method shows a remarkable improvement in computational efficiency for fluence map optimization, while maintaining the conformal dose distribution. Compared with QP-based algorithms, the computational speed using TFOCS for fluence optimization is increased by a factor of 4 to 6, and at the same time the memory requirement is reduced by a factor of 3 to 4. Therefore, TFOCS provides an effective, fast and memory-efficient method for IMRT inverse planning. The unique features of the approach should be particularly important in inverse planning involving a large number of beams, such as in VMAT and dense angularly sampled and sparse intensity modulated radiation therapy (DASSIM-RT). PMID:22683930

  15. Computations of two-fluid models based on a simple and robust hybrid primitive variable Riemann solver with AUSMD

    NASA Astrophysics Data System (ADS)

    Niu, Yang-Yao

    2016-03-01

    This paper is to continue our previous work in 2008 on solving a two-fluid model for compressible liquid-gas flows. We proposed a pressure-velocity based diffusion term original derived from AUSMD scheme of Wada and Liou in 1997 to enhance its robustness. The proposed AUSMD schemes have been applied to gas and liquid fluids universally to capture fluid discontinuities, such as the fluid interfaces and shock waves, accurately for the Ransom's faucet problem, air-water shock tube problems and 2D shock-water liquid interaction problems. However, the proposed scheme failed at computing liquid-gas interfaces in problems under large ratios of pressure, density and volume of fraction. The numerical instability has been remedied by Chang and Liou in 2007 using the exact Riemann solver to enhance the accuracy and stability of numerical flux across the liquid-gas interface. Here, instead of the exact Riemann solver, we propose a simple AUSMD type primitive variable Riemann solver (PVRS) which can successfully solve 1D stiffened water-air shock tube and 2D shock-gas interaction problems under large ratios of pressure, density and volume of fraction without the expensive cost of tedious computer time. In addition, the proposed approach is shown to deliver a good resolution of the shock-front, rarefaction and cavitation inside the evolution of high-speed droplet impact on the wall.

  16. Changing Channels: Activities Promoting Media Smarts and Creative Problem Solving for Kids.

    ERIC Educational Resources Information Center

    Hoffman, Eric

    When children have healthy ways to process the news and information they see on television, they are better prepared to approach conflict peacefully and solve problems in their everyday lives. This guide presents activities for children to help them learn to think critically about what they see on television, to resolve conflicts productively, and…

  17. Perceived Affordances of a Technology-Enhanced Active Learning Classroom in Promoting Collaborative Problem Solving

    ERIC Educational Resources Information Center

    Ge, Xun; Yang, Yu Jin; Liao, Lihui; Wolfe, Erin G.

    2013-01-01

    This study explored students and instructors' perceptions and experience of technology affordances in an technology-enhanced Active Learning Classroom (ALC) to promote students' collaborative problem solving. Multiple case studies were conducted. Five classes of 92 students and five professors participated in this study. The data sources were…

  18. Can Mood-Inducing Videos Affect Problem-Solving Activities in a Web-Based Environment?

    ERIC Educational Resources Information Center

    Verleur, Ria; Verhagen, Plon W.; Heuvelman, Ard

    2007-01-01

    The purpose of this study was to examine whether a video-induced positive and negative mood has a differential effect on subsequent problem-solving activities in a web-based environment. The study also examined whether task conditions (task demands) moderated the mood effect. As in traditional experimental mood-effect studies, the affective video…

  19. Alternative Fuels and Hybrid Technology: A Classroom Activity Designed to Evaluate a Contemporary Problem

    ERIC Educational Resources Information Center

    Roy MacArthur, Amy H.; Copper, Christine L.

    2009-01-01

    As petroleum reserves are being depleted worldwide and energy costs are increasing, the use of alternative fuels is being more widely considered as a solution to the impending energy crisis. In this classroom activity students are presented with a real-world problem in which they must evaluate the properties and environmental impacts of a variety…

  20. "Sustainability on Earth" Webquests: Do They Qualify as Problem-Based Learning Activities?

    ERIC Educational Resources Information Center

    Leite, Laurinda; Dourado, Luís; Morgado, Sofia

    2015-01-01

    Information and communication technologies (ICT), namely the Internet, can play a valuable educational role in several school subjects, including science education. The same applies to problem-based learning (PBL), that is, a student-centered active learning methodology that can prepare students for lifelong learning. WebQuests (WQs) combine PBL…

  1. The Use of a Real Life Simulated Problem Based Learning Activity in a Corporate Environment

    ERIC Educational Resources Information Center

    Laurent, Mark A.

    2013-01-01

    This narrative study examines using a real life simulated problem base learning activity during education of clinical staff, which is expected to design and develop clinically correct electronic charting systems. Expertise in healthcare does not readily transcend to the realm of manipulating software to collect patient data that is pertinent to…

  2. ABO/Rh Blood-Typing Model: A Problem-Solving Activity

    ERIC Educational Resources Information Center

    Wake, Carol

    2005-01-01

    An ARO/Rh Blood-Typing kit useful for students to visualize blood-typing activities and practice problem-solving skills with transfusion reactions is presented. The model also enables students to identify relationships between A, B, and Rh antigens and antibodies in blood and to understand molecular mechanisms involved in transfusion agglutination…

  3. Creative Multimodal Learning Environments and Blended Interaction for Problem-Based Activity in HCI Education

    ERIC Educational Resources Information Center

    Ioannou, Andri; Vasiliou, Christina; Zaphiris, Panayiotis; Arh, Tanja; Klobucar, Tomaž; Pipan, Matija

    2015-01-01

    This exploratory case study aims to examine how students benefit from a multimodal learning environment while they engage in collaborative problem-based activity in a Human Computer Interaction (HCI) university course. For 12 weeks, 30 students, in groups of 5-7 each, participated in weekly face-to-face meetings and online interactions.…

  4. Longitudinal Modeling of Adolescents' Activity Involvement, Problem Peer Associations, and Youth Smoking

    ERIC Educational Resources Information Center

    Metzger, Aaron; Dawes, Nickki; Mermelstein, Robin; Wakschlag, Lauren

    2011-01-01

    Longitudinal associations among different types of organized activity involvement, problem peer associations, and cigarette smoking were examined in a sample of 1040 adolescents (mean age = 15.62 at baseline, 16.89 at 15-month assessment, 17.59 at 24 months) enriched for smoking experimentation (83% had tried smoking). A structural equation model…

  5. The Influence of Achievement Goals on the Constructive Activity of Low Achievers during Collaborative Problem Solving

    ERIC Educational Resources Information Center

    Gabriele, Anthony J.

    2007-01-01

    Background: Previous research on small-group learning has found that level of constructive activity (solving or explaining how to solve problems using ideas stated or implied in the explanation provided by a partner) was a better predictor of post-test achievement than either a student's prior achievement or the quality of help received (Webb,…

  6. Predicting Early Sexual Activity with Behavior Problems Exhibited at School Entry and in Early Adolescence

    ERIC Educational Resources Information Center

    Schofield, Hannah-Lise T.; Bierman, Karen L.; Heinrichs, Brenda; Nix, Robert L.

    2008-01-01

    Youth who initiate sexual intercourse in early adolescence (age 11-14) experience multiple risks, including concurrent adjustment problems and unsafe sexual practices. The current study tested two models describing the links between childhood precursors, early adolescent risk factors, and adolescent sexual activity: a cumulative model and a…

  7. Using Computers to Initiate Active Learning for Students with Severe Behavior Problems.

    ERIC Educational Resources Information Center

    Reganick, Karol A.

    1994-01-01

    Describes a desktop publishing project that uses computer-assisted instruction to engage students with severe behavioral problems in a more active learning environment. Topics discussed include the reinforcement from computers; benefits of computer-assisted instruction; hardware and software selection; staff training; evaluation; and future…

  8. A Proposal for Teaching Undergraduate Chemistry Students Carbohydrate Biochemistry by Problem-Based Learning Activities

    ERIC Educational Resources Information Center

    Figueira, Angela C. M.; Rocha, Joao B. T.

    2014-01-01

    This article presents a problem-based learning (PBL) approach to teaching elementary biochemistry to undergraduate students. The activity was based on "the foods we eat." It was used to engage students' curiosity and to initiate learning about a subject that could be used by the future teachers in the high school. The experimental…

  9. Feedback during Active Learning: Elementary School Teachers' Beliefs and Perceived Problems

    ERIC Educational Resources Information Center

    van den Bergh, Linda; Ros, Anje; Beijaard, Douwe

    2013-01-01

    Giving feedback during active learning is an important, though difficult, task for teachers. In the present study, the problems elementary school teachers perceive and the beliefs they hold regarding this task were investigated. It appeared that teachers believe conditional teacher skills, especially time management, hinder them most from giving…

  10. Participation in Organized Activities and Conduct Problems in Elementary School: The Mediating Effect of Social Skills

    ERIC Educational Resources Information Center

    Denault, Anne-Sophie; Déry, Michèle

    2015-01-01

    The goal of this study was to test a mediation model in which social skills mediate the relationship between participation in organized activities and conduct problems among elementary school children. Two moderators of these associations were also examined, namely, gender and reception of special education services. A total of 563 children (45%…

  11. 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…

  12. Problems Encountered by Religious Vocational Secondary School and Other Secondary School Students in Physical Education and Sports Activities

    ERIC Educational Resources Information Center

    Bar, Mustafa; Yaman, Menzure Sibel; Hergüner, Gülten

    2016-01-01

    The study aimed to determine problems encountered by Religious Vocational Secondary School and other Secondary School students in physical education and sports activities and to compare these problems according to school type and gender. A questionnaire named "Problems encountered in attending to physical education and sports activities"…

  13. LSRN: A PARALLEL ITERATIVE SOLVER FOR STRONGLY OVER- OR UNDERDETERMINED SYSTEMS*

    PubMed Central

    Meng, Xiangrui; Saunders, Michael A.; Mahoney, Michael W.

    2014-01-01

    We describe a parallel iterative least squares solver named LSRN that is based on random normal projection. LSRN computes the min-length solution to minx∈ℝn ‖Ax − b‖2, where A ∈ ℝm × n with m ≫ n or m ≪ n, and where A may be rank-deficient. Tikhonov regularization may also be included. Since A is involved only in matrix-matrix and matrix-vector multiplications, it can be a dense or sparse matrix or a linear operator, and LSRN automatically speeds up when A is sparse or a fast linear operator. The preconditioning phase consists of a random normal projection, which is embarrassingly parallel, and a singular value decomposition of size ⌈γ min(m, n)⌉ × min(m, n), where γ is moderately larger than 1, e.g., γ = 2. We prove that the preconditioned system is well-conditioned, with a strong concentration result on the extreme singular values, and hence that the number of iterations is fully predictable when we apply LSQR or the Chebyshev semi-iterative method. As we demonstrate, the Chebyshev method is particularly efficient for solving large problems on clusters with high communication cost. Numerical results show that on a shared-memory machine, LSRN is very competitive with LAPACK’s DGELSD and a fast randomized least squares solver called Blendenpik on large dense problems, and it outperforms the least squares solver from SuiteSparseQR on sparse problems without sparsity patterns that can be exploited to reduce fill-in. Further experiments show that LSRN scales well on an Amazon Elastic Compute Cloud cluster. PMID:25419094

  14. Description and use of LSODE, the Livermore Solver for Ordinary Differential Equations

    NASA Technical Reports Server (NTRS)

    Radhakrishnan, Krishnan; Hindmarsh, Alan C.

    1993-01-01

    LSODE, the Livermore Solver for Ordinary Differential Equations, is a package of FORTRAN subroutines designed for the numerical solution of the initial value problem for a system of ordinary differential equations. It is particularly well suited for 'stiff' differential systems, for which the backward differentiation formula method of orders 1 to 5 is provided. The code includes the Adams-Moulton method of orders 1 to 12, so it can be used for nonstiff problems as well. In addition, the user can easily switch methods to increase computational efficiency for problems that change character. For both methods a variety of corrector iteration techniques is included in the code. Also, to minimize computational work, both the step size and method order are varied dynamically. This report presents complete descriptions of the code and integration methods, including their implementation. It also provides a detailed guide to the use of the code, as well as an illustrative example problem.

  15. Final Report for "Implimentation and Evaluation of Multigrid Linear Solvers into Extended Magnetohydrodynamic Codes for Petascale Computing"

    SciTech Connect

    Srinath Vadlamani; Scott Kruger; Travis Austin

    2008-06-19

    Extended magnetohydrodynamic (MHD) codes are used to model the large, slow-growing instabilities that are projected to limit the performance of International Thermonuclear Experimental Reactor (ITER). The multiscale nature of the extended MHD equations requires an implicit approach. The current linear solvers needed for the implicit algorithm scale poorly because the resultant matrices are so ill-conditioned. A new solver is needed, especially one that scales to the petascale. The most successful scalable parallel processor solvers to date are multigrid solvers. Applying multigrid techniques to a set of equations whose fundamental modes are dispersive waves is a promising solution to CEMM problems. For the Phase 1, we implemented multigrid preconditioners from the HYPRE project of the Center for Applied Scientific Computing at LLNL via PETSc of the DOE SciDAC TOPS for the real matrix systems of the extended MHD code NIMROD which is a one of the primary modeling codes of the OFES-funded Center for Extended Magnetohydrodynamic Modeling (CEMM) SciDAC. We implemented the multigrid solvers on the fusion test problem that allows for real matrix systems with success, and in the process learned about the details of NIMROD data structures and the difficulties of inverting NIMROD operators. The further success of this project will allow for efficient usage of future petascale computers at the National Leadership Facilities: Oak Ridge National Laboratory, Argonne National Laboratory, and National Energy Research Scientific Computing Center. The project will be a collaborative effort between computational plasma physicists and applied mathematicians at Tech-X Corporation, applied mathematicians Front Range Scientific Computations, Inc. (who are collaborators on the HYPRE project), and other computational plasma physicists involved with the CEMM project.

  16. Performance of Nonlinear Finite-Difference Poisson-Boltzmann Solvers.

    PubMed

    Cai, Qin; Hsieh, Meng-Juei; Wang, Jun; Luo, Ray

    2010-01-12

    We implemented and optimized seven finite-difference solvers for the full nonlinear Poisson-Boltzmann equation in biomolecular applications, including four relaxation methods, one conjugate gradient method, and two inexact Newton methods. The performance of the seven solvers was extensively evaluated with a large number of nucleic acids and proteins. Worth noting is the inexact Newton method in our analysis. We investigated the role of linear solvers in its performance by incorporating the incomplete Cholesky conjugate gradient and the geometric multigrid into its inner linear loop. We tailored and optimized both linear solvers for faster convergence rate. In addition, we explored strategies to optimize the successive over-relaxation method to reduce its convergence failures without too much sacrifice in its convergence rate. Specifically we attempted to adaptively change the relaxation parameter and to utilize the damping strategy from the inexact Newton method to improve the successive over-relaxation method. Our analysis shows that the nonlinear methods accompanied with a functional-assisted strategy, such as the conjugate gradient method and the inexact Newton method, can guarantee convergence in the tested molecules. Especially the inexact Newton method exhibits impressive performance when it is combined with highly efficient linear solvers that are tailored for its special requirement. PMID:24723843

  17. Adaptive kinetic-fluid solvers for heterogeneous computing architectures

    NASA Astrophysics Data System (ADS)

    Zabelok, Sergey; Arslanbekov, Robert; Kolobov, Vladimir

    2015-12-01

    We show feasibility and benefits of porting an adaptive multi-scale kinetic-fluid code to CPU-GPU systems. Challenges are due to the irregular data access for adaptive Cartesian mesh, vast difference of computational cost between kinetic and fluid cells, and desire to evenly load all CPUs and GPUs during grid adaptation and algorithm refinement. Our Unified Flow Solver (UFS) combines Adaptive Mesh Refinement (AMR) with automatic cell-by-cell selection of kinetic or fluid solvers based on continuum breakdown criteria. Using GPUs enables hybrid simulations of mixed rarefied-continuum flows with a million of Boltzmann cells each having a 24 × 24 × 24 velocity mesh. We describe the implementation of CUDA kernels for three modules in UFS: the direct Boltzmann solver using the discrete velocity method (DVM), the Direct Simulation Monte Carlo (DSMC) solver, and a mesoscopic solver based on the Lattice Boltzmann Method (LBM), all using adaptive Cartesian mesh. Double digit speedups on single GPU and good scaling for multi-GPUs have been demonstrated.

  18. On the Performance of an Algebraic MultigridSolver on Multicore Clusters

    SciTech Connect

    Baker, A H; Schulz, M; Yang, U M

    2010-04-29

    Algebraic multigrid (AMG) solvers have proven to be extremely efficient on distributed-memory architectures. However, when executed on modern multicore cluster architectures, we face new challenges that can significantly harm AMG's performance. We discuss our experiences on such an architecture and present a set of techniques that help users to overcome the associated problems, including thread and process pinning and correct memory associations. We have implemented most of the techniques in a MultiCore SUPport library (MCSup), which helps to map OpenMP applications to multicore machines. We present results using both an MPI-only and a hybrid MPI/OpenMP model.

  19. Multilevel solvers of first-order system least-squares for Stokes equations

    SciTech Connect

    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.

  20. On the Performance of an Algebraic Multigrid Solver on Multicore Clusters

    SciTech Connect

    Baker, A; Schulz, M; Yang, U M

    2009-11-24

    Algebraic multigrid (AMG) solvers have proven to be extremely efficient on distributed-memory architectures. However, when executed on modern multicore cluster architectures, we face new challenges that can significantly harm AMG's performance. We discuss our experiences on such an architecture and present a set of techniques that help users to overcome the associated problems, including thread and process pinning and correct memory associations. We have implemented most of the techniques in a MultiCore SUPport library (MCSup), which helps to map OpenMP applications to multicore machines. We present results using both an MPI-only and a hybrid MPI/OpenMP model.

  1. Application of a Scalable, Parallel, Unstructured-Grid-Based Navier-Stokes Solver

    NASA Technical Reports Server (NTRS)

    Parikh, Paresh

    2001-01-01

    A parallel version of an unstructured-grid based Navier-Stokes solver, USM3Dns, previously developed for efficient operation on a variety of parallel computers, has been enhanced to incorporate upgrades made to the serial version. The resultant parallel code has been extensively tested on a variety of problems of aerospace interest and on two sets of parallel computers to understand and document its characteristics. An innovative grid renumbering construct and use of non-blocking communication are shown to produce superlinear computing performance. Preliminary results from parallelization of a recently introduced "porous surface" boundary condition are also presented.

  2. A speciation solver for cement paste modeling and the semismooth Newton method

    SciTech Connect

    Georget, Fabien; Prévost, Jean H.; Vanderbei, Robert J.

    2015-02-15

    The mineral assemblage of a cement paste may vary considerably with its environment. In addition, the water content of a cement paste is relatively low and the ionic strength of the interstitial solution is often high. These conditions are extreme conditions with respect to the common assumptions made in speciation problem. Furthermore the common trial and error algorithm to find the phase assemblage does not provide any guarantee of convergence. We propose a speciation solver based on a semismooth Newton method adapted to the thermodynamic modeling of cement paste. The strong theoretical properties associated with these methods offer practical advantages. Results of numerical experiments indicate that the algorithm is reliable, robust, and efficient.

  3. An efficient procedure for cascade aeroelastic stability determination using nonlinear, time-marching aerodynamic solvers

    NASA Technical Reports Server (NTRS)

    Mahajan, Aparajit J.; Bakhle, Milind A.; Dowell, Earl H.

    1993-01-01

    A numerical eigenvalue problem formulation and a practical calculation procedure for exact eigenvalues and corresponding eigenvectors are developed and applied to a nonlinear, two-dimensional, time-marching full potential solver for cascade aeroelastic stability analysis. This procedure is based on the Lanczos recursive method and it directly calculates stability information about a nonlinear steady state. It is compared to conventional approaches in the frequency and time domains developed earlier and is found to be 100-10.000 times more computationally efficient. Eigenvalue constellations and the flutter results for flow through a cascade SR5 propfan airfoil are presented.

  4. Can Organized Youth Activities Protect Against Internalizing Problems Among Adolescents Living in Violent Homes?

    PubMed

    Gardner, Margo; Browning, Christopher; Brooks-Gunn, Jeanne

    2012-12-01

    Using longitudinal data from a subsample of Hispanic, African American, and white youth enrolled in the Project on Human Development in Chicago Neighborhoods (N = 1,419), we examined the effects of both parental involvement in domestic violence and youth participation in organized out-of-school-time activities on internalizing symptoms during adolescence. We also examined the extent to which participation in organized activities protected youth against the internalizing consequences of domestic violence. We found that intensive participation in either afterschool programs or extracurricular activities was inversely associated with youth internalizing problems. Moreover, we found that intensive participation in afterschool programs weakened the association between parents' domestic violence and youths' internalizing problems. PMID:23162370

  5. A three-dimensional explicit sphere function-based gas-kinetic flux solver for simulation of inviscid compressible flows

    NASA Astrophysics Data System (ADS)

    Yang, L. M.; Shu, C.; Wu, J.

    2015-08-01

    In this work, a truly three-dimensional (3D) flux solver is presented for simulation of inviscid compressible flows. Like the conventional multi-dimensional gas-kinetic scheme, in the present work, the local solution of 3D Boltzmann equation at the cell interface is used to evaluate the flux. On the other hand, different from most of the existing gas-kinetic schemes, which are constructed from Maxwellian distribution function, the present flux solver is derived from a simple distribution function defined on the spherical surface in the phase velocity space. As a result, the explicit expression of flux vector at the cell interface can be simply given. Since the simple distribution function is defined on the spherical surface, for simplicity, it is termed as sphere function hereafter. In addition, to simulate fluid flow problems with strong shock waves, the non-equilibrium part of the distribution function is regarded as numerical dissipation and involved in evaluating the inviscid flux at the cell interface. The weight of the non-equilibrium part is controlled by introducing a switch function which ranges from 0 to 1. In the smooth region, the switch function takes a value close to zero, while around the strong shock wave, it tends to one. To validate the proposed flux solver, several transonic, supersonic and hypersonic inviscid flows are simulated. Numerical results showed that the present solver can provide accurate numerical results for three-dimensional inviscid flows with strong shock waves.

  6. Selectively active markers for solving of the partial occlusion problem in matchmoving and chromakeying workflow

    NASA Astrophysics Data System (ADS)

    Mazurek, Przemysław

    2013-09-01

    Matchmoving (Match Moving) is the process used for the estimation of camera movements for further integration of acquired video image with computer graphics. The estimation of movements is possible using pattern recognition, 2D and 3D tracking algorithms. The main problem for the workflow is the partial occlusion of markers by the actor, because manual rotoscoping is necessary for fixing of the chroma-keyed footage. In the paper, the partial occlusion problem is solved using the invented, selectively active electronic markers. The sensor network with multiple infrared links detects occlusion state (no-occlusion, partial, full) and switch LED's based markers.

  7. 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.

  8. TemperSAT: A new efficient fair-sampling random k-SAT solver

    NASA Astrophysics Data System (ADS)

    Fang, Chao; Zhu, Zheng; Katzgraber, Helmut G.

    The set membership problem is of great importance to many applications and, in particular, database searches for target groups. Recently, an approach to speed up set membership searches based on the NP-hard constraint-satisfaction problem (random k-SAT) has been developed. However, the bottleneck of the approach lies in finding the solution to a large SAT formula efficiently and, in particular, a large number of independent solutions is needed to reduce the probability of false positives. Unfortunately, traditional random k-SAT solvers such as WalkSAT are biased when seeking solutions to the Boolean formulas. By porting parallel tempering Monte Carlo to the sampling of binary optimization problems, we introduce a new algorithm (TemperSAT) whose performance is comparable to current state-of-the-art SAT solvers for large k with the added benefit that theoretically it can find many independent solutions quickly. We illustrate our results by comparing to the currently fastest implementation of WalkSAT, WalkSATlm.

  9. Open Collaboration: A Problem Solving Strategy That is Redefining NASA's Innovative Spirit

    NASA Technical Reports Server (NTRS)

    Rando, Cynthia M.; Fogarty, Jennifer A.; Richard, E. E.; Davis, Jeffrey R.

    2011-01-01

    In 2010, NASA's Space Life Sciences Directorate announced the successful results from pilot experiments with open innovation methodologies. Specifically, utilization of internet based external crowdsourcing platforms to solve challenging problems in human health and performance related to the future of spaceflight. The follow-up to this success was an internal crowdsourcing pilot program entitled NASA@work, which was supported by the InnoCentive@work software platform. The objective of the NASA@work pilot was to connect the collective knowledge of individuals from all areas within the NASA organization via a private web based environment. The platform provided a venue for NASA Challenge Owners, those looking for solutions or new ideas, to pose challenges to internal solvers, those within NASA with the skill and desire to create solutions. The pilot was launched in 57 days, a record for InnoCentive and NASA, and ran for three months with a total of 20 challenges posted Agency wide. The NASA@work pilot attracted over 6,000 participants throughout NASA with a total of 183 contributing solvers for the 20 challenges posted. At the time of the pilot's closure, solvers provided viable solutions and ideas for 17 of the 20 posted challenges. The solver community provided feedback on the pilot describing it as a barrier breaking activity, conveying that there was a satisfaction associated with helping co-workers, that it was fun to think about problems outside normal work boundaries, and it was nice to learn what challenges others were facing across the agency. The results and the feedback from the solver community have demonstrated the power and utility of an internal collaboration tool, such as NASA@work.

  10. Open Collaboration: A Problem Solving Strategy That Is Redefining NASA's Innovative Spirit

    NASA Technical Reports Server (NTRS)

    Rando, Cynthia M.; Fogarty, Jennifer A.; Richard, Elizabeth E.; Davis, Jeffrey R.

    2011-01-01

    In 2010, NASA?s Space Life Sciences Directorate announced the successful results from pilot experiments with open innovation methodologies. Specifically, utilization of internet based external crowd sourcing platforms to solve challenging problems in human health and performance related to the future of spaceflight. The follow-up to this success was an internal crowd sourcing pilot program entitled NASA@work, which was supported by the InnoCentive@work software platform. The objective of the NASA@work pilot was to connect the collective knowledge of individuals from all areas within the NASA organization via a private web based environment. The platform provided a venue for NASA Challenge Owners, those looking for solutions or new ideas, to pose challenges to internal solvers, those within NASA with the skill and desire to create solutions. The pilot was launched in 57 days, a record for InnoCentive and NASA, and ran for three months with a total of 20 challenges posted Agency wide. The NASA@work pilot attracted over 6000 participants throughout NASA with a total of 183 contributing solvers for the 20 challenges posted. At the time of the pilot?s closure, solvers provided viable solutions and ideas for 17 of the 20 posted challenges. The solver community provided feedback on the pilot describing it as a barrier breaking activity, conveying that there was a satisfaction associated with helping co-workers, that it was "fun" to think about problems outside normal work boundaries, and it was nice to learn what challenges others were facing across the agency. The results and the feedback from the solver community have demonstrated the power and utility of an internal collaboration tool, such as NASA@work.

  11. 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.

  12. Gpu Implementation of a Viscous Flow Solver on Unstructured Grids

    NASA Astrophysics Data System (ADS)

    Xu, Tianhao; Chen, Long

    2016-06-01

    Graphics processing units have gained popularities in scientific computing over past several years due to their outstanding parallel computing capability. Computational fluid dynamics applications involve large amounts of calculations, therefore a latest GPU card is preferable of which the peak computing performance and memory bandwidth are much better than a contemporary high-end CPU. We herein focus on the detailed implementation of our GPU targeting Reynolds-averaged Navier-Stokes equations solver based on finite-volume method. The solver employs a vertex-centered scheme on unstructured grids for the sake of being capable of handling complex topologies. Multiple optimizations are carried out to improve the memory accessing performance and kernel utilization. Both steady and unsteady flow simulation cases are carried out using explicit Runge-Kutta scheme. The solver with GPU acceleration in this paper is demonstrated to have competitive advantages over the CPU targeting one.

  13. 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.

  14. Problem solving stages in the five square problem.

    PubMed

    Fedor, Anna; Szathmáry, Eörs; Öllinger, Michael

    2015-01-01

    According to the restructuring hypothesis, insight problem solving typically progresses through consecutive stages of search, impasse, insight, and search again for someone, who solves the task. The order of these stages was determined through self-reports of problem solvers and has never been verified behaviorally. We asked whether individual analysis of problem solving attempts of participants revealed the same order of problem solving stages as defined by the theory and whether their subjective feelings corresponded to the problem solving stages they were in. Our participants tried to solve the Five-Square problem in an online task, while we recorded the time and trajectory of their stick movements. After the task they were asked about their feelings related to insight and some of them also had the possibility of reporting impasse while working on the task. We found that the majority of participants did not follow the classic four-stage model of insight, but had more complex sequences of problem solving stages, with search and impasse recurring several times. This means that the classic four-stage model is not sufficient to describe variability on the individual level. We revised the classic model and we provide a new model that can generate all sequences found. Solvers reported insight more often than non-solvers and non-solvers reported impasse more often than solvers, as expected; but participants did not report impasse more often during behaviorally defined impasse stages than during other stages. This shows that impasse reports might be unreliable indicators of impasse. Our study highlights the importance of individual analysis of problem solving behavior to verify insight theory. PMID:26300794

  15. Problem solving stages in the five square problem

    PubMed Central

    Fedor, Anna; Szathmáry, Eörs; Öllinger, Michael

    2015-01-01

    According to the restructuring hypothesis, insight problem solving typically progresses through consecutive stages of search, impasse, insight, and search again for someone, who solves the task. The order of these stages was determined through self-reports of problem solvers and has never been verified behaviorally. We asked whether individual analysis of problem solving attempts of participants revealed the same order of problem solving stages as defined by the theory and whether their subjective feelings corresponded to the problem solving stages they were in. Our participants tried to solve the Five-Square problem in an online task, while we recorded the time and trajectory of their stick movements. After the task they were asked about their feelings related to insight and some of them also had the possibility of reporting impasse while working on the task. We found that the majority of participants did not follow the classic four-stage model of insight, but had more complex sequences of problem solving stages, with search and impasse recurring several times. This means that the classic four-stage model is not sufficient to describe variability on the individual level. We revised the classic model and we provide a new model that can generate all sequences found. Solvers reported insight more often than non-solvers and non-solvers reported impasse more often than solvers, as expected; but participants did not report impasse more often during behaviorally defined impasse stages than during other stages. This shows that impasse reports might be unreliable indicators of impasse. Our study highlights the importance of individual analysis of problem solving behavior to verify insight theory. PMID:26300794

  16. Albany/FELIX: A parallel, scalable and robust, finite element, first-order Stokes approximation ice sheet solver built for advanced analysis

    DOE PAGESBeta

    Tezaur, I. K.; Perego, M.; Salinger, A. G.; Tuminaro, R. S.; Price, S. F.

    2015-04-27

    This paper describes a new parallel, scalable and robust finite element based solver for the first-order Stokes momentum balance equations for ice flow. The solver, known as Albany/FELIX, is constructed using the component-based approach to building application codes, in which mature, modular libraries developed as a part of the Trilinos project are combined using abstract interfaces and template-based generic programming, resulting in a final code with access to dozens of algorithmic and advanced analysis capabilities. Following an overview of the relevant partial differential equations and boundary conditions, the numerical methods chosen to discretize the ice flow equations are described, alongmore » with their implementation. The results of several verification studies of the model accuracy are presented using (1) new test cases for simplified two-dimensional (2-D) versions of the governing equations derived using the method of manufactured solutions, and (2) canonical ice sheet modeling benchmarks. Model accuracy and convergence with respect to mesh resolution are then studied on problems involving a realistic Greenland ice sheet geometry discretized using hexahedral and tetrahedral meshes. Also explored as a part of this study is the effect of vertical mesh resolution on the solution accuracy and solver performance. The robustness and scalability of our solver on these problems is demonstrated. Lastly, we show that good scalability can be achieved by preconditioning the iterative linear solver using a new algebraic multilevel preconditioner, constructed based on the idea of semi-coarsening.« less

  17. Albany/FELIX: A parallel, scalable and robust, finite element, first-order Stokes approximation ice sheet solver built for advanced analysis

    SciTech Connect

    Tezaur, I. K.; Perego, M.; Salinger, A. G.; Tuminaro, R. S.; Price, S. F.

    2015-04-27

    This paper describes a new parallel, scalable and robust finite element based solver for the first-order Stokes momentum balance equations for ice flow. The solver, known as Albany/FELIX, is constructed using the component-based approach to building application codes, in which mature, modular libraries developed as a part of the Trilinos project are combined using abstract interfaces and template-based generic programming, resulting in a final code with access to dozens of algorithmic and advanced analysis capabilities. Following an overview of the relevant partial differential equations and boundary conditions, the numerical methods chosen to discretize the ice flow equations are described, along with their implementation. The results of several verification studies of the model accuracy are presented using (1) new test cases for simplified two-dimensional (2-D) versions of the governing equations derived using the method of manufactured solutions, and (2) canonical ice sheet modeling benchmarks. Model accuracy and convergence with respect to mesh resolution are then studied on problems involving a realistic Greenland ice sheet geometry discretized using hexahedral and tetrahedral meshes. Also explored as a part of this study is the effect of vertical mesh resolution on the solution accuracy and solver performance. The robustness and scalability of our solver on these problems is demonstrated. Lastly, we show that good scalability can be achieved by preconditioning the iterative linear solver using a new algebraic multilevel preconditioner, constructed based on the idea of semi-coarsening.

  18. Albany/FELIX: a parallel, scalable and robust, finite element, first-order Stokes approximation ice sheet solver built for advanced analysis

    NASA Astrophysics Data System (ADS)

    Tezaur, I. K.; Perego, M.; Salinger, A. G.; Tuminaro, R. S.; Price, S. F.

    2015-04-01

    This paper describes a new parallel, scalable and robust finite element based solver for the first-order Stokes momentum balance equations for ice flow. The solver, known as Albany/FELIX, is constructed using the component-based approach to building application codes, in which mature, modular libraries developed as a part of the Trilinos project are combined using abstract interfaces and template-based generic programming, resulting in a final code with access to dozens of algorithmic and advanced analysis capabilities. Following an overview of the relevant partial differential equations and boundary conditions, the numerical methods chosen to discretize the ice flow equations are described, along with their implementation. The results of several verification studies of the model accuracy are presented using (1) new test cases for simplified two-dimensional (2-D) versions of the governing equations derived using the method of manufactured solutions, and (2) canonical ice sheet modeling benchmarks. Model accuracy and convergence with respect to mesh resolution are then studied on problems involving a realistic Greenland ice sheet geometry discretized using hexahedral and tetrahedral meshes. Also explored as a part of this study is the effect of vertical mesh resolution on the solution accuracy and solver performance. The robustness and scalability of our solver on these problems is demonstrated. Lastly, we show that good scalability can be achieved by preconditioning the iterative linear solver using a new algebraic multilevel preconditioner, constructed based on the idea of semi-coarsening.

  19. Purposeful activity for people with enduring mental health problems: reflections from a case study.

    PubMed

    Mitchell, D

    1998-10-01

    The desire to work is deeply rooted in the human psyche and involves both intrinsic and extrinsic factors. If this is indeed the case, then this form of human activity should be considered to be an important element of our lives and therefore worthy of intervention when circumstances restrict an individual's engagement with it. To investigate the therapeutic nature of work for people with enduring mental health problems, the author conducted a pilot case study of a work rehabilitation scheme in the United Kingdom. The main theme to emerge from the study was that of purposeful activity. PMID:9793215

  20. Selected topics on the active control of helicopter aeromechanical and vibration problems

    NASA Technical Reports Server (NTRS)

    Friedmann, Peretz P.

    1994-01-01

    This paper describes in a concise manner three selected topics on the active control of helicopter aeromechanical and vibration problems. The three topics are as follows: (1) the active control of helicopter air-resonance using an LQG/LTR approach; (2) simulation of higher harmonic control (HHC) applied to a four bladed hingeless helicopter rotor in forward flight; and (3) vibration suppression in forward flight on a hingeless helicopter rotor using an actively controlled, partial span, trailing edge flap, which is mounted on the blade. Only a few selected illustrative results are presented. The results obtained clearly indicate that the partial span, actively controlled flap has considerable potential for vibration reduction in helicopter rotors.

  1. Viscous Driven-Cavity Solver: User's Manual

    NASA Technical Reports Server (NTRS)

    Wood, William A.

    1997-01-01

    The viscous driven-cavity problem is solved using a stream-function and vorticity formulation for the incompressible Navier-Stokes equations. This report provides the user's manual and FORTRAN code for the set of governing equations presented in NASA TM-110262.

  2. A Comparison of Updating Processes in Children Good or Poor in Arithmetic Word Problem-Solving

    ERIC Educational Resources Information Center

    Passolunghi, Maria Chiara; Pazzaglia, Francesca

    2005-01-01

    This study examines the updating ability of poor or good problem solvers. Seventy-eight fourth-graders, 43 good and 35 poor arithmetic word problem-solvers, performed the Updating Test used in Palladino et al. [Palladino, P., Cornoldi, C., De Beni, R., and Pazzaglia F. (2002). Working memory and updating processes in reading comprehension. Memory…

  3. Generalized methods and solvers for noise removal from piecewise constant signals. II. New methods

    PubMed Central

    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

  4. An Extension of the Time-Spectral Method to Overset Solvers

    NASA Technical Reports Server (NTRS)

    Leffell, Joshua Isaac; Murman, Scott M.; Pulliam, Thomas

    2013-01-01

    Relative motion in the Cartesian or overset framework causes certain spatial nodes to move in and out of the physical domain as they are dynamically blanked by moving solid bodies. This poses a problem for the conventional Time-Spectral approach, which expands the solution at every spatial node into a Fourier series spanning the period of motion. The proposed extension to the Time-Spectral method treats unblanked nodes in the conventional manner but expands the solution at dynamically blanked nodes in a basis of barycentric rational polynomials spanning partitions of contiguously defined temporal intervals. Rational polynomials avoid Runge's phenomenon on the equidistant time samples of these sub-periodic intervals. Fourier- and rational polynomial-based differentiation operators are used in tandem to provide a consistent hybrid Time-Spectral overset scheme capable of handling relative motion. The hybrid scheme is tested with a linear model problem and implemented within NASA's OVERFLOW Reynolds-averaged Navier- Stokes (RANS) solver. The hybrid Time-Spectral solver is then applied to inviscid and turbulent RANS cases of plunging and pitching airfoils and compared to time-accurate and experimental data. A limiter was applied in the turbulent case to avoid undershoots in the undamped turbulent eddy viscosity while maintaining accuracy. The hybrid scheme matches the performance of the conventional Time-Spectral method and converges to the time-accurate results with increased temporal resolution.

  5. Error Detection Processes in Problem Solving.

    ERIC Educational Resources Information Center

    Allwood, Carl Martin

    1984-01-01

    Describes a study which analyzed problem solvers' error detection processes by instructing subjects to think aloud when solving statistical problems. Effects of evaluative episodes on error detection, detection of different error types, error detection processes per se, and relationship of error detection behavior to problem-solving proficiency…

  6. 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

  7. Assessment of Linear Finite-Difference Poisson-Boltzmann Solvers

    PubMed Central

    Wang, Jun; Luo, Ray

    2009-01-01

    CPU time and memory usage are two vital issues that any numerical solvers for the Poisson-Boltzmann equation have to face in biomolecular applications. In this study we systematically analyzed the CPU time and memory usage of five commonly used finite-difference solvers with a large and diversified set of biomolecular structures. Our comparative analysis shows that modified incomplete Cholesky conjugate gradient and geometric multigrid are the most efficient in the diversified test set. For the two efficient solvers, our test shows that their CPU times increase approximately linearly with the numbers of grids. Their CPU times also increase almost linearly with the negative logarithm of the convergence criterion at very similar rate. Our comparison further shows that geometric multigrid performs better in the large set of tested biomolecules. However, modified incomplete Cholesky conjugate gradient is superior to geometric multigrid in molecular dynamics simulations of tested molecules. We also investigated other significant components in numerical solutions of the Poisson-Boltzmann equation. It turns out that the time-limiting step is the free boundary condition setup for the linear systems for the selected proteins if the electrostatic focusing is not used. Thus, development of future numerical solvers for the Poisson-Boltzmann equation should balance all aspects of the numerical procedures in realistic biomolecular applications. PMID:20063271

  8. Assessment of linear finite-difference Poisson-Boltzmann solvers.

    PubMed

    Wang, Jun; Luo, Ray

    2010-06-01

    CPU time and memory usage are two vital issues that any numerical solvers for the Poisson-Boltzmann equation have to face in biomolecular applications. In this study, we systematically analyzed the CPU time and memory usage of five commonly used finite-difference solvers with a large and diversified set of biomolecular structures. Our comparative analysis shows that modified incomplete Cholesky conjugate gradient and geometric multigrid are the most efficient in the diversified test set. For the two efficient solvers, our test shows that their CPU times increase approximately linearly with the numbers of grids. Their CPU times also increase almost linearly with the negative logarithm of the convergence criterion at very similar rate. Our comparison further shows that geometric multigrid performs better in the large set of tested biomolecules. However, modified incomplete Cholesky conjugate gradient is superior to geometric multigrid in molecular dynamics simulations of tested molecules. We also investigated other significant components in numerical solutions of the Poisson-Boltzmann equation. It turns out that the time-limiting step is the free boundary condition setup for the linear systems for the selected proteins if the electrostatic focusing is not used. Thus, development of future numerical solvers for the Poisson-Boltzmann equation should balance all aspects of the numerical procedures in realistic biomolecular applications. PMID:20063271

  9. Coordinate Projection-based Solver for ODE with Invariants

    SciTech Connect

    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.

  10. 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.

  11. A Navier-Stokes boundary element solver

    NASA Technical Reports Server (NTRS)

    Reddy, D. R.; Lafe, O.; Cheng, A. H-D.

    1995-01-01

    Using global interpolation functions (GIF's) boundary element solutions are obtained for two-dimensional laminar flows. Two schemes are proposed for handling the convective terms. The first treats convection as a forcing function, and converts the flow equations to pseudo-Poisson equations. In the second scheme, some convective effect is incorporated into the fundamental solution used in constructing the pertinent integral equations. The lid-driven cavity flow is selected as the benchmark problem.

  12. Physical activity, emotional and behavioural problems, maternal education and self-reported educational performance of adolescents.

    PubMed

    Kantomaa, M T; Tammelin, T H; Demakakos, P; Ebeling, H E; Taanila, A M

    2010-04-01

    This study examined whether physical activity, mental health and socio-economic position were associated with the overall academic performance and future educational plans of adolescents aged 15-16 years. We used a sample of 7002 boys and girls from the Northern Finland Birth Cohort 1986. Data were collected by a postal enquiry in 2001-02. Multivariable logistic regression models were estimated and adjusted for family structure and all variables in the models. In the fully adjusted models, higher levels of physical activity and high parental socio-economic position were associated with higher overall academic performance and future plans for higher education. High scoring on behavioural problems was related to lower overall academic performance and poorer future academic plans. In summary, a higher level of physical activity, fewer behavioural problems and higher socio-economic position were independently associated with high self-perceived overall academic performance and plans for higher education among adolescents. The interrelations of these factors and the positive relationship between physical activity, mental health and school outcomes provide a context of critical importance for future research, intervention programming and policy directed at improving the educational attainment of adolescents. PMID:19762353

  13. A Multi-Level Parallelization Concept for High-Fidelity Multi-Block Solvers

    NASA Technical Reports Server (NTRS)

    Hatay, Ferhat F.; Jespersen, Dennis C.; Guruswamy, Guru P.; Rizk, Yehia M.; Byun, Chansup; Gee, Ken; VanDalsem, William R. (Technical Monitor)

    1997-01-01

    The integration of high-fidelity Computational Fluid Dynamics (CFD) analysis tools with the industrial design process benefits greatly from the robust implementations that are transportable across a wide range of computer architectures. In the present work, a hybrid domain-decomposition and parallelization concept was developed and implemented into the widely-used NASA multi-block Computational Fluid Dynamics (CFD) packages implemented in ENSAERO and OVERFLOW. The new parallel solver concept, PENS (Parallel Euler Navier-Stokes Solver), employs both fine and coarse granularity in data partitioning as well as data coalescing to obtain the desired load-balance characteristics on the available computer platforms. This multi-level parallelism implementation itself introduces no changes to the numerical results, hence the original fidelity of the packages are identically preserved. The present implementation uses the Message Passing Interface (MPI) library for interprocessor message passing and memory accessing. By choosing an appropriate combination of the available partitioning and coalescing capabilities only during the execution stage, the PENS solver becomes adaptable to different computer architectures from shared-memory to distributed-memory platforms with varying degrees of parallelism. The PENS implementation on the IBM SP2 distributed memory environment at the NASA Ames Research Center obtains 85 percent scalable parallel performance using fine-grain partitioning of single-block CFD domains using up to 128 wide computational nodes. Multi-block CFD simulations of complete aircraft simulations achieve 75 percent perfect load-balanced executions using data coalescing and the two levels of parallelism. SGI PowerChallenge, SGI Origin 2000, and a cluster of workstations are the other platforms where the robustness of the implementation is tested. The performance behavior on the other computer platforms with a variety of realistic problems will be included as this on

  14. 2d PDE Linear Symmetric Matrix Solver

    1983-10-01

    ICCG2 (Incomplete Cholesky factorized Conjugate Gradient algorithm for 2d symmetric problems) was developed to solve a linear symmetric matrix system arising from a 9-point discretization of two-dimensional elliptic and parabolic partial differential equations found in plasma physics applications, such as resistive MHD, spatial diffusive transport, and phase space transport (Fokker-Planck equation) problems. These problems share the common feature of being stiff and requiring implicit solution techniques. When these parabolic or elliptic PDE''s are discretized withmore » finite-difference or finite-element methods,the resulting matrix system is frequently of block-tridiagonal form. To use ICCG2, the discretization of the two-dimensional partial differential equation and its boundary conditions must result in a block-tridiagonal supermatrix composed of elementary tridiagonal matrices. The incomplete Cholesky conjugate gradient algorithm is used to solve the linear symmetric matrix equation. Loops are arranged to vectorize on the Cray1 with the CFT compiler, wherever possible. Recursive loops, which cannot be vectorized, are written for optimum scalar speed. For matrices lacking symmetry, ILUCG2 should be used. Similar methods in three dimensions are available in ICCG3 and ILUCG3. A general source containing extensions and macros, which must be processed by a pre-compiler to obtain the standard FORTRAN source, is provided along with the standard FORTRAN source because it is believed to be more readable. The pre-compiler is not included, but pre-compilation may be performed by a text editor as described in the UCRL-88746 Preprint.« less

  15. 2d PDE Linear Asymmetric Matrix Solver

    1983-10-01

    ILUCG2 (Incomplete LU factorized Conjugate Gradient algorithm for 2d problems) was developed to solve a linear asymmetric matrix system arising from a 9-point discretization of two-dimensional elliptic and parabolic partial differential equations found in plasma physics applications, such as plasma diffusion, equilibria, and phase space transport (Fokker-Planck equation) problems. These equations share the common feature of being stiff and requiring implicit solution techniques. When these parabolic or elliptic PDE''s are discretized with finite-difference or finite-elementmore » methods, the resulting matrix system is frequently of block-tridiagonal form. To use ILUCG2, the discretization of the two-dimensional partial differential equation and its boundary conditions must result in a block-tridiagonal supermatrix composed of elementary tridiagonal matrices. A generalization of the incomplete Cholesky conjugate gradient algorithm is used to solve the matrix equation. Loops are arranged to vectorize on the Cray1 with the CFT compiler, wherever possible. Recursive loops, which cannot be vectorized, are written for optimum scalar speed. For problems having a symmetric matrix ICCG2 should be used since it runs up to four times faster and uses approximately 30% less storage. Similar methods in three dimensions are available in ICCG3 and ILUCG3. A general source, containing extensions and macros, which must be processed by a pre-compiler to obtain the standard FORTRAN source, is provided along with the standard FORTRAN source because it is believed to be more readable. The pre-compiler is not included, but pre-compilation may be performed by a text editor as described in the UCRL-88746 Preprint.« less

  16. A modelization of the task allocation problem for prescribing activity in an ICU.

    PubMed Central

    Renard, J. M.; Bricon-Souf, N.; Guigue, L.; Beuscart, R.

    2000-01-01

    The improvement of coordination between Health Care Professionals belonging different specialities and who are extremely mobile, is a crucial problem in Medicine. A workflow System is one example of the new informatics tools which facilitate the transfer of information and responsibility between health care providers. Medical informatics systems in particular should be reactive enough to cope with the flexibility of real work situations: in this paper, we present the task allocation problem. We distinguish between the workflow control process and the notifying process, which concerns the sharing out of the tasks between the actors concerned. We focus on the impact of strategies of notification on the progress of coordinated work. We propose a simulator to model and study the different ways of sharing tasks between actors in an Intensive Care Unit's activity of prescription. PMID:11079971

  17. Toward robust scalable algebraic multigrid solvers.

    SciTech Connect

    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.

  18. 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.

  19. Efficient three-dimensional Poisson solvers in open rectangular conducting pipe

    NASA Astrophysics Data System (ADS)

    Qiang, Ji

    2016-06-01

    Three-dimensional (3D) Poisson solver plays an important role in the study of space-charge effects on charged particle beam dynamics in particle accelerators. In this paper, we propose three new 3D Poisson solvers for a charged particle beam in an open rectangular conducting pipe. These three solvers include a spectral integrated Green function (IGF) solver, a 3D spectral solver, and a 3D integrated Green function solver. These solvers effectively handle the longitudinal open boundary condition using a finite computational domain that contains the beam itself. This saves the computational cost of using an extra larger longitudinal domain in order to set up an appropriate finite boundary condition. Using an integrated Green function also avoids the need to resolve rapid variation of the Green function inside the beam. The numerical operational cost of the spectral IGF solver and the 3D IGF solver scales as O(N log(N)) , where N is the number of grid points. The cost of the 3D spectral solver scales as O(Nn N) , where Nn is the maximum longitudinal mode number. We compare these three solvers using several numerical examples and discuss the advantageous regime of each solver in the physical application.

  20. Parallel implicit unstructured grid Euler solvers

    NASA Technical Reports Server (NTRS)

    Venkatakrishnan, V.

    1994-01-01

    A mesh-vertex finite volume scheme for solving the Euler equations on triangular unstructured meshes is implemented on an MIMD (multiple instruction/multiple data stream) parallel computer. An explicit four-stage Runge-Kutta scheme is used to solve two-dimensional flow problems. A family of implicit schemes is also developed to solve these problems, where the linear system that arises at each time step is solved by a preconditioned GMRES algorithm. Two partitioning strategies are employed, one that partitions triangles and the other that partitions vertices. The choice of the preconditioner in a distributed memory setting is discussed. All the methods are compared both in terms of elapsed times and convergence rates. It is shown that the implicit schemes offer adequate parallelism at the expense of minimal sequential overhead. The use of a global coarse grid to further minimize this overhead is also investigated. The schemes are implemented on a distributed memory parallel computer, the iPSC/860.

  1. Parallel implicit unstructured grid Euler solvers

    NASA Technical Reports Server (NTRS)

    Venkatakrishnan, V.

    1994-01-01

    A mesh-vertex finite volume scheme for solving the Euler equations on triangular unstructured meshes is implemented on a multiple-instruction/multiple-data stream parallel computer. An explicit four-stage Runge-Kutta scheme is used to solve two-dimensional flow problems. A family of implicit schemes is also developed to solve these problems, where the linear system that arises at each time step is solved by a preconditioned GMRES algorithm. Two partitioning strategies are employed: one that partitions triangles and the other that partitions vertices. The choice of the preconditioner in a distributed memory setting is discussed. All of the methods are compared both in terms of elapsed times and convergence rates. It is shown that the implicit schemes offer adequate parallelism at the expense of minimal sequential overhead. The use of a global coarse grid to further minimize this overhead is also investigated. The schemes are implemented on a distributed memory parallel computer, the Intel iPSC/860.

  2. Variational elliptic solver for atmospheric applications

    SciTech Connect

    Smolarkiewicz, P.K.; Margolin, L.G.

    1994-03-01

    We discuss a conjugate gradient type method -- the conjugate residual -- suitable for solving linear elliptic equations that result from discretization of complex atmospheric dynamical problems. Rotation and irregular boundaries typically lead to nonself-adjoint elliptic operators whose matrix representation on the grid is definite but not symmetric. On the other hand, most established methods for solving large sparse matrix equations depend on the symmetry and definiteness of the matrix. Furthermore, the explicit construction of the matrix can be both difficult and computationally expensive. An attractive feature of conjugate gradient methods in general is that they do not require any knowledge of the matrix; and in particular, convergence of conjugate residual algorithms do not rely on symmetry for definite operators. We begin by reviewing some basic concepts of variational algorithms from the perspective of a physical analogy to the damped wave equation, which is a simple alternative to the traditional abstract framework of the Krylov subspace methods. We derive two conjugate residual schemes from variational principles, and prove that either definiteness or symmetry ensures their convergence. We discuss issues related to computational efficiency and illustrate our theoretical considerations with a test problem of the potential flow of a Boussinesq fluid flow past a steep, three-dimensional obstacle.

  3. Evaluating sedimentation problems in activated sludge treatment plants operating at complete sludge retention time.

    PubMed

    Amanatidou, Elisavet; Samiotis, Georgios; Trikoilidou, Eleni; Pekridis, George; Taousanidis, Nikolaos

    2015-02-01

    Zero net sludge growth can be achieved by complete retention of solids in activated sludge wastewater treatment, especially in high strength and biodegradable wastewaters. When increasing the solids retention time, MLSS and MLVSS concentrations reach a plateau phase and observed growth yields values tend to zero (Yobs ≈ 0). In this work, in order to evaluate sedimentation problems arised due to high MLSS concentrations and complete sludge retention operational conditions, two identical innovative slaughterhouse wastewater treatment plants were studied. Measurements of wastewaters' quality characteristics, treatment plant's operational conditions, sludge microscopic analysis and state point analysis were conducted. Results have shown that low COD/Nitrogen ratios increase sludge bulking and flotation phenomena due to accidental denitrification in clarifiers. High return activated sludge rate is essential in complete retention systems as it reduces sludge condensation and hydraulic retention time in the clarifiers. Under certain operational conditions sludge loading rates can greatly exceed literature limit values. The presented methodology is a useful tool for estimation of sedimentation problems encountered in activated sludge wastewater treatment plants with complete retention time. PMID:25463928

  4. Efficient Parallel Kernel Solvers for Computational Fluid Dynamics Applications

    NASA Technical Reports Server (NTRS)

    Sun, Xian-He

    1997-01-01

    Distributed-memory parallel computers dominate today's parallel computing arena. These machines, such as Intel Paragon, IBM SP2, and Cray Origin2OO, have successfully delivered high performance computing power for solving some of the so-called "grand-challenge" problems. Despite initial success, parallel machines have not been widely accepted in production engineering environments due to the complexity of parallel programming. On a parallel computing system, a task has to be partitioned and distributed appropriately among processors to reduce communication cost and to attain load balance. More importantly, even with careful partitioning and mapping, the performance of an algorithm may still be unsatisfactory, since conventional sequential algorithms may be serial in nature and may not be implemented efficiently on parallel machines. In many cases, new algorithms have to be introduced to increase parallel performance. In order to achieve optimal performance, in addition to partitioning and mapping, a careful performance study should be conducted for a given application to find a good algorithm-machine combination. This process, however, is usually painful and elusive. The goal of this project is to design and develop efficient parallel algorithms for highly accurate Computational Fluid Dynamics (CFD) simulations and other engineering applications. The work plan is 1) developing highly accurate parallel numerical algorithms, 2) conduct preliminary testing to verify the effectiveness and potential of these algorithms, 3) incorporate newly developed algorithms into actual simulation packages. The work plan has well achieved. Two highly accurate, efficient Poisson solvers have been developed and tested based on two different approaches: (1) Adopting a mathematical geometry which has a better capacity to describe the fluid, (2) Using compact scheme to gain high order accuracy in numerical discretization. The previously developed Parallel Diagonal Dominant (PDD) algorithm

  5. Solving Upwind-Biased Discretizations. 2; Multigrid Solver Using Semicoarsening

    NASA Technical Reports Server (NTRS)

    Diskin, Boris

    1999-01-01

    This paper studies a novel multigrid approach to the solution for a second order upwind biased discretization of the convection equation in two dimensions. This approach is based on semi-coarsening and well balanced explicit correction terms added to coarse-grid operators to maintain on coarse-grid the same cross-characteristic interaction as on the target (fine) grid. Colored relaxation schemes are used on all the levels allowing a very efficient parallel implementation. The results of the numerical tests can be summarized as follows: 1) The residual asymptotic convergence rate of the proposed V(0, 2) multigrid cycle is about 3 per cycle. This convergence rate far surpasses the theoretical limit (4/3) predicted for standard multigrid algorithms using full coarsening. The reported efficiency does not deteriorate with increasing the cycle, depth (number of levels) and/or refining the target-grid mesh spacing. 2) The full multi-grid algorithm (FMG) with two V(0, 2) cycles on the target grid and just one V(0, 2) cycle on all the coarse grids always provides an approximate solution with the algebraic error less than the discretization error. Estimates of the total work in the FMG algorithm are ranged between 18 and 30 minimal work units (depending on the target (discretizatioin). Thus, the overall efficiency of the FMG solver closely approaches (if does not achieve) the goal of the textbook multigrid efficiency. 3) A novel approach to deriving a discrete solution approximating the true continuous solution with a relative accuracy given in advance is developed. An adaptive multigrid algorithm (AMA) using comparison of the solutions on two successive target grids to estimate the accuracy of the current target-grid solution is defined. A desired relative accuracy is accepted as an input parameter. The final target grid on which this accuracy can be achieved is chosen automatically in the solution process. the actual relative accuracy of the discrete solution approximation

  6. Activity Structures and the Unfolding of Problem-Solving Actions in High-School Chemistry Classrooms

    NASA Astrophysics Data System (ADS)

    Criswell, Brett A.; Rushton, Greg T.

    2014-02-01

    In this paper, we argue for a more systematic approach for studying the relationship between classroom practices and scientific practices—an approach that will likely better support the systemic reforms being promoted in the Next Generation Science Standards in the USA and similar efforts in other countries. One component of that approach is looking at how the nature of the activity structure may influence the relative alignment between classroom and scientific practices. To that end, we build on previously published research related to the practices utilized by five high-school chemistry teachers as they enacted problem-solving activities in which students were likely to generate proposals that were not aligned with normative scientific understandings. In that prior work, our analysis had emphasized micro-level features of the talk interactions and how they related to the way students' ideas were explored; in the current paper, the analysis zooms out to consider the macro-level nature of the enactments associated with the activity structure of each lesson examined. Our data show that there were two general patterns to the activity structure across the 14 lessons scrutinized, and that each pattern had associated with it a constellation of features that impinged on the way the problem space was navigated. A key finding is that both activity structures (the expansive and the open) had features that aligned with scientific practices espoused in the Next Generation Science Standards—and both had features that were not aligned with those practices. We discuss the nature of these two structures, evidence of the relationship of each structure to key features of how the lessons unfolded, and the implications of these findings for both future research and the training of teachers.

  7. Implementation of Implicit Adaptive Mesh Refinement in an Unstructured Finite-Volume Flow Solver

    NASA Technical Reports Server (NTRS)

    Schwing, Alan M.; Nompelis, Ioannis; Candler, Graham V.

    2013-01-01

    This paper explores the implementation of adaptive mesh refinement in an unstructured, finite-volume solver. Unsteady and steady problems are considered. The effect on the recovery of high-order numerics is explored and the results are favorable. Important to this work is the ability to provide a path for efficient, implicit time advancement. A method using a simple refinement sensor based on undivided differences is discussed and applied to a practical problem: a shock-shock interaction on a hypersonic, inviscid double-wedge. Cases are compared to uniform grids without the use of adapted meshes in order to assess error and computational expense. Discussion of difficulties, advances, and future work prepare this method for additional research. The potential for this method in more complicated flows is described.

  8. Gust Acoustics Computation with a Space-Time CE/SE Parallel 3D Solver

    NASA Technical Reports Server (NTRS)

    Wang, X. Y.; Himansu, A.; Chang, S. C.; Jorgenson, P. C. E.; Reddy, D. R. (Technical Monitor)

    2002-01-01

    The benchmark Problem 2 in Category 3 of the Third Computational Aero-Acoustics (CAA) Workshop is solved using the space-time conservation element and solution element (CE/SE) method. This problem concerns the unsteady response of an isolated finite-span swept flat-plate airfoil bounded by two parallel walls to an incident gust. The acoustic field generated by the interaction of the gust with the flat-plate airfoil is computed by solving the 3D (three-dimensional) Euler equations in the time domain using a parallel version of a 3D CE/SE solver. The effect of the gust orientation on the far-field directivity is studied. Numerical solutions are presented and compared with analytical solutions, showing a reasonable agreement.

  9. Recent Enhancements to USM3D Unstructured Flow Solver for Unsteady Flows

    NASA Technical Reports Server (NTRS)

    Pandya, Mohagna J.; Frink, Neal T.; Abdol-Hamid, Khaled S.; Chung, James J.

    2004-01-01

    The NASA USM3D unstructured flow solver is undergoing extensions to address dynamic flow problems in support of NASA and NAVAIR efforts to study the applicability of Computational Fluid Dynamics tools for the prediction of aircraft stability and control characteristics. The initial extensions reported herein include two second-order time stepping schemes, Detached-Eddy Simulation, and grid motion. This paper reports the initial code verification and validation assessment of the dynamic flow capabilities of USM3D. The cases considered are the classic inviscid shock-tube problem, low Reynolds number wake shedding from a NACA 0012 airfoil, high Reynolds number DES-based wake shedding from a 4-to-1 length-to-diameter cylinder, and forced pitch oscillation of a NACA 0012 airfoil with inviscid and turbulent flow.

  10. Performance Comparison of a Set of Periodic and Non-Periodic Tridiagonal Solvers on SP2 and Paragon Parallel Computers

    NASA Technical Reports Server (NTRS)

    Sun, Xian-He; Moitra, Stuti

    1996-01-01

    Various tridiagonal solvers have been proposed in recent years for different parallel platforms. In this paper, the performance of three tridiagonal solvers, namely, the parallel partition LU algorithm, the parallel diagonal dominant algorithm, and the reduced diagonal dominant algorithm, is studied. These algorithms are designed for distributed-memory machines and are tested on an Intel Paragon and an IBM SP2 machines. Measured results are reported in terms of execution time and speedup. Analytical study are conducted for different communication topologies and for different tridiagonal systems. The measured results match the analytical results closely. In addition to address implementation issues, performance considerations such as problem sizes and models of speedup are also discussed.

  11. Parallel first-order linear recurrence solver

    SciTech Connect

    Meyer, G.G.L.; Podrazik, L.

    1987-04-01

    In this paper the authors present a parallel procedure for the solution of first-order linear recurrence systems of size N when the number or processors rho is small in relation to N. They show that when 1 < rho/sup 2/ less than or equal to N, a first-order linear recurrence system of size N can be solved in 5(N - 1)(rho + 1) steps on a p processor SIMD machine and at most 5(N - 1/2)/(rho + 3/2) steps on a p processor MIMD machine. As a special case, they show that their approach precisely achieves the lower bound 2(N - 1)/(rho + 1) for solving the parallel prefix problem on a p processor machine.

  12. Application of Semi Active Control Techniques to the Damping Suppression Problem of Solar Sail Booms

    NASA Technical Reports Server (NTRS)

    Adetona, O.; Keel, L. H.; Whorton, M. S.

    2007-01-01

    Solar sails provide a propellant free form for space propulsion. These are large flat surfaces that generate thrust when they are impacted by light. When attached to a space vehicle, the thrust generated can propel the space vehicle to great distances at significant speeds. For optimal performance the sail must be kept from excessive vibration. Active control techniques can provide the best performance. However, they require an external power-source that may create significant parasitic mass to the solar sail. However, solar sails require low mass for optimal performance. Secondly, active control techniques typically require a good system model to ensure stability and performance. However, the accuracy of solar sail models validated on earth for a space environment is questionable. An alternative approach is passive vibration techniques. These do not require an external power supply, and do not destabilize the system. A third alternative is referred to as semi-active control. This approach tries to get the best of both active and passive control, while avoiding their pitfalls. In semi-active control, an active control law is designed for the system, and passive control techniques are used to implement it. As a result, no external power supply is needed so the system is not destabilize-able. Though it typically underperforms active control techniques, it has been shown to out-perform passive control approaches and can be unobtrusively installed on a solar sail boom. Motivated by this, the objective of this research is to study the suitability of a Piezoelectric (PZT) patch actuator/sensor based semi-active control system for the vibration suppression problem of solar sail booms. Accordingly, we develop a suitable mathematical and computer model for such studies and demonstrate the capabilities of the proposed approach with computer simulations.

  13. The role of physical activity to control obesity problem in Malaysia

    NASA Astrophysics Data System (ADS)

    Abidin, Norhaslinda Zainal; Zaibidi, Nerda Zura; Zulkepli, Jafri Hj

    2014-07-01

    Obesity is defined as a condition in which an individual has an excess of body fat and it is accumulated to the extent that it can lead to numerous health problems and decreases the quality and length of life. Overall, the contributing factor to obesity varies. Lack of physical activity and increased sedentary behaviour has been identified as the causes of weight gain and various health implications including obesity. Rapid development in industrialization and urbanization has brought Malaysia to be the next millennium country in the world, and this causes changes in the country's socioeconomic, especially the lifestyles of Malaysians. In conjunction with this, the aim of this paper is to simulate the changes in physical activities and to highlight its implication on body weight and prevalence of overweight and obesity in a Malaysian adult population. This study combines different strands of knowledge consisting of nutrition, physical activity and body metabolism, and these elements have been synthesised into a system dynamics model called SIMULObese. The development of this model has considered the interrelations between those various strands in one multifaceted human weight regulation system. Findings from this study revealed that Malaysian adults perform less physical activity and this has resulted in weight gain and increase in prevalence of overweight and obesity. Therefore, findings from this study bring the important message to various parties such as practitioners, researchers, educators and publics about the importance of focusing on combinations of intensity, frequency and duration of moderate-vigorous activity for adult obesity control in Malaysia.

  14. An Extended Membrane System with Active Membranes to Solve Automatic Fuzzy Clustering Problems.

    PubMed

    Peng, Hong; Wang, Jun; Shi, Peng; Pérez-Jiménez, Mario J; Riscos-Núñez, Agustín

    2016-05-01

    This paper focuses on automatic fuzzy clustering problem and proposes a novel automatic fuzzy clustering method that employs an extended membrane system with active membranes that has been designed as its computing framework. The extended membrane system has a dynamic membrane structure; since membranes can evolve, it is particularly suitable for processing the automatic fuzzy clustering problem. A modification of a differential evolution (DE) mechanism was developed as evolution rules for objects according to membrane structure and object communication mechanisms. Under the control of both the object's evolution-communication mechanism and the membrane evolution mechanism, the extended membrane system can effectively determine the most appropriate number of clusters as well as the corresponding optimal cluster centers. The proposed method was evaluated over 13 benchmark problems and was compared with four state-of-the-art automatic clustering methods, two recently developed clustering methods and six classification techniques. The comparison results demonstrate the superiority of the proposed method in terms of effectiveness and robustness. PMID:26790484

  15. Local Attitudes towards Bear Management after Illegal Feeding and Problem Bear Activity.

    PubMed

    Dubois, Sara; Fraser, David

    2013-01-01

    The "pot bears" received international media attention in 2010 after police discovered the intentional feeding of over 20 black bears during the investigation of an alleged marijuana-growing operation in Christina Lake, British Columbia, Canada. A two-phase random digit dialing survey of the community was conducted in 2011 to understand local perspectives on bear policy and management, before and after a summer of problem bear activity and government interventions. Of the 159 households surveyed in February 2011, most had neutral or positive attitudes towards bears in general, and supported the initial decision to feed the food-conditioned bears until the autumn hibernation. In contrast to wildlife experts however, most participants supported relocating the problem bears, or allowing them to remain in the area, ahead of killing; in part this arose from notions of fairness despite the acknowledged problems of relocation. Most locals were aware of the years of feeding but did not report it, evidently failing to see it as a serious form of harm, even after many bears had been killed. This underscores the importance of preventive action on wildlife feeding and the need to narrow the gap between public and expert opinion on the likely effects of relocation versus killing. PMID:26479542

  16. Intervertebral disc creep behavior assessment through an open source finite element solver.

    PubMed

    Castro, A P G; Wilson, W; Huyghe, J M; Ito, K; Alves, J L

    2014-01-01

    Degenerative Disc Disease (DDD) is one of the largest health problems faced worldwide, based on lost working time and associated costs. By means of this motivation, this work aims to evaluate a biomimetic Finite Element (FE) model of the Intervertebral Disc (IVD). Recent studies have emphasized the importance of an accurate biomechanical modeling of the IVD, as it is a highly complex multiphasic medium. Poroelastic models of the disc are mostly implemented in commercial finite element packages with limited access to the algorithms. Therefore, a novel poroelastic formulation implemented on a home-developed open source FE solver is briefly addressed throughout this paper. The combination of this formulation with biphasic osmotic swelling behavior is also taken into account. Numerical simulations were devoted to the analysis of the non-degenerated human lumbar IVD time-dependent behavior. The results of the tests performed for creep assessment were inside the scope of the experimental data, with a remarkable improvement of the numerical accuracy when compared with previously published results obtained with ABAQUS(®). In brief, this in-development open-source FE solver was validated with literature experimental data and aims to be a valuable tool to study the IVD biomechanics and DDD mechanisms. PMID:24210477

  17. Simulation of three-component fluid flows using the multiphase lattice Boltzmann flux solver

    NASA Astrophysics Data System (ADS)

    Shi, Y.; Tang, G. H.; Wang, Y.

    2016-06-01

    In this work, we extend the multiphase lattice Boltzmann flux solver, which was proposed in [1] for simulating incompressible flows of binary fluids based on two-component Cahn-Hilliard model, to three-component fluid flows. In the present method, the multiphase lattice Boltzmann flux solver is applied to solve for the flow field and the three-component Cahn-Hilliard model is used to predict the evolution of the interfaces. The proposed method is first validated through the classical problem of simulation of partial spreading of a liquid lens between the other two components. Numerical results of interface shapes and contact angles agree well with theoretical solutions. After that, to further demonstrate the capability of the present method, several numerical examples of three-component fluid flows are presented, including a bubble rising across a fluid-fluid interface, single droplet falling through a fluid-fluid interface, the collision-coalescence of two droplets, and the non-contact collision of two droplets. It is shown that the present method can successfully handle complex interactions among three components.

  18. Computational modelling of cardiac electrophysiology: explanation of the variability of results from different numerical solvers.

    PubMed

    Pathmanathan, P; Bernabeu, M O; Niederer, S A; Gavaghan, D J; Kay, D

    2012-08-01

    A recent verification study compared 11 large-scale cardiac electrophysiology solvers on an unambiguously defined common problem. An unexpected amount of variation was observed between the codes, including significant error in conduction velocity in the majority of the codes at certain spatial resolutions. In particular, the results of the six finite element codes varied considerably despite each using the same order of interpolation. In this present study, we compare various algorithms for cardiac electrophysiological simulation, which allows us to fully explain the differences between the solvers. We identify the use of mass lumping as the fundamental cause of the largest variations, specifically the combination of the commonly used techniques of mass lumping and operator splitting, which results in a slightly different form of mass lumping to that supported by theory and leads to increased numerical error. Other variations are explained through the manner in which the ionic current is interpolated. We also investigate the effect of different forms of mass lumping in various types of simulation. PMID:25099569

  19. A modern solver framework to manage solution algorithms in the Community Earth System Model

    SciTech Connect

    Evans, Katherine J; Worley, Patrick H; Nichols, Dr Jeff A; WhiteIII, James B; Salinger, Andy; Price, Stephen; Lemieux, Jean-Francois; Lipscomb, William; Perego, Mauro; Vertenstein, Mariana; Edwards, Jim

    2012-01-01

    Global Earth-system models (ESM) can now produce simulations that resolve ~50 km features and include finer-scale, interacting physical processes. In order to achieve these scale-length solutions, ESMs require smaller time steps, which limits parallel performance. Solution methods that overcome these bottlenecks can be quite intricate, and there is no single set of algorithms that perform well across the range of problems of interest. This creates significant implementation challenges, which is further compounded by complexity of ESMs. Therefore, prototyping and evaluating new algorithms in these models requires a software framework that is flexible, extensible, and easily introduced into the existing software. We describe our efforts to create a parallel solver framework that links the Trilinos library of solvers to Glimmer-CISM, a continental ice sheet model used in the Community Earth System Model (CESM). We demonstrate this framework within both current and developmental versions of Glimmer-CISM and provide strategies for its integration into the rest of the CESM.

  20. Accelerating the Gauss-Seidel Power Flow Solver on a High Performance Reconfigurable Computer

    SciTech Connect

    Byun, Jong-Ho; Ravindran, Arun; Mukherjee, Arindam; Joshi, Bharat; Chassin, David P.

    2009-09-01

    The computationally intensive power flow problem determines the voltage magnitude and phase angle at each bus in a power system for hundreds of thousands of buses under balanced three-phase steady-state conditions. We report an FPGA acceleration of the Gauss-Seidel based power flow solver employed in the transmission module of the GridLAB-D power distribution simulator and analysis tool. The prototype hardware is implemented on an SGI Altix-RASC system equipped with a Xilinx Virtex II 6000 FPGA. Due to capacity limitations of the FPGA, only the bus voltage calculations of the power network are implemented on hardware while the branch current calculations are implemented in software. For a 200,000 bus system, the bus voltage calculation on the FPGA achieves a 48x speed-up with PQ buses and a 62 times for PV over an equivalent sequential software implementation. The average overall speed up of the FPGA-CPU implementation with 100 iterations of the Gauss-Seidel power solver is 2.6x over a software implementation, with the branch calculations on the CPU accounting for 85% of the total execution time. The FPGA-CPU implementation also shows linear scaling with increase in the size of the input power network.

  1. Multilayer shallow shelf approximation: Minimisation formulation, finite element solvers and applications

    NASA Astrophysics Data System (ADS)

    Jouvet, Guillaume

    2015-04-01

    In this paper, a multilayer generalisation of the Shallow Shelf Approximation (SSA) is considered. In this recent hybrid ice flow model, the ice thickness is divided into thin layers, which can spread out, contract and slide over each other in such a way that the velocity profile is layer-wise constant. Like the SSA (1-layer model), the multilayer model can be reformulated as a minimisation problem. However, unlike the SSA, the functional to be minimised involves a new penalisation term for the interlayer jumps of the velocity, which represents the vertical shear stresses induced by interlayer sliding. Taking advantage of this reformulation, numerical solvers developed for the SSA can be naturally extended layer-wise or column-wise. Numerical results show that the column-wise extension of a Newton multigrid solver proves to be robust in the sense that its convergence is barely influenced by the number of layers and the type of ice flow. In addition, the multilayer formulation appears to be naturally better conditioned than the one of the first-order approximation to face the anisotropic conditions of the sliding-dominant ice flow of ISMIP-HOM experiments.

  2. A point implicit unstructured grid solver for the Euler and Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Thareja, Rajiv R.; Stewart, James R.; Hassan, Obey; Morgan, Ken; Peraire, Jaime

    1988-01-01

    An upwind finite element technique that uses cell centered quantities and implicit and/or explicit time marching has been developed for computing hypersonic laminar viscous flows using adaptive unstructured triangular grids. A structured grid of quadrilaterals is laid out near the body surface. For inviscid flows the method is stable at Courant numbers of over 100,000. A first order basic scheme and a higher order flux corrected transport (FCT) scheme have been implemented. This technique has been applied to the problem of predicting type III and IV shock wave interactions on a cylinder, with a view of simulating the pressure and heating rate augmentation caused by an impinging shock on the leading edge of a cowl lip of an engine inlet. The predictions of wall pressure and heating rates compare very well with experimental data. The flow features are very distinctly captured with a sequence of adaptively generated grids. The adaptive mesh generator and the upwind Navier-Stokes solver are combined in a set of programs called LARCNESS, an acronym for Langley Adaptive Remeshing Code and Navier-Stokes Solver.

  3. Multilayer shallow shelf approximation: Minimisation formulation, finite element solvers and applications

    SciTech Connect

    Jouvet, Guillaume

    2015-04-15

    In this paper, a multilayer generalisation of the Shallow Shelf Approximation (SSA) is considered. In this recent hybrid ice flow model, the ice thickness is divided into thin layers, which can spread out, contract and slide over each other in such a way that the velocity profile is layer-wise constant. Like the SSA (1-layer model), the multilayer model can be reformulated as a minimisation problem. However, unlike the SSA, the functional to be minimised involves a new penalisation term for the interlayer jumps of the velocity, which represents the vertical shear stresses induced by interlayer sliding. Taking advantage of this reformulation, numerical solvers developed for the SSA can be naturally extended layer-wise or column-wise. Numerical results show that the column-wise extension of a Newton multigrid solver proves to be robust in the sense that its convergence is barely influenced by the number of layers and the type of ice flow. In addition, the multilayer formulation appears to be naturally better conditioned than the one of the first-order approximation to face the anisotropic conditions of the sliding-dominant ice flow of ISMIP-HOM experiments.

  4. Approximate Harten-Lax-van Leer Riemann solvers for relativistic magnetohydrodynamics

    NASA Astrophysics Data System (ADS)

    Mignone, Andrea; Bodo, G.; Ugliano, M.

    2012-11-01

    We review a particular class of approximate Riemann solvers in the context of the equations of ideal relativistic magnetohydrodynamics. Commonly prefixed as Harten-Lax-van Leer (HLL), this family of solvers approaches the solution of the Riemann problem by providing suitable guesses to the outermots characteristic speeds, without any prior knowledge of the solution. By requiring consistency with the integral form of the conservation law, a simplified set of jump conditions with a reduced number of characteristic waves may be obtained. The degree of approximation crucially depends on the wave pattern used in prepresnting the Riemann fan arising from the initial discontinuity breakup. In the original HLL scheme, the solution is approximated by collapsing the full characteristic structure into a single average state enclosed by two outermost fast mangnetosonic speeds. On the other hand, HLLC and HLLD improves the accuracy of the solution by restoring the tangential and Alfvén modes therefore leading to a representation of the Riemann fan in terms of 3 and 5 waves, respectively.

  5. Towards Verification of Unstructured-Grid Solvers

    NASA Technical Reports Server (NTRS)

    Thomas, James L.; Diskin, Boris; Rumsey, Christopher L.

    2008-01-01

    New methodology for verification of finite-volume computational methods using unstructured grids is presented. The discretization order properties are studied in computational windows, easily constructed within a collection of grids or a single grid. Tests are performed within each window and address a combination of problem-, solution-, and discretization/grid-related features affecting discretization error convergence. The windows can be adjusted to isolate particular elements of the computational scheme, such as the interior discretization, the boundary discretization, or singularities. Studies can use traditional grid-refinement computations within a fixed window or downscaling, a recently-introduced technique in which computations are made within windows contracting toward a focal point of interest. Grids within the windows are constrained to be consistently refined, allowing a meaningful assessment of asymptotic error convergence on unstructured grids. Demonstrations of the method are shown, including a comparative accuracy assessment of commonly-used schemes on general mixed grids and the identification of local accuracy deterioration at boundary intersections. Recommendations to enable attainment of design-order discretization errors for large-scale computational simulations are given.

  6. Local Attitudes towards Bear Management after Illegal Feeding and Problem Bear Activity

    PubMed Central

    Dubois, Sara; Fraser, David

    2013-01-01

    Simple Summary The “pot bears” received international media attention in 2010 after police discovered the intentional feeding of black bears during the investigation of an alleged marijuana-growing operation in Christina Lake, British Columbia. Residents of this small community were surveyed by phone twice over the following year, before and after government actions. This study aimed to understand local attitudes on how these bears should be managed and whether they differed from existing bear management policy. Results indicate a significant problem with the public view of wildlife feeding and a gap between public and expert opinion on relocation and killing of food-conditioned wildlife. Abstract The “pot bears” received international media attention in 2010 after police discovered the intentional feeding of over 20 black bears during the investigation of an alleged marijuana-growing operation in Christina Lake, British Columbia, Canada. A two-phase random digit dialing survey of the community was conducted in 2011 to understand local perspectives on bear policy and management, before and after a summer of problem bear activity and government interventions. Of the 159 households surveyed in February 2011, most had neutral or positive attitudes towards bears in general, and supported the initial decision to feed the food-conditioned bears until the autumn hibernation. In contrast to wildlife experts however, most participants supported relocating the problem bears, or allowing them to remain in the area, ahead of killing; in part this arose from notions of fairness despite the acknowledged problems of relocation. Most locals were aware of the years of feeding but did not report it, evidently failing to see it as a serious form of harm, even after many bears had been killed. This underscores the importance of preventive action on wildlife feeding and the need to narrow the gap between public and expert opinion on the likely effects of relocation versus

  7. A Problem-Solving Conceptual Framework and Its Implications in Designing Problem-Posing Tasks

    ERIC Educational Resources Information Center

    Singer, Florence Mihaela; Voica, Cristian

    2013-01-01

    The links between the mathematical and cognitive models that interact during problem solving are explored with the purpose of developing a reference framework for designing problem-posing tasks. When the process of solving is a successful one, a solver successively changes his/her cognitive stances related to the problem via transformations that…

  8. The Effect of Learning Environments Based on Problem Solving on Students' Achievements of Problem Solving

    ERIC Educational Resources Information Center

    Karatas, Ilhan; Baki, Adnan

    2013-01-01

    Problem solving is recognized as an important life skill involving a range of processes including analyzing, interpreting, reasoning, predicting, evaluating and reflecting. For that reason educating students as efficient problem solvers is an important role of mathematics education. Problem solving skill is the centre of mathematics curriculum.…

  9. Impact of data distribution on the parallel performance of iterative linear solvers with emphasis on CFD of incompressible flows

    NASA Astrophysics Data System (ADS)

    Esmaily-Moghadam, M.; Bazilevs, Y.; Marsden, A. L.

    2015-01-01

    A parallel data structure that gives optimized memory layout for problems involving iterative solution of sparse linear systems is developed, and its efficient implementation is presented. The proposed method assigns a processor to a problem subdomain, and sorts data based on the shared entries with the adjacent subdomains. Matrix-vector-product communication overhead is reduced and parallel scalability is improved by overlapping inter-processor communications and local computations. The proposed method simplifies the implementation of parallel iterative linear equation solver algorithms and reduces the computational cost of vector inner products and matrix-vector products. Numerical results demonstrate very good performance of the proposed technique.

  10. Comparison between the NWF and DC methods for implementing HR Schemes within a Fully Coupled Finite Volume Solver

    SciTech Connect

    Moukalled, F.; Aziz, A. Abdel; Darwish, M.

    2009-09-09

    This paper reports on the performance of a high resolution implemented as part of an implicit fully coupled velocity-pressure algorithm for the solution of laminar incompressible flow problems. The numerical implementation of high resolution convective schemes follows two techniques; (i) the Deferred Correction (DC) approach, and (ii) the Normalized Weighting Factor (NWF) method. The superiority of the NWF method over the DC approach is demonstrated by solving the sudden expansion in a square cavity problem. Results indicate that the number of iterations needed by the NWF solver is grid independent. Moreover, recorded CPU time values reveal that the NWF method substantially reduces the computational cost.

  11. Computer Problem-Solving Coaches

    NASA Astrophysics Data System (ADS)

    Hsu, Leon; Heller, Kenneth

    2005-09-01

    Computers might be able to play an important role in physics instruction by coaching students to develop good problem-solving skills. Building on previous research on student problem solving and on designing computer programs to teach cognitive skills, we are developing a prototype computer coach to provide students with guided practice in solving problems. In addition to helping students become better problem solvers, such programs can be useful in studying how students learn to solve problems and how and if problem-solving skills can be transferred from a computer to a pencil-and-paper environment.

  12. Performance of Basic Geodynamic Solvers on BG/p and on Modern Mid-sized CPU Clusters

    NASA Astrophysics Data System (ADS)

    Omlin, S.; Keller, V.; Podladchikov, Y.

    2012-04-01

    Nowadays, most researchers have access to computer clusters. For the community developing numerical applications in geodynamics, this constitutes a very important potential: besides that current applications can be speeded up, much bigger problems can be solved. This is particularly relevant in 3D applications. However, current practical experiments in geodynamic high-performance applications normally end with the successful demonstration of the potential by exploring the performance of the simplest example (typically the Poisson solver); more advanced practical examples are rare. For this reason, we optimize algorithms for 3D scalar problems and 3D mechanics and design concise, educational Fortran 90 templates that allow other researchers to easily plug in their own geodynamic computations: in these templates, the geodynamic computations are entirely separated from the technical programming needed for the parallelized running on a computer cluster; additionally, we develop our code with minimal syntactical differences from the MATLAB language, such that prototypes of the desired geodynamic computations can be programmed in MATLAB and then copied into the template with only minimal syntactical changes. High-performance programming requires to a big extent taking into account the specificities of the available hardware. The hardware of the world's largest CPU clusters is very different from the one of a modern mid-sized CPU cluster. In this context, we investigate the performance of basic memory-bounded geodynamic solvers on the large-sized BlueGene/P cluster, having 13 Gb/s peak memory bandwidth, and compare it with the performance of a typical modern mid-sized CPU cluster, having 100 Gb/s peak memory bandwidth. A memory-bounded solver's performance depends only on the amount of data required for its computations and on the speed this data can be read from memory (or from the CPUs' cache). In consequence, we speed up the solvers by optimizing memory access and CPU

  13. An Upwind Solver for the National Combustion Code

    NASA Technical Reports Server (NTRS)

    Sockol, Peter M.

    2011-01-01

    An upwind solver is presented for the unstructured grid National Combustion Code (NCC). The compressible Navier-Stokes equations with time-derivative preconditioning and preconditioned flux-difference splitting of the inviscid terms are used. First order derivatives are computed on cell faces and used to evaluate the shear stresses and heat fluxes. A new flux limiter uses these same first order derivatives in the evaluation of left and right states used in the flux-difference splitting. The k-epsilon turbulence equations are solved with the same second-order method. The new solver has been installed in a recent version of NCC and the resulting code has been tested successfully in 2D on two laminar cases with known solutions and one turbulent case with experimental data.

  14. CASTRO: A NEW COMPRESSIBLE ASTROPHYSICAL SOLVER. II. GRAY RADIATION HYDRODYNAMICS

    SciTech Connect

    Zhang, W.; Almgren, A.; Bell, J.; Howell, L.; Burrows, A.

    2011-10-01

    We describe the development of a flux-limited gray radiation solver for the compressible astrophysics code, CASTRO. CASTRO uses an Eulerian grid with block-structured adaptive mesh refinement based on a nested hierarchy of logically rectangular variable-sized grids with simultaneous refinement in both space and time. The gray radiation solver is based on a mixed-frame formulation of radiation hydrodynamics. In our approach, the system is split into two parts, one part that couples the radiation and fluid in a hyperbolic subsystem, and another parabolic part that evolves radiation diffusion and source-sink terms. The hyperbolic subsystem is solved explicitly with a high-order Godunov scheme, whereas the parabolic part is solved implicitly with a first-order backward Euler method.

  15. Verification and Validation Studies for the LAVA CFD Solver

    NASA Technical Reports Server (NTRS)

    Moini-Yekta, Shayan; Barad, Michael F; Sozer, Emre; Brehm, Christoph; Housman, Jeffrey A.; Kiris, Cetin C.

    2013-01-01

    The verification and validation of the Launch Ascent and Vehicle Aerodynamics (LAVA) computational fluid dynamics (CFD) solver is presented. A modern strategy for verification and validation is described incorporating verification tests, validation benchmarks, continuous integration and version control methods for automated testing in a collaborative development environment. The purpose of the approach is to integrate the verification and validation process into the development of the solver and improve productivity. This paper uses the Method of Manufactured Solutions (MMS) for the verification of 2D Euler equations, 3D Navier-Stokes equations as well as turbulence models. A method for systematic refinement of unstructured grids is also presented. Verification using inviscid vortex propagation and flow over a flat plate is highlighted. Simulation results using laminar and turbulent flow past a NACA 0012 airfoil and ONERA M6 wing are validated against experimental and numerical data.

  16. A functional implementation of the Jacobi eigen-solver

    SciTech Connect

    Boehm, A.P.W.; Hiromoto, R.E.

    1993-02-01

    In this paper, we describe the systematic development of two implementations of the Jacobi eigen-solver and give performance results for the MIT/Motorola Monsoon dataflow machine. Our study is carried out using MINT, the MIT Monsoon simulator. The design of these implementations follows from the mathematics of the Jacobi method, and not from a translation of an existing sequential code. The functional semantics with respect to array updates, which cause excessive array copying, has lead us to a new implementation of a parallel ``group-rotations`` algorithm first described by Sameh. Our version of this algorithm requires 0(n{sup 3}) operations, whereas Sameh`s original version requires 0(n{sup 4}) operations. The implementations are programmed in the language Id, and although Id has non-functional features, we have restricted the development of our eigen-solvers to the functional sub-set of the language.

  17. A functional implementation of the Jacobi eigen-solver

    SciTech Connect

    Boehm, A.P.W. . Dept. of Computer Science); Hiromoto, R.E. )

    1993-01-01

    In this paper, we describe the systematic development of two implementations of the Jacobi eigen-solver and give performance results for the MIT/Motorola Monsoon dataflow machine. Our study is carried out using MINT, the MIT Monsoon simulator. The design of these implementations follows from the mathematics of the Jacobi method, and not from a translation of an existing sequential code. The functional semantics with respect to array updates, which cause excessive array copying, has lead us to a new implementation of a parallel group-rotations'' algorithm first described by Sameh. Our version of this algorithm requires 0(n[sup 3]) operations, whereas Sameh's original version requires 0(n[sup 4]) operations. The implementations are programmed in the language Id, and although Id has non-functional features, we have restricted the development of our eigen-solvers to the functional sub-set of the language.

  18. LDRD report : parallel repartitioning for optimal solver performance.

    SciTech Connect

    Heaphy, Robert; Devine, Karen Dragon; Preis, Robert; Hendrickson, Bruce Alan; Heroux, Michael Allen; Boman, Erik Gunnar

    2004-02-01

    We have developed infrastructure, utilities and partitioning methods to improve data partitioning in linear solvers and preconditioners. Our efforts included incorporation of data repartitioning capabilities from the Zoltan toolkit into the Trilinos solver framework, (allowing dynamic repartitioning of Trilinos matrices); implementation of efficient distributed data directories and unstructured communication utilities in Zoltan and Trilinos; development of a new multi-constraint geometric partitioning algorithm (which can generate one decomposition that is good with respect to multiple criteria); and research into hypergraph partitioning algorithms (which provide up to 56% reduction of communication volume compared to graph partitioning for a number of emerging applications). This report includes descriptions of the infrastructure and algorithms developed, along with results demonstrating the effectiveness of our approaches.

  19. 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.

  20. Scalable Out-of-Core Solvers on Xeon Phi Cluster

    SciTech Connect

    D'Azevedo, Ed F; Chan, Ki Shing; Su, Shiquan; Wong, Kwai

    2015-01-01

    This paper documents the implementation of a distributive out-of-core (OOC) solver for performing LU and Cholesky factorizations of a large dense matrix on clusters of many-core programmable co-processors. The out-of- core algorithm combines both the left-looking and right-looking schemes aimed to minimize the movement of data between the CPU host and the co-processor, optimizing data locality as well as computing throughput. The OOC solver is built to align with the format of the ScaLAPACK software library, making it readily portable to any existing codes using ScaLAPACK. A runtime analysis conducted on Beacon (an Intel Xeon plus Intel Xeon Phi cluster which composed of 48 nodes of multi-core CPU and MIC) at the Na- tional Institute for Computational Sciences is presented. Comparison of the performance on the Intel Xeon Phi and GPU clusters are also provided.

  1. Scaling Algebraic Multigrid Solvers: On the Road to Exascale

    SciTech Connect

    Baker, A H; Falgout, R D; Gamblin, T; Kolev, T; Schulz, M; Yang, U M

    2010-12-12

    Algebraic Multigrid (AMG) solvers are an essential component of many large-scale scientific simulation codes. Their continued numerical scalability and efficient implementation is critical for preparing these codes for exascale. Our experiences on modern multi-core machines show that significant challenges must be addressed for AMG to perform well on such machines. We discuss our experiences and describe the techniques we have used to overcome scalability challenges for AMG on hybrid architectures in preparation for exascale.

  2. Boltzmann Solver with Adaptive Mesh in Velocity Space

    SciTech Connect

    Kolobov, Vladimir I.; Arslanbekov, Robert R.; Frolova, Anna A.

    2011-05-20

    We describe the implementation of direct Boltzmann solver with Adaptive Mesh in Velocity Space (AMVS) using quad/octree data structure. The benefits of the AMVS technique are demonstrated for the charged particle transport in weakly ionized plasmas where the collision integral is linear. We also describe the implementation of AMVS for the nonlinear Boltzmann collision integral. Test computations demonstrate both advantages and deficiencies of the current method for calculations of narrow-kernel distributions.

  3. A contribution to the great Riemann solver debate

    NASA Technical Reports Server (NTRS)

    Quirk, James J.

    1992-01-01

    The aims of this paper are threefold: to increase the level of awareness within the shock capturing community to the fact that many Godunov-type methods contain subtle flaws that can cause spurious solutions to be computed; to identify one mechanism that might thwart attempts to produce very high resolution simulations; and to proffer a simple strategy for overcoming the specific failings of individual Riemann solvers.

  4. Effects of Cooperative Grouping on Stoichiometric Problem Solving in High School Chemistry.

    ERIC Educational Resources Information Center

    Tingle, Joy B.; Good, Ron

    1990-01-01

    Determined was the effect that cooperative groups heterogeneously based on proportional reasoning ability have on problem solving in regular and honors high school chemistry. Characteristics of successful and unsuccessful problem solvers individually and in groups are discussed. (KR)

  5. Transonic Drag Prediction Using an Unstructured Multigrid Solver

    NASA Technical Reports Server (NTRS)

    Mavriplis, D. J.; Levy, David W.

    2001-01-01

    This paper summarizes the results obtained with the NSU-3D unstructured multigrid solver for the AIAA Drag Prediction Workshop held in Anaheim, CA, June 2001. The test case for the workshop consists of a wing-body configuration at transonic flow conditions. Flow analyses for a complete test matrix of lift coefficient values and Mach numbers at a constant Reynolds number are performed, thus producing a set of drag polars and drag rise curves which are compared with experimental data. Results were obtained independently by both authors using an identical baseline grid and different refined grids. Most cases were run in parallel on commodity cluster-type machines while the largest cases were run on an SGI Origin machine using 128 processors. The objective of this paper is to study the accuracy of the subject unstructured grid solver for predicting drag in the transonic cruise regime, to assess the efficiency of the method in terms of convergence, cpu time, and memory, and to determine the effects of grid resolution on this predictive ability and its computational efficiency. A good predictive ability is demonstrated over a wide range of conditions, although accuracy was found to degrade for cases at higher Mach numbers and lift values where increasing amounts of flow separation occur. The ability to rapidly compute large numbers of cases at varying flow conditions using an unstructured solver on inexpensive clusters of commodity computers is also demonstrated.

  6. 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.

  7. Comparison of an algebraic multigrid algorithm to two iterative solvers used for modeling ground water flow and transport

    USGS Publications Warehouse

    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.

  8. Comparison of an algebraic multigrid algorithm to two iterative solvers used for modeling ground water flow and transport.

    PubMed

    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

  9. Adaptive multi-resolution 3D Hartree-Fock-Bogoliubov solver for nuclear structure

    NASA Astrophysics Data System (ADS)

    Pei, J. C.; Fann, G. I.; Harrison, R. J.; Nazarewicz, W.; Shi, Yue; Thornton, S.

    2014-08-01

    Background: Complex many-body systems, such as triaxial and reflection-asymmetric nuclei, weakly bound halo states, cluster configurations, nuclear fragments produced in heavy-ion fusion reactions, cold Fermi gases, and pasta phases in neutron star crust, are all characterized by large sizes and complex topologies in which many geometrical symmetries characteristic of ground-state configurations are broken. A tool of choice to study such complex forms of matter is an adaptive multi-resolution wavelet analysis. This method has generated much excitement since it provides a common framework linking many diversified methodologies across different fields, including signal processing, data compression, harmonic analysis and operator theory, fractals, and quantum field theory. Purpose: To describe complex superfluid many-fermion systems, we introduce an adaptive pseudospectral method for solving self-consistent equations of nuclear density functional theory in three dimensions, without symmetry restrictions. Methods: The numerical method is based on the multi-resolution and computational harmonic analysis techniques with a multi-wavelet basis. The application of state-of-the-art parallel programming techniques include sophisticated object-oriented templates which parse the high-level code into distributed parallel tasks with a multi-thread task queue scheduler for each multi-core node. The internode communications are asynchronous. The algorithm is variational and is capable of solving coupled complex-geometric systems of equations adaptively, with functional and boundary constraints, in a finite spatial domain of very large size, limited by existing parallel computer memory. For smooth functions, user-defined finite precision is guaranteed. Results: The new adaptive multi-resolution Hartree-Fock-Bogoliubov (HFB) solver madness-hfb is benchmarked against a two-dimensional coordinate-space solver hfb-ax that is based on the B-spline technique and a three-dimensional solver

  10. A Hybrid, Parallel Krylov Solver for MODFLOW using Schwarz Domain Decomposition

    NASA Astrophysics Data System (ADS)

    Sutanudjaja, E.; Verkaik, J.; Hughes, J. D.

    2015-12-01

    In order to support decision makers in solving hydrological problems, detailed high-resolution models are often needed. These models typically consist of a large number of computational cells and have large memory requirements and long run times. An efficient technique for obtaining realistic run times and memory requirements is parallel computing, where the problem is divided over multiple processor cores. The new Parallel Krylov Solver (PKS) for MODFLOW-USG is presented. It combines both distributed memory parallelization by the Message Passing Interface (MPI) and shared memory parallelization by Open Multi-Processing (OpenMP). PKS includes conjugate gradient and biconjugate gradient stabilized linear accelerators that are both preconditioned by an overlapping additive Schwarz preconditioner in a way that: a) subdomains are partitioned using the METIS library; b) each subdomain uses local memory only and communicates with other subdomains by MPI within the linear accelerator; c) is fully integrated in the MODFLOW-USG code. PKS is based on the unstructured PCGU-solver, and supports OpenMP. Depending on the available hardware, PKS can run exclusively with MPI, exclusively with OpenMP, or with a hybrid MPI/OpenMP approach. Benchmarks were performed on the Cartesius Dutch supercomputer (https://userinfo.surfsara.nl/systems/cartesius) using up to 144 cores, for a synthetic test (~112 million cells) and the Indonesia groundwater model (~4 million 1km cells). The latter, which includes all islands in the Indonesian archipelago, was built using publically available global datasets, and is an ideal test bed for evaluating the applicability of PKS parallelization techniques to a global groundwater model consisting of multiple continents and islands. Results show that run time reductions can be greatest with the hybrid parallelization approach for the problems tested.

  11. A Breach in the Relationship between Correctness and Scientific Conceptual Knowledge for the Meaningful Solving of a Problem about Osmosis.

    ERIC Educational Resources Information Center

    Zuckerman, June T.

    Expert/novice studies of conceptually rich problem solving have demonstrated a relationship between the correctness of a solution and the extent and organization of the solver's conceptual knowledge. This study examines meaningful problem solving and the relationship between the correctness of a solution and the extent of the solver's scientific…

  12. Using Bibliotherapy To Teach Problem Solving.

    ERIC Educational Resources Information Center

    Forgan, James W.

    2002-01-01

    This article discusses how students with high-incidence disabilities can benefit from using bibliotherapy by learning to become proactive problem solvers. A sample lesson plan is presented based on a teaching framework for bibliotherapy and problem solving that contains the elements of prereading, guided reading, post-reading discussion, and a…

  13. Activity Theory as a Tool to Address the Problem of Chemistry's Lack of Relevance in Secondary School Chemical Education

    ERIC Educational Resources Information Center

    Van Aalsvoort, Joke

    2004-01-01

    In a previous article, the problem of chemistry's lack of relevance in secondary chemical education was analysed using logical positivism as a tool. This article starts with the hypothesis that the problem can be addressed by means of activity theory, one of the important theories within the sociocultural school. The reason for this expectation is…

  14. Riding the Active Learning Wave: Problem-Based Learning as a Catalyst for Creating Faculty-Librarian Instructional Partnerships.

    ERIC Educational Resources Information Center

    Fosmire, Michael; Macklin, Alexius

    2002-01-01

    Discusses active learning as a technique to improve learning outcomes; describes the background and history of problem-based learning, explaining why information skills are an integral part; and relates the experiences of librarians at Purdue University in forming collaborations with subject faculty and in the development of problem-based learning…

  15. Problem-Based Learning Revisited, Introduction of Active and Self-Directed Learning to Reduce Fatigue among Students

    ERIC Educational Resources Information Center

    Czabanowska, Katarzyna; Moust, Jos H. C.; Meijer, Andre W. M.; Schroder-Back, Peter; Roebertsen, Herma

    2012-01-01

    Despite several years of successfully applying problem-based learning at Maastricht University, the Faculty of Medicine observed a slow erosion of problem-based practices and "PBL fatigue" among themselves and students. In response to this fatigue and new research into the development of the young adult brain, Active Self-Directed Learning was…

  16. An AMR capable finite element diffusion solver for ALE hydrocodes [An AMR capable diffusion solver for ALE-AMR

    SciTech Connect

    Fisher, A. C.; Bailey, D. S.; Kaiser, T. B.; Eder, D. C.; Gunney, B. T. N.; Masters, N. D.; Koniges, A. E.; Anderson, R. W.

    2015-02-01

    Here, we present a novel method for the solution of the diffusion equation on a composite AMR mesh. This approach is suitable for including diffusion based physics modules to hydrocodes that support ALE and AMR capabilities. To illustrate, we proffer our implementations of diffusion based radiation transport and heat conduction in a hydrocode called ALE-AMR. Numerical experiments conducted with the diffusion solver and associated physics packages yield 2nd order convergence in the L2 norm.

  17. Inverse eigenvalue problems in vibration absorption: Passive modification and active control

    NASA Astrophysics Data System (ADS)

    Mottershead, John E.; Ram, Yitshak M.

    2006-01-01

    The abiding problem of vibration absorption has occupied engineering scientists for over a century and there remain abundant examples of the need for vibration suppression in many industries. For example, in the automotive industry the resolution of noise, vibration and harshness (NVH) problems is of extreme importance to customer satisfaction. In rotorcraft it is vital to avoid resonance close to the blade passing speed and its harmonics. An objective of the greatest importance, and extremely difficult to achieve, is the isolation of the pilot's seat in a helicopter. It is presently impossible to achieve the objectives of vibration absorption in these industries at the design stage because of limitations inherent in finite element models. Therefore, it is necessary to develop techniques whereby the dynamic of the system (possibly a car or a helicopter) can be adjusted after it has been built. There are two main approaches: structural modification by passive elements and active control. The state of art of the mathematical theory of vibration absorption is presented and illustrated for the benefit of the reader with numerous simple examples.

  18. 3D frequency modeling of elastic seismic wave propagation via a structured massively parallel direct Helmholtz solver

    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.

  19. Adaptation of a Multi-Block Structured Solver for Effective Use in a Hybrid CPU/GPU Massively Parallel Environment

    NASA Astrophysics Data System (ADS)

    Gutzwiller, David; Gontier, Mathieu; Demeulenaere, Alain

    2014-11-01

    Multi-Block structured solvers hold many advantages over their unstructured counterparts, such as a smaller memory footprint and efficient serial performance. Historically, multi-block structured solvers have not been easily adapted for use in a High Performance Computing (HPC) environment, and the recent trend towards hybrid GPU/CPU architectures has further complicated the situation. This paper will elaborate on developments and innovations applied to the NUMECA FINE/Turbo solver that have allowed near-linear scalability with real-world problems on over 250 hybrid GPU/GPU cluster nodes. Discussion will focus on the implementation of virtual partitioning and load balancing algorithms using a novel meta-block concept. This implementation is transparent to the user, allowing all pre- and post-processing steps to be performed using a simple, unpartitioned grid topology. Additional discussion will elaborate on developments that have improved parallel performance, including fully parallel I/O with the ADIOS API and the GPU porting of the computationally heavy CPUBooster convergence acceleration module. Head of HPC and Release Management, Numeca International.

  20. "Sustainability On Earth" WebQuests: Do They Qualify as Problem-Based Learning Activities?

    NASA Astrophysics Data System (ADS)

    Leite, Laurinda; Dourado, Luís; Morgado, Sofia

    2015-02-01

    Information and communication technologies (ICT), namely the Internet, can play a valuable educational role in several school subjects, including science education. The same applies to problem-based learning (PBL), that is, a student-centered active learning methodology that can prepare students for lifelong learning. WebQuests (WQs) combine PBL and Internet use, and they can reduce the probability of having students surfing the Internet without any clear purpose. The objective of this paper is to investigate to what extent WQs available from Portuguese schools' and universities' websites, focusing on the "Sustainability on Earth" eighth-grade school science theme, are consistent with a PBL perspective. Results from content analysis of 92 WQs indicate that the WQs selected for this paper are rarely consistent with PBL requirements. Teachers should be both aware of this issue and ready to improve the WQs available before using them in their science classes so that greater educational advantage can be generated from this powerful tool.

  1. MARS-KS code validation activity through the atlas domestic standard problem

    SciTech Connect

    Choi, K. Y.; Kim, Y. S.; Kang, K. H.; Park, H. S.; Cho, S.

    2012-07-01

    The 2 nd Domestic Standard Problem (DSP-02) exercise using the ATLAS integral effect test data was executed to transfer the integral effect test data to domestic nuclear industries and to contribute to improving the safety analysis methodology for PWRs. A small break loss of coolant accident of a 6-inch break at the cold leg was determined as a target scenario by considering its technical importance and by incorporating interests from participants. Ten calculation results using MARS-KS code were collected, major prediction results were described qualitatively and code prediction accuracy was assessed quantitatively using the FFTBM. In addition, special code assessment activities were carried out to find out the area where the model improvement is required in the MARS-KS code. The lessons from this DSP-02 and recommendations to code developers are described in this paper. (authors)

  2. Numerical Solution of the k-Eigenvalue Problem

    NASA Astrophysics Data System (ADS)

    Hamilton, Steven Paul

    2011-12-01

    Obtaining solutions to the k-eigenvalue form of the radiation transport equation is an important topic in the design and analysis of nuclear reactors. Although this has been an area of active interest in the nuclear engineering community for several decades, to date no truly satisfactory solution strategies exist. In general, existing techniques are either slow to converge for difficult problems or suffer from stability and robustness issues that can cause solvers to diverge for some problems. This work provides a comparison between a variety of methods and introduces a new strategy based on the Davidson method that has been used in other fields for many years but never for this problem. The Davidson method offers an alternative to the nested iteration structure inherent to standard approaches and allows expensive linear solvers to be replaced by a potentially cheap preconditioner. To fill the role of this preconditioner, a strategy based on a multigrid treatment of the energy variable is developed. Numerical experiments using the 2-D NEWT transport package are presented, demonstrating the effectiveness of the proposed strategy.

  3. A biomolecular electrostatics solver using Python, GPUs and boundary elements that can handle solvent-filled cavities and Stern layers

    NASA Astrophysics Data System (ADS)

    Cooper, Christopher D.; Bardhan, Jaydeep P.; Barba, L. A.

    2014-03-01

    The continuum theory applied to biomolecular electrostatics leads to an implicit-solvent model governed by the Poisson-Boltzmann equation. Solvers relying on a boundary integral representation typically do not consider features like solvent-filled cavities or ion-exclusion (Stern) layers, due to the added difficulty of treating multiple boundary surfaces. This has hindered meaningful comparisons with volume-based methods, and the effects on accuracy of including these features has remained unknown. This work presents a solver called PyGBe that uses a boundary-element formulation and can handle multiple interacting surfaces. It was used to study the effects of solvent-filled cavities and Stern layers on the accuracy of calculating solvation energy and binding energy of proteins, using the well-known APBS finite-difference code for comparison. The results suggest that if required accuracy for an application allows errors larger than about 2% in solvation energy, then the simpler, single-surface model can be used. When calculating binding energies, the need for a multi-surface model is problem-dependent, becoming more critical when ligand and receptor are of comparable size. Comparing with the APBS solver, the boundary-element solver is faster when the accuracy requirements are higher. The cross-over point for the PyGBe code is on the order of 1-2% error, when running on one GPU card (NVIDIA Tesla C2075), compared with APBS running on six Intel Xeon CPU cores. PyGBe achieves algorithmic acceleration of the boundary element method using a treecode, and hardware acceleration using GPUs via PyCuda from a user-visible code that is all Python. The code is open-source under MIT license.

  4. A biomolecular electrostatics solver using Python, GPUs and boundary elements that can handle solvent-filled cavities and Stern layers.

    PubMed

    Cooper, Christopher D; Bardhan, Jaydeep P; Barba, L A

    2014-03-01

    The continuum theory applied to biomolecular electrostatics leads to an implicit-solvent model governed by the Poisson-Boltzmann equation. Solvers relying on a boundary integral representation typically do not consider features like solvent-filled cavities or ion-exclusion (Stern) layers, due to the added difficulty of treating multiple boundary surfaces. This has hindered meaningful comparisons with volume-based methods, and the effects on accuracy of including these features has remained unknown. This work presents a solver called PyGBe that uses a boundary-element formulation and can handle multiple interacting surfaces. It was used to study the effects of solvent-filled cavities and Stern layers on the accuracy of calculating solvation energy and binding energy of proteins, using the well-known apbs finite-difference code for comparison. The results suggest that if required accuracy for an application allows errors larger than about 2% in solvation energy, then the simpler, single-surface model can be used. When calculating binding energies, the need for a multi-surface model is problem-dependent, becoming more critical when ligand and receptor are of comparable size. Comparing with the apbs solver, the boundary-element solver is faster when the accuracy requirements are higher. The cross-over point for the PyGBe code is in the order of 1-2% error, when running on one gpu card (nvidia Tesla C2075), compared with apbs running on six Intel Xeon cpu cores. PyGBe achieves algorithmic acceleration of the boundary element method using a treecode, and hardware acceleration using gpus via PyCuda from a user-visible code that is all Python. The code is open-source under MIT license. PMID:25284826

  5. Modeling of laser wakefield acceleration in Lorentz boosted frame using EM-PIC code with spectral solver

    NASA Astrophysics Data System (ADS)

    Yu, Peicheng; Xu, Xinlu; Decyk, Viktor K.; An, Weiming; Vieira, Jorge; Tsung, Frank S.; Fonseca, Ricardo A.; Lu, Wei; Silva, Luis O.; Mori, Warren B.

    2014-06-01

    Simulating laser wakefield acceleration (LWFA) in a Lorentz boosted frame in which the plasma drifts towards the laser with vb can speed up the simulation by factors of γb2=(1. In these simulations the relativistic drifting plasma inevitably induces a high frequency numerical instability that contaminates the interesting physics. Various approaches have been proposed to mitigate this instability. One approach is to solve Maxwell equations in Fourier space (a spectral solver) as this has been shown to suppress the fastest growing modes of this instability in simple test problems using a simple low pass or "ring" or "shell" like filters in Fourier space. We describe the development of a fully parallelized, multi-dimensional, particle-in-cell code that uses a spectral solver to solve Maxwell's equations and that includes the ability to launch a laser using a moving antenna. This new EM-PIC code is called UPIC-EMMA and it is based on the components of the UCLA PIC framework (UPIC). We show that by using UPIC-EMMA, LWFA simulations in the boosted frames with arbitrary γb can be conducted without the presence of the numerical instability. We also compare the results of a few LWFA cases for several values of γb, including lab frame simulations using OSIRIS, an EM-PIC code with a finite-difference time domain (FDTD) Maxwell solver. These comparisons include cases in both linear and nonlinear regimes. We also investigate some issues associated with numerical dispersion in lab and boosted frame simulations and between FDTD and spectral solvers.

  6. A biomolecular electrostatics solver using Python, GPUs and boundary elements that can handle solvent-filled cavities and Stern layers

    PubMed Central

    Cooper, Christopher D.; Bardhan, Jaydeep P.; Barba, L. A.

    2014-01-01

    The continuum theory applied to biomolecular electrostatics leads to an implicit-solvent model governed by the Poisson-Boltzmann equation. Solvers relying on a boundary integral representation typically do not consider features like solvent-filled cavities or ion-exclusion (Stern) layers, due to the added difficulty of treating multiple boundary surfaces. This has hindered meaningful comparisons with volume-based methods, and the effects on accuracy of including these features has remained unknown. This work presents a solver called PyGBe that uses a boundary-element formulation and can handle multiple interacting surfaces. It was used to study the effects of solvent-filled cavities and Stern layers on the accuracy of calculating solvation energy and binding energy of proteins, using the well-known apbs finite-difference code for comparison. The results suggest that if required accuracy for an application allows errors larger than about 2% in solvation energy, then the simpler, single-surface model can be used. When calculating binding energies, the need for a multi-surface model is problem-dependent, becoming more critical when ligand and receptor are of comparable size. Comparing with the apbs solver, the boundary-element solver is faster when the accuracy requirements are higher. The cross-over point for the PyGBe code is in the order of 1–2% error, when running on one gpu card (nvidia Tesla C2075), compared with apbs running on six Intel Xeon cpu cores. PyGBe achieves algorithmic acceleration of the boundary element method using a treecode, and hardware acceleration using gpus via PyCuda from a user-visible code that is all Python. The code is open-source under MIT license. PMID:25284826

  7. Problem Solving and Chemical Equilibrium: Successful versus Unsuccessful Performance.

    ERIC Educational Resources Information Center

    Camacho, Moises; Good, Ron

    1989-01-01

    Describes the problem-solving behaviors of experts and novices engaged in solving seven chemical equilibrium problems. Lists 27 behavioral tendencies of successful and unsuccessful problem solvers. Discusses several implications for a problem solving theory, think-aloud techniques, adequacy of the chemistry domain, and chemistry instruction.…

  8. Three-Dimensional High-Lift Analysis Using a Parallel Unstructured Multigrid Solver

    NASA Technical Reports Server (NTRS)

    Mavriplis, Dimitri J.

    1998-01-01

    A directional implicit unstructured agglomeration multigrid solver is ported to shared and distributed memory massively parallel machines using the explicit domain-decomposition and message-passing approach. Because the algorithm operates on local implicit lines in the unstructured mesh, special care is required in partitioning the problem for parallel computing. A weighted partitioning strategy is described which avoids breaking the implicit lines across processor boundaries, while incurring minimal additional communication overhead. Good scalability is demonstrated on a 128 processor SGI Origin 2000 machine and on a 512 processor CRAY T3E machine for reasonably fine grids. The feasibility of performing large-scale unstructured grid calculations with the parallel multigrid algorithm is demonstrated by computing the flow over a partial-span flap wing high-lift geometry on a highly resolved grid of 13.5 million points in approximately 4 hours of wall clock time on the CRAY T3E.

  9. 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.

  10. SpectralPlasmaSolver: a Spectral Code for Multiscale Simulations of Collisionless, Magnetized Plasmas

    NASA Astrophysics Data System (ADS)

    Vencels, Juris; Delzanno, Gian Luca; Manzini, Gianmarco; Markidis, Stefano; Peng, Ivy Bo; Roytershteyn, Vadim

    2016-05-01

    We present the design and implementation of a spectral code, called SpectralPlasmaSolver (SPS), for the solution of the multi-dimensional Vlasov-Maxwell equations. The method is based on a Hermite-Fourier decomposition of the particle distribution function. The code is written in Fortran and uses the PETSc library for solving the non-linear equations and preconditioning and the FFTW library for the convolutions. SPS is parallelized for shared- memory machines using OpenMP. As a verification example, we discuss simulations of the two-dimensional Orszag-Tang vortex problem and successfully compare them against a fully kinetic Particle-In-Cell simulation. An assessment of the performance of the code is presented, showing a significant improvement in the code running-time achieved by preconditioning, while strong scaling tests show a factor of 10 speed-up using 16 threads.

  11. MosaicSolver: a tool for determining recombinants of viral genomes from pileup data

    PubMed Central

    Wood, Graham R.; Ryabov, Eugene V.; Fannon, Jessica M.; Moore, Jonathan D.; Evans, David J.; Burroughs, Nigel

    2014-01-01

    Viral recombination is a key evolutionary mechanism, aiding escape from host immunity, contributing to changes in tropism and possibly assisting transmission across species barriers. The ability to determine whether recombination has occurred and to locate associated specific recombination junctions is thus of major importance in understanding emerging diseases and pathogenesis. This paper describes a method for determining recombinant mosaics (and their proportions) originating from two parent genomes, using high-throughput sequence data. The method involves setting the problem geometrically and the use of appropriately constrained quadratic programming. Recombinants of the honeybee deformed wing virus and the Varroa destructor virus-1 are inferred to illustrate the method from both siRNAs and reads sampling the viral genome population (cDNA library); our results are confirmed experimentally. Matlab software (MosaicSolver) is available. PMID:25120266

  12. Virtual Petaflop Simulation: Parallel Potential Solvers and New Integrators for Gravitational Systems

    NASA Technical Reports Server (NTRS)

    Lake, George; Quinn, Thomas; Richardson, Derek C.; Stadel, Joachim

    1999-01-01

    "The orbit of any one planet depends on the combined motion of all the planets, not to mention the actions of all these on each other. To consider simultaneously all these causes of motion and to define these motions by exact laws allowing of convenient calculation exceeds, unless I am mistaken, the forces of the entire human intellect" -Isaac Newton 1687. Epochal surveys are throwing down the gauntlet for cosmological simulation. We describe three keys to meeting the challenge of N-body simulation: adaptive potential solvers, adaptive integrators and volume renormalization. With these techniques and a dedicated Teraflop facility, simulation can stay even with observation of the Universe. We also describe some problems in the formation and stability of planetary systems. Here, the challenge is to perform accurate integrations that retain Hamiltonian properties for 10(exp 13) timesteps.

  13. A parallel implementation of an EBE solver for the finite element method

    SciTech Connect

    Silva, R.P.; Las Casas, E.B.; Carvalho, M.L.B.

    1994-12-31

    A parallel implementation using PVM on a cluster of workstations of an Element By Element (EBE) solver using the Preconditioned Conjugate Gradient (PCG) method is described, along with an application in the solution of the linear systems generated from finite element analysis of a problem in three dimensional linear elasticity. The PVM (Parallel Virtual Machine) system, developed at the Oak Ridge Laboratory, allows the construction of a parallel MIMD machine by connecting heterogeneous computers linked through a network. In this implementation, version 3.1 of PVM is used, and 11 SLC Sun workstations and a Sun SPARC-2 model are connected through Ethernet. The finite element program is based on SDP, System for Finite Element Based Software Development, developed at the Brazilian National Laboratory for Scientific Computation (LNCC). SDP provides the basic routines for a finite element application program, as well as a standard for programming and documentation, intended to allow exchanges between research groups in different centers.

  14. ISIS++Reference Guide (Iterative Scalable Implicit Solver in C++) Version 1.1

    SciTech Connect

    Alan B. Williams; Benjamin A. Allan; Kyran D. Mish; Robert L. Clay

    1999-04-01

    ISIS++ (Iterative Scalable Implicit Solver in C++) Version 1.1 is a portable, object-oriented framework for solving sparse linear systems of equations. It includes a collection of Krylov solution methods and preconditioners, as well as both uni-processor (serial) and multi-processor (scalable) matrix and vector classes. Though it was developed to solve systems of equations originating from large-scale, 3-D, finite element analyses, it has application in many other fields. This document supersedes the ISIS++ V1.0 Reference Guide, defines the V1. 1 interface specification, and includes the necessary instructions for building and running ISIS++ v 1.1 on Unix platforms. The interface is presented in annotated header format, along with background on design and implementation considerations. A finite difference modeling example problem is included to demonstrate the overall setup and use.

  15. Average synaptic activity and neural networks topology: a global inverse problem

    NASA Astrophysics Data System (ADS)

    Burioni, Raffaella; Casartelli, Mario; di Volo, Matteo; Livi, Roberto; Vezzani, Alessandro

    2014-03-01

    The dynamics of neural networks is often characterized by collective behavior and quasi-synchronous events, where a large fraction of neurons fire in short time intervals, separated by uncorrelated firing activity. These global temporal signals are crucial for brain functioning. They strongly depend on the topology of the network and on the fluctuations of the connectivity. We propose a heterogeneous mean-field approach to neural dynamics on random networks, that explicitly preserves the disorder in the topology at growing network sizes, and leads to a set of self-consistent equations. Within this approach, we provide an effective description of microscopic and large scale temporal signals in a leaky integrate-and-fire model with short term plasticity, where quasi-synchronous events arise. Our equations provide a clear analytical picture of the dynamics, evidencing the contributions of both periodic (locked) and aperiodic (unlocked) neurons to the measurable average signal. In particular, we formulate and solve a global inverse problem of reconstructing the in-degree distribution from the knowledge of the average activity field. Our method is very general and applies to a large class of dynamical models on dense random networks.

  16. Marine Invertebrate Metabolites with Anticancer Activities: Solutions to the "Supply Problem".

    PubMed

    Gomes, Nelson G M; Dasari, Ramesh; Chandra, Sunena; Kiss, Robert; Kornienko, Alexander

    2016-05-01

    Marine invertebrates provide a rich source of metabolites with anticancer activities and several marine-derived agents have been approved for the treatment of cancer. However, the limited supply of promising anticancer metabolites from their natural sources is a major hurdle to their preclinical and clinical development. Thus, the lack of a sustainable large-scale supply has been an important challenge facing chemists and biologists involved in marine-based drug discovery. In the current review we describe the main strategies aimed to overcome the supply problem. These include: marine invertebrate aquaculture, invertebrate and symbiont cell culture, culture-independent strategies, total chemical synthesis, semi-synthesis, and a number of hybrid strategies. We provide examples illustrating the application of these strategies for the supply of marine invertebrate-derived anticancer agents. Finally, we encourage the scientific community to develop scalable methods to obtain selected metabolites, which in the authors' opinion should be pursued due to their most promising anticancer activities. PMID:27213412

  17. Patterns of Organized Activity Participation in Urban, Early Adolescents: Associations with Academic Achievement, Problem Behaviors, and Perceived Adult Support

    ERIC Educational Resources Information Center

    Metzger, Aaron; Crean, Hugh F.; Forbes-Jones, Emma L.

    2009-01-01

    This study examines patterns of organized activity and their concurrent association with academic achievement, problem behavior, and perceived adult support in a sample of urban, early adolescent, middle school students (mean age = 13.01; N = 2,495). Cluster analyses yielded six activity profiles: an uninvolved group (n = 775, 31.1%), a multiply…

  18. Future Scenario Writing as a Family Problem Solving Activity: If Today Were Tomorrow.

    ERIC Educational Resources Information Center

    Murdock, Mary C.

    1993-01-01

    Future scenario writing is presented as a combined writing and problem-solving technique that identifies alternative ways of thinking about situations. Uses of future scenario writing in family problem solving include setting family goals, communicating growth resulting from new experiences, resolving family problems, encouraging family…

  19. Object-Oriented Design for Sparse Direct Solvers

    NASA Technical Reports Server (NTRS)

    Dobrian, Florin; Kumfert, Gary; Pothen, Alex

    1999-01-01

    We discuss the object-oriented design of a software package for solving sparse, symmetric systems of equations (positive definite and indefinite) by direct methods. At the highest layers, we decouple data structure classes from algorithmic classes for flexibility. We describe the important structural and algorithmic classes in our design, and discuss the trade-offs we made for high performance. The kernels at the lower layers were optimized by hand. Our results show no performance loss from our object-oriented design, while providing flexibility, case of use, and extensibility over solvers using procedural design.

  20. FDIPS: Finite Difference Iterative Potential-field Solver

    NASA Astrophysics Data System (ADS)

    Toth, Gabor; van der Holst, Bartholomeus; Huang, Zhenguang

    2016-06-01

    FDIPS is a finite difference iterative potential-field solver that can generate the 3D potential magnetic field solution based on a magnetogram. It is offered as an alternative to the spherical harmonics approach, as when the number of spherical harmonics is increased, using the raw magnetogram data given on a grid that is uniform in the sine of the latitude coordinate can result in inaccurate and unreliable results, especially in the polar regions close to the Sun. FDIPS is written in Fortran 90 and uses the MPI library for parallel execution.