Conjugate gradient coupled with multigrid for an indefinite problem

NASA Technical Reports Server (NTRS)

Gozani, J.; Nachshon, A.; Turkel, E.

1984-01-01

An iterative algorithm for the Helmholtz equation is presented. This scheme was based on the preconditioned conjugate gradient method for the normal equations. The preconditioning is one cycle of a multigrid method for the discrete Laplacian. The smoothing algorithm is red-black Gauss-Seidel and is constructed so it is a symmetric operator. The total number of iterations needed by the algorithm is independent of h. By varying the number of grids, the number of iterations depends only weakly on k when k(3)h(2) is constant. Comparisons with a SSOR preconditioner are presented.

Rapidly converging multigrid reconstruction of cone-beam tomographic data

NASA Astrophysics Data System (ADS)

Myers, Glenn R.; Kingston, Andrew M.; Latham, Shane J.; Recur, Benoit; Li, Thomas; Turner, Michael L.; Beeching, Levi; Sheppard, Adrian P.

2016-10-01

In the context of large-angle cone-beam tomography (CBCT), we present a practical iterative reconstruction (IR) scheme designed for rapid convergence as required for large datasets. The robustness of the reconstruction is provided by the "space-filling" source trajectory along which the experimental data is collected. The speed of convergence is achieved by leveraging the highly isotropic nature of this trajectory to design an approximate deconvolution filter that serves as a pre-conditioner in a multi-grid scheme. We demonstrate this IR scheme for CBCT and compare convergence to that of more traditional techniques.

Scalable smoothing strategies for a geometric multigrid method for the immersed boundary equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bhalla, Amneet Pal Singh; Knepley, Matthew G.; Adams, Mark F.

2016-12-20

The immersed boundary (IB) method is a widely used approach to simulating fluid-structure interaction (FSI). Although explicit versions of the IB method can suffer from severe time step size restrictions, these methods remain popular because of their simplicity and generality. In prior work (Guy et al., Adv Comput Math, 2015), some of us developed a geometric multigrid preconditioner for a stable semi-implicit IB method under Stokes flow conditions; however, this solver methodology used a Vanka-type smoother that presented limited opportunities for parallelization. This work extends this Stokes-IB solver methodology by developing smoothing techniques that are suitable for parallel implementation. Specifically,more » we demonstrate that an additive version of the Vanka smoother can yield an effective multigrid preconditioner for the Stokes-IB equations, and we introduce an efficient Schur complement-based smoother that is also shown to be effective for the Stokes-IB equations. We investigate the performance of these solvers for a broad range of material stiffnesses, both for Stokes flows and flows at nonzero Reynolds numbers, and for thick and thin structural models. We show here that linear solver performance degrades with increasing Reynolds number and material stiffness, especially for thin interface cases. Nonetheless, the proposed approaches promise to yield effective solution algorithms, especially at lower Reynolds numbers and at modest-to-high elastic stiffnesses.« less

A Study of Multigrid Preconditioners Using Eigensystem Analysis

NASA Technical Reports Server (NTRS)

Roberts, Thomas W.; Swanson, R. C.

2005-01-01

The convergence properties of numerical schemes for partial differential equations are studied by examining the eigensystem of the discrete operator. This method of analysis is very general, and allows the effects of boundary conditions and grid nonuniformities to be examined directly. Algorithms for the Laplace equation and a two equation model hyperbolic system are examined.

A preconditioner for the finite element computation of incompressible, nonlinear elastic deformations

NASA Astrophysics Data System (ADS)

Whiteley, J. P.

2017-10-01

Large, incompressible elastic deformations are governed by a system of nonlinear partial differential equations. The finite element discretisation of these partial differential equations yields a system of nonlinear algebraic equations that are usually solved using Newton's method. On each iteration of Newton's method, a linear system must be solved. We exploit the structure of the Jacobian matrix to propose a preconditioner, comprising two steps. The first step is the solution of a relatively small, symmetric, positive definite linear system using the preconditioned conjugate gradient method. This is followed by a small number of multigrid V-cycles for a larger linear system. Through the use of exemplar elastic deformations, the preconditioner is demonstrated to facilitate the iterative solution of the linear systems arising. The number of GMRES iterations required has only a very weak dependence on the number of degrees of freedom of the linear systems.

Multigrid Strategies for Viscous Flow Solvers on Anisotropic Unstructured Meshes

NASA Technical Reports Server (NTRS)

Movriplis, Dimitri J.

1998-01-01

Unstructured multigrid techniques for relieving the stiffness associated with high-Reynolds number viscous flow simulations on extremely stretched grids are investigated. One approach consists of employing a semi-coarsening or directional-coarsening technique, based on the directions of strong coupling within the mesh, in order to construct more optimal coarse grid levels. An alternate approach is developed which employs directional implicit smoothing with regular fully coarsened multigrid levels. The directional implicit smoothing is obtained by constructing implicit lines in the unstructured mesh based on the directions of strong coupling. Both approaches yield large increases in convergence rates over the traditional explicit full-coarsening multigrid algorithm. However, maximum benefits are achieved by combining the two approaches in a coupled manner into a single algorithm. An order of magnitude increase in convergence rate over the traditional explicit full-coarsening algorithm is demonstrated, and convergence rates for high-Reynolds number viscous flows which are independent of the grid aspect ratio are obtained. Further acceleration is provided by incorporating low-Mach-number preconditioning techniques, and a Newton-GMRES strategy which employs the multigrid scheme as a preconditioner. The compounding effects of these various techniques on speed of convergence is documented through several example test cases.

Performance of fully-coupled algebraic multigrid preconditioners for large-scale VMS resistive MHD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lin, P. T.; Shadid, J. N.; Hu, J. J.

Here, we explore the current performance and scaling of a fully-implicit stabilized unstructured finite element (FE) variational multiscale (VMS) capability for large-scale simulations of 3D incompressible resistive magnetohydrodynamics (MHD). The large-scale linear systems that are generated by a Newton nonlinear solver approach are iteratively solved by preconditioned Krylov subspace methods. The efficiency of this approach is critically dependent on the scalability and performance of the algebraic multigrid preconditioner. Our study considers the performance of the numerical methods as recently implemented in the second-generation Trilinos implementation that is 64-bit compliant and is not limited by the 32-bit global identifiers of themore » original Epetra-based Trilinos. The study presents representative results for a Poisson problem on 1.6 million cores of an IBM Blue Gene/Q platform to demonstrate very large-scale parallel execution. Additionally, results for a more challenging steady-state MHD generator and a transient solution of a benchmark MHD turbulence calculation for the full resistive MHD system are also presented. These results are obtained on up to 131,000 cores of a Cray XC40 and one million cores of a BG/Q system.« less

Performance of fully-coupled algebraic multigrid preconditioners for large-scale VMS resistive MHD

DOE PAGES

Lin, P. T.; Shadid, J. N.; Hu, J. J.; ...

2017-11-06

Here, we explore the current performance and scaling of a fully-implicit stabilized unstructured finite element (FE) variational multiscale (VMS) capability for large-scale simulations of 3D incompressible resistive magnetohydrodynamics (MHD). The large-scale linear systems that are generated by a Newton nonlinear solver approach are iteratively solved by preconditioned Krylov subspace methods. The efficiency of this approach is critically dependent on the scalability and performance of the algebraic multigrid preconditioner. Our study considers the performance of the numerical methods as recently implemented in the second-generation Trilinos implementation that is 64-bit compliant and is not limited by the 32-bit global identifiers of themore » original Epetra-based Trilinos. The study presents representative results for a Poisson problem on 1.6 million cores of an IBM Blue Gene/Q platform to demonstrate very large-scale parallel execution. Additionally, results for a more challenging steady-state MHD generator and a transient solution of a benchmark MHD turbulence calculation for the full resistive MHD system are also presented. These results are obtained on up to 131,000 cores of a Cray XC40 and one million cores of a BG/Q system.« less

FaCSI: A block parallel preconditioner for fluid-structure interaction in hemodynamics

NASA Astrophysics Data System (ADS)

Deparis, Simone; Forti, Davide; Grandperrin, Gwenol; Quarteroni, Alfio

2016-12-01

Modeling Fluid-Structure Interaction (FSI) in the vascular system is mandatory to reliably compute mechanical indicators in vessels undergoing large deformations. In order to cope with the computational complexity of the coupled 3D FSI problem after discretizations in space and time, a parallel solution is often mandatory. In this paper we propose a new block parallel preconditioner for the coupled linearized FSI system obtained after space and time discretization. We name it FaCSI to indicate that it exploits the Factorized form of the linearized FSI matrix, the use of static Condensation to formally eliminate the interface degrees of freedom of the fluid equations, and the use of a SIMPLE preconditioner for saddle-point problems. FaCSI is built upon a block Gauss-Seidel factorization of the FSI Jacobian matrix and it uses ad-hoc preconditioners for each physical component of the coupled problem, namely the fluid, the structure and the geometry. In the fluid subproblem, after operating static condensation of the interface fluid variables, we use a SIMPLE preconditioner on the reduced fluid matrix. Moreover, to efficiently deal with a large number of processes, FaCSI exploits efficient single field preconditioners, e.g., based on domain decomposition or the multigrid method. We measure the parallel performances of FaCSI on a benchmark cylindrical geometry and on a problem of physiological interest, namely the blood flow through a patient-specific femoropopliteal bypass. We analyze the dependence of the number of linear solver iterations on the cores count (scalability of the preconditioner) and on the mesh size (optimality).

ML 3.0 smoothed aggregation user's guide.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sala, Marzio; Hu, Jonathan Joseph; Tuminaro, Raymond Stephen

2004-05-01

ML is a multigrid preconditioning package intended to solve linear systems of equations Az = b where A is a user supplied n x n sparse matrix, b is a user supplied vector of length n and x is a vector of length n to be computed. ML should be used on large sparse linear systems arising from partial differential equation (PDE) discretizations. While technically any linear system can be considered, ML should be used on linear systems that correspond to things that work well with multigrid methods (e.g. elliptic PDEs). ML can be used as a stand-alone package ormore » to generate preconditioners for a traditional iterative solver package (e.g. Krylov methods). We have supplied support for working with the AZTEC 2.1 and AZTECOO iterative package [15]. However, other solvers can be used by supplying a few functions. This document describes one specific algebraic multigrid approach: smoothed aggregation. This approach is used within several specialized multigrid methods: one for the eddy current formulation for Maxwell's equations, and a multilevel and domain decomposition method for symmetric and non-symmetric systems of equations (like elliptic equations, or compressible and incompressible fluid dynamics problems). Other methods exist within ML but are not described in this document. Examples are given illustrating the problem definition and exercising multigrid options.« less

ML 3.1 smoothed aggregation user's guide.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sala, Marzio; Hu, Jonathan Joseph; Tuminaro, Raymond Stephen

2004-10-01

ML is a multigrid preconditioning package intended to solve linear systems of equations Ax = b where A is a user supplied n x n sparse matrix, b is a user supplied vector of length n and x is a vector of length n to be computed. ML should be used on large sparse linear systems arising from partial differential equation (PDE) discretizations. While technically any linear system can be considered, ML should be used on linear systems that correspond to things that work well with multigrid methods (e.g. elliptic PDEs). ML can be used as a stand-alone package ormore » to generate preconditioners for a traditional iterative solver package (e.g. Krylov methods). We have supplied support for working with the Aztec 2.1 and AztecOO iterative package [16]. However, other solvers can be used by supplying a few functions. This document describes one specific algebraic multigrid approach: smoothed aggregation. This approach is used within several specialized multigrid methods: one for the eddy current formulation for Maxwell's equations, and a multilevel and domain decomposition method for symmetric and nonsymmetric systems of equations (like elliptic equations, or compressible and incompressible fluid dynamics problems). Other methods exist within ML but are not described in this document. Examples are given illustrating the problem definition and exercising multigrid options.« less

Efficient solvers for coupled models in respiratory mechanics.

PubMed

Verdugo, Francesc; Roth, Christian J; Yoshihara, Lena; Wall, Wolfgang A

2017-02-01

We present efficient preconditioners for one of the most physiologically relevant pulmonary models currently available. Our underlying motivation is to enable the efficient simulation of such a lung model on high-performance computing platforms in order to assess mechanical ventilation strategies and contributing to design more protective patient-specific ventilation treatments. The system of linear equations to be solved using the proposed preconditioners is essentially the monolithic system arising in fluid-structure interaction (FSI) extended by additional algebraic constraints. The introduction of these constraints leads to a saddle point problem that cannot be solved with usual FSI preconditioners available in the literature. The key ingredient in this work is to use the idea of the semi-implicit method for pressure-linked equations (SIMPLE) for getting rid of the saddle point structure, resulting in a standard FSI problem that can be treated with available techniques. The numerical examples show that the resulting preconditioners approach the optimal performance of multigrid methods, even though the lung model is a complex multiphysics problem. Moreover, the preconditioners are robust enough to deal with physiologically relevant simulations involving complex real-world patient-specific lung geometries. The same approach is applicable to other challenging biomedical applications where coupling between flow and tissue deformations is modeled with additional algebraic constraints. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Convergence Acceleration of Runge-Kutta Schemes for Solving the Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Swanson, Roy C., Jr.; Turkel, Eli; Rossow, C.-C.

2007-01-01

The convergence of a Runge-Kutta (RK) scheme with multigrid is accelerated by preconditioning with a fully implicit operator. With the extended stability of the Runge-Kutta scheme, CFL numbers as high as 1000 can be used. The implicit preconditioner addresses the stiffness in the discrete equations associated with stretched meshes. This RK/implicit scheme is used as a smoother for multigrid. Fourier analysis is applied to determine damping properties. Numerical dissipation operators based on the Roe scheme, a matrix dissipation, and the CUSP scheme are considered in evaluating the RK/implicit scheme. In addition, the effect of the number of RK stages is examined. Both the numerical and computational efficiency of the scheme with the different dissipation operators are discussed. The RK/implicit scheme is used to solve the two-dimensional (2-D) and three-dimensional (3-D) compressible, Reynolds-averaged Navier-Stokes equations. Turbulent flows over an airfoil and wing at subsonic and transonic conditions are computed. The effects of the cell aspect ratio on convergence are investigated for Reynolds numbers between 5:7 x 10(exp 6) and 100 x 10(exp 6). It is demonstrated that the implicit preconditioner can reduce the computational time of a well-tuned standard RK scheme by a factor between four and ten.

Numerical Methods for Forward and Inverse Problems in Discontinuous Media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chartier, Timothy P.

The research emphasis under this grant's funding is in the area of algebraic multigrid methods. The research has two main branches: 1) exploring interdisciplinary applications in which algebraic multigrid can make an impact and 2) extending the scope of algebraic multigrid methods with algorithmic improvements that are based in strong analysis.The work in interdisciplinary applications falls primarily in the field of biomedical imaging. Work under this grant demonstrated the effectiveness and robustness of multigrid for solving linear systems that result from highly heterogeneous finite element method models of the human head. The results in this work also give promise tomore » medical advances possible with software that may be developed. Research to extend the scope of algebraic multigrid has been focused in several areas. In collaboration with researchers at the University of Colorado, Lawrence Livermore National Laboratory, and Los Alamos National Laboratory, the PI developed an adaptive multigrid with subcycling via complementary grids. This method has very cheap computing costs per iterate and is showing promise as a preconditioner for conjugate gradient. Recent work with Los Alamos National Laboratory concentrates on developing algorithms that take advantage of the recent advances in adaptive multigrid research. The results of the various efforts in this research could ultimately have direct use and impact to researchers for a wide variety of applications, including, astrophysics, neuroscience, contaminant transport in porous media, bi-domain heart modeling, modeling of tumor growth, and flow in heterogeneous porous media. This work has already led to basic advances in computational mathematics and numerical linear algebra and will continue to do so into the future.« less

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.

Layer-oriented multigrid wavefront reconstruction algorithms for multi-conjugate adaptive optics

NASA Astrophysics Data System (ADS)

Gilles, Luc; Ellerbroek, Brent L.; Vogel, Curtis R.

2003-02-01

Multi-conjugate adaptive optics (MCAO) systems with 104-105 degrees of freedom have been proposed for future giant telescopes. Using standard matrix methods to compute, optimize, and implement wavefront control algorithms for these systems is impractical, since the number of calculations required to compute and apply the reconstruction matrix scales respectively with the cube and the square of the number of AO degrees of freedom. In this paper, we develop an iterative sparse matrix implementation of minimum variance wavefront reconstruction for telescope diameters up to 32m with more than 104 actuators. The basic approach is the preconditioned conjugate gradient method, using a multigrid preconditioner incorporating a layer-oriented (block) symmetric Gauss-Seidel iterative smoothing operator. We present open-loop numerical simulation results to illustrate algorithm convergence.

Performance of a parallel algebraic multilevel preconditioner for stabilized finite element semiconductor device modeling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lin, Paul T.; Shadid, John N.; Sala, Marzio

In this study results are presented for the large-scale parallel performance of an algebraic multilevel preconditioner for solution of the drift-diffusion model for semiconductor devices. The preconditioner is the key numerical procedure determining the robustness, efficiency and scalability of the fully-coupled Newton-Krylov based, nonlinear solution method that is employed for this system of equations. The coupled system is comprised of a source term dominated Poisson equation for the electric potential, and two convection-diffusion-reaction type equations for the electron and hole concentration. The governing PDEs are discretized in space by a stabilized finite element method. Solution of the discrete system ismore » obtained through a fully-implicit time integrator, a fully-coupled Newton-based nonlinear solver, and a restarted GMRES Krylov linear system solver. The algebraic multilevel preconditioner is based on an aggressive coarsening graph partitioning of the nonzero block structure of the Jacobian matrix. Representative performance results are presented for various choices of multigrid V-cycles and W-cycles and parameter variations for smoothers based on incomplete factorizations. Parallel scalability results are presented for solution of up to 10{sup 8} unknowns on 4096 processors of a Cray XT3/4 and an IBM POWER eServer system.« less

Construction, classification and parametrization of complex Hadamard matrices

NASA Astrophysics Data System (ADS)

Szöllősi, Ferenc

To improve the design of nuclear systems, high-fidelity neutron fluxes are required. Leadership-class machines provide platforms on which very large problems can be solved. Computing such fluxes efficiently requires numerical methods with good convergence properties and algorithms that can scale to hundreds of thousands of cores. Many 3-D deterministic transport codes are decomposable in space and angle only, limiting them to tens of thousands of cores. Most codes rely on methods such as Gauss Seidel for fixed source problems and power iteration for eigenvalue problems, which can be slow to converge for challenging problems like those with highly scattering materials or high dominance ratios. Three methods have been added to the 3-D SN transport code Denovo that are designed to improve convergence and enable the full use of cutting-edge computers. The first is a multigroup Krylov solver that converges more quickly than Gauss Seidel and parallelizes the code in energy such that Denovo can use hundreds of thousand of cores effectively. The second is Rayleigh quotient iteration (RQI), an old method applied in a new context. This eigenvalue solver finds the dominant eigenvalue in a mathematically optimal way and should converge in fewer iterations than power iteration. RQI creates energy-block-dense equations that the new Krylov solver treats efficiently. However, RQI can have convergence problems because it creates poorly conditioned systems. This can be overcome with preconditioning. The third method is a multigrid-in-energy preconditioner. The preconditioner takes advantage of the new energy decomposition because the grids are in energy rather than space or angle. The preconditioner greatly reduces iteration count for many problem types and scales well in energy. It also allows RQI to be successful for problems it could not solve otherwise. The methods added to Denovo accomplish the goals of this work. They converge in fewer iterations than traditional methods and enable the use of hundreds of thousands of cores. Each method can be used individually, with the multigroup Krylov solver and multigrid-in-energy preconditioner being particularly successful on their own. The largest benefit, though, comes from using these methods in concert.

The numerical solution of the Helmholtz equation for wave propagation problems in underwater acoustics

NASA Technical Reports Server (NTRS)

Bayliss, A.; Goldstein, C. I.; Turkel, E.

1984-01-01

The Helmholtz Equation (-delta-K(2)n(2))u=0 with a variable index of refraction, n, and a suitable radiation condition at infinity serves as a model for a wide variety of wave propagation problems. A numerical algorithm was developed and a computer code implemented that can effectively solve this equation in the intermediate frequency range. The equation is discretized using the finite element method, thus allowing for the modeling of complicated geometrices (including interfaces) and complicated boundary conditions. A global radiation boundary condition is imposed at the far field boundary that is exact for an arbitrary number of propagating modes. The resulting large, non-selfadjoint system of linear equations with indefinite symmetric part is solved using the preconditioned conjugate gradient method applied to the normal equations. A new preconditioner is developed based on the multigrid method. This preconditioner is vectorizable and is extremely effective over a wide range of frequencies provided the number of grid levels is reduced for large frequencies. A heuristic argument is given that indicates the superior convergence properties of this preconditioner.

A Note on Substructuring Preconditioning for Nonconforming Finite Element Approximations of Second Order Elliptic Problems

NASA Technical Reports Server (NTRS)

Maliassov, Serguei

1996-01-01

In this paper an algebraic substructuring preconditioner is considered for nonconforming finite element approximations of second order elliptic problems in 3D domains with a piecewise constant diffusion coefficient. Using a substructuring idea and a block Gauss elimination, part of the unknowns is eliminated and the Schur complement obtained is preconditioned by a spectrally equivalent very sparse matrix. In the case of quasiuniform tetrahedral mesh an appropriate algebraic multigrid solver can be used to solve the problem with this matrix. Explicit estimates of condition numbers and implementation algorithms are established for the constructed preconditioner. It is shown that the condition number of the preconditioned matrix does not depend on either the mesh step size or the jump of the coefficient. Finally, numerical experiments are presented to illustrate the theory being developed.

Fully anisotropic 3-D EM modelling on a Lebedev grid with a multigrid pre-conditioner

NASA Astrophysics Data System (ADS)

Jaysaval, Piyoosh; Shantsev, Daniil V.; de la Kethulle de Ryhove, Sébastien; Bratteland, Tarjei

2016-12-01

We present a numerical algorithm for 3-D electromagnetic (EM) simulations in conducting media with general electric anisotropy. The algorithm is based on the finite-difference discretization of frequency-domain Maxwell's equations on a Lebedev grid, in which all components of the electric field are collocated but half a spatial step staggered with respect to the magnetic field components, which also are collocated. This leads to a system of linear equations that is solved using a stabilized biconjugate gradient method with a multigrid preconditioner. We validate the accuracy of the numerical results for layered and 3-D tilted transverse isotropic (TTI) earth models representing typical scenarios used in the marine controlled-source EM method. It is then demonstrated that not taking into account the full anisotropy of the conductivity tensor can lead to misleading inversion results. For synthetic data corresponding to a 3-D model with a TTI anticlinal structure, a standard vertical transverse isotropic (VTI) inversion is not able to image a resistor, while for a 3-D model with a TTI synclinal structure it produces a false resistive anomaly. However, if the VTI forward solver used in the inversion is replaced by the proposed TTI solver with perfect knowledge of the strike and dip of the dipping structures, the resulting resistivity images become consistent with the true models.

Geometric multigrid for an implicit-time immersed boundary method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guy, Robert D.; Philip, Bobby; Griffith, Boyce E.

2014-10-12

The immersed boundary (IB) method is an approach to fluid-structure interaction that uses Lagrangian variables to describe the deformations and resulting forces of the structure and Eulerian variables to describe the motion and forces of the fluid. Explicit time stepping schemes for the IB method require solvers only for Eulerian equations, for which fast Cartesian grid solution methods are available. Such methods are relatively straightforward to develop and are widely used in practice but often require very small time steps to maintain stability. Implicit-time IB methods permit the stable use of large time steps, but efficient implementations of such methodsmore » require significantly more complex solvers that effectively treat both Lagrangian and Eulerian variables simultaneously. Moreover, several different approaches to solving the coupled Lagrangian-Eulerian equations have been proposed, but a complete understanding of this problem is still emerging. This paper presents a geometric multigrid method for an implicit-time discretization of the IB equations. This multigrid scheme uses a generalization of box relaxation that is shown to handle problems in which the physical stiffness of the structure is very large. Numerical examples are provided to illustrate the effectiveness and efficiency of the algorithms described herein. Finally, these tests show that using multigrid as a preconditioner for a Krylov method yields improvements in both robustness and efficiency as compared to using multigrid as a solver. They also demonstrate that with a time step 100–1000 times larger than that permitted by an explicit IB method, the multigrid-preconditioned implicit IB method is approximately 50–200 times more efficient than the explicit method.« less

A fast and robust computational method for the ionization cross sections of the driven Schrödinger equation using an O (N) multigrid-based scheme

NASA Astrophysics Data System (ADS)

Cools, S.; Vanroose, W.

2016-03-01

This paper improves the convergence and robustness of a multigrid-based solver for the cross sections of the driven Schrödinger equation. Adding a Coupled Channel Correction Step (CCCS) after each multigrid (MG) V-cycle efficiently removes the errors that remain after the V-cycle sweep. The combined iterative solution scheme (MG-CCCS) is shown to feature significantly improved convergence rates over the classical MG method at energies where bound states dominate the solution, resulting in a fast and scalable solution method for the complex-valued Schrödinger break-up problem for any energy regime. The proposed solver displays optimal scaling; a solution is found in a time that is linear in the number of unknowns. The method is validated on a 2D Temkin-Poet model problem, and convergence results both as a solver and preconditioner are provided to support the O (N) scalability of the method. This paper extends the applicability of the complex contour approach for far field map computation (Cools et al. (2014) [10]).

Layout optimization with algebraic multigrid methods

NASA Technical Reports Server (NTRS)

Regler, Hans; Ruede, Ulrich

1993-01-01

Finding the optimal position for the individual cells (also called functional modules) on the chip surface is an important and difficult step in the design of integrated circuits. This paper deals with the problem of relative placement, that is the minimization of a quadratic functional with a large, sparse, positive definite system matrix. The basic optimization problem must be augmented by constraints to inhibit solutions where cells overlap. Besides classical iterative methods, based on conjugate gradients (CG), we show that algebraic multigrid methods (AMG) provide an interesting alternative. For moderately sized examples with about 10000 cells, AMG is already competitive with CG and is expected to be superior for larger problems. Besides the classical 'multiplicative' AMG algorithm where the levels are visited sequentially, we propose an 'additive' variant of AMG where levels may be treated in parallel and that is suitable as a preconditioner in the CG algorithm.

Three-dimensional forward modeling of DC resistivity using the aggregation-based algebraic multigrid method

NASA Astrophysics Data System (ADS)

Chen, Hui; Deng, Ju-Zhi; Yin, Min; Yin, Chang-Chun; Tang, Wen-Wu

2017-03-01

To speed up three-dimensional (3D) DC resistivity modeling, we present a new multigrid method, the aggregation-based algebraic multigrid method (AGMG). We first discretize the differential equation of the secondary potential field with mixed boundary conditions by using a seven-point finite-difference method to obtain a large sparse system of linear equations. Then, we introduce the theory behind the pairwise aggregation algorithms for AGMG and use the conjugate-gradient method with the V-cycle AGMG preconditioner (AGMG-CG) to solve the linear equations. We use typical geoelectrical models to test the proposed AGMG-CG method and compare the results with analytical solutions and the 3DDCXH algorithm for 3D DC modeling (3DDCXH). In addition, we apply the AGMG-CG method to different grid sizes and geoelectrical models and compare it to different iterative methods, such as ILU-BICGSTAB, ILU-GCR, and SSOR-CG. The AGMG-CG method yields nearly linearly decreasing errors, whereas the number of iterations increases slowly with increasing grid size. The AGMG-CG method is precise and converges fast, and thus can improve the computational efficiency in forward modeling of three-dimensional DC resistivity.

Performance Models for the Spike Banded Linear System Solver

DOE PAGES

Manguoglu, Murat; Saied, Faisal; Sameh, Ahmed; ...

2011-01-01

With availability of large-scale parallel platforms comprised of tens-of-thousands of processors and beyond, there is significant impetus for the development of scalable parallel sparse linear system solvers and preconditioners. An integral part of this design process is the development of performance models capable of predicting performance and providing accurate cost models for the solvers and preconditioners. There has been some work in the past on characterizing performance of the iterative solvers themselves. In this paper, we investigate the problem of characterizing performance and scalability of banded preconditioners. Recent work has demonstrated the superior convergence properties and robustness of banded preconditioners,more » compared to state-of-the-art ILU family of preconditioners as well as algebraic multigrid preconditioners. Furthermore, when used in conjunction with efficient banded solvers, banded preconditioners are capable of significantly faster time-to-solution. Our banded solver, the Truncated Spike algorithm is specifically designed for parallel performance and tolerance to deep memory hierarchies. Its regular structure is also highly amenable to accurate performance characterization. Using these characteristics, we derive the following results in this paper: (i) we develop parallel formulations of the Truncated Spike solver, (ii) we develop a highly accurate pseudo-analytical parallel performance model for our solver, (iii) we show excellent predication capabilities of our model – based on which we argue the high scalability of our solver. Our pseudo-analytical performance model is based on analytical performance characterization of each phase of our solver. These analytical models are then parameterized using actual runtime information on target platforms. An important consequence of our performance models is that they reveal underlying performance bottlenecks in both serial and parallel formulations. All of our results are validated on diverse heterogeneous multiclusters – platforms for which performance prediction is particularly challenging. Finally, we provide predict the scalability of the Spike algorithm using up to 65,536 cores with our model. In this paper we extend the results presented in the Ninth International Symposium on Parallel and Distributed Computing.« less

Algebraic multigrid preconditioners for two-phase flow in porous media with phase transitions

NASA Astrophysics Data System (ADS)

Bui, Quan M.; Wang, Lu; Osei-Kuffuor, Daniel

2018-04-01

Multiphase flow is a critical process in a wide range of applications, including oil and gas recovery, carbon sequestration, and contaminant remediation. Numerical simulation of multiphase flow requires solving of a large, sparse linear system resulting from the discretization of the partial differential equations modeling the flow. In the case of multiphase multicomponent flow with miscible effect, this is a very challenging task. The problem becomes even more difficult if phase transitions are taken into account. A new approach to handle phase transitions is to formulate the system as a nonlinear complementarity problem (NCP). Unlike in the primary variable switching technique, the set of primary variables in this approach is fixed even when there is phase transition. Not only does this improve the robustness of the nonlinear solver, it opens up the possibility to use multigrid methods to solve the resulting linear system. The disadvantage of the complementarity approach, however, is that when a phase disappears, the linear system has the structure of a saddle point problem and becomes indefinite, and current algebraic multigrid (AMG) algorithms cannot be applied directly. In this study, we explore the effectiveness of a new multilevel strategy, based on the multigrid reduction technique, to deal with problems of this type. We demonstrate the effectiveness of the method through numerical results for the case of two-phase, two-component flow with phase appearance/disappearance. We also show that the strategy is efficient and scales optimally with problem size.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Srinath Vadlamani; Scott Kruger; Travis Austin

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.more » 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.« less

Preconditioned conjugate gradient wave-front reconstructors for multiconjugate adaptive optics

NASA Astrophysics Data System (ADS)

Gilles, Luc; Ellerbroek, Brent L.; Vogel, Curtis R.

2003-09-01

Multiconjugate adaptive optics (MCAO) systems with 104-105 degrees of freedom have been proposed for future giant telescopes. Using standard matrix methods to compute, optimize, and implement wave-front control algorithms for these systems is impractical, since the number of calculations required to compute and apply the reconstruction matrix scales respectively with the cube and the square of the number of adaptive optics degrees of freedom. We develop scalable open-loop iterative sparse matrix implementations of minimum variance wave-front reconstruction for telescope diameters up to 32 m with more than 104 actuators. The basic approach is the preconditioned conjugate gradient method with an efficient preconditioner, whose block structure is defined by the atmospheric turbulent layers very much like the layer-oriented MCAO algorithms of current interest. Two cost-effective preconditioners are investigated: a multigrid solver and a simpler block symmetric Gauss-Seidel (BSGS) sweep. Both options require off-line sparse Cholesky factorizations of the diagonal blocks of the matrix system. The cost to precompute these factors scales approximately as the three-halves power of the number of estimated phase grid points per atmospheric layer, and their average update rate is typically of the order of 10-2 Hz, i.e., 4-5 orders of magnitude lower than the typical 103 Hz temporal sampling rate. All other computations scale almost linearly with the total number of estimated phase grid points. We present numerical simulation results to illustrate algorithm convergence. Convergence rates of both preconditioners are similar, regardless of measurement noise level, indicating that the layer-oriented BSGS sweep is as effective as the more elaborated multiresolution preconditioner.

Implicit adaptive mesh refinement for 2D reduced resistive magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Philip, Bobby; Chacón, Luis; Pernice, Michael

2008-10-01

An implicit structured adaptive mesh refinement (SAMR) solver for 2D reduced magnetohydrodynamics (MHD) is described. The time-implicit discretization is able to step over fast normal modes, while the spatial adaptivity resolves thin, dynamically evolving features. A Jacobian-free Newton-Krylov method is used for the nonlinear solver engine. For preconditioning, we have extended the optimal "physics-based" approach developed in [L. Chacón, D.A. Knoll, J.M. Finn, An implicit, nonlinear reduced resistive MHD solver, J. Comput. Phys. 178 (2002) 15-36] (which employed multigrid solver technology in the preconditioner for scalability) to SAMR grids using the well-known Fast Adaptive Composite grid (FAC) method [S. McCormick, Multilevel Adaptive Methods for Partial Differential Equations, SIAM, Philadelphia, PA, 1989]. A grid convergence study demonstrates that the solver performance is independent of the number of grid levels and only depends on the finest resolution considered, and that it scales well with grid refinement. The study of error generation and propagation in our SAMR implementation demonstrates that high-order (cubic) interpolation during regridding, combined with a robustly damping second-order temporal scheme such as BDF2, is required to minimize impact of grid errors at coarse-fine interfaces on the overall error of the computation for this MHD application. We also demonstrate that our implementation features the desired property that the overall numerical error is dependent only on the finest resolution level considered, and not on the base-grid resolution or on the number of refinement levels present during the simulation. We demonstrate the effectiveness of the tool on several challenging problems.

Preconditioned conjugate gradient wave-front reconstructors for multiconjugate adaptive optics.

PubMed

Gilles, Luc; Ellerbroek, Brent L; Vogel, Curtis R

2003-09-10

Multiconjugate adaptive optics (MCAO) systems with 10(4)-10(5) degrees of freedom have been proposed for future giant telescopes. Using standard matrix methods to compute, optimize, and implement wavefront control algorithms for these systems is impractical, since the number of calculations required to compute and apply the reconstruction matrix scales respectively with the cube and the square of the number of adaptive optics degrees of freedom. We develop scalable open-loop iterative sparse matrix implementations of minimum variance wave-front reconstruction for telescope diameters up to 32 m with more than 10(4) actuators. The basic approach is the preconditioned conjugate gradient method with an efficient preconditioner, whose block structure is defined by the atmospheric turbulent layers very much like the layer-oriented MCAO algorithms of current interest. Two cost-effective preconditioners are investigated: a multigrid solver and a simpler block symmetric Gauss-Seidel (BSGS) sweep. Both options require off-line sparse Cholesky factorizations of the diagonal blocks of the matrix system. The cost to precompute these factors scales approximately as the three-halves power of the number of estimated phase grid points per atmospheric layer, and their average update rate is typically of the order of 10(-2) Hz, i.e., 4-5 orders of magnitude lower than the typical 10(3) Hz temporal sampling rate. All other computations scale almost linearly with the total number of estimated phase grid points. We present numerical simulation results to illustrate algorithm convergence. Convergence rates of both preconditioners are similar, regardless of measurement noise level, indicating that the layer-oriented BSGS sweep is as effective as the more elaborated multiresolution preconditioner.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lin, Paul T.; Shadid, John N.; Tsuji, Paul H.

Here, this study explores the performance and scaling of a GMRES Krylov method employed as a smoother for an algebraic multigrid (AMG) preconditioned Newton- Krylov solution approach applied to a fully-implicit variational multiscale (VMS) nite element (FE) resistive magnetohydrodynamics (MHD) formulation. In this context a Newton iteration is used for the nonlinear system and a Krylov (GMRES) method is employed for the linear subsystems. The efficiency of this approach is critically dependent on the scalability and performance of the AMG preconditioner for the linear solutions and the performance of the smoothers play a critical role. Krylov smoothers are considered inmore » an attempt to reduce the time and memory requirements of existing robust smoothers based on additive Schwarz domain decomposition (DD) with incomplete LU factorization solves on each subdomain. Three time dependent resistive MHD test cases are considered to evaluate the method. The results demonstrate that the GMRES smoother can be faster due to a decrease in the preconditioner setup time and a reduction in outer GMRESR solver iterations, and requires less memory (typically 35% less memory for global GMRES smoother) than the DD ILU smoother.« less

Array-based, parallel hierarchical mesh refinement algorithms for unstructured meshes

DOE PAGES

Ray, Navamita; Grindeanu, Iulian; Zhao, Xinglin; ...

2016-08-18

In this paper, we describe an array-based hierarchical mesh refinement capability through uniform refinement of unstructured meshes for efficient solution of PDE's using finite element methods and multigrid solvers. A multi-degree, multi-dimensional and multi-level framework is designed to generate the nested hierarchies from an initial coarse mesh that can be used for a variety of purposes such as in multigrid solvers/preconditioners, to do solution convergence and verification studies and to improve overall parallel efficiency by decreasing I/O bandwidth requirements (by loading smaller meshes and in memory refinement). We also describe a high-order boundary reconstruction capability that can be used tomore » project the new points after refinement using high-order approximations instead of linear projection in order to minimize and provide more control on geometrical errors introduced by curved boundaries.The capability is developed under the parallel unstructured mesh framework "Mesh Oriented dAtaBase" (MOAB Tautges et al. (2004)). We describe the underlying data structures and algorithms to generate such hierarchies in parallel and present numerical results for computational efficiency and effect on mesh quality. Furthermore, we also present results to demonstrate the applicability of the developed capability to study convergence properties of different point projection schemes for various mesh hierarchies and to a multigrid finite-element solver for elliptic problems.« less

Efficient solution of the simplified P N equations

DOE PAGES

Hamilton, Steven P.; Evans, Thomas M.

2014-12-23

We show new solver strategies for the multigroup SPN equations for nuclear reactor analysis. By forming the complete matrix over space, moments, and energy a robust set of solution strategies may be applied. Moreover, power iteration, shifted power iteration, Rayleigh quotient iteration, Arnoldi's method, and a generalized Davidson method, each using algebraic and physics-based multigrid preconditioners, have been compared on C5G7 MOX test problem as well as an operational PWR model. These results show that the most ecient approach is the generalized Davidson method, that is 30-40 times faster than traditional power iteration and 6-10 times faster than Arnoldi's method.

Fast solution of elliptic partial differential equations using linear combinations of plane waves.

PubMed

Pérez-Jordá, José M

2016-02-01

Given an arbitrary elliptic partial differential equation (PDE), a procedure for obtaining its solution is proposed based on the method of Ritz: the solution is written as a linear combination of plane waves and the coefficients are obtained by variational minimization. The PDE to be solved is cast as a system of linear equations Ax=b, where the matrix A is not sparse, which prevents the straightforward application of standard iterative methods in order to solve it. This sparseness problem can be circumvented by means of a recursive bisection approach based on the fast Fourier transform, which makes it possible to implement fast versions of some stationary iterative methods (such as Gauss-Seidel) consuming O(NlogN) memory and executing an iteration in O(Nlog(2)N) time, N being the number of plane waves used. In a similar way, fast versions of Krylov subspace methods and multigrid methods can also be implemented. These procedures are tested on Poisson's equation expressed in adaptive coordinates. It is found that the best results are obtained with the GMRES method using a multigrid preconditioner with Gauss-Seidel relaxation steps.

Eigenvalue Solvers for Modeling Nuclear Reactors on Leadership Class Machines

DOE PAGES

Slaybaugh, R. N.; Ramirez-Zweiger, M.; Pandya, Tara; ...

2018-02-20

In this paper, three complementary methods have been implemented in the code Denovo that accelerate neutral particle transport calculations with methods that use leadership-class computers fully and effectively: a multigroup block (MG) Krylov solver, a Rayleigh quotient iteration (RQI) eigenvalue solver, and a multigrid in energy (MGE) preconditioner. The MG Krylov solver converges more quickly than Gauss Seidel and enables energy decomposition such that Denovo can scale to hundreds of thousands of cores. RQI should converge in fewer iterations than power iteration (PI) for large and challenging problems. RQI creates shifted systems that would not be tractable without the MGmore » Krylov solver. It also creates ill-conditioned matrices. The MGE preconditioner reduces iteration count significantly when used with RQI and takes advantage of the new energy decomposition such that it can scale efficiently. Each individual method has been described before, but this is the first time they have been demonstrated to work together effectively. The combination of solvers enables the RQI eigenvalue solver to work better than the other available solvers for large reactors problems on leadership-class machines. Using these methods together, RQI converged in fewer iterations and in less time than PI for a full pressurized water reactor core. These solvers also performed better than an Arnoldi eigenvalue solver for a reactor benchmark problem when energy decomposition is needed. The MG Krylov, MGE preconditioner, and RQI solver combination also scales well in energy. Finally, this solver set is a strong choice for very large and challenging problems.« less

Eigenvalue Solvers for Modeling Nuclear Reactors on Leadership Class Machines

DOE Office of Scientific and Technical Information (OSTI.GOV)

Slaybaugh, R. N.; Ramirez-Zweiger, M.; Pandya, Tara

In this paper, three complementary methods have been implemented in the code Denovo that accelerate neutral particle transport calculations with methods that use leadership-class computers fully and effectively: a multigroup block (MG) Krylov solver, a Rayleigh quotient iteration (RQI) eigenvalue solver, and a multigrid in energy (MGE) preconditioner. The MG Krylov solver converges more quickly than Gauss Seidel and enables energy decomposition such that Denovo can scale to hundreds of thousands of cores. RQI should converge in fewer iterations than power iteration (PI) for large and challenging problems. RQI creates shifted systems that would not be tractable without the MGmore » Krylov solver. It also creates ill-conditioned matrices. The MGE preconditioner reduces iteration count significantly when used with RQI and takes advantage of the new energy decomposition such that it can scale efficiently. Each individual method has been described before, but this is the first time they have been demonstrated to work together effectively. The combination of solvers enables the RQI eigenvalue solver to work better than the other available solvers for large reactors problems on leadership-class machines. Using these methods together, RQI converged in fewer iterations and in less time than PI for a full pressurized water reactor core. These solvers also performed better than an Arnoldi eigenvalue solver for a reactor benchmark problem when energy decomposition is needed. The MG Krylov, MGE preconditioner, and RQI solver combination also scales well in energy. Finally, this solver set is a strong choice for very large and challenging problems.« less

Numerical Solution of the Gyrokinetic Poisson Equation in TEMPEST

NASA Astrophysics Data System (ADS)

Dorr, Milo; Cohen, Bruce; Cohen, Ronald; Dimits, Andris; Hittinger, Jeffrey; Kerbel, Gary; Nevins, William; Rognlien, Thomas; Umansky, Maxim; Xiong, Andrew; Xu, Xueqiao

2006-10-01

The gyrokinetic Poisson (GKP) model in the TEMPEST continuum gyrokinetic edge plasma code yields the electrostatic potential due to the charge density of electrons and an arbitrary number of ion species including the effects of gyroaveraging in the limit kρ1. The TEMPEST equations are integrated as a differential algebraic system involving a nonlinear system solve via Newton-Krylov iteration. The GKP preconditioner block is inverted using a multigrid preconditioned conjugate gradient (CG) algorithm. Electrons are treated as kinetic or adiabatic. The Boltzmann relation in the adiabatic option employs flux surface averaging to maintain neutrality within field lines and is solved self-consistently with the GKP equation. A decomposition procedure circumvents the near singularity of the GKP Jacobian block that otherwise degrades CG convergence.

Anatomically accurate high resolution modeling of human whole heart electromechanics: A strongly scalable algebraic multigrid solver method for nonlinear deformation

NASA Astrophysics Data System (ADS)

Augustin, Christoph M.; Neic, Aurel; Liebmann, Manfred; Prassl, Anton J.; Niederer, Steven A.; Haase, Gundolf; Plank, Gernot

2016-01-01

Electromechanical (EM) models of the heart have been used successfully to study fundamental mechanisms underlying a heart beat in health and disease. However, in all modeling studies reported so far numerous simplifications were made in terms of representing biophysical details of cellular function and its heterogeneity, gross anatomy and tissue microstructure, as well as the bidirectional coupling between electrophysiology (EP) and tissue distension. One limiting factor is the employed spatial discretization methods which are not sufficiently flexible to accommodate complex geometries or resolve heterogeneities, but, even more importantly, the limited efficiency of the prevailing solver techniques which is not sufficiently scalable to deal with the incurring increase in degrees of freedom (DOF) when modeling cardiac electromechanics at high spatio-temporal resolution. This study reports on the development of a novel methodology for solving the nonlinear equation of finite elasticity using human whole organ models of cardiac electromechanics, discretized at a high para-cellular resolution. Three patient-specific, anatomically accurate, whole heart EM models were reconstructed from magnetic resonance (MR) scans at resolutions of 220 μm, 440 μm and 880 μm, yielding meshes of approximately 184.6, 24.4 and 3.7 million tetrahedral elements and 95.9, 13.2 and 2.1 million displacement DOF, respectively. The same mesh was used for discretizing the governing equations of both electrophysiology (EP) and nonlinear elasticity. A novel algebraic multigrid (AMG) preconditioner for an iterative Krylov solver was developed to deal with the resulting computational load. The AMG preconditioner was designed under the primary objective of achieving favorable strong scaling characteristics for both setup and solution runtimes, as this is key for exploiting current high performance computing hardware. Benchmark results using the 220 μm, 440 μm and 880 μm meshes demonstrate efficient scaling up to 1024, 4096 and 8192 compute cores which allowed the simulation of a single heart beat in 44.3, 87.8 and 235.3 minutes, respectively. The efficiency of the method allows fast simulation cycles without compromising anatomical or biophysical detail.

Anatomically accurate high resolution modeling of human whole heart electromechanics: A strongly scalable algebraic multigrid solver method for nonlinear deformation

PubMed Central

Augustin, Christoph M.; Neic, Aurel; Liebmann, Manfred; Prassl, Anton J.; Niederer, Steven A.; Haase, Gundolf; Plank, Gernot

2016-01-01

Electromechanical (EM) models of the heart have been used successfully to study fundamental mechanisms underlying a heart beat in health and disease. However, in all modeling studies reported so far numerous simplifications were made in terms of representing biophysical details of cellular function and its heterogeneity, gross anatomy and tissue microstructure, as well as the bidirectional coupling between electrophysiology (EP) and tissue distension. One limiting factor is the employed spatial discretization methods which are not sufficiently flexible to accommodate complex geometries or resolve heterogeneities, but, even more importantly, the limited efficiency of the prevailing solver techniques which are not sufficiently scalable to deal with the incurring increase in degrees of freedom (DOF) when modeling cardiac electromechanics at high spatio-temporal resolution. This study reports on the development of a novel methodology for solving the nonlinear equation of finite elasticity using human whole organ models of cardiac electromechanics, discretized at a high para-cellular resolution. Three patient-specific, anatomically accurate, whole heart EM models were reconstructed from magnetic resonance (MR) scans at resolutions of 220 μm, 440 μm and 880 μm, yielding meshes of approximately 184.6, 24.4 and 3.7 million tetrahedral elements and 95.9, 13.2 and 2.1 million displacement DOF, respectively. The same mesh was used for discretizing the governing equations of both electrophysiology (EP) and nonlinear elasticity. A novel algebraic multigrid (AMG) preconditioner for an iterative Krylov solver was developed to deal with the resulting computational load. The AMG preconditioner was designed under the primary objective of achieving favorable strong scaling characteristics for both setup and solution runtimes, as this is key for exploiting current high performance computing hardware. Benchmark results using the 220 μm, 440 μm and 880 μm meshes demonstrate efficient scaling up to 1024, 4096 and 8192 compute cores which allowed the simulation of a single heart beat in 44.3, 87.8 and 235.3 minutes, respectively. The efficiency of the method allows fast simulation cycles without compromising anatomical or biophysical detail. PMID:26819483

Large Scale, High Resolution, Mantle Dynamics Modeling

NASA Astrophysics Data System (ADS)

Geenen, T.; Berg, A. V.; Spakman, W.

2007-12-01

To model the geodynamic evolution of plate convergence, subduction and collision and to allow for a connection to various types of observational data, geophysical, geodetical and geological, we developed a 4D (space-time) numerical mantle convection code. The model is based on a spherical 3D Eulerian fem model, with quadratic elements, on top of which we constructed a 3D Lagrangian particle in cell(PIC) method. We use the PIC method to transport material properties and to incorporate a viscoelastic rheology. Since capturing small scale processes associated with localization phenomena require a high resolution, we spend a considerable effort on implementing solvers suitable to solve for models with over 100 million degrees of freedom. We implemented Additive Schwartz type ILU based methods in combination with a Krylov solver, GMRES. However we found that for problems with over 500 thousend degrees of freedom the convergence of the solver degraded severely. This observation is known from the literature [Saad, 2003] and results from the local character of the ILU preconditioner resulting in a poor approximation of the inverse of A for large A. The size of A for which ILU is no longer usable depends on the condition of A and on the amount of fill in allowed for the ILU preconditioner. We found that for our problems with over 5×105 degrees of freedom convergence became to slow to solve the system within an acceptable amount of walltime, one minute, even when allowing for considerable amount of fill in. We also implemented MUMPS and found good scaling results for problems up to 107 degrees of freedom for up to 32 CPU¡¯s. For problems with over 100 million degrees of freedom we implemented Algebraic Multigrid type methods (AMG) from the ML library [Sala, 2006]. Since multigrid methods are most effective for single parameter problems, we rebuild our model to use the SIMPLE method in the Stokes solver [Patankar, 1980]. We present scaling results from these solvers for 3D spherical models. We also applied the above mentioned method to a high resolution (~ 1 km) 2D mantle convection model with temperature, pressure and phase dependent rheology including several phase transitions. We focus on a model of a subducting lithospheric slab which is subject to strong folding at the bottom of the mantle's D" region which includes the postperovskite phase boundary. For a detailed description of this model we refer to poster [Mantel convection models of the D" region, U17] [Saad, 2003] Saad, Y. (2003). Iterative methods for sparse linear systems. [Sala, 2006] Sala. M (2006) An Object-Oriented Framework for the Development of Scalable Parallel Multilevel Preconditioners. ACM Transactions on Mathematical Software, 32 (3), 2006 [Patankar, 1980] Patankar, S. V.(1980) Numerical Heat Transfer and Fluid Flow, Hemisphere, Washington.

A scalable parallel black oil simulator on distributed memory parallel computers

NASA Astrophysics Data System (ADS)

Wang, Kun; Liu, Hui; Chen, Zhangxin

2015-11-01

This paper presents our work on developing a parallel black oil simulator for distributed memory computers based on our in-house parallel platform. The parallel simulator is designed to overcome the performance issues of common simulators that are implemented for personal computers and workstations. The finite difference method is applied to discretize the black oil model. In addition, some advanced techniques are employed to strengthen the robustness and parallel scalability of the simulator, including an inexact Newton method, matrix decoupling methods, and algebraic multigrid methods. A new multi-stage preconditioner is proposed to accelerate the solution of linear systems from the Newton methods. Numerical experiments show that our simulator is scalable and efficient, and is capable of simulating extremely large-scale black oil problems with tens of millions of grid blocks using thousands of MPI processes on parallel computers.

An algebraic multigrid method for Q2-Q1 mixed discretizations of the Navier-Stokes equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Prokopenko, Andrey; Tuminaro, Raymond S.

Algebraic multigrid (AMG) preconditioners are considered for discretized systems of partial differential equations (PDEs) where unknowns associated with different physical quantities are not necessarily co-located at mesh points. Speci cally, we investigate a Q 2-Q 1 mixed finite element discretization of the incompressible Navier-Stokes equations where the number of velocity nodes is much greater than the number of pressure nodes. Consequently, some velocity degrees-of-freedom (dofs) are defined at spatial locations where there are no corresponding pressure dofs. Thus, AMG approaches lever- aging this co-located structure are not applicable. This paper instead proposes an automatic AMG coarsening that mimics certain pressure/velocitymore » dof relationships of the Q 2-Q 1 discretization. The main idea is to first automatically define coarse pressures in a somewhat standard AMG fashion and then to carefully (but automatically) choose coarse velocity unknowns so that the spatial location relationship between pressure and velocity dofs resembles that on the nest grid. To define coefficients within the inter-grid transfers, an energy minimization AMG (EMIN-AMG) is utilized. EMIN-AMG is not tied to specific coarsening schemes and grid transfer sparsity patterns, and so it is applicable to the proposed coarsening. Numerical results highlighting solver performance are given on Stokes and incompressible Navier-Stokes problems.« less

Architecting the Finite Element Method Pipeline for the GPU.

PubMed

Fu, Zhisong; Lewis, T James; Kirby, Robert M; Whitaker, Ross T

2014-02-01

The finite element method (FEM) is a widely employed numerical technique for approximating the solution of partial differential equations (PDEs) in various science and engineering applications. Many of these applications benefit from fast execution of the FEM pipeline. One way to accelerate the FEM pipeline is by exploiting advances in modern computational hardware, such as the many-core streaming processors like the graphical processing unit (GPU). In this paper, we present the algorithms and data-structures necessary to move the entire FEM pipeline to the GPU. First we propose an efficient GPU-based algorithm to generate local element information and to assemble the global linear system associated with the FEM discretization of an elliptic PDE. To solve the corresponding linear system efficiently on the GPU, we implement a conjugate gradient method preconditioned with a geometry-informed algebraic multi-grid (AMG) method preconditioner. We propose a new fine-grained parallelism strategy, a corresponding multigrid cycling stage and efficient data mapping to the many-core architecture of GPU. Comparison of our on-GPU assembly versus a traditional serial implementation on the CPU achieves up to an 87 × speedup. Focusing on the linear system solver alone, we achieve a speedup of up to 51 × versus use of a comparable state-of-the-art serial CPU linear system solver. Furthermore, the method compares favorably with other GPU-based, sparse, linear solvers.

An algebraic multigrid method for Q2-Q1 mixed discretizations of the Navier-Stokes equations

DOE PAGES

Prokopenko, Andrey; Tuminaro, Raymond S.

2016-07-01

Algebraic multigrid (AMG) preconditioners are considered for discretized systems of partial differential equations (PDEs) where unknowns associated with different physical quantities are not necessarily co-located at mesh points. Speci cally, we investigate a Q 2-Q 1 mixed finite element discretization of the incompressible Navier-Stokes equations where the number of velocity nodes is much greater than the number of pressure nodes. Consequently, some velocity degrees-of-freedom (dofs) are defined at spatial locations where there are no corresponding pressure dofs. Thus, AMG approaches lever- aging this co-located structure are not applicable. This paper instead proposes an automatic AMG coarsening that mimics certain pressure/velocitymore » dof relationships of the Q 2-Q 1 discretization. The main idea is to first automatically define coarse pressures in a somewhat standard AMG fashion and then to carefully (but automatically) choose coarse velocity unknowns so that the spatial location relationship between pressure and velocity dofs resembles that on the nest grid. To define coefficients within the inter-grid transfers, an energy minimization AMG (EMIN-AMG) is utilized. EMIN-AMG is not tied to specific coarsening schemes and grid transfer sparsity patterns, and so it is applicable to the proposed coarsening. Numerical results highlighting solver performance are given on Stokes and incompressible Navier-Stokes problems.« less

SymPix: A Spherical Grid for Efficient Sampling of Rotationally Invariant Operators

NASA Astrophysics Data System (ADS)

Seljebotn, D. S.; Eriksen, H. K.

2016-02-01

We present SymPix, a special-purpose spherical grid optimized for efficiently sampling rotationally invariant linear operators. This grid is conceptually similar to the Gauss-Legendre (GL) grid, aligning sample points with iso-latitude rings located on Legendre polynomial zeros. Unlike the GL grid, however, the number of grid points per ring varies as a function of latitude, avoiding expensive oversampling near the poles and ensuring nearly equal sky area per grid point. The ratio between the number of grid points in two neighboring rings is required to be a low-order rational number (3, 2, 1, 4/3, 5/4, or 6/5) to maintain a high degree of symmetries. Our main motivation for this grid is to solve linear systems using multi-grid methods, and to construct efficient preconditioners through pixel-space sampling of the linear operator in question. As a benchmark and representative example, we compute a preconditioner for a linear system that involves the operator \\widehat{{\\boldsymbol{D}}}+{\\widehat{{\\boldsymbol{B}}}}T{{\\boldsymbol{N}}}-1\\widehat{{\\boldsymbol{B}}}, where \\widehat{{\\boldsymbol{B}}} and \\widehat{{\\boldsymbol{D}}} may be described as both local and rotationally invariant operators, and {\\boldsymbol{N}} is diagonal in the pixel domain. For a bandwidth limit of {{\\ell }}{max} = 3000, we find that our new SymPix implementation yields average speed-ups of 360 and 23 for {\\widehat{{\\boldsymbol{B}}}}T{{\\boldsymbol{N}}}-1\\widehat{{\\boldsymbol{B}}} and \\widehat{{\\boldsymbol{D}}}, respectively, compared with the previous state-of-the-art implementation.

On some variational acceleration techniques and related methods for local refinement

NASA Astrophysics Data System (ADS)

Teigland, Rune

1998-10-01

This paper shows that the well-known variational acceleration method described by Wachspress (E. Wachspress, Iterative Solution of Elliptic Systems and Applications to the Neutron Diffusion Equations of Reactor Physics, Prentice-Hall, Englewood Cliffs, NJ, 1966) and later generalized to multilevels (known as the additive correction multigrid method (B.R Huthchinson and G.D. Raithby, Numer. Heat Transf., 9, 511-537 (1986))) is similar to the FAC method of McCormick and Thomas (S.F McCormick and J.W. Thomas, Math. Comput., 46, 439-456 (1986)) and related multilevel methods. The performance of the method is demonstrated for some simple model problems using local refinement and suggestions for improving the performance of the method are given.

Multilevel acceleration of scattering-source iterations with application to electron transport

DOE PAGES

Drumm, Clif; Fan, Wesley

2017-08-18

Acceleration/preconditioning strategies available in the SCEPTRE radiation transport code are described. A flexible transport synthetic acceleration (TSA) algorithm that uses a low-order discrete-ordinates (S N) or spherical-harmonics (P N) solve to accelerate convergence of a high-order S N source-iteration (SI) solve is described. Convergence of the low-order solves can be further accelerated by applying off-the-shelf incomplete-factorization or algebraic-multigrid methods. Also available is an algorithm that uses a generalized minimum residual (GMRES) iterative method rather than SI for convergence, using a parallel sweep-based solver to build up a Krylov subspace. TSA has been applied as a preconditioner to accelerate the convergencemore » of the GMRES iterations. The methods are applied to several problems involving electron transport and problems with artificial cross sections with large scattering ratios. These methods were compared and evaluated by considering material discontinuities and scattering anisotropy. Observed accelerations obtained are highly problem dependent, but speedup factors around 10 have been observed in typical applications.« less

StagBL : A Scalable, Portable, High-Performance Discretization and Solver Layer for Geodynamic Simulation

NASA Astrophysics Data System (ADS)

Sanan, P.; Tackley, P. J.; Gerya, T.; Kaus, B. J. P.; May, D.

2017-12-01

StagBL is an open-source parallel solver and discretization library for geodynamic simulation,encapsulating and optimizing operations essential to staggered-grid finite volume Stokes flow solvers.It provides a parallel staggered-grid abstraction with a high-level interface in C and Fortran.On top of this abstraction, tools are available to define boundary conditions and interact with particle systems.Tools and examples to efficiently solve Stokes systems defined on the grid are provided in small (direct solver), medium (simple preconditioners), and large (block factorization and multigrid) model regimes.By working directly with leading application codes (StagYY, I3ELVIS, and LaMEM) and providing an API and examples to integrate with others, StagBL aims to become a community tool supplying scalable, portable, reproducible performance toward novel science in regional- and planet-scale geodynamics and planetary science.By implementing kernels used by many research groups beneath a uniform abstraction layer, the library will enable optimization for modern hardware, thus reducing community barriers to large- or extreme-scale parallel simulation on modern architectures. In particular, the library will include CPU-, Manycore-, and GPU-optimized variants of matrix-free operators and multigrid components.The common layer provides a framework upon which to introduce innovative new tools.StagBL will leverage p4est to provide distributed adaptive meshes, and incorporate a multigrid convergence analysis tool.These options, in addition to a wealth of solver options provided by an interface to PETSc, will make the most modern solution techniques available from a common interface. StagBL in turn provides a PETSc interface, DMStag, to its central staggered grid abstraction.We present public version 0.5 of StagBL, including preliminary integration with application codes and demonstrations with its own demonstration application, StagBLDemo. Central to StagBL is the notion of an uninterrupted pipeline from toy/teaching codes to high-performance, extreme-scale solves. StagBLDemo replicates the functionality of an advanced MATLAB-style regional geodynamics code, thus providing users with a concrete procedure to exceed the performance and scalability limitations of smaller-scale tools.

A Spectral Element Discretisation on Unstructured Triangle / Tetrahedral Meshes for Elastodynamics

NASA Astrophysics Data System (ADS)

May, Dave A.; Gabriel, Alice-A.

2017-04-01

The spectral element method (SEM) defined over quadrilateral and hexahedral element geometries has proven to be a fast, accurate and scalable approach to study wave propagation phenomena. In the context of regional scale seismology and or simulations incorporating finite earthquake sources, the geometric restrictions associated with hexahedral elements can limit the applicability of the classical quad./hex. SEM. Here we describe a continuous Galerkin spectral element discretisation defined over unstructured meshes composed of triangles (2D), or tetrahedra (3D). The method uses a stable, nodal basis constructed from PKD polynomials and thus retains the spectral accuracy and low dispersive properties of the classical SEM, in addition to the geometric versatility provided by unstructured simplex meshes. For the particular basis and quadrature rule we have adopted, the discretisation results in a mass matrix which is not diagonal, thereby mandating linear solvers be utilised. To that end, we have developed efficient solvers and preconditioners which are robust with respect to the polynomial order (p), and possess high arithmetic intensity. Furthermore, we also consider using implicit time integrators, together with a p-multigrid preconditioner to circumvent the CFL condition. Implicit time integrators become particularly relevant when considering solving problems on poor quality meshes, or meshes containing elements with a widely varying range of length scales - both of which frequently arise when meshing non-trivial geometries. We demonstrate the applicability of the new method by examining a number of two- and three-dimensional wave propagation scenarios. These scenarios serve to characterise the accuracy and cost of the new method. Lastly, we will assess the potential benefits of using implicit time integrators for regional scale wave propagation simulations.

Keeping it Together: Advanced algorithms and software for magma dynamics (and other coupled multi-physics problems)

NASA Astrophysics Data System (ADS)

Spiegelman, M.; Wilson, C. R.

2011-12-01

A quantitative theory of magma production and transport is essential for understanding the dynamics of magmatic plate boundaries, intra-plate volcanism and the geochemical evolution of the planet. It also provides one of the most challenging computational problems in solid Earth science, as it requires consistent coupling of fluid and solid mechanics together with the thermodynamics of melting and reactive flows. Considerable work on these problems over the past two decades shows that small changes in assumptions of coupling (e.g. the relationship between melt fraction and solid rheology), can have profound changes on the behavior of these systems which in turn affects critical computational choices such as discretizations, solvers and preconditioners. To make progress in exploring and understanding this physically rich system requires a computational framework that allows more flexible, high-level description of multi-physics problems as well as increased flexibility in composing efficient algorithms for solution of the full non-linear coupled system. Fortunately, recent advances in available computational libraries and algorithms provide a platform for implementing such a framework. We present results from a new model building system that leverages functionality from both the FEniCS project (www.fenicsproject.org) and PETSc libraries (www.mcs.anl.gov/petsc) along with a model independent options system and gui, Spud (amcg.ese.ic.ac.uk/Spud). Key features from FEniCS include fully unstructured FEM with a wide range of elements; a high-level language (ufl) and code generation compiler (FFC) for describing the weak forms of residuals and automatic differentiation for calculation of exact and approximate jacobians. The overall strategy is to monitor/calculate residuals and jacobians for the entire non-linear system of equations within a global non-linear solve based on PETSc's SNES routines. PETSc already provides a wide range of solvers and preconditioners, from parallel sparse direct to algebraic multigrid, that can be chosen at runtime. In particular, we make extensive use of PETSc's FieldSplit block preconditioners that allow us to use optimal solvers for subproblems (such as Stokes, or advection/diffusion of temperature) as preconditioners for the full problem. Thus these routines let us reuse effective solving recipes/splittings from previous experience while monitoring the convergence of the global problem. These techniques often yield quadratic (Newton like) convergence for the work of standard Picard schemes. We will illustrate this new framework with examples from the Magma Dynamic Demonstration suite (MADDs) of well understood magma dynamics benchmark problems including stokes flow in ridge geometries, magmatic solitary waves and shear-driven melt bands. While development of this system has been driven by magma dynamics, this framework is much more general and can be used for a wide range of PDE based multi-physics models.

Electrical Resistivity Tomography using a finite element based BFGS algorithm with algebraic multigrid preconditioning

NASA Astrophysics Data System (ADS)

Codd, A. L.; Gross, L.

2018-03-01

We present a new inversion method for Electrical Resistivity Tomography which, in contrast to established approaches, minimizes the cost function prior to finite element discretization for the unknown electric conductivity and electric potential. Minimization is performed with the Broyden-Fletcher-Goldfarb-Shanno method (BFGS) in an appropriate function space. BFGS is self-preconditioning and avoids construction of the dense Hessian which is the major obstacle to solving large 3-D problems using parallel computers. In addition to the forward problem predicting the measurement from the injected current, the so-called adjoint problem also needs to be solved. For this problem a virtual current is injected through the measurement electrodes and an adjoint electric potential is obtained. The magnitude of the injected virtual current is equal to the misfit at the measurement electrodes. This new approach has the advantage that the solution process of the optimization problem remains independent to the meshes used for discretization and allows for mesh adaptation during inversion. Computation time is reduced by using superposition of pole loads for the forward and adjoint problems. A smoothed aggregation algebraic multigrid (AMG) preconditioned conjugate gradient is applied to construct the potentials for a given electric conductivity estimate and for constructing a first level BFGS preconditioner. Through the additional reuse of AMG operators and coarse grid solvers inversion time for large 3-D problems can be reduced further. We apply our new inversion method to synthetic survey data created by the resistivity profile representing the characteristics of subsurface fluid injection. We further test it on data obtained from a 2-D surface electrode survey on Heron Island, a small tropical island off the east coast of central Queensland, Australia.

Final Report - Subcontract B623760

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bank, R.

2017-11-17

During my visit to LLNL during July 17{27, 2017, I worked on linear system solvers. The two level hierarchical solver that initiated our study was developed to solve linear systems arising from hp adaptive finite element calculations, and is implemented in the PLTMG software package, version 12. This preconditioner typically requires 3-20% of the space used by the stiffness matrix for higher order elements. It has multigrid like convergence rates for a wide variety of PDEs (self-adjoint positive de nite elliptic equations, convection dominated convection-diffusion equations, and highly indefinite Helmholtz equations, among others). The convergence rate is not independent ofmore » the polynomial degree p as p ! 1, but but remains strong for p 9, which is the highest polynomial degree allowed in PLTMG, due to limitations of the numerical quadrature rules implemented in the software package. A more complete description of the method and some numerical experiments illustrating its effectiveness appear in. Like traditional geometric multilevel methods, this scheme relies on knowledge of the underlying finite element space in order to construct the smoother and the coarse grid correction.« less

Optimization of Regional Geodynamic Models for Mantle Dynamics

NASA Astrophysics Data System (ADS)

Knepley, M.; Isaac, T.; Jadamec, M. A.

2016-12-01

The SubductionGenerator program is used to construct high resolution, 3D regional thermal structures for mantle convection simulations using a variety of data sources, including sea floor ages and geographically referenced 3D slab locations based on seismic observations. The initial bulk temperature field is constructed using a half-space cooling model or plate cooling model, and related smoothing functions based on a diffusion length-scale analysis. In this work, we seek to improve the 3D thermal model and test different model geometries and dynamically driven flow fields using constraints from observed seismic velocities and plate motions. Through a formal adjoint analysis, we construct the primal-dual version of the multi-objective PDE-constrained optimization problem for the plate motions and seismic misfit. We have efficient, scalable preconditioners for both the forward and adjoint problems based upon a block preconditioning strategy, and a simple gradient update is used to improve the control residual. The full optimal control problem is formulated on a nested hierarchy of grids, allowing a nonlinear multigrid method to accelerate the solution.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chacon, Luis; Stanier, Adam John

Here, we demonstrate a scalable fully implicit algorithm for the two-field low-β extended MHD model. This reduced model describes plasma behavior in the presence of strong guide fields, and is of significant practical impact both in nature and in laboratory plasmas. The model displays strong hyperbolic behavior, as manifested by the presence of fast dispersive waves, which make a fully implicit treatment very challenging. In this study, we employ a Jacobian-free Newton–Krylov nonlinear solver, for which we propose a physics-based preconditioner that renders the linearized set of equations suitable for inversion with multigrid methods. As a result, the algorithm ismore » shown to scale both algorithmically (i.e., the iteration count is insensitive to grid refinement and timestep size) and in parallel in a weak-scaling sense, with the wall-clock time scaling weakly with the number of cores for up to 4096 cores. For a 4096 × 4096 mesh, we demonstrate a wall-clock-time speedup of ~6700 with respect to explicit algorithms. The model is validated linearly (against linear theory predictions) and nonlinearly (against fully kinetic simulations), demonstrating excellent agreement.« less

Curvilinear immersed-boundary method for simulating unsteady flows in shallow natural streams with arbitrarily complex obstacles

NASA Astrophysics Data System (ADS)

Kang, Seokkoo; Borazjani, Iman; Sotiropoulos, Fotis

2008-11-01

Unsteady 3D simulations of flows in natural streams is a challenging task due to the complexity of the bathymetry, the shallowness of the flow, and the presence of multiple nature- and man-made obstacles. This work is motivated by the need to develop a powerful numerical method for simulating such flows using coherent-structure-resolving turbulence models. We employ the curvilinear immersed boundary method of Ge and Sotiropoulos (Journal of Computational Physics, 2007) and address the critical issue of numerical efficiency in large aspect ratio computational domains and grids such as those encountered in long and shallow open channels. We show that the matrix-free Newton-Krylov method for solving the momentum equations coupled with an algebraic multigrid method with incomplete LU preconditioner for solving the Poisson equation yield a robust and efficient procedure for obtaining time-accurate solutions in such problems. We demonstrate the potential of the numerical approach by carrying out a direct numerical simulation of flow in a long and shallow meandering stream with multiple hydraulic structures.

CPIC: a curvilinear Particle-In-Cell code for plasma-material interaction studies

NASA Astrophysics Data System (ADS)

Delzanno, G.; Camporeale, E.; Moulton, J. D.; Borovsky, J. E.; MacDonald, E.; Thomsen, M. F.

2012-12-01

We present a recently developed Particle-In-Cell (PIC) code in curvilinear geometry called CPIC (Curvilinear PIC) [1], where the standard PIC algorithm is coupled with a grid generation/adaptation strategy. Through the grid generator, which maps the physical domain to a logical domain where the grid is uniform and Cartesian, the code can simulate domains of arbitrary complexity, including the interaction of complex objects with a plasma. At present the code is electrostatic. Poisson's equation (in logical space) can be solved with either an iterative method based on the Conjugate Gradient (CG) or the Generalized Minimal Residual (GMRES) coupled with a multigrid solver used as a preconditioner, or directly with multigrid. The multigrid strategy is critical for the solver to perform optimally or nearly optimally as the dimension of the problem increases. CPIC also features a hybrid particle mover, where the computational particles are characterized by position in logical space and velocity in physical space. The advantage of a hybrid mover, as opposed to more conventional movers that move particles directly in the physical space, is that the interpolation of the particles in logical space is straightforward and computationally inexpensive, since one does not have to track the position of the particle. We will present our latest progress on the development of the code and document the code performance on standard plasma-physics tests. Then we will present the (preliminary) application of the code to a basic dynamic-charging problem, namely the charging and shielding of a spherical spacecraft in a magnetized plasma for various level of magnetization and including the pulsed emission of an electron beam from the spacecraft. The dynamical evolution of the sheath and the time-dependent current collection will be described. This study is in support of the ConnEx mission concept to use an electron beam from a magnetospheric spacecraft to trace magnetic field lines from the magnetosphere to the ionosphere [2]. [1] G.L. Delzanno, E. Camporeale, "CPIC: a new Particle-in-Cell code for plasma-material interaction studies", in preparation (2012). [2] J.E. Borovsky, D.J. McComas, M.F. Thomsen, J.L. Burch, J. Cravens, C.J. Pollock, T.E. Moore, and S.B. Mende, "Magnetosphere-Ionosphere Observatory (MIO): A multisatellite mission designed to solve the problem of what generates auroral arcs," Eos. Trans. Amer. Geophys. Union 79 (45), F744 (2000).

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-suited to solution on hybrid computational clusters. To manage the combinatorial explosion of solver options (which include hybridizations of all the approaches mentioned above), we leverage the modularity of the PETSc library.

Recovery Discontinuous Galerkin Jacobian-Free Newton-Krylov Method for All-Speed Flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

HyeongKae Park; Robert Nourgaliev; Vincent Mousseau

2008-07-01

A novel numerical algorithm (rDG-JFNK) for all-speed fluid flows with heat conduction and viscosity is introduced. The rDG-JFNK combines the Discontinuous Galerkin spatial discretization with the implicit Runge-Kutta time integration under the Jacobian-free Newton-Krylov framework. We solve fully-compressible Navier-Stokes equations without operator-splitting of hyperbolic, diffusion and reaction terms, which enables fully-coupled high-order temporal discretization. The stability constraint is removed due to the L-stable Explicit, Singly Diagonal Implicit Runge-Kutta (ESDIRK) scheme. The governing equations are solved in the conservative form, which allows one to accurately compute shock dynamics, as well as low-speed flows. For spatial discretization, we develop a “recovery” familymore » of DG, exhibiting nearly-spectral accuracy. To precondition the Krylov-based linear solver (GMRES), we developed an “Operator-Split”-(OS) Physics Based Preconditioner (PBP), in which we transform/simplify the fully-coupled system to a sequence of segregated scalar problems, each can be solved efficiently with Multigrid method. Each scalar problem is designed to target/cluster eigenvalues of the Jacobian matrix associated with a specific physics.« less

A scalable, fully implicit algorithm for the reduced two-field low-β extended MHD model

DOE PAGES

Chacon, Luis; Stanier, Adam John

2016-12-01

Here, we demonstrate a scalable fully implicit algorithm for the two-field low-β extended MHD model. This reduced model describes plasma behavior in the presence of strong guide fields, and is of significant practical impact both in nature and in laboratory plasmas. The model displays strong hyperbolic behavior, as manifested by the presence of fast dispersive waves, which make a fully implicit treatment very challenging. In this study, we employ a Jacobian-free Newton–Krylov nonlinear solver, for which we propose a physics-based preconditioner that renders the linearized set of equations suitable for inversion with multigrid methods. As a result, the algorithm ismore » shown to scale both algorithmically (i.e., the iteration count is insensitive to grid refinement and timestep size) and in parallel in a weak-scaling sense, with the wall-clock time scaling weakly with the number of cores for up to 4096 cores. For a 4096 × 4096 mesh, we demonstrate a wall-clock-time speedup of ~6700 with respect to explicit algorithms. The model is validated linearly (against linear theory predictions) and nonlinearly (against fully kinetic simulations), demonstrating excellent agreement.« less

Preconditioned augmented Lagrangian formulation for nearly incompressible cardiac mechanics.

PubMed

Campos, Joventino Oliveira; Dos Santos, Rodrigo Weber; Sundnes, Joakim; Rocha, Bernardo Martins

2018-04-01

Computational modeling of the heart is a subject of substantial medical and scientific interest, which may contribute to increase the understanding of several phenomena associated with cardiac physiological and pathological states. Modeling the mechanics of the heart have led to considerable insights, but it still represents a complex and a demanding computational problem, especially in a strongly coupled electromechanical setting. Passive cardiac tissue is commonly modeled as hyperelastic and is characterized by quasi-incompressible, orthotropic, and nonlinear material behavior. These factors are known to be very challenging for the numerical solution of the model. The near-incompressibility is known to cause numerical issues such as the well-known locking phenomenon and ill-conditioning of the stiffness matrix. In this work, the augmented Lagrangian method is used to handle the nearly incompressible condition. This approach can potentially improve computational performance by reducing the condition number of the stiffness matrix and thereby improving the convergence of iterative solvers. We also improve the performance of iterative solvers by the use of an algebraic multigrid preconditioner. Numerical results of the augmented Lagrangian method combined with a preconditioned iterative solver for a cardiac mechanics benchmark suite are presented to show its improved performance. Copyright © 2017 John Wiley & Sons, Ltd.

Convergence Acceleration for Multistage Time-Stepping Schemes

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Turkel, Eli L.; Rossow, C-C; Vasta, V. N.

2006-01-01

The convergence of a Runge-Kutta (RK) scheme with multigrid is accelerated by preconditioning with a fully implicit operator. With the extended stability of the Runge-Kutta scheme, CFL numbers as high as 1000 could be used. The implicit preconditioner addresses the stiffness in the discrete equations associated with stretched meshes. Numerical dissipation operators (based on the Roe scheme, a matrix formulation, and the CUSP scheme) as well as the number of RK stages are considered in evaluating the RK/implicit scheme. Both the numerical and computational efficiency of the scheme with the different dissipation operators are discussed. The RK/implicit scheme is used to solve the two-dimensional (2-D) and three-dimensional (3-D) compressible, Reynolds-averaged Navier-Stokes equations. In two dimensions, turbulent flows over an airfoil at subsonic and transonic conditions are computed. The effects of mesh cell aspect ratio on convergence are investigated for Reynolds numbers between 5.7 x 10(exp 6) and 100.0 x 10(exp 6). Results are also obtained for a transonic wing flow. For both 2-D and 3-D problems, the computational time of a well-tuned standard RK scheme is reduced at least a factor of four.

Optimization-based mesh correction with volume and convexity constraints

DOE PAGES

D'Elia, Marta; Ridzal, Denis; Peterson, Kara J.; ...

2016-02-24

In this study, we consider the problem of finding a mesh such that 1) it is the closest, with respect to a suitable metric, to a given source mesh having the same connectivity, and 2) the volumes of its cells match a set of prescribed positive values that are not necessarily equal to the cell volumes in the source mesh. This volume correction problem arises in important simulation contexts, such as satisfying a discrete geometric conservation law and solving transport equations by incremental remapping or similar semi-Lagrangian transport schemes. In this paper we formulate volume correction as a constrained optimizationmore » problem in which the distance to the source mesh defines an optimization objective, while the prescribed cell volumes, mesh validity and/or cell convexity specify the constraints. We solve this problem numerically using a sequential quadratic programming (SQP) method whose performance scales with the mesh size. To achieve scalable performance we develop a specialized multigrid-based preconditioner for optimality systems that arise in the application of the SQP method to the volume correction problem. Numerical examples illustrate the importance of volume correction, and showcase the accuracy, robustness and scalability of our approach.« less

Approximate tensor-product preconditioners for very high order discontinuous Galerkin methods

NASA Astrophysics Data System (ADS)

Pazner, Will; Persson, Per-Olof

2018-02-01

In this paper, we develop a new tensor-product based preconditioner for discontinuous Galerkin methods with polynomial degrees higher than those typically employed. This preconditioner uses an automatic, purely algebraic method to approximate the exact block Jacobi preconditioner by Kronecker products of several small, one-dimensional matrices. Traditional matrix-based preconditioners require O (p2d) storage and O (p3d) computational work, where p is the degree of basis polynomials used, and d is the spatial dimension. Our SVD-based tensor-product preconditioner requires O (p d + 1) storage, O (p d + 1) work in two spatial dimensions, and O (p d + 2) work in three spatial dimensions. Combined with a matrix-free Newton-Krylov solver, these preconditioners allow for the solution of DG systems in linear time in p per degree of freedom in 2D, and reduce the computational complexity from O (p9) to O (p5) in 3D. Numerical results are shown in 2D and 3D for the advection, Euler, and Navier-Stokes equations, using polynomials of degree up to p = 30. For many test cases, the preconditioner results in similar iteration counts when compared with the exact block Jacobi preconditioner, and performance is significantly improved for high polynomial degrees p.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

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 formore » 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 problem of evaluating f(A)v which arises in statistical sampling. 11. As an application to the methods we developed, we tackled the problem of computing the diagonal of the inverse of a matrix. This arises in statistical applications as well as in many applications in physics. We explored probing methods as well as domain-decomposition type methods. 12. A collaboration with researchers from Toulouse, France, considered the important problem of computing the Schur complement in a domain-decomposition approach. 13. We explored new ways of preconditioning linear systems, based on low-rank approximations.« less

Evaluating Sparse Linear System Solvers on Scalable Parallel Architectures

DTIC Science & Technology

2008-10-01

42 3.4 Residual history of WSO banded preconditioner for problem 2D 54019 HIGHK . . . . . . . . . . . . . . . . . . . . . . . . . . 43...3.5 Residual history of WSO banded preconditioner for problem Appu 43 3.6 Residual history of WSO banded preconditioner for problem ASIC 680k...44 3.7 Residual history of WSO banded preconditioner for problem BUN- DLE1

On the implementation of an accurate and efficient solver for convection-diffusion equations

NASA Astrophysics Data System (ADS)

Wu, Chin-Tien

In this dissertation, we examine several different aspects of computing the numerical solution of the convection-diffusion equation. The solution of this equation often exhibits sharp gradients due to Dirichlet outflow boundaries or discontinuities in boundary conditions. Because of the singular-perturbed nature of the equation, numerical solutions often have severe oscillations when grid sizes are not small enough to resolve sharp gradients. To overcome such difficulties, the streamline diffusion discretization method can be used to obtain an accurate approximate solution in regions where the solution is smooth. To increase accuracy of the solution in the regions containing layers, adaptive mesh refinement and mesh movement based on a posteriori error estimations can be employed. An error-adapted mesh refinement strategy based on a posteriori error estimations is also proposed to resolve layers. For solving the sparse linear systems that arise from discretization, goemetric multigrid (MG) and algebraic multigrid (AMG) are compared. In addition, both methods are also used as preconditioners for Krylov subspace methods. We derive some convergence results for MG with line Gauss-Seidel smoothers and bilinear interpolation. Finally, while considering adaptive mesh refinement as an integral part of the solution process, it is natural to set a stopping tolerance for the iterative linear solvers on each mesh stage so that the difference between the approximate solution obtained from iterative methods and the finite element solution is bounded by an a posteriori error bound. Here, we present two stopping criteria. The first is based on a residual-type a posteriori error estimator developed by Verfurth. The second is based on an a posteriori error estimator, using local solutions, developed by Kay and Silvester. Our numerical results show the refined mesh obtained from the iterative solution which satisfies the second criteria is similar to the refined mesh obtained from the finite element solution.

Element-topology-independent preconditioners for parallel finite element computations

NASA Technical Reports Server (NTRS)

Park, K. C.; Alexander, Scott

1992-01-01

A family of preconditioners for the solution of finite element equations are presented, which are element-topology independent and thus can be applicable to element order-free parallel computations. A key feature of the present preconditioners is the repeated use of element connectivity matrices and their left and right inverses. The properties and performance of the present preconditioners are demonstrated via beam and two-dimensional finite element matrices for implicit time integration computations.

On optimal improvements of classical iterative schemes for Z-matrices

NASA Astrophysics Data System (ADS)

Noutsos, D.; Tzoumas, M.

2006-04-01

Many researchers have considered preconditioners, applied to linear systems, whose matrix coefficient is a Z- or an M-matrix, that make the associated Jacobi and Gauss-Seidel methods converge asymptotically faster than the unpreconditioned ones. Such preconditioners are chosen so that they eliminate the off-diagonal elements of the same column or the elements of the first upper diagonal [Milaszewicz, LAA 93 (1987) 161-170], Gunawardena et al. [LAA 154-156 (1991) 123-143]. In this work we generalize the previous preconditioners to obtain optimal methods. "Good" Jacobi and Gauss-Seidel algorithms are given and preconditioners, that eliminate more than one entry per row, are also proposed and analyzed. Moreover, the behavior of the above preconditioners to the Krylov subspace methods is studied.

3D electromagnetic modelling of a TTI medium and TTI effects in inversion

NASA Astrophysics Data System (ADS)

Jaysaval, Piyoosh; Shantsev, Daniil; de la Kethulle de Ryhove, Sébastien

2016-04-01

We present a numerical algorithm for 3D electromagnetic (EM) forward modelling in conducting media with general electric anisotropy. The algorithm is based on the finite-difference discretization of frequency-domain Maxwell's equations on a Lebedev grid, in which all components of the electric field are collocated but half a spatial step staggered with respect to the magnetic field components, which also are collocated. This leads to a system of linear equations that is solved using a stabilized biconjugate gradient method with a multigrid preconditioner. We validate the accuracy of the numerical results for layered and 3D tilted transverse isotropic (TTI) earth models representing typical scenarios used in the marine controlled-source EM method. It is then demonstrated that not taking into account the full anisotropy of the conductivity tensor can lead to misleading inversion results. For simulation data corresponding to a 3D model with a TTI anticlinal structure, a standard vertical transverse isotropic inversion is not able to image a resistor, while for a 3D model with a TTI synclinal structure the inversion produces a false resistive anomaly. If inversion uses the proposed forward solver that can handle TTI anisotropy, it produces resistivity images consistent with the true models.

Multigrid techniques for unstructured meshes

NASA Technical Reports Server (NTRS)

Mavriplis, D. J.

1995-01-01

An overview of current multigrid techniques for unstructured meshes is given. The basic principles of the multigrid approach are first outlined. Application of these principles to unstructured mesh problems is then described, illustrating various different approaches, and giving examples of practical applications. Advanced multigrid topics, such as the use of algebraic multigrid methods, and the combination of multigrid techniques with adaptive meshing strategies are dealt with in subsequent sections. These represent current areas of research, and the unresolved issues are discussed. The presentation is organized in an educational manner, for readers familiar with computational fluid dynamics, wishing to learn more about current unstructured mesh techniques.

Multigrid calculation of three-dimensional turbomachinery flows

NASA Technical Reports Server (NTRS)

Caughey, David A.

1989-01-01

Research was performed in the general area of computational aerodynamics, with particular emphasis on the development of efficient techniques for the solution of the Euler and Navier-Stokes equations for transonic flows through the complex blade passages associated with turbomachines. In particular, multigrid methods were developed, using both explicit and implicit time-stepping schemes as smoothing algorithms. The specific accomplishments of the research have included: (1) the development of an explicit multigrid method to solve the Euler equations for three-dimensional turbomachinery flows based upon the multigrid implementation of Jameson's explicit Runge-Kutta scheme (Jameson 1983); (2) the development of an implicit multigrid scheme for the three-dimensional Euler equations based upon lower-upper factorization; (3) the development of a multigrid scheme using a diagonalized alternating direction implicit (ADI) algorithm; (4) the extension of the diagonalized ADI multigrid method to solve the Euler equations of inviscid flow for three-dimensional turbomachinery flows; and also (5) the extension of the diagonalized ADI multigrid scheme to solve the Reynolds-averaged Navier-Stokes equations for two-dimensional turbomachinery flows.

Conjugate-gradient preconditioning methods for shift-variant PET image reconstruction.

PubMed

Fessler, J A; Booth, S D

1999-01-01

Gradient-based iterative methods often converge slowly for tomographic image reconstruction and image restoration problems, but can be accelerated by suitable preconditioners. Diagonal preconditioners offer some improvement in convergence rate, but do not incorporate the structure of the Hessian matrices in imaging problems. Circulant preconditioners can provide remarkable acceleration for inverse problems that are approximately shift-invariant, i.e., for those with approximately block-Toeplitz or block-circulant Hessians. However, in applications with nonuniform noise variance, such as arises from Poisson statistics in emission tomography and in quantum-limited optical imaging, the Hessian of the weighted least-squares objective function is quite shift-variant, and circulant preconditioners perform poorly. Additional shift-variance is caused by edge-preserving regularization methods based on nonquadratic penalty functions. This paper describes new preconditioners that approximate more accurately the Hessian matrices of shift-variant imaging problems. Compared to diagonal or circulant preconditioning, the new preconditioners lead to significantly faster convergence rates for the unconstrained conjugate-gradient (CG) iteration. We also propose a new efficient method for the line-search step required by CG methods. Applications to positron emission tomography (PET) illustrate the method.

Black box multigrid

NASA Technical Reports Server (NTRS)

Dendy, J. E., Jr.

1981-01-01

The black box multigrid (BOXMG) code, which only needs specification of the matrix problem for application in the multigrid method was investigated. It is contended that a major problem with the multigrid method is that each new grid configuration requires a major programming effort to develop a code that specifically handles that grid configuration. The SOR and ICCG methods only specify the matrix problem, no matter what the grid configuration. It is concluded that the BOXMG does everything else necessary to set up the auxiliary coarser problems to achieve a multigrid solution.

On several aspects and applications of the multigrid method for solving partial differential equations

NASA Technical Reports Server (NTRS)

Dinar, N.

1978-01-01

Several aspects of multigrid methods are briefly described. The main subjects include the development of very efficient multigrid algorithms for systems of elliptic equations (Cauchy-Riemann, Stokes, Navier-Stokes), as well as the development of control and prediction tools (based on local mode Fourier analysis), used to analyze, check and improve these algorithms. Preliminary research on multigrid algorithms for time dependent parabolic equations is also described. Improvements in existing multigrid processes and algorithms for elliptic equations were studied.

Application of multi-grid methods for solving the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Demuren, A. O.

1989-01-01

The application of a class of multi-grid methods to the solution of the Navier-Stokes equations for two-dimensional laminar flow problems is discussed. The methods consist of combining the full approximation scheme-full multi-grid technique (FAS-FMG) with point-, line-, or plane-relaxation routines for solving the Navier-Stokes equations in primitive variables. The performance of the multi-grid methods is compared to that of several single-grid methods. The results show that much faster convergence can be procured through the use of the multi-grid approach than through the various suggestions for improving single-grid methods. The importance of the choice of relaxation scheme for the multi-grid method is illustrated.

Application of multi-grid methods for solving the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Demuren, A. O.

1989-01-01

This paper presents the application of a class of multi-grid methods to the solution of the Navier-Stokes equations for two-dimensional laminar flow problems. The methods consists of combining the full approximation scheme-full multi-grid technique (FAS-FMG) with point-, line- or plane-relaxation routines for solving the Navier-Stokes equations in primitive variables. The performance of the multi-grid methods is compared to those of several single-grid methods. The results show that much faster convergence can be procured through the use of the multi-grid approach than through the various suggestions for improving single-grid methods. The importance of the choice of relaxation scheme for the multi-grid method is illustrated.

Agglomeration Multigrid for an Unstructured-Grid Flow Solver

NASA Technical Reports Server (NTRS)

Frink, Neal; Pandya, Mohagna J.

2004-01-01

An agglomeration multigrid scheme has been implemented into the sequential version of the NASA code USM3Dns, tetrahedral cell-centered finite volume Euler/Navier-Stokes flow solver. Efficiency and robustness of the multigrid-enhanced flow solver have been assessed for three configurations assuming an inviscid flow and one configuration assuming a viscous fully turbulent flow. The inviscid studies include a transonic flow over the ONERA M6 wing and a generic business jet with flow-through nacelles and a low subsonic flow over a high-lift trapezoidal wing. The viscous case includes a fully turbulent flow over the RAE 2822 rectangular wing. The multigrid solutions converged with 12%-33% of the Central Processing Unit (CPU) time required by the solutions obtained without multigrid. For all of the inviscid cases, multigrid in conjunction with an explicit time-stepping scheme performed the best with regard to the run time memory and CPU time requirements. However, for the viscous case multigrid had to be used with an implicit backward Euler time-stepping scheme that increased the run time memory requirement by 22% as compared to the run made without multigrid.

Large-Scale Parallel Viscous Flow Computations using an Unstructured Multigrid Algorithm

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.

1999-01-01

The development and testing of a parallel unstructured agglomeration multigrid algorithm for steady-state aerodynamic flows is discussed. The agglomeration multigrid strategy uses a graph algorithm to construct the coarse multigrid levels from the given fine grid, similar to an algebraic multigrid approach, but operates directly on the non-linear system using the FAS (Full Approximation Scheme) approach. The scalability and convergence rate of the multigrid algorithm are examined on the SGI Origin 2000 and the Cray T3E. An argument is given which indicates that the asymptotic scalability of the multigrid algorithm should be similar to that of its underlying single grid smoothing scheme. For medium size problems involving several million grid points, near perfect scalability is obtained for the single grid algorithm, while only a slight drop-off in parallel efficiency is observed for the multigrid V- and W-cycles, using up to 128 processors on the SGI Origin 2000, and up to 512 processors on the Cray T3E. For a large problem using 25 million grid points, good scalability is observed for the multigrid algorithm using up to 1450 processors on a Cray T3E, even when the coarsest grid level contains fewer points than the total number of processors.

Two new modified Gauss-Seidel methods for linear system with M-matrices

NASA Astrophysics Data System (ADS)

Zheng, Bing; Miao, Shu-Xin

2009-12-01

In 2002, H. Kotakemori et al. proposed the modified Gauss-Seidel (MGS) method for solving the linear system with the preconditioner [H. Kotakemori, K. Harada, M. Morimoto, H. Niki, A comparison theorem for the iterative method with the preconditioner () J. Comput. Appl. Math. 145 (2002) 373-378]. Since this preconditioner is constructed by only the largest element on each row of the upper triangular part of the coefficient matrix, the preconditioning effect is not observed on the nth row. In the present paper, to deal with this drawback, we propose two new preconditioners. The convergence and comparison theorems of the modified Gauss-Seidel methods with these two preconditioners for solving the linear system are established. The convergence rates of the new proposed preconditioned methods are compared. In addition, numerical experiments are used to show the effectiveness of the new MGS methods.

Block recursive LU preconditioners for the thermally coupled incompressible inductionless MHD problem

NASA Astrophysics Data System (ADS)

Badia, Santiago; Martín, Alberto F.; Planas, Ramon

2014-10-01

The thermally coupled incompressible inductionless magnetohydrodynamics (MHD) problem models the flow of an electrically charged fluid under the influence of an external electromagnetic field with thermal coupling. This system of partial differential equations is strongly coupled and highly nonlinear for real cases of interest. Therefore, fully implicit time integration schemes are very desirable in order to capture the different physical scales of the problem at hand. However, solving the multiphysics linear systems of equations resulting from such algorithms is a very challenging task which requires efficient and scalable preconditioners. In this work, a new family of recursive block LU preconditioners is designed and tested for solving the thermally coupled inductionless MHD equations. These preconditioners are obtained after splitting the fully coupled matrix into one-physics problems for every variable (velocity, pressure, current density, electric potential and temperature) that can be optimally solved, e.g., using preconditioned domain decomposition algorithms. The main idea is to arrange the original matrix into an (arbitrary) 2 × 2 block matrix, and consider an LU preconditioner obtained by approximating the corresponding Schur complement. For every one of the diagonal blocks in the LU preconditioner, if it involves more than one type of unknowns, we proceed the same way in a recursive fashion. This approach is stated in an abstract way, and can be straightforwardly applied to other multiphysics problems. Further, we precisely explain a flexible and general software design for the code implementation of this type of preconditioners.

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.

On polynomial preconditioning for indefinite Hermitian matrices

NASA Technical Reports Server (NTRS)

Freund, Roland W.

1989-01-01

The minimal residual method is studied combined with polynomial preconditioning for solving large linear systems (Ax = b) with indefinite Hermitian coefficient matrices (A). The standard approach for choosing the polynomial preconditioners leads to preconditioned systems which are positive definite. Here, a different strategy is studied which leaves the preconditioned coefficient matrix indefinite. More precisely, the polynomial preconditioner is designed to cluster the positive, resp. negative eigenvalues of A around 1, resp. around some negative constant. In particular, it is shown that such indefinite polynomial preconditioners can be obtained as the optimal solutions of a certain two parameter family of Chebyshev approximation problems. Some basic results are established for these approximation problems and a Remez type algorithm is sketched for their numerical solution. The problem of selecting the parameters such that the resulting indefinite polynomial preconditioners speeds up the convergence of minimal residual method optimally is also addressed. An approach is proposed based on the concept of asymptotic convergence factors. Finally, some numerical examples of indefinite polynomial preconditioners are given.

Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Adams, Mark F.; Samtaney, Ravi, E-mail: samtaney@pppl.go; Brandt, Achi

2010-09-01

Multigrid methods can solve some classes of elliptic and parabolic equations to accuracy below the truncation error with a work-cost equivalent to a few residual calculations - so-called 'textbook' multigrid efficiency. We investigate methods to solve the system of equations that arise in time dependent magnetohydrodynamics (MHD) simulations with textbook multigrid efficiency. We apply multigrid techniques such as geometric interpolation, full approximate storage, Gauss-Seidel smoothers, and defect correction for fully implicit, nonlinear, second-order finite volume discretizations of MHD. We apply these methods to a standard resistive MHD benchmark problem, the GEM reconnection problem, and add a strong magnetic guide field,more » which is a critical characteristic of magnetically confined fusion plasmas. We show that our multigrid methods can achieve near textbook efficiency on fully implicit resistive MHD simulations.« less

Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Adams, Mark F.; Samtaney, Ravi; Brandt, Achi

2010-09-01

Multigrid methods can solve some classes of elliptic and parabolic equations to accuracy below the truncation error with a work-cost equivalent to a few residual calculations – so-called ‘‘textbook” multigrid efficiency. We investigate methods to solve the system of equations that arise in time dependent magnetohydrodynamics (MHD) simulations with textbook multigrid efficiency. We apply multigrid techniques such as geometric interpolation, full approximate storage, Gauss–Seidel smoothers, and defect correction for fully implicit, nonlinear, second-order finite volume discretizations of MHD. We apply these methods to a standard resistive MHD benchmark problem, the GEM reconnection problem, and add a strong magnetic guide field,more » which is a critical characteristic of magnetically confined fusion plasmas. We show that our multigrid methods can achieve near textbook efficiency on fully implicit resistive MHD simulations.« less

Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Adams, Mark F.; Samtaney, Ravi; Brandt, Achi

2013-12-14

Multigrid methods can solve some classes of elliptic and parabolic equations to accuracy below the truncation error with a work-cost equivalent to a few residual calculations – so-called “textbook” multigrid efficiency. We investigate methods to solve the system of equations that arise in time dependent magnetohydrodynamics (MHD) simulations with textbook multigrid efficiency. We apply multigrid techniques such as geometric interpolation, full approximate storage, Gauss-Seidel smoothers, and defect correction for fully implicit, nonlinear, second-order finite volume discretizations of MHD. We apply these methods to a standard resistive MHD benchmark problem, the GEM reconnection problem, and add a strong magnetic guide field,more » which is a critical characteristic of magnetically confined fusion plasmas. We show that our multigrid methods can achieve near textbook efficiency on fully implicit resistive MHD simulations.« less

Evaluation of a Multigrid Scheme for the Incompressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Swanson, R. C.

2004-01-01

A fast multigrid solver for the steady, incompressible Navier-Stokes equations is presented. The multigrid solver is based upon a factorizable discrete scheme for the velocity-pressure form of the Navier-Stokes equations. This scheme correctly distinguishes between the advection-diffusion and elliptic parts of the operator, allowing efficient smoothers to be constructed. To evaluate the multigrid algorithm, solutions are computed for flow over a flat plate, parabola, and a Karman-Trefftz airfoil. Both nonlifting and lifting airfoil flows are considered, with a Reynolds number range of 200 to 800. Convergence and accuracy of the algorithm are discussed. Using Gauss-Seidel line relaxation in alternating directions, multigrid convergence behavior approaching that of O(N) methods is achieved. The computational efficiency of the numerical scheme is compared with that of Runge-Kutta and implicit upwind based multigrid methods.

Incomplete augmented Lagrangian preconditioner for steady incompressible Navier-Stokes equations.

PubMed

Tan, Ning-Bo; Huang, Ting-Zhu; Hu, Ze-Jun

2013-01-01

An incomplete augmented Lagrangian preconditioner, for the steady incompressible Navier-Stokes equations discretized by stable finite elements, is proposed. The eigenvalues of the preconditioned matrix are analyzed. Numerical experiments show that the incomplete augmented Lagrangian-based preconditioner proposed is very robust and performs quite well by the Picard linearization or the Newton linearization over a wide range of values of the viscosity on both uniform and stretched grids.

Formulation of boundary conditions for the multigrid acceleration of the Euler and Navier Stokes equations

NASA Technical Reports Server (NTRS)

Jentink, Thomas Neil; Usab, William J., Jr.

1990-01-01

An explicit, Multigrid algorithm was written to solve the Euler and Navier-Stokes equations with special consideration given to the coarse mesh boundary conditions. These are formulated in a manner consistent with the interior solution, utilizing forcing terms to prevent coarse-mesh truncation error from affecting the fine-mesh solution. A 4-Stage Hybrid Runge-Kutta Scheme is used to advance the solution in time, and Multigrid convergence is further enhanced by using local time-stepping and implicit residual smoothing. Details of the algorithm are presented along with a description of Jameson's standard Multigrid method and a new approach to formulating the Multigrid equations.

Introduction to multigrid methods

NASA Technical Reports Server (NTRS)

Wesseling, P.

1995-01-01

These notes were written for an introductory course on the application of multigrid methods to elliptic and hyperbolic partial differential equations for engineers, physicists and applied mathematicians. The use of more advanced mathematical tools, such as functional analysis, is avoided. The course is intended to be accessible to a wide audience of users of computational methods. We restrict ourselves to finite volume and finite difference discretization. The basic principles are given. Smoothing methods and Fourier smoothing analysis are reviewed. The fundamental multigrid algorithm is studied. The smoothing and coarse grid approximation properties are discussed. Multigrid schedules and structured programming of multigrid algorithms are treated. Robustness and efficiency are considered.

A Critical Study of Agglomerated Multigrid Methods for Diffusion

NASA Technical Reports Server (NTRS)

Nishikawa, Hiroaki; Diskin, Boris; Thomas, James L.

2011-01-01

Agglomerated multigrid techniques used in unstructured-grid methods are studied critically for a model problem representative of laminar diffusion in the incompressible limit. The studied target-grid discretizations and discretizations used on agglomerated grids are typical of current node-centered formulations. Agglomerated multigrid convergence rates are presented using a range of two- and three-dimensional randomly perturbed unstructured grids for simple geometries with isotropic and stretched grids. Two agglomeration techniques are used within an overall topology-preserving agglomeration framework. The results show that multigrid with an inconsistent coarse-grid scheme using only the edge terms (also referred to in the literature as a thin-layer formulation) provides considerable speedup over single-grid methods but its convergence deteriorates on finer grids. Multigrid with a Galerkin coarse-grid discretization using piecewise-constant prolongation and a heuristic correction factor is slower and also grid-dependent. In contrast, grid-independent convergence rates are demonstrated for multigrid with consistent coarse-grid discretizations. Convergence rates of multigrid cycles are verified with quantitative analysis methods in which parts of the two-grid cycle are replaced by their idealized counterparts.

The Mixed Finite Element Multigrid Method for Stokes Equations

PubMed Central

Muzhinji, K.; Shateyi, S.; Motsa, S. S.

2015-01-01

The stable finite element discretization of the Stokes problem produces a symmetric indefinite system of linear algebraic equations. A variety of iterative solvers have been proposed for such systems in an attempt to construct efficient, fast, and robust solution techniques. This paper investigates one of such iterative solvers, the geometric multigrid solver, to find the approximate solution of the indefinite systems. The main ingredient of the multigrid method is the choice of an appropriate smoothing strategy. This study considers the application of different smoothers and compares their effects in the overall performance of the multigrid solver. We study the multigrid method with the following smoothers: distributed Gauss Seidel, inexact Uzawa, preconditioned MINRES, and Braess-Sarazin type smoothers. A comparative study of the smoothers shows that the Braess-Sarazin smoothers enhance good performance of the multigrid method. We study the problem in a two-dimensional domain using stable Hood-Taylor Q 2-Q 1 pair of finite rectangular elements. We also give the main theoretical convergence results. We present the numerical results to demonstrate the efficiency and robustness of the multigrid method and confirm the theoretical results. PMID:25945361

A minimally-resolved immersed boundary model for reaction-diffusion problems

NASA Astrophysics Data System (ADS)

Pal Singh Bhalla, Amneet; Griffith, Boyce E.; Patankar, Neelesh A.; Donev, Aleksandar

2013-12-01

We develop an immersed boundary approach to modeling reaction-diffusion processes in dispersions of reactive spherical particles, from the diffusion-limited to the reaction-limited setting. We represent each reactive particle with a minimally-resolved "blob" using many fewer degrees of freedom per particle than standard discretization approaches. More complicated or more highly resolved particle shapes can be built out of a collection of reactive blobs. We demonstrate numerically that the blob model can provide an accurate representation at low to moderate packing densities of the reactive particles, at a cost not much larger than solving a Poisson equation in the same domain. Unlike multipole expansion methods, our method does not require analytically computed Green's functions, but rather, computes regularized discrete Green's functions on the fly by using a standard grid-based discretization of the Poisson equation. This allows for great flexibility in implementing different boundary conditions, coupling to fluid flow or thermal transport, and the inclusion of other effects such as temporal evolution and even nonlinearities. We develop multigrid-based preconditioners for solving the linear systems that arise when using implicit temporal discretizations or studying steady states. In the diffusion-limited case the resulting linear system is a saddle-point problem, the efficient solution of which remains a challenge for suspensions of many particles. We validate our method by comparing to published results on reaction-diffusion in ordered and disordered suspensions of reactive spheres.

An Initial Investigation of the Effects of Turbulence Models on the Convergence of the RK/Implicit Scheme

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Rossow, C.-C.

2008-01-01

A three-stage Runge-Kutta (RK) scheme with multigrid and an implicit preconditioner has been shown to be an effective solver for the fluid dynamic equations. This scheme has been applied to both the compressible and essentially incompressible Reynolds-averaged Navier-Stokes (RANS) equations using the algebraic turbulence model of Baldwin and Lomax (BL). In this paper we focus on the convergence of the RK/implicit scheme when the effects of turbulence are represented by either the Spalart-Allmaras model or the Wilcox k-! model, which are frequently used models in practical fluid dynamic applications. Convergence behavior of the scheme with these turbulence models and the BL model are directly compared. For this initial investigation we solve the flow equations and the partial differential equations of the turbulence models indirectly coupled. With this approach we examine the convergence behavior of each system. Both point and line symmetric Gauss-Seidel are considered for approximating the inverse of the implicit operator of the flow solver. To solve the turbulence equations we use a diagonally dominant alternating direction implicit (DDADI) scheme. Computational results are presented for three airfoil flow cases and comparisons are made with experimental data. We demonstrate that the two-dimensional RANS equations and transport-type equations for turbulence modeling can be efficiently solved with an indirectly coupled algorithm that uses the RK/implicit scheme for the flow equations.

Recent Advances in Agglomerated Multigrid

NASA Technical Reports Server (NTRS)

Nishikawa, Hiroaki; Diskin, Boris; Thomas, James L.; Hammond, Dana P.

2013-01-01

We report recent advancements of the agglomerated multigrid methodology for complex flow simulations on fully unstructured grids. An agglomerated multigrid solver is applied to a wide range of test problems from simple two-dimensional geometries to realistic three- dimensional configurations. The solver is evaluated against a single-grid solver and, in some cases, against a structured-grid multigrid solver. Grid and solver issues are identified and overcome, leading to significant improvements over single-grid solvers.

New Nonlinear Multigrid Analysis

NASA Technical Reports Server (NTRS)

Xie, Dexuan

1996-01-01

The nonlinear multigrid is an efficient algorithm for solving the system of nonlinear equations arising from the numerical discretization of nonlinear elliptic boundary problems. In this paper, we present a new nonlinear multigrid analysis as an extension of the linear multigrid theory presented by Bramble. In particular, we prove the convergence of the nonlinear V-cycle method for a class of mildly nonlinear second order elliptic boundary value problems which do not have full elliptic regularity.

Incomplete Augmented Lagrangian Preconditioner for Steady Incompressible Navier-Stokes Equations

PubMed Central

Tan, Ning-Bo; Huang, Ting-Zhu; Hu, Ze-Jun

2013-01-01

An incomplete augmented Lagrangian preconditioner, for the steady incompressible Navier-Stokes equations discretized by stable finite elements, is proposed. The eigenvalues of the preconditioned matrix are analyzed. Numerical experiments show that the incomplete augmented Lagrangian-based preconditioner proposed is very robust and performs quite well by the Picard linearization or the Newton linearization over a wide range of values of the viscosity on both uniform and stretched grids. PMID:24235888

Multigrid approaches to non-linear diffusion problems on unstructured meshes

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.; Bushnell, Dennis M. (Technical Monitor)

2001-01-01

The efficiency of three multigrid methods for solving highly non-linear diffusion problems on two-dimensional unstructured meshes is examined. The three multigrid methods differ mainly in the manner in which the nonlinearities of the governing equations are handled. These comprise a non-linear full approximation storage (FAS) multigrid method which is used to solve the non-linear equations directly, a linear multigrid method which is used to solve the linear system arising from a Newton linearization of the non-linear system, and a hybrid scheme which is based on a non-linear FAS multigrid scheme, but employs a linear solver on each level as a smoother. Results indicate that all methods are equally effective at converging the non-linear residual in a given number of grid sweeps, but that the linear solver is more efficient in cpu time due to the lower cost of linear versus non-linear grid sweeps.

Multigrid schemes for viscous hypersonic flows

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Radespiel, R.

1993-01-01

Several multigrid schemes are considered for the numerical computation of viscous hypersonic flows. For each scheme, the basic solution algorithm employs upwind spatial discretization with explicit multistage time stepping. Two-level versions of the various multigrid algorithms are applied to the two-dimensional advection equation, and Fourier analysis is used to determine their damping properties. The capabilities of the multigrid methods are assessed by solving two different hypersonic flow problems. Some new multigrid schemes, based on semicoarsening strategies, are shown to be quite effective in relieving the stiffness caused by the high-aspect-ratio cells required to resolve high Reynolds number flows. These schemes exhibit good convergence rates for Reynolds numbers up to 200 x 10(exp 6).

Convergence acceleration of the Proteus computer code with multigrid methods

NASA Technical Reports Server (NTRS)

Demuren, A. O.; Ibraheem, S. O.

1995-01-01

This report presents the results of a study to implement convergence acceleration techniques based on the multigrid concept in the two-dimensional and three-dimensional versions of the Proteus computer code. The first section presents a review of the relevant literature on the implementation of the multigrid methods in computer codes for compressible flow analysis. The next two sections present detailed stability analysis of numerical schemes for solving the Euler and Navier-Stokes equations, based on conventional von Neumann analysis and the bi-grid analysis, respectively. The next section presents details of the computational method used in the Proteus computer code. Finally, the multigrid implementation and applications to several two-dimensional and three-dimensional test problems are presented. The results of the present study show that the multigrid method always leads to a reduction in the number of iterations (or time steps) required for convergence. However, there is an overhead associated with the use of multigrid acceleration. The overhead is higher in 2-D problems than in 3-D problems, thus overall multigrid savings in CPU time are in general better in the latter. Savings of about 40-50 percent are typical in 3-D problems, but they are about 20-30 percent in large 2-D problems. The present multigrid method is applicable to steady-state problems and is therefore ineffective in problems with inherently unstable solutions.

The role of grape seed extract in the remineralization of demineralized dentine: micromorphological and physical analyses.

PubMed

Tang, Cheng-fang; Fang, Ming; Liu, Rui-rui; Dou, Qi; Chai, Zhi-guo; Xiao, Yu-hong; Chen, Ji-hua

2013-12-01

Grape seed extract (GSE) is known to have a positive effect on the demineralization and/or remineralization of artificial root caries lesions. The present study aimed to investigate whether biomodification of caries-like acid-etched demineralized dentine, using proanthocyanidins-rich GSE, would promote its remineralization potential. Dentine specimens were acid-etched for 30s, then biomodified using proanthocyanidin-based preconditioners (at different concentrations and pH values) for 2min, followed by a 15-day artificial remineralization regimen. They were subsequently subjected to microhardness measurements, micromorphological evaluation and X-ray diffraction analyses. Stability of the preconditioners was also analyzed, spectrophotometrically. A concentration-dependent increase was observed in the microhardness of the specimens that were biomodified using GSE preconditioners, without pH adjustment. Field emission scanning electron microscopy revealed greater mineral deposition on their surfaces, which was further identified mainly as hydroxylapatite. The absorbances of preconditioner dilutions at pH 7.4 and pH 10.0 decreased at the two typical polyphenol bands. Transient GSE biomodification promoted remineralization on the surface of demineralized dentine, and this process was influenced by the concentration and pH value of the preconditioner. GSE preconditioner at a concentration of 15%, without pH adjustment, presented with the best results, and this may be attributed to its high polyphenolic content. Copyright © 2013 Elsevier Ltd. All rights reserved.

Solving the Fluid Pressure Poisson Equation Using Multigrid-Evaluation and Improvements.

PubMed

Dick, Christian; Rogowsky, Marcus; Westermann, Rudiger

2016-11-01

In many numerical simulations of fluids governed by the incompressible Navier-Stokes equations, the pressure Poisson equation needs to be solved to enforce mass conservation. Multigrid solvers show excellent convergence in simple scenarios, yet they can converge slowly in domains where physically separated regions are combined at coarser scales. Moreover, existing multigrid solvers are tailored to specific discretizations of the pressure Poisson equation, and they cannot easily be adapted to other discretizations. In this paper we analyze the convergence properties of existing multigrid solvers for the pressure Poisson equation in different simulation domains, and we show how to further improve the multigrid convergence rate by using a graph-based extension to determine the coarse grid hierarchy. The proposed multigrid solver is generic in that it can be applied to different kinds of discretizations of the pressure Poisson equation, by using solely the specification of the simulation domain and pre-assembled computational stencils. We analyze the proposed solver in combination with finite difference and finite volume discretizations of the pressure Poisson equation. Our evaluations show that, despite the common assumption, multigrid schemes can exploit their potential even in the most complicated simulation scenarios, yet this behavior is obtained at the price of higher memory consumption.

A universal preconditioner for simulating condensed phase materials.

PubMed

Packwood, David; Kermode, James; Mones, Letif; Bernstein, Noam; Woolley, John; Gould, Nicholas; Ortner, Christoph; Csányi, Gábor

2016-04-28

We introduce a universal sparse preconditioner that accelerates geometry optimisation and saddle point search tasks that are common in the atomic scale simulation of materials. Our preconditioner is based on the neighbourhood structure and we demonstrate the gain in computational efficiency in a wide range of materials that include metals, insulators, and molecular solids. The simple structure of the preconditioner means that the gains can be realised in practice not only when using expensive electronic structure models but also for fast empirical potentials. Even for relatively small systems of a few hundred atoms, we observe speedups of a factor of two or more, and the gain grows with system size. An open source Python implementation within the Atomic Simulation Environment is available, offering interfaces to a wide range of atomistic codes.

A universal preconditioner for simulating condensed phase materials

NASA Astrophysics Data System (ADS)

Packwood, David; Kermode, James; Mones, Letif; Bernstein, Noam; Woolley, John; Gould, Nicholas; Ortner, Christoph; Csányi, Gábor

2016-04-01

We introduce a universal sparse preconditioner that accelerates geometry optimisation and saddle point search tasks that are common in the atomic scale simulation of materials. Our preconditioner is based on the neighbourhood structure and we demonstrate the gain in computational efficiency in a wide range of materials that include metals, insulators, and molecular solids. The simple structure of the preconditioner means that the gains can be realised in practice not only when using expensive electronic structure models but also for fast empirical potentials. Even for relatively small systems of a few hundred atoms, we observe speedups of a factor of two or more, and the gain grows with system size. An open source Python implementation within the Atomic Simulation Environment is available, offering interfaces to a wide range of atomistic codes.

The MueLu Tutorial

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hu, Jonathan Joseph; Wiesner, Tobias A.; Prokopenko, Andrey

2014-10-01

The MueLu tutorial is written as a hands-on tutorial for MueLu, the next generation multigrid framework in Trilinos. It covers the whole spectrum from absolute beginners’ topics to expert level. Since the focus of this tutorial is on practical and technical aspects of multigrid methods in general and MueLu in particular, the reader is expected to have a basic understanding of multigrid methods and its general underlying concepts. Please refer to multigrid textbooks (e.g. [1]) for the theoretical background.

Progress with multigrid schemes for hypersonic flow problems

NASA Technical Reports Server (NTRS)

Radespiel, R.; Swanson, R. C.

1991-01-01

Several multigrid schemes are considered for the numerical computation of viscous hypersonic flows. For each scheme, the basic solution algorithm uses upwind spatial discretization with explicit multistage time stepping. Two level versions of the various multigrid algorithms are applied to the two dimensional advection equation, and Fourier analysis is used to determine their damping properties. The capabilities of the multigrid methods are assessed by solving three different hypersonic flow problems. Some new multigrid schemes based on semicoarsening strategies are shown to be quite effective in relieving the stiffness caused by the high aspect ratio cells required to resolve high Reynolds number flows. These schemes exhibit good convergence rates for Reynolds numbers up to 200 x 10(exp 6) and Mach numbers up to 25.

Incomplete Gröbner basis as a preconditioner for polynomial systems

NASA Astrophysics Data System (ADS)

Sun, Yang; Tao, Yu-Hui; Bai, Feng-Shan

2009-04-01

Precondition plays a critical role in the numerical methods for large and sparse linear systems. It is also true for nonlinear algebraic systems. In this paper incomplete Gröbner basis (IGB) is proposed as a preconditioner of homotopy methods for polynomial systems of equations, which transforms a deficient system into a system with the same finite solutions, but smaller degree. The reduced system can thus be solved faster. Numerical results show the efficiency of the preconditioner.

A universal preconditioner for simulating condensed phase materials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Packwood, David; Ortner, Christoph, E-mail: c.ortner@warwick.ac.uk; Kermode, James, E-mail: j.r.kermode@warwick.ac.uk

2016-04-28

We introduce a universal sparse preconditioner that accelerates geometry optimisation and saddle point search tasks that are common in the atomic scale simulation of materials. Our preconditioner is based on the neighbourhood structure and we demonstrate the gain in computational efficiency in a wide range of materials that include metals, insulators, and molecular solids. The simple structure of the preconditioner means that the gains can be realised in practice not only when using expensive electronic structure models but also for fast empirical potentials. Even for relatively small systems of a few hundred atoms, we observe speedups of a factor ofmore » two or more, and the gain grows with system size. An open source Python implementation within the Atomic Simulation Environment is available, offering interfaces to a wide range of atomistic codes.« less

Annual Copper Mountain Conferences on Multigrid and Iterative Methods, Copper Mountain, Colorado

DOE Office of Scientific and Technical Information (OSTI.GOV)

McCormick, Stephen F.

This project supported the Copper Mountain Conference on Multigrid and Iterative Methods, held from 2007 to 2015, at Copper Mountain, Colorado. The subject of the Copper Mountain Conference Series alternated between Multigrid Methods in odd-numbered years and Iterative Methods in even-numbered years. Begun in 1983, the Series represents an important forum for the exchange of ideas in these two closely related fields. This report describes the Copper Mountain Conference on Multigrid and Iterative Methods, 2007-2015. Information on the conference series is available at http://grandmaster.colorado.edu/~copper/.

Graph Embedding Techniques for Bounding Condition Numbers of Incomplete Factor Preconditioning

NASA Technical Reports Server (NTRS)

Guattery, Stephen

1997-01-01

We extend graph embedding techniques for bounding the spectral condition number of preconditioned systems involving symmetric, irreducibly diagonally dominant M-matrices to systems where the preconditioner is not diagonally dominant. In particular, this allows us to bound the spectral condition number when the preconditioner is based on an incomplete factorization. We provide a review of previous techniques, describe our extension, and give examples both of a bound for a model problem, and of ways in which our techniques give intuitive way of looking at incomplete factor preconditioners.

High order multi-grid methods to solve the Poisson equation

NASA Technical Reports Server (NTRS)

Schaffer, S.

1981-01-01

High order multigrid methods based on finite difference discretization of the model problem are examined. The following methods are described: (1) a fixed high order FMG-FAS multigrid algorithm; (2) the high order methods; and (3) results are presented on four problems using each method with the same underlying fixed FMG-FAS algorithm.

Vectorized multigrid Poisson solver for the CDC CYBER 205

NASA Technical Reports Server (NTRS)

Barkai, D.; Brandt, M. A.

1984-01-01

The full multigrid (FMG) method is applied to the two dimensional Poisson equation with Dirichlet boundary conditions. This has been chosen as a relatively simple test case for examining the efficiency of fully vectorizing of the multigrid method. Data structure and programming considerations and techniques are discussed, accompanied by performance details.

A Critical Study of Agglomerated Multigrid Methods for Diffusion

NASA Technical Reports Server (NTRS)

Thomas, James L.; Nishikawa, Hiroaki; Diskin, Boris

2009-01-01

Agglomerated multigrid techniques used in unstructured-grid methods are studied critically for a model problem representative of laminar diffusion in the incompressible limit. The studied target-grid discretizations and discretizations used on agglomerated grids are typical of current node-centered formulations. Agglomerated multigrid convergence rates are presented using a range of two- and three-dimensional randomly perturbed unstructured grids for simple geometries with isotropic and highly stretched grids. Two agglomeration techniques are used within an overall topology-preserving agglomeration framework. The results show that multigrid with an inconsistent coarse-grid scheme using only the edge terms (also referred to in the literature as a thin-layer formulation) provides considerable speedup over single-grid methods but its convergence deteriorates on finer grids. Multigrid with a Galerkin coarse-grid discretization using piecewise-constant prolongation and a heuristic correction factor is slower and also grid-dependent. In contrast, grid-independent convergence rates are demonstrated for multigrid with consistent coarse-grid discretizations. Actual cycle results are verified using quantitative analysis methods in which parts of the cycle are replaced by their idealized counterparts.

Multigrid solution of the Navier-Stokes equations on highly stretched grids with defect correction

NASA Technical Reports Server (NTRS)

Sockol, Peter M.

1993-01-01

Relaxation-based multigrid solvers for the steady incompressible Navier-Stokes equations are examined to determine their computational speed and robustness. Four relaxation methods with a common discretization have been used as smoothers in a single tailored multigrid procedure. The equations are discretized on a staggered grid with first order upwind used for convection in the relaxation process on all grids and defect correction to second order central on the fine grid introduced once per multigrid cycle. A fixed W(1,1) cycle with full weighting of residuals is used in the FAS multigrid process. The resulting solvers have been applied to three 2D flow problems, over a range of Reynolds numbers, on both uniform and highly stretched grids. In all cases the L(sub 2) norm of the velocity changes is reduced to 10(exp -6) in a few 10's of fine grid sweeps. The results from this study are used to draw conclusions on the strengths and weaknesses of the individual relaxation schemes as well as those of the overall multigrid procedure when used as a solver on highly stretched grids.

Multigrid accelerated simulations for Twisted Mass fermions

NASA Astrophysics Data System (ADS)

Bacchio, Simone; Alexandrou, Constantia; Finkerath, Jacob

2018-03-01

Simulations at physical quark masses are affected by the critical slowing down of the solvers. Multigrid preconditioning has proved to deal effectively with this problem. Multigrid accelerated simulations at the physical value of the pion mass are being performed to generate Nf = 2 and Nf = 2 + 1 + 1 gauge ensembles using twisted mass fermions. The adaptive aggregation-based domain decomposition multigrid solver, referred to as DD-αAMG method, is employed for these simulations. Our simulation strategy consists of an hybrid approach of different solvers, involving the Conjugate Gradient (CG), multi-mass-shift CG and DD-αAMG solvers. We present an analysis of the multigrid performance during the simulations discussing the stability of the method. This significant speeds up the Hybrid Monte Carlo simulation by more than a factor 4 at physical pion mass compared to the usage of the CG solver.

On the connection between multigrid and cyclic reduction

NASA Technical Reports Server (NTRS)

Merriam, M. L.

1984-01-01

A technique is shown whereby it is possible to relate a particular multigrid process to cyclic reduction using purely mathematical arguments. This technique suggest methods for solving Poisson's equation in 1-, 2-, or 3-dimensions with Dirichlet or Neumann boundary conditions. In one dimension the method is exact and, in fact, reduces to cyclic reduction. This provides a valuable reference point for understanding multigrid techniques. The particular multigrid process analyzed is referred to here as Approximate Cyclic Reduction (ACR) and is one of a class known as Multigrid Reduction methods in the literature. It involves one approximation with a known error term. It is possible to relate the error term in this approximation with certain eigenvector components of the error. These are sharply reduced in amplitude by classical relaxation techniques. The approximation can thus be made a very good one.

Algorithmically scalable block preconditioner for fully implicit shallow-water equations in CAM-SE

DOE PAGES

Lott, P. Aaron; Woodward, Carol S.; Evans, Katherine J.

2014-10-19

Performing accurate and efficient numerical simulation of global atmospheric climate models is challenging due to the disparate length and time scales over which physical processes interact. Implicit solvers enable the physical system to be integrated with a time step commensurate with processes being studied. The dominant cost of an implicit time step is the ancillary linear system solves, so we have developed a preconditioner aimed at improving the efficiency of these linear system solves. Our preconditioner is based on an approximate block factorization of the linearized shallow-water equations and has been implemented within the spectral element dynamical core within themore » Community Atmospheric Model (CAM-SE). Furthermore, in this paper we discuss the development and scalability of the preconditioner for a suite of test cases with the implicit shallow-water solver within CAM-SE.« less

Solving Graph Laplacian Systems Through Recursive Bisections and Two-Grid Preconditioning

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ponce, Colin; Vassilevski, Panayot S.

2016-02-18

We present a parallelizable direct method for computing the solution to graph Laplacian-based linear systems derived from graphs that can be hierarchically bipartitioned with small edge cuts. For a graph of size n with constant-size edge cuts, our method decomposes a graph Laplacian in time O(n log n), and then uses that decomposition to perform a linear solve in time O(n log n). We then use the developed technique to design a preconditioner for graph Laplacians that do not have this property. Finally, we augment this preconditioner with a two-grid method that accounts for much of the preconditioner's weaknesses. Wemore » present an analysis of this method, as well as a general theorem for the condition number of a general class of two-grid support graph-based preconditioners. Numerical experiments illustrate the performance of the studied methods.« less

A note on the preconditioner Pm=(I+Sm)

NASA Astrophysics Data System (ADS)

Kohno, Toshiyuki; Niki, Hiroshi

2009-03-01

Kotakemori et al. [H. Kotakemori, K. Harada, M. Morimoto, H. Niki, A comparison theorem for the iterative method with the preconditioner (I+Smax), Journal of Computational and Applied Mathematics 145 (2002) 373-378] have reported that the convergence rate of the iterative method with a preconditioner Pm=(I+Sm) was superior to one of the modified Gauss-Seidel method under the condition. These authors derived a theorem comparing the Gauss-Seidel method with the proposed method. However, through application of a counter example, Wen Li [Wen Li, A note on the preconditioned GaussSeidel (GS) method for linear systems, Journal of Computational and Applied Mathematics 182 (2005) 81-91] pointed out that there exists a special matrix that does not satisfy this comparison theorem. In this note, we analyze the reason why such a to counter example may be produced, and propose a preconditioner to overcome this problem.

Local multiplicative Schwarz algorithms for convection-diffusion equations

NASA Technical Reports Server (NTRS)

Cai, Xiao-Chuan; Sarkis, Marcus

1995-01-01

We develop a new class of overlapping Schwarz type algorithms for solving scalar convection-diffusion equations discretized by finite element or finite difference methods. The preconditioners consist of two components, namely, the usual two-level additive Schwarz preconditioner and the sum of some quadratic terms constructed by using products of ordered neighboring subdomain preconditioners. The ordering of the subdomain preconditioners is determined by considering the direction of the flow. We prove that the algorithms are optimal in the sense that the convergence rates are independent of the mesh size, as well as the number of subdomains. We show by numerical examples that the new algorithms are less sensitive to the direction of the flow than either the classical multiplicative Schwarz algorithms, and converge faster than the additive Schwarz algorithms. Thus, the new algorithms are more suitable for fluid flow applications than the classical additive or multiplicative Schwarz algorithms.

Convergence acceleration of the Proteus computer code with multigrid methods

NASA Technical Reports Server (NTRS)

Demuren, A. O.; Ibraheem, S. O.

1992-01-01

Presented here is the first part of a study to implement convergence acceleration techniques based on the multigrid concept in the Proteus computer code. A review is given of previous studies on the implementation of multigrid methods in computer codes for compressible flow analysis. Also presented is a detailed stability analysis of upwind and central-difference based numerical schemes for solving the Euler and Navier-Stokes equations. Results are given of a convergence study of the Proteus code on computational grids of different sizes. The results presented here form the foundation for the implementation of multigrid methods in the Proteus code.

Multigrid method for the equilibrium equations of elasticity using a compact scheme

NASA Technical Reports Server (NTRS)

Taasan, S.

1986-01-01

A compact difference scheme is derived for treating the equilibrium equations of elasticity. The scheme is inconsistent and unstable. A multigrid method which takes into account these properties is described. The solution of the discrete equations, up to the level of discretization errors, is obtained by this method in just two multigrid cycles.

Unweighted least squares phase unwrapping by means of multigrid techniques

NASA Astrophysics Data System (ADS)

Pritt, Mark D.

1995-11-01

We present a multigrid algorithm for unweighted least squares phase unwrapping. This algorithm applies Gauss-Seidel relaxation schemes to solve the Poisson equation on smaller, coarser grids and transfers the intermediate results to the finer grids. This approach forms the basis of our multigrid algorithm for weighted least squares phase unwrapping, which is described in a separate paper. The key idea of our multigrid approach is to maintain the partial derivatives of the phase data in separate arrays and to correct these derivatives at the boundaries of the coarser grids. This maintains the boundary conditions necessary for rapid convergence to the correct solution. Although the multigrid algorithm is an iterative algorithm, we demonstrate that it is nearly as fast as the direct Fourier-based method. We also describe how to parallelize the algorithm for execution on a distributed-memory parallel processor computer or a network-cluster of workstations.

On a multigrid method for the coupled Stokes and porous media flow problem

NASA Astrophysics Data System (ADS)

Luo, P.; Rodrigo, C.; Gaspar, F. J.; Oosterlee, C. W.

2017-07-01

The multigrid solution of coupled porous media and Stokes flow problems is considered. The Darcy equation as the saturated porous medium model is coupled to the Stokes equations by means of appropriate interface conditions. We focus on an efficient multigrid solution technique for the coupled problem, which is discretized by finite volumes on staggered grids, giving rise to a saddle point linear system. Special treatment is required regarding the discretization at the interface. An Uzawa smoother is employed in multigrid, which is a decoupled procedure based on symmetric Gauss-Seidel smoothing for velocity components and a simple Richardson iteration for the pressure field. Since a relaxation parameter is part of a Richardson iteration, Local Fourier Analysis (LFA) is applied to determine the optimal parameters. Highly satisfactory multigrid convergence is reported, and, moreover, the algorithm performs well for small values of the hydraulic conductivity and fluid viscosity, that are relevant for applications.

Uniform convergence of multigrid V-cycle iterations for indefinite and nonsymmetric problems

NASA Technical Reports Server (NTRS)

Bramble, James H.; Kwak, Do Y.; Pasciak, Joseph E.

1993-01-01

In this paper, we present an analysis of a multigrid method for nonsymmetric and/or indefinite elliptic problems. In this multigrid method various types of smoothers may be used. One type of smoother which we consider is defined in terms of an associated symmetric problem and includes point and line, Jacobi, and Gauss-Seidel iterations. We also study smoothers based entirely on the original operator. One is based on the normal form, that is, the product of the operator and its transpose. Other smoothers studied include point and line, Jacobi, and Gauss-Seidel. We show that the uniform estimates for symmetric positive definite problems carry over to these algorithms. More precisely, the multigrid iteration for the nonsymmetric and/or indefinite problem is shown to converge at a uniform rate provided that the coarsest grid in the multilevel iteration is sufficiently fine (but not depending on the number of multigrid levels).

A new scripting library for modeling flow and transport in fractured rock with channel networks

NASA Astrophysics Data System (ADS)

Dessirier, Benoît; Tsang, Chin-Fu; Niemi, Auli

2018-02-01

Deep crystalline bedrock formations are targeted to host spent nuclear fuel owing to their overall low permeability. They are however highly heterogeneous and only a few preferential paths pertaining to a small set of dominant rock fractures usually carry most of the flow or mass fluxes, a behavior known as channeling that needs to be accounted for in the performance assessment of repositories. Channel network models have been developed and used to investigate the effect of channeling. They are usually simpler than discrete fracture networks based on rock fracture mappings and rely on idealized full or sparsely populated lattices of channels. This study reexamines the fundamental parameter structure required to describe a channel network in terms of groundwater flow and solute transport, leading to an extended description suitable for unstructured arbitrary networks of channels. An implementation of this formalism in a Python scripting library is presented and released along with this article. A new algebraic multigrid preconditioner delivers a significant speedup in the flow solution step compared to previous channel network codes. 3D visualization is readily available for verification and interpretation of the results by exporting the results to an open and free dedicated software. The new code is applied to three example cases to verify its results on full uncorrelated lattices of channels, sparsely populated percolation lattices and to exemplify the use of unstructured networks to accommodate knowledge on local rock fractures.

Un-collided-flux preconditioning for the first order transport equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rigley, M.; Koebbe, J.; Drumm, C.

2013-07-01

Two codes were tested for the first order neutron transport equation using finite element methods. The un-collided-flux solution is used as a preconditioner for each of these methods. These codes include a least squares finite element method and a discontinuous finite element method. The performance of each code is shown on problems in one and two dimensions. The un-collided-flux preconditioner shows good speedup on each of the given methods. The un-collided-flux preconditioner has been used on the second-order equation, and here we extend those results to the first order equation. (authors)

An iterative solver for the 3D Helmholtz equation

NASA Astrophysics Data System (ADS)

Belonosov, Mikhail; Dmitriev, Maxim; Kostin, Victor; Neklyudov, Dmitry; Tcheverda, Vladimir

2017-09-01

We develop a frequency-domain iterative solver for numerical simulation of acoustic waves in 3D heterogeneous media. It is based on the application of a unique preconditioner to the Helmholtz equation that ensures convergence for Krylov subspace iteration methods. Effective inversion of the preconditioner involves the Fast Fourier Transform (FFT) and numerical solution of a series of boundary value problems for ordinary differential equations. Matrix-by-vector multiplication for iterative inversion of the preconditioned matrix involves inversion of the preconditioner and pointwise multiplication of grid functions. Our solver has been verified by benchmarking against exact solutions and a time-domain solver.

A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier-Stokes equations.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shadid, John Nicolas; Elman, Howard; Shuttleworth, Robert R.

2007-04-01

In recent years, considerable effort has been placed on developing efficient and robust solution algorithms for the incompressible Navier-Stokes equations based on preconditioned Krylov methods. These include physics-based methods, such as SIMPLE, and purely algebraic preconditioners based on the approximation of the Schur complement. All these techniques can be represented as approximate block factorization (ABF) type preconditioners. The goal is to decompose the application of the preconditioner into simplified sub-systems in which scalable multi-level type solvers can be applied. In this paper we develop a taxonomy of these ideas based on an adaptation of a generalized approximate factorization of themore » Navier-Stokes system first presented in [25]. This taxonomy illuminates the similarities and differences among these preconditioners and the central role played by efficient approximation of certain Schur complement operators. We then present a parallel computational study that examines the performance of these methods and compares them to an additive Schwarz domain decomposition (DD) algorithm. Results are presented for two and three-dimensional steady state problems for enclosed domains and inflow/outflow systems on both structured and unstructured meshes. The numerical experiments are performed using MPSalsa, a stabilized finite element code.« less

Distributed Relaxation Multigrid and Defect Correction Applied to the Compressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Thomas, J. L.; Diskin, B.; Brandt, A.

1999-01-01

The distributed-relaxation multigrid and defect- correction methods are applied to the two- dimensional compressible Navier-Stokes equations. The formulation is intended for high Reynolds number applications and several applications are made at a laminar Reynolds number of 10,000. A staggered- grid arrangement of variables is used; the coupled pressure and internal energy equations are solved together with multigrid, requiring a block 2x2 matrix solution. Textbook multigrid efficiencies are attained for incompressible and slightly compressible simulations of the boundary layer on a flat plate. Textbook efficiencies are obtained for compressible simulations up to Mach numbers of 0.7 for a viscous wake simulation.

3D Parallel Multigrid Methods for Real-Time Fluid Simulation

NASA Astrophysics Data System (ADS)

Wan, Feifei; Yin, Yong; Zhang, Suiyu

2018-03-01

The multigrid method is widely used in fluid simulation because of its strong convergence. In addition to operating accuracy, operational efficiency is also an important factor to consider in order to enable real-time fluid simulation in computer graphics. For this problem, we compared the performance of the Algebraic Multigrid and the Geometric Multigrid in the V-Cycle and Full-Cycle schemes respectively, and analyze the convergence and speed of different methods. All the calculations are done on the parallel computing of GPU in this paper. Finally, we experiment with the 3D-grid for each scale, and give the exact experimental results.

New multigrid approach for three-dimensional unstructured, adaptive grids

NASA Technical Reports Server (NTRS)

Parthasarathy, Vijayan; Kallinderis, Y.

1994-01-01

A new multigrid method with adaptive unstructured grids is presented. The three-dimensional Euler equations are solved on tetrahedral grids that are adaptively refined or coarsened locally. The multigrid method is employed to propagate the fine grid corrections more rapidly by redistributing the changes-in-time of the solution from the fine grid to the coarser grids to accelerate convergence. A new approach is employed that uses the parent cells of the fine grid cells in an adapted mesh to generate successively coaser levels of multigrid. This obviates the need for the generation of a sequence of independent, nonoverlapping grids as well as the relatively complicated operations that need to be performed to interpolate the solution and the residuals between the independent grids. The solver is an explicit, vertex-based, finite volume scheme that employs edge-based data structures and operations. Spatial discretization is of central-differencing type combined with a special upwind-like smoothing operators. Application cases include adaptive solutions obtained with multigrid acceleration for supersonic and subsonic flow over a bump in a channel, as well as transonic flow around the ONERA M6 wing. Two levels of multigrid resulted in reduction in the number of iterations by a factor of 5.

Multigrid Methods for Fully Implicit Oil Reservoir Simulation

NASA Technical Reports Server (NTRS)

Molenaar, J.

1996-01-01

In this paper we consider the simultaneous flow of oil and water in reservoir rock. This displacement process is modeled by two basic equations: the material balance or continuity equations and the equation of motion (Darcy's law). For the numerical solution of this system of nonlinear partial differential equations there are two approaches: the fully implicit or simultaneous solution method and the sequential solution method. In the sequential solution method the system of partial differential equations is manipulated to give an elliptic pressure equation and a hyperbolic (or parabolic) saturation equation. In the IMPES approach the pressure equation is first solved, using values for the saturation from the previous time level. Next the saturations are updated by some explicit time stepping method; this implies that the method is only conditionally stable. For the numerical solution of the linear, elliptic pressure equation multigrid methods have become an accepted technique. On the other hand, the fully implicit method is unconditionally stable, but it has the disadvantage that in every time step a large system of nonlinear algebraic equations has to be solved. The most time-consuming part of any fully implicit reservoir simulator is the solution of this large system of equations. Usually this is done by Newton's method. The resulting systems of linear equations are then either solved by a direct method or by some conjugate gradient type method. In this paper we consider the possibility of applying multigrid methods for the iterative solution of the systems of nonlinear equations. There are two ways of using multigrid for this job: either we use a nonlinear multigrid method or we use a linear multigrid method to deal with the linear systems that arise in Newton's method. So far only a few authors have reported on the use of multigrid methods for fully implicit simulations. Two-level FAS algorithm is presented for the black-oil equations, and linear multigrid for two-phase flow problems with strong heterogeneities and anisotropies is studied. Here we consider both possibilities. Moreover we present a novel way for constructing the coarse grid correction operator in linear multigrid algorithms. This approach has the advantage in that it preserves the sparsity pattern of the fine grid matrix and it can be extended to systems of equations in a straightforward manner. We compare the linear and nonlinear multigrid algorithms by means of a numerical experiment.

Applications of multigrid software in the atmospheric sciences

NASA Technical Reports Server (NTRS)

Adams, J.; Garcia, R.; Gross, B.; Hack, J.; Haidvogel, D.; Pizzo, V.

1992-01-01

Elliptic partial differential equations from different areas in the atmospheric sciences are efficiently and easily solved utilizing the multigrid software package named MUDPACK. It is demonstrated that the multigrid method is more efficient than other commonly employed techniques, such as Gaussian elimination and fixed-grid relaxation. The efficiency relative to other techniques, both in terms of storage requirement and computational time, increases quickly with grid size.

Repeated Red-Black ordering

NASA Astrophysics Data System (ADS)

Ciarlet, P.

1994-09-01

Hereafter, we describe and analyze, from both a theoretical and a numerical point of view, an iterative method for efficiently solving symmetric elliptic problems with possibly discontinuous coefficients. In the following, we use the Preconditioned Conjugate Gradient method to solve the symmetric positive definite linear systems which arise from the finite element discretization of the problems. We focus our interest on sparse and efficient preconditioners. In order to define the preconditioners, we perform two steps: first we reorder the unknowns and then we carry out a (modified) incomplete factorization of the original matrix. We study numerically and theoretically two preconditioners, the second preconditioner corresponding to the one investigated by Brand and Heinemann [2]. We prove convergence results about the Poisson equation with either Dirichlet or periodic boundary conditions. For a meshsizeh, Brand proved that the condition number of the preconditioned system is bounded byO(h-1/2) for Dirichlet boundary conditions. By slightly modifying the preconditioning process, we prove that the condition number is bounded byO(h-1/3).

A Pseudo-Temporal Multi-Grid Relaxation Scheme for Solving the Parabolized Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

White, J. A.; Morrison, J. H.

1999-01-01

A multi-grid, flux-difference-split, finite-volume code, VULCAN, is presented for solving the elliptic and parabolized form of the equations governing three-dimensional, turbulent, calorically perfect and non-equilibrium chemically reacting flows. The space marching algorithms developed to improve convergence rate and or reduce computational cost are emphasized. The algorithms presented are extensions to the class of implicit pseudo-time iterative, upwind space-marching schemes. A full approximate storage, full multi-grid scheme is also described which is used to accelerate the convergence of a Gauss-Seidel relaxation method. The multi-grid algorithm is shown to significantly improve convergence on high aspect ratio grids.

Textbook Multigrid Efficiency for Leading Edge Stagnation

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.; Mineck, Raymond E.

2004-01-01

A multigrid solver is defined as having textbook multigrid efficiency (TME) if the solutions to the governing system of equations are attained in a computational work which is a small (less than 10) multiple of the operation count in evaluating the discrete residuals. TME in solving the incompressible inviscid fluid equations is demonstrated for leading-edge stagnation flows. The contributions of this paper include (1) a special formulation of the boundary conditions near stagnation allowing convergence of the Newton iterations on coarse grids, (2) the boundary relaxation technique to facilitate relaxation and residual restriction near the boundaries, (3) a modified relaxation scheme to prevent initial error amplification, and (4) new general analysis techniques for multigrid solvers. Convergence of algebraic errors below the level of discretization errors is attained by a full multigrid (FMG) solver with one full approximation scheme (FAS) cycle per grid. Asymptotic convergence rates of the FAS cycles for the full system of flow equations are very fast, approaching those for scalar elliptic equations.

Textbook Multigrid Efficiency for Leading Edge Stagnation

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.; Mineck, Raymond E.

2004-01-01

A multigrid solver is defined as having textbook multigrid efficiency (TME) if the solutions to the governing system of equations are attained in a computational work which is a small (less than 10) multiple of the operation count in evaluating the discrete residuals. TME in solving the incompressible inviscid fluid equations is demonstrated for leading- edge stagnation flows. The contributions of this paper include (1) a special formulation of the boundary conditions near stagnation allowing convergence of the Newton iterations on coarse grids, (2) the boundary relaxation technique to facilitate relaxation and residual restriction near the boundaries, (3) a modified relaxation scheme to prevent initial error amplification, and (4) new general analysis techniques for multigrid solvers. Convergence of algebraic errors below the level of discretization errors is attained by a full multigrid (FMG) solver with one full approximation scheme (F.4S) cycle per grid. Asymptotic convergence rates of the F.4S cycles for the full system of flow equations are very fast, approaching those for scalar elliptic equations.

Numerical Evaluation of P-Multigrid Method for the Solution of Discontinuous Galerkin Discretizations of Diffusive Equations

NASA Technical Reports Server (NTRS)

Atkins, H. L.; Helenbrook, B. T.

2005-01-01

This paper describes numerical experiments with P-multigrid to corroborate analysis, validate the present implementation, and to examine issues that arise in the implementations of the various combinations of relaxation schemes, discretizations and P-multigrid methods. The two approaches to implement P-multigrid presented here are equivalent for most high-order discretization methods such as spectral element, SUPG, and discontinuous Galerkin applied to advection; however it is discovered that the approach that mimics the common geometric multigrid implementation is less robust, and frequently unstable when applied to discontinuous Galerkin discretizations of di usion. Gauss-Seidel relaxation converges 40% faster than block Jacobi, as predicted by analysis; however, the implementation of Gauss-Seidel is considerably more expensive that one would expect because gradients in most neighboring elements must be updated. A compromise quasi Gauss-Seidel relaxation method that evaluates the gradient in each element twice per iteration converges at rates similar to those predicted for true Gauss-Seidel.

A multigrid nonoscillatory method for computing high speed flows

NASA Technical Reports Server (NTRS)

Li, C. P.; Shieh, T. H.

1993-01-01

A multigrid method using different smoothers has been developed to solve the Euler equations discretized by a nonoscillatory scheme up to fourth order accuracy. The best smoothing property is provided by a five-stage Runge-Kutta technique with optimized coefficients, yet the most efficient smoother is a backward Euler technique in factored and diagonalized form. The singlegrid solution for a hypersonic, viscous conic flow is in excellent agreement with the solution obtained by the third order MUSCL and Roe's method. Mach 8 inviscid flow computations for a complete entry probe have shown that the accuracy is at least as good as the symmetric TVD scheme of Yee and Harten. The implicit multigrid method is four times more efficient than the explicit multigrid technique and 3.5 times faster than the single-grid implicit technique. For a Mach 8.7 inviscid flow over a blunt delta wing at 30 deg incidence, the CPU reduction factor from the three-level multigrid computation is 2.2 on a grid of 37 x 41 x 73 nodes.

A Conforming Multigrid Method for the Pure Traction Problem of Linear Elasticity: Mixed Formulation

NASA Technical Reports Server (NTRS)

Lee, Chang-Ock

1996-01-01

A multigrid method using conforming P-1 finite element is developed for the two-dimensional pure traction boundary value problem of linear elasticity. The convergence is uniform even as the material becomes nearly incompressible. A heuristic argument for acceleration of the multigrid method is discussed as well. Numerical results with and without this acceleration as well as performance estimates on a parallel computer are included.

A matrix dependent/algebraic multigrid approach for extruded meshes with applications to ice sheet modeling

DOE PAGES

Tuminaro, Raymond S.; Perego, Mauro; Tezaur, Irina Kalashnikova; ...

2016-10-06

A multigrid method is proposed that combines ideas from matrix dependent multigrid for structured grids and algebraic multigrid for unstructured grids. It targets problems where a three-dimensional mesh can be viewed as an extrusion of a two-dimensional, unstructured mesh in a third dimension. Our motivation comes from the modeling of thin structures via finite elements and, more specifically, the modeling of ice sheets. Extruded meshes are relatively common for thin structures and often give rise to anisotropic problems when the thin direction mesh spacing is much smaller than the broad direction mesh spacing. Within our approach, the first few multigridmore » hierarchy levels are obtained by applying matrix dependent multigrid to semicoarsen in a structured thin direction fashion. After sufficient structured coarsening, the resulting mesh contains only a single layer corresponding to a two-dimensional, unstructured mesh. Algebraic multigrid can then be employed in a standard manner to create further coarse levels, as the anisotropic phenomena is no longer present in the single layer problem. The overall approach remains fully algebraic, with the minor exception that some additional information is needed to determine the extruded direction. Furthermore, this facilitates integration of the solver with a variety of different extruded mesh applications.« less

Multigrid methods in structural mechanics

NASA Technical Reports Server (NTRS)

Raju, I. S.; Bigelow, C. A.; Taasan, S.; Hussaini, M. Y.

1986-01-01

Although the application of multigrid methods to the equations of elasticity has been suggested, few such applications have been reported in the literature. In the present work, multigrid techniques are applied to the finite element analysis of a simply supported Bernoulli-Euler beam, and various aspects of the multigrid algorithm are studied and explained in detail. In this study, six grid levels were used to model half the beam. With linear prolongation and sequential ordering, the multigrid algorithm yielded results which were of machine accuracy with work equivalent to 200 standard Gauss-Seidel iterations on the fine grid. Also with linear prolongation and sequential ordering, the V(1,n) cycle with n greater than 2 yielded better convergence rates than the V(n,1) cycle. The restriction and prolongation operators were derived based on energy principles. Conserving energy during the inter-grid transfers required that the prolongation operator be the transpose of the restriction operator, and led to improved convergence rates. With energy-conserving prolongation and sequential ordering, the multigrid algorithm yielded results of machine accuracy with a work equivalent to 45 Gauss-Seidel iterations on the fine grid. The red-black ordering of relaxations yielded solutions of machine accuracy in a single V(1,1) cycle, which required work equivalent to about 4 iterations on the finest grid level.

Implementation and Optimization of miniGMG - a Compact Geometric Multigrid Benchmark

DOE Office of Scientific and Technical Information (OSTI.GOV)

Williams, Samuel; Kalamkar, Dhiraj; Singh, Amik

2012-12-01

Multigrid methods are widely used to accelerate the convergence of iterative solvers for linear systems used in a number of different application areas. In this report, we describe miniGMG, our compact geometric multigrid benchmark designed to proxy the multigrid solves found in AMR applications. We explore optimization techniques for geometric multigrid on existing and emerging multicore systems including the Opteron-based Cray XE6, Intel Sandy Bridge and Nehalem-based Infiniband clusters, as well as manycore-based architectures including NVIDIA's Fermi and Kepler GPUs and Intel's Knights Corner (KNC) co-processor. This report examines a variety of novel techniques including communication-aggregation, threaded wavefront-based DRAM communication-avoiding,more » dynamic threading decisions, SIMDization, and fusion of operators. We quantify performance through each phase of the V-cycle for both single-node and distributed-memory experiments and provide detailed analysis for each class of optimization. Results show our optimizations yield significant speedups across a variety of subdomain sizes while simultaneously demonstrating the potential of multi- and manycore processors to dramatically accelerate single-node performance. However, our analysis also indicates that improvements in networks and communication will be essential to reap the potential of manycore processors in large-scale multigrid calculations.« less

Wetland Plants of Specialized Habitats in the Arid West

DTIC Science & Technology

2007-06-01

NO FACW NO NO FACW Xanthium strumarium L. FAC- NI FAC FAC FAC+ Yucca brevifolia Engelm. UPL UPL UPL UPL UPL 1 Barbour and Billings (1988) 7...FACW FAC Washingtonia filifera (L. Linden) H. Wendl. 2,7 NO FACW NO NO FACW Xanthium strumarium L. FAC- NI FAC FAC FAC+ Yucca brevifolia

Recent Development of Multigrid Algorithms for Mixed and Noncomforming Methods for Second Order Elliptical Problems

NASA Technical Reports Server (NTRS)

Chen, Zhangxin; Ewing, Richard E.

1996-01-01

Multigrid algorithms for nonconforming and mixed finite element methods for second order elliptic problems on triangular and rectangular finite elements are considered. The construction of several coarse-to-fine intergrid transfer operators for nonconforming multigrid algorithms is discussed. The equivalence between the nonconforming and mixed finite element methods with and without projection of the coefficient of the differential problems into finite element spaces is described.

Stability analysis of multigrid acceleration methods for the solution of partial differential equations

NASA Technical Reports Server (NTRS)

Fay, John F.

1990-01-01

A calculation is made of the stability of various relaxation schemes for the numerical solution of partial differential equations. A multigrid acceleration method is introduced, and its effects on stability are explored. A detailed stability analysis of a simple case is carried out and verified by numerical experiment. It is shown that the use of multigrids can speed convergence by several orders of magnitude without adversely affecting stability.

Segmental Refinement: A Multigrid Technique for Data Locality

DOE PAGES

Adams, Mark F.; Brown, Jed; Knepley, Matt; ...

2016-08-04

In this paper, we investigate a domain decomposed multigrid technique, termed segmental refinement, for solving general nonlinear elliptic boundary value problems. We extend the method first proposed in 1994 by analytically and experimentally investigating its complexity. We confirm that communication of traditional parallel multigrid is eliminated on fine grids, with modest amounts of extra work and storage, while maintaining the asymptotic exactness of full multigrid. We observe an accuracy dependence on the segmental refinement subdomain size, which was not considered in the original analysis. Finally, we present a communication complexity analysis that quantifies the communication costs ameliorated by segmental refinementmore » and report performance results with up to 64K cores on a Cray XC30.« less

Textbook Multigrid Efficiency for the Steady Euler Equations

NASA Technical Reports Server (NTRS)

Roberts, Thomas W.; Sidilkover, David; Swanson, R. C.

2004-01-01

A fast multigrid solver for the steady incompressible Euler equations is presented. Unlike time-marching schemes, this approach uses relaxation of the steady equations. Application of this method results in a discretization that correctly distinguishes between the advection and elliptic parts of the operator, allowing efficient smoothers to be constructed. Solvers for both unstructured triangular grids and structured quadrilateral grids have been written. Computations for channel flow and flow over a nonlifting airfoil have computed. Using Gauss-Seidel relaxation ordered in the flow direction, textbook multigrid convergence rates of nearly one order-of-magnitude residual reduction per multigrid cycle are achieved, independent of the grid spacing. This approach also may be applied to the compressible Euler equations and the incompressible Navier-Stokes equations.

New Multigrid Method Including Elimination Algolithm Based on High-Order Vector Finite Elements in Three Dimensional Magnetostatic Field Analysis

NASA Astrophysics Data System (ADS)

Hano, Mitsuo; Hotta, Masashi

A new multigrid method based on high-order vector finite elements is proposed in this paper. Low level discretizations in this method are obtained by using low-order vector finite elements for the same mesh. Gauss-Seidel method is used as a smoother, and a linear equation of lowest level is solved by ICCG method. But it is often found that multigrid solutions do not converge into ICCG solutions. An elimination algolithm of constant term using a null space of the coefficient matrix is also described. In three dimensional magnetostatic field analysis, convergence time and number of iteration of this multigrid method are discussed with the convectional ICCG method.

Algorithms for parallel and vector computations

NASA Technical Reports Server (NTRS)

Ortega, James M.

1995-01-01

This is a final report on work performed under NASA grant NAG-1-1112-FOP during the period March, 1990 through February 1995. Four major topics are covered: (1) solution of nonlinear poisson-type equations; (2) parallel reduced system conjugate gradient method; (3) orderings for conjugate gradient preconditioners, and (4) SOR as a preconditioner.

A highly parallel multigrid-like method for the solution of the Euler equations

NASA Technical Reports Server (NTRS)

Tuminaro, Ray S.

1989-01-01

We consider a highly parallel multigrid-like method for the solution of the two dimensional steady Euler equations. The new method, introduced as filtering multigrid, is similar to a standard multigrid scheme in that convergence on the finest grid is accelerated by iterations on coarser grids. In the filtering method, however, additional fine grid subproblems are processed concurrently with coarse grid computations to further accelerate convergence. These additional problems are obtained by splitting the residual into a smooth and an oscillatory component. The smooth component is then used to form a coarse grid problem (similar to standard multigrid) while the oscillatory component is used for a fine grid subproblem. The primary advantage in the filtering approach is that fewer iterations are required and that most of the additional work per iteration can be performed in parallel with the standard coarse grid computations. We generalize the filtering algorithm to a version suitable for nonlinear problems. We emphasize that this generalization is conceptually straight-forward and relatively easy to implement. In particular, no explicit linearization (e.g., formation of Jacobians) needs to be performed (similar to the FAS multigrid approach). We illustrate the nonlinear version by applying it to the Euler equations, and presenting numerical results. Finally, a performance evaluation is made based on execution time models and convergence information obtained from numerical experiments.

A scalable block-preconditioning strategy for divergence-conforming B-spline discretizations of the Stokes problem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cortes, Adriano M.; Dalcin, Lisandro; Sarmiento, Adel F.

The recently introduced divergence-conforming B-spline discretizations allow the construction of smooth discrete velocity–pressure pairs for viscous incompressible flows that are at the same time inf–sup stable and pointwise divergence-free. When applied to the discretized Stokes problem, these spaces generate a symmetric and indefinite saddle-point linear system. The iterative method of choice to solve such system is the Generalized Minimum Residual Method. This method lacks robustness, and one remedy is to use preconditioners. For linear systems of saddle-point type, a large family of preconditioners can be obtained by using a block factorization of the system. In this paper, we show howmore » the nesting of “black-box” solvers and preconditioners can be put together in a block triangular strategy to build a scalable block preconditioner for the Stokes system discretized by divergence-conforming B-splines. Lastly, besides the known cavity flow problem, we used for benchmark flows defined on complex geometries: an eccentric annulus and hollow torus of an eccentric annular cross-section.« less

Assessment of Preconditioner for a USM3D Hierarchical Adaptive Nonlinear Method (HANIM) (Invited)

NASA Technical Reports Server (NTRS)

Pandya, Mohagna J.; Diskin, Boris; Thomas, James L.; Frink, Neal T.

2016-01-01

Enhancements to the previously reported mixed-element USM3D Hierarchical Adaptive Nonlinear Iteration Method (HANIM) framework have been made to further improve robustness, efficiency, and accuracy of computational fluid dynamic simulations. The key enhancements include a multi-color line-implicit preconditioner, a discretely consistent symmetry boundary condition, and a line-mapping method for the turbulence source term discretization. The USM3D iterative convergence for the turbulent flows is assessed on four configurations. The configurations include a two-dimensional (2D) bump-in-channel, the 2D NACA 0012 airfoil, a three-dimensional (3D) bump-in-channel, and a 3D hemisphere cylinder. The Reynolds Averaged Navier Stokes (RANS) solutions have been obtained using a Spalart-Allmaras turbulence model and families of uniformly refined nested grids. Two types of HANIM solutions using line- and point-implicit preconditioners have been computed. Additional solutions using the point-implicit preconditioner alone (PA) method that broadly represents the baseline solver technology have also been computed. The line-implicit HANIM shows superior iterative convergence in most cases with progressively increasing benefits on finer grids.

A scalable block-preconditioning strategy for divergence-conforming B-spline discretizations of the Stokes problem

DOE PAGES

Cortes, Adriano M.; Dalcin, Lisandro; Sarmiento, Adel F.; ...

2016-10-19

The recently introduced divergence-conforming B-spline discretizations allow the construction of smooth discrete velocity–pressure pairs for viscous incompressible flows that are at the same time inf–sup stable and pointwise divergence-free. When applied to the discretized Stokes problem, these spaces generate a symmetric and indefinite saddle-point linear system. The iterative method of choice to solve such system is the Generalized Minimum Residual Method. This method lacks robustness, and one remedy is to use preconditioners. For linear systems of saddle-point type, a large family of preconditioners can be obtained by using a block factorization of the system. In this paper, we show howmore » the nesting of “black-box” solvers and preconditioners can be put together in a block triangular strategy to build a scalable block preconditioner for the Stokes system discretized by divergence-conforming B-splines. Lastly, besides the known cavity flow problem, we used for benchmark flows defined on complex geometries: an eccentric annulus and hollow torus of an eccentric annular cross-section.« less

An overlapped grid method for multigrid, finite volume/difference flow solvers: MaGGiE

NASA Technical Reports Server (NTRS)

Baysal, Oktay; Lessard, Victor R.

1990-01-01

The objective is to develop a domain decomposition method via overlapping/embedding the component grids, which is to be used by upwind, multi-grid, finite volume solution algorithms. A computer code, given the name MaGGiE (Multi-Geometry Grid Embedder) is developed to meet this objective. MaGGiE takes independently generated component grids as input, and automatically constructs the composite mesh and interpolation data, which can be used by the finite volume solution methods with or without multigrid convergence acceleration. Six demonstrative examples showing various aspects of the overlap technique are presented and discussed. These cases are used for developing the procedure for overlapping grids of different topologies, and to evaluate the grid connection and interpolation data for finite volume calculations on a composite mesh. Time fluxes are transferred between mesh interfaces using a trilinear interpolation procedure. Conservation losses are minimal at the interfaces using this method. The multi-grid solution algorithm, using the coaser grid connections, improves the convergence time history as compared to the solution on composite mesh without multi-gridding.

Multigrid methods for bifurcation problems: The self adjoint case

NASA Technical Reports Server (NTRS)

Taasan, Shlomo

1987-01-01

This paper deals with multigrid methods for computational problems that arise in the theory of bifurcation and is restricted to the self adjoint case. The basic problem is to solve for arcs of solutions, a task that is done successfully with an arc length continuation method. Other important issues are, for example, detecting and locating singular points as part of the continuation process, switching branches at bifurcation points, etc. Multigrid methods have been applied to continuation problems. These methods work well at regular points and at limit points, while they may encounter difficulties in the vicinity of bifurcation points. A new continuation method that is very efficient also near bifurcation points is presented here. The other issues mentioned above are also treated very efficiently with appropriate multigrid algorithms. For example, it is shown that limit points and bifurcation points can be solved for directly by a multigrid algorithm. Moreover, the algorithms presented here solve the corresponding problems in just a few work units (about 10 or less), where a work unit is the work involved in one local relaxation on the finest grid.

Conduct of the International Multigrid Conference

NASA Technical Reports Server (NTRS)

Mccormick, S.

1984-01-01

The 1983 International Multigrid Conference was held at Colorado's Copper Mountain Ski Resort, April 5-8. It was organized jointly by the Institute for Computational Studies at Colorado State University, U.S.A., and the Gasellschaft fur Mathematik und Datenverarbeitung Bonn, F.R. Germany, and was sponsored by the Air Force Office of Sponsored Research and National Aeronautics and Space Administration Headquarters. The conference was attended by 80 scientists, divided by institution almost equally into private industry, research laboratories, and academia. Fifteen attendees came from countries other than the U.S.A. In addition to the fruitful discussions, the most significant factor of the conference was of course the lectures. The lecturers include most of the leaders in the field of multigrid research. The program offered a nice integrated blend of theory, numerical studies, basic research, and applications. Some of the new areas of research that have surfaced since the Koln-Porz conference include: the algebraic multigrid approach; multigrid treatment of Euler equations for inviscid fluid flow problems; 3-D problems; and the application of MG methods on vector and parallel computers.

An O(Nm(sup 2)) Plane Solver for the Compressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Thomas, J. L.; Bonhaus, D. L.; Anderson, W. K.; Rumsey, C. L.; Biedron, R. T.

1999-01-01

A hierarchical multigrid algorithm for efficient steady solutions to the two-dimensional compressible Navier-Stokes equations is developed and demonstrated. The algorithm applies multigrid in two ways: a Full Approximation Scheme (FAS) for a nonlinear residual equation and a Correction Scheme (CS) for a linearized defect correction implicit equation. Multigrid analyses which include the effect of boundary conditions in one direction are used to estimate the convergence rate of the algorithm for a model convection equation. Three alternating-line- implicit algorithms are compared in terms of efficiency. The analyses indicate that full multigrid efficiency is not attained in the general case; the number of cycles to attain convergence is dependent on the mesh density for high-frequency cross-stream variations. However, the dependence is reasonably small and fast convergence is eventually attained for any given frequency with either the FAS or the CS scheme alone. The paper summarizes numerical computations for which convergence has been attained to within truncation error in a few multigrid cycles for both inviscid and viscous ow simulations on highly stretched meshes.

Directional Agglomeration Multigrid Techniques for High Reynolds Number Viscous Flow Solvers

NASA Technical Reports Server (NTRS)

1998-01-01

A preconditioned directional-implicit agglomeration algorithm is developed for solving two- and three-dimensional viscous flows on highly anisotropic unstructured meshes of mixed-element types. The multigrid smoother consists of a pre-conditioned point- or line-implicit solver which operates on lines constructed in the unstructured mesh using a weighted graph algorithm. Directional coarsening or agglomeration is achieved using a similar weighted graph algorithm. A tight coupling of the line construction and directional agglomeration algorithms enables the use of aggressive coarsening ratios in the multigrid algorithm, which in turn reduces the cost of a multigrid cycle. Convergence rates which are independent of the degree of grid stretching are demonstrated in both two and three dimensions. Further improvement of the three-dimensional convergence rates through a GMRES technique is also demonstrated.

Directional Agglomeration Multigrid Techniques for High-Reynolds Number Viscous Flows

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.

1998-01-01

A preconditioned directional-implicit agglomeration algorithm is developed for solving two- and three-dimensional viscous flows on highly anisotropic unstructured meshes of mixed-element types. The multigrid smoother consists of a pre-conditioned point- or line-implicit solver which operates on lines constructed in the unstructured mesh using a weighted graph algorithm. Directional coarsening or agglomeration is achieved using a similar weighted graph algorithm. A tight coupling of the line construction and directional agglomeration algorithms enables the use of aggressive coarsening ratios in the multigrid algorithm, which in turn reduces the cost of a multigrid cycle. Convergence rates which are independent of the degree of grid stretching are demonstrated in both two and three dimensions. Further improvement of the three-dimensional convergence rates through a GMRES technique is also demonstrated.

Hydrodynamics of suspensions of passive and active rigid particles: a rigid multiblob approach

DOE PAGES

Usabiaga, Florencio Balboa; Kallemov, Bakytzhan; Delmotte, Blaise; ...

2016-01-12

We develop a rigid multiblob method for numerically solving the mobility problem for suspensions of passive and active rigid particles of complex shape in Stokes flow in unconfined, partially confined, and fully confined geometries. As in a number of existing methods, we discretize rigid bodies using a collection of minimally resolved spherical blobs constrained to move as a rigid body, to arrive at a potentially large linear system of equations for the unknown Lagrange multipliers and rigid-body motions. Here we develop a block-diagonal preconditioner for this linear system and show that a standard Krylov solver converges in a modest numbermore » of iterations that is essentially independent of the number of particles. Key to the efficiency of the method is a technique for fast computation of the product of the blob-blob mobility matrix and a vector. For unbounded suspensions, we rely on existing analytical expressions for the Rotne-Prager-Yamakawa tensor combined with a fast multipole method (FMM) to obtain linear scaling in the number of particles. For suspensions sedimented against a single no-slip boundary, we use a direct summation on a graphical processing unit (GPU), which gives quadratic asymptotic scaling with the number of particles. For fully confined domains, such as periodic suspensions or suspensions confined in slit and square channels, we extend a recently developed rigid-body immersed boundary method by B. Kallemov, A. P. S. Bhalla, B. E. Griffith, and A. Donev (Commun. Appl. Math. Comput. Sci. 11 (2016), no. 1, 79-141) to suspensions of freely moving passive or active rigid particles at zero Reynolds number. We demonstrate that the iterative solver for the coupled fluid and rigid-body equations converges in a bounded number of iterations regardless of the system size. In our approach, each iteration only requires a few cycles of a geometric multigrid solver for the Poisson equation, and an application of the block-diagonal preconditioner, leading to linear scaling with the number of particles. We optimize a number of parameters in the iterative solvers and apply our method to a variety of benchmark problems to carefully assess the accuracy of the rigid multiblob approach as a function of the resolution. We also model the dynamics of colloidal particles studied in recent experiments, such as passive boomerangs in a slit channel, as well as a pair of non-Brownian active nanorods sedimented against a wall.« less

Multigrid-based reconstruction algorithm for quantitative photoacoustic tomography

PubMed Central

Li, Shengfu; Montcel, Bruno; Yuan, Zhen; Liu, Wanyu; Vray, Didier

2015-01-01

This paper proposes a multigrid inversion framework for quantitative photoacoustic tomography reconstruction. The forward model of optical fluence distribution and the inverse problem are solved at multiple resolutions. A fixed-point iteration scheme is formulated for each resolution and used as a cost function. The simulated and experimental results for quantitative photoacoustic tomography reconstruction show that the proposed multigrid inversion can dramatically reduce the required number of iterations for the optimization process without loss of reliability in the results. PMID:26203371

Multigrid solution of internal flows using unstructured solution adaptive meshes

NASA Technical Reports Server (NTRS)

Smith, Wayne A.; Blake, Kenneth R.

1992-01-01

This is the final report of the NASA Lewis SBIR Phase 2 Contract Number NAS3-25785, Multigrid Solution of Internal Flows Using Unstructured Solution Adaptive Meshes. The objective of this project, as described in the Statement of Work, is to develop and deliver to NASA a general three-dimensional Navier-Stokes code using unstructured solution-adaptive meshes for accuracy and multigrid techniques for convergence acceleration. The code will primarily be applied, but not necessarily limited, to high speed internal flows in turbomachinery.

Techniques and Software for Monolithic Preconditioning of Moderately-sized Geodynamic Stokes Flow Problems

NASA Astrophysics Data System (ADS)

Sanan, Patrick; May, Dave A.; Schenk, Olaf; Bollhöffer, Matthias

2017-04-01

Geodynamics simulations typically involve the repeated solution of saddle-point systems arising from the Stokes equations. These computations often dominate the time to solution. Direct solvers are known for their robustness and ``black box'' properties, yet exhibit superlinear memory requirements and time to solution. More complex multilevel-preconditioned iterative solvers have been very successful for large problems, yet their use can require more effort from the practitioner in terms of setting up a solver and choosing its parameters. We champion an intermediate approach, based on leveraging the power of modern incomplete factorization techniques for indefinite symmetric matrices. These provide an interesting alternative in situations in between the regimes where direct solvers are an obvious choice and those where complex, scalable, iterative solvers are an obvious choice. That is, much like their relatives for definite systems, ILU/ICC-preconditioned Krylov methods and ILU/ICC-smoothed multigrid methods, the approaches demonstrated here provide a useful addition to the solver toolkit. We present results with a simple, PETSc-based, open-source Q2-Q1 (Taylor-Hood) finite element discretization, in 2 and 3 dimensions, with the Stokes and Lamé (linear elasticity) saddle point systems. Attention is paid to cases in which full-operator incomplete factorization gives an improvement in time to solution over direct solution methods (which may not even be feasible due to memory limitations), without the complication of more complex (or at least, less-automatic) preconditioners or smoothers. As an important factor in the relevance of these tools is their availability in portable software, we also describe open-source PETSc interfaces to the factorization routines.

Incomplete Sparse Approximate Inverses for Parallel Preconditioning

DOE PAGES

Anzt, Hartwig; Huckle, Thomas K.; Bräckle, Jürgen; ...

2017-10-28

In this study, we propose a new preconditioning method that can be seen as a generalization of block-Jacobi methods, or as a simplification of the sparse approximate inverse (SAI) preconditioners. The “Incomplete Sparse Approximate Inverses” (ISAI) is in particular efficient in the solution of sparse triangular linear systems of equations. Those arise, for example, in the context of incomplete factorization preconditioning. ISAI preconditioners can be generated via an algorithm providing fine-grained parallelism, which makes them attractive for hardware with a high concurrency level. Finally, in a study covering a large number of matrices, we identify the ISAI preconditioner as anmore » attractive alternative to exact triangular solves in the context of incomplete factorization preconditioning.« less

Efficient Implementation of Multigrid Solvers on Message-Passing Parrallel Systems

NASA Technical Reports Server (NTRS)

Lou, John

1994-01-01

We discuss our implementation strategies for finite difference multigrid partial differential equation (PDE) solvers on message-passing systems. Our target parallel architecture is Intel parallel computers: the Delta and Paragon system.

Multistage Schemes with Multigrid for Euler and Navier-Strokes Equations: Components and Analysis

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Turkel, Eli

1997-01-01

A class of explicit multistage time-stepping schemes with centered spatial differencing and multigrids are considered for the compressible Euler and Navier-Stokes equations. These schemes are the basis for a family of computer programs (flow codes with multigrid (FLOMG) series) currently used to solve a wide range of fluid dynamics problems, including internal and external flows. In this paper, the components of these multistage time-stepping schemes are defined, discussed, and in many cases analyzed to provide additional insight into their behavior. Special emphasis is given to numerical dissipation, stability of Runge-Kutta schemes, and the convergence acceleration techniques of multigrid and implicit residual smoothing. Both the Baldwin and Lomax algebraic equilibrium model and the Johnson and King one-half equation nonequilibrium model are used to establish turbulence closure. Implementation of these models is described.

Higher-order differencing method with a multigrid approach for the solution of the incompressible flow equations at high Reynolds numbers

NASA Astrophysics Data System (ADS)

Tzanos, Constantine P.

1992-10-01

A higher-order differencing scheme (Tzanos, 1990) is used in conjunction with a multigrid approach to obtain accurate solutions of the Navier-Stokes convection-diffusion equations at high Re numbers. Flow in a square cavity with a moving lid is used as a test problem. a multigrid approach based on the additive correction method (Settari and Aziz) and an iterative incomplete lower and upper solver demonstrated good performance for the whole range of Re number under consideration (from 1000 to 10,000) and for both uniform and nonuniform grids. It is concluded that the combination of the higher-order differencing scheme with a multigrid approach proved to be an effective technique for giving accurate solutions of the Navier-Stokes equations at high Re numbers.

Adjudication Decision Support (ADS) System Automated Approval Estimates for NACLC Investigations

DTIC Science & Technology

2007-05-01

each less than 1 week • Credit status: 21 open accounts Case 459 • Child born abroad of U.S. parents • Parent-in-law born in Hungary, said to...WAC attorney WAC chat room FAC account FAC authenticat FAC child custody WAC accus FAC avenge FAC child endangerment WAC addict FAC B&E WAC Child ...enforcement WAC adjournment WAC bad WAC child support WAC adjudicat FAC bail WAC chronic WAC advers FAC balance WAC civil case WAC advis WAC

Generation of field-aligned currents and Alfven waves by 3D magnetic reconnection

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ma, Z.W.; Lee, L.C.; Otto, A.

1995-07-01

The authors have carried out a three-dimensional compressible MHD simulation to study the generation of field-aligned currents (FAC`s) and Alfven waves by magnetic reconnection for locally antiparallel magnetic fields across the current sheet. Reconnection is triggered by a localized resistivity. The results indicate that both FAC`s and Alfven waves are generated by the three-dimensional reconnection process. Two pairs of FAC`s are generated on each side of current sheet. The polarities of the resulting FAC pair in the leading bulge region are opposite to those of a FAC pair in the trailing quasi-steady region. It is further found that a largemore » portion of the FAC`s ({approximately}40%) is located in the closed field line region. They examine the Walen relation between FAC and parallel vorticity and find that Alfven waves are generated and propagate away from the reconnection site. They discuss the relevance of the results to the observed Region 1 FAC`s at noon. 15 refs., 4 figs.« less

Multigrid Approach to Incompressible Viscous Cavity Flows

NASA Technical Reports Server (NTRS)

Wood, William A.

1996-01-01

Two-dimensional incompressible viscous driven-cavity flows are computed for Reynolds numbers on the range 100-20,000 using a loosely coupled, implicit, second-order centrally-different scheme. Mesh sequencing and three-level V-cycle multigrid error smoothing are incorporated into the symmetric Gauss-Seidel time-integration algorithm. Parametrics on the numerical parameters are performed, achieving reductions in solution times by more than 60 percent with the full multigrid approach. Details of the circulation patterns are investigated in cavities of 2-to-1, 1-to-1, and 1-to-2 depth to width ratios.

Multigrid Methods: Proceedings of the Copper Mountain Conference on Multigrid Methods (3rd) Held in Copper Mountain, Colorado on April 5-10, 1987

DTIC Science & Technology

1988-08-01

Time Series 53. J. Barros-Neto and R. A. Artino, Hypoelliptic Boundary-Value Problems 54. R. L. Sternberg, A. J. Kalinowski, and J. S. Papadakis... Systems 95. C E. AuL Rings of Continuous Functions 96. R. Chuaqui, Analysis , Geometry, and Probability 97. L. Fuchs and L. Sace, Modules Over...Local Refinements for a Class of Nonshared Memory Systems 449 Hermann Mierendorif Analysis of a Multigrid Method for the Euler Equations of Gas Dynamics

An Upwind Multigrid Algorithm for Calculating Flows on Unstructured Grids

NASA Technical Reports Server (NTRS)

Bonhaus, Daryl L.

1993-01-01

An algorithm is described that calculates inviscid, laminar, and turbulent flows on triangular meshes with an upwind discretization. A brief description of the base solver and the multigrid implementation is given, followed by results that consist mainly of convergence rates for inviscid and viscous flows over a NACA four-digit airfoil section. The results show that multigrid does accelerate convergence when the same relaxation parameters that yield good single-grid performance are used; however, larger gains in performance can be realized by doing less work in the relaxation scheme.

A positivity-preserving, implicit defect-correction multigrid method for turbulent combustion

NASA Astrophysics Data System (ADS)

Wasserman, M.; Mor-Yossef, Y.; Greenberg, J. B.

2016-07-01

A novel, robust multigrid method for the simulation of turbulent and chemically reacting flows is developed. A survey of previous attempts at implementing multigrid for the problems at hand indicated extensive use of artificial stabilization to overcome numerical instability arising from non-linearity of turbulence and chemistry model source-terms, small-scale physics of combustion, and loss of positivity. These issues are addressed in the current work. The highly stiff Reynolds-averaged Navier-Stokes (RANS) equations, coupled with turbulence and finite-rate chemical kinetics models, are integrated in time using the unconditionally positive-convergent (UPC) implicit method. The scheme is successfully extended in this work for use with chemical kinetics models, in a fully-coupled multigrid (FC-MG) framework. To tackle the degraded performance of multigrid methods for chemically reacting flows, two major modifications are introduced with respect to the basic, Full Approximation Storage (FAS) approach. First, a novel prolongation operator that is based on logarithmic variables is proposed to prevent loss of positivity due to coarse-grid corrections. Together with the extended UPC implicit scheme, the positivity-preserving prolongation operator guarantees unconditional positivity of turbulence quantities and species mass fractions throughout the multigrid cycle. Second, to improve the coarse-grid-correction obtained in localized regions of high chemical activity, a modified defect correction procedure is devised, and successfully applied for the first time to simulate turbulent, combusting flows. The proposed modifications to the standard multigrid algorithm create a well-rounded and robust numerical method that provides accelerated convergence, while unconditionally preserving the positivity of model equation variables. Numerical simulations of various flows involving premixed combustion demonstrate that the proposed MG method increases the efficiency by a factor of up to eight times with respect to an equivalent single-grid method, and by two times with respect to an artificially-stabilized MG method.

Preconditioner and convergence study for the Quantum Computer Aided Design (QCAD) nonlinear poisson problem posed on the Ottawa Flat 270 design geometry.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kalashnikova, Irina

2012-05-01

A numerical study aimed to evaluate different preconditioners within the Trilinos Ifpack and ML packages for the Quantum Computer Aided Design (QCAD) non-linear Poisson problem implemented within the Albany code base and posed on the Ottawa Flat 270 design geometry is performed. This study led to some new development of Albany that allows the user to select an ML preconditioner with Zoltan repartitioning based on nodal coordinates, which is summarized. Convergence of the numerical solutions computed within the QCAD computational suite with successive mesh refinement is examined in two metrics, the mean value of the solution (an L{sup 1} norm)more » and the field integral of the solution (L{sup 2} norm).« less

Tensor-product preconditioners for higher-order space-time discontinuous Galerkin methods

NASA Astrophysics Data System (ADS)

Diosady, Laslo T.; Murman, Scott M.

2017-02-01

A space-time discontinuous-Galerkin spectral-element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equations. An efficient solution technique based on a matrix-free Newton-Krylov method is developed in order to overcome the stiffness associated with high solution order. The use of tensor-product basis functions is key to maintaining efficiency at high-order. Efficient preconditioning methods are presented which can take advantage of the tensor-product formulation. A diagonalized Alternating-Direction-Implicit (ADI) scheme is extended to the space-time discontinuous Galerkin discretization. A new preconditioner for the compressible Euler/Navier-Stokes equations based on the fast-diagonalization method is also presented. Numerical results demonstrate the effectiveness of these preconditioners for the direct numerical simulation of subsonic turbulent flows.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lott, P. Aaron; Woodward, Carol S.; Evans, Katherine J.

Performing accurate and efficient numerical simulation of global atmospheric climate models is challenging due to the disparate length and time scales over which physical processes interact. Implicit solvers enable the physical system to be integrated with a time step commensurate with processes being studied. The dominant cost of an implicit time step is the ancillary linear system solves, so we have developed a preconditioner aimed at improving the efficiency of these linear system solves. Our preconditioner is based on an approximate block factorization of the linearized shallow-water equations and has been implemented within the spectral element dynamical core within themore » Community Atmospheric Model (CAM-SE). Furthermore, in this paper we discuss the development and scalability of the preconditioner for a suite of test cases with the implicit shallow-water solver within CAM-SE.« less

Tensor-Product Preconditioners for Higher-Order Space-Time Discontinuous Galerkin Methods

NASA Technical Reports Server (NTRS)

Diosady, Laslo T.; Murman, Scott M.

2016-01-01

space-time discontinuous-Galerkin spectral-element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equat ions. An efficient solution technique based on a matrix-free Newton-Krylov method is developed in order to overcome the stiffness associated with high solution order. The use of tensor-product basis functions is key to maintaining efficiency at high order. Efficient preconditioning methods are presented which can take advantage of the tensor-product formulation. A diagonalized Alternating-Direction-Implicit (ADI) scheme is extended to the space-time discontinuous Galerkin discretization. A new preconditioner for the compressible Euler/Navier-Stokes equations based on the fast-diagonalization method is also presented. Numerical results demonstrate the effectiveness of these preconditioners for the direct numerical simulation of subsonic turbulent flows.

Parallel multigrid smoothing: polynomial versus Gauss-Seidel

NASA Astrophysics Data System (ADS)

Adams, Mark; Brezina, Marian; Hu, Jonathan; Tuminaro, Ray

2003-07-01

Gauss-Seidel is often the smoother of choice within multigrid applications. In the context of unstructured meshes, however, maintaining good parallel efficiency is difficult with multiplicative iterative methods such as Gauss-Seidel. This leads us to consider alternative smoothers. We discuss the computational advantages of polynomial smoothers within parallel multigrid algorithms for positive definite symmetric systems. Two particular polynomials are considered: Chebyshev and a multilevel specific polynomial. The advantages of polynomial smoothing over traditional smoothers such as Gauss-Seidel are illustrated on several applications: Poisson's equation, thin-body elasticity, and eddy current approximations to Maxwell's equations. While parallelizing the Gauss-Seidel method typically involves a compromise between a scalable convergence rate and maintaining high flop rates, polynomial smoothers achieve parallel scalable multigrid convergence rates without sacrificing flop rates. We show that, although parallel computers are the main motivation, polynomial smoothers are often surprisingly competitive with Gauss-Seidel smoothers on serial machines.

Multigrid methods for isogeometric discretization

PubMed Central

Gahalaut, K.P.S.; Kraus, J.K.; Tomar, S.K.

2013-01-01

We present (geometric) multigrid methods for isogeometric discretization of scalar second order elliptic problems. The smoothing property of the relaxation method, and the approximation property of the intergrid transfer operators are analyzed. These properties, when used in the framework of classical multigrid theory, imply uniform convergence of two-grid and multigrid methods. Supporting numerical results are provided for the smoothing property, the approximation property, convergence factor and iterations count for V-, W- and F-cycles, and the linear dependence of V-cycle convergence on the smoothing steps. For two dimensions, numerical results include the problems with variable coefficients, simple multi-patch geometry, a quarter annulus, and the dependence of convergence behavior on refinement levels ℓ, whereas for three dimensions, only the constant coefficient problem in a unit cube is considered. The numerical results are complete up to polynomial order p=4, and for C0 and Cp-1 smoothness. PMID:24511168

Geometric multigrid to accelerate the solution of the quasi-static electric field problem by tetrahedral finite elements.

PubMed

Hollaus, K; Weiss, B; Magele, Ch; Hutten, H

2004-02-01

The acceleration of the solution of the quasi-static electric field problem considering anisotropic complex conductivity simulated by tetrahedral finite elements of first order is investigated by geometric multigrid.

Domain decomposition preconditioners for the spectral collocation method

NASA Technical Reports Server (NTRS)

Quarteroni, Alfio; Sacchilandriani, Giovanni

1988-01-01

Several block iteration preconditioners are proposed and analyzed for the solution of elliptic problems by spectral collocation methods in a region partitioned into several rectangles. It is shown that convergence is achieved with a rate which does not depend on the polynomial degree of the spectral solution. The iterative methods here presented can be effectively implemented on multiprocessor systems due to their high degree of parallelism.

A hierarchical preconditioner for the electric field integral equation on unstructured meshes based on primal and dual Haar bases

NASA Astrophysics Data System (ADS)

Adrian, S. B.; Andriulli, F. P.; Eibert, T. F.

2017-02-01

A new hierarchical basis preconditioner for the electric field integral equation (EFIE) operator is introduced. In contrast to existing hierarchical basis preconditioners, it works on arbitrary meshes and preconditions both the vector and the scalar potential within the EFIE operator. This is obtained by taking into account that the vector and the scalar potential discretized with loop-star basis functions are related to the hypersingular and the single layer operator (i.e., the well known integral operators from acoustics). For the single layer operator discretized with piecewise constant functions, a hierarchical preconditioner can easily be constructed. Thus the strategy we propose in this work for preconditioning the EFIE is the transformation of the scalar and the vector potential into operators equivalent to the single layer operator and to its inverse. More specifically, when the scalar potential is discretized with star functions as source and testing functions, the resulting matrix is a single layer operator discretized with piecewise constant functions and multiplied left and right with two additional graph Laplacian matrices. By inverting these graph Laplacian matrices, the discretized single layer operator is obtained, which can be preconditioned with the hierarchical basis. Dually, when the vector potential is discretized with loop functions, the resulting matrix can be interpreted as a hypersingular operator discretized with piecewise linear functions. By leveraging on a scalar Calderón identity, we can interpret this operator as spectrally equivalent to the inverse single layer operator. Then we use a linear-in-complexity, closed-form inverse of the dual hierarchical basis to precondition the hypersingular operator. The numerical results show the effectiveness of the proposed preconditioner and the practical impact of theoretical developments in real case scenarios.

The block adaptive multigrid method applied to the solution of the Euler equations

NASA Technical Reports Server (NTRS)

Pantelelis, Nikos

1993-01-01

In the present study, a scheme capable of solving very fast and robust complex nonlinear systems of equations is presented. The Block Adaptive Multigrid (BAM) solution method offers multigrid acceleration and adaptive grid refinement based on the prediction of the solution error. The proposed solution method was used with an implicit upwind Euler solver for the solution of complex transonic flows around airfoils. Very fast results were obtained (18-fold acceleration of the solution) using one fourth of the volumes of a global grid with the same solution accuracy for two test cases.

Multigrid Methods for Aerodynamic Problems in Complex Geometries

NASA Technical Reports Server (NTRS)

Caughey, David A.

1995-01-01

Work has been directed at the development of efficient multigrid methods for the solution of aerodynamic problems involving complex geometries, including the development of computational methods for the solution of both inviscid and viscous transonic flow problems. The emphasis is on problems of complex, three-dimensional geometry. The methods developed are based upon finite-volume approximations to both the Euler and the Reynolds-Averaged Navier-Stokes equations. The methods are developed for use on multi-block grids using diagonalized implicit multigrid methods to achieve computational efficiency. The work is focused upon aerodynamic problems involving complex geometries, including advanced engine inlets.

Robust Multigrid Smoothers for Three Dimensional Elliptic Equations with Strong Anisotropies

NASA Technical Reports Server (NTRS)

Llorente, Ignacio M.; Melson, N. Duane

1998-01-01

We discuss the behavior of several plane relaxation methods as multigrid smoothers for the solution of a discrete anisotropic elliptic model problem on cell-centered grids. The methods compared are plane Jacobi with damping, plane Jacobi with partial damping, plane Gauss-Seidel, plane zebra Gauss-Seidel, and line Gauss-Seidel. Based on numerical experiments and local mode analysis, we compare the smoothing factor of the different methods in the presence of strong anisotropies. A four-color Gauss-Seidel method is found to have the best numerical and architectural properties of the methods considered in the present work. Although alternating direction plane relaxation schemes are simpler and more robust than other approaches, they are not currently used in industrial and production codes because they require the solution of a two-dimensional problem for each plane in each direction. We verify the theoretical predictions of Thole and Trottenberg that an exact solution of each plane is not necessary and that a single two-dimensional multigrid cycle gives the same result as an exact solution, in much less execution time. Parallelization of the two-dimensional multigrid cycles, the kernel of the three-dimensional implicit solver, is also discussed. Alternating-plane smoothers are found to be highly efficient multigrid smoothers for anisotropic elliptic problems.

A multigrid method for steady Euler equations on unstructured adaptive grids

NASA Technical Reports Server (NTRS)

Riemslagh, Kris; Dick, Erik

1993-01-01

A flux-difference splitting type algorithm is formulated for the steady Euler equations on unstructured grids. The polynomial flux-difference splitting technique is used. A vertex-centered finite volume method is employed on a triangular mesh. The multigrid method is in defect-correction form. A relaxation procedure with a first order accurate inner iteration and a second-order correction performed only on the finest grid, is used. A multi-stage Jacobi relaxation method is employed as a smoother. Since the grid is unstructured a Jacobi type is chosen. The multi-staging is necessary to provide sufficient smoothing properties. The domain is discretized using a Delaunay triangular mesh generator. Three grids with more or less uniform distribution of nodes but with different resolution are generated by successive refinement of the coarsest grid. Nodes of coarser grids appear in the finer grids. The multigrid method is started on these grids. As soon as the residual drops below a threshold value, an adaptive refinement is started. The solution on the adaptively refined grid is accelerated by a multigrid procedure. The coarser multigrid grids are generated by successive coarsening through point removement. The adaption cycle is repeated a few times. Results are given for the transonic flow over a NACA-0012 airfoil.

Domain decomposition algorithms and computation fluid dynamics

NASA Technical Reports Server (NTRS)

Chan, Tony F.

1988-01-01

In the past several years, domain decomposition was a very popular topic, partly motivated by the potential of parallelization. While a large body of theory and algorithms were developed for model elliptic problems, they are only recently starting to be tested on realistic applications. The application of some of these methods to two model problems in computational fluid dynamics are investigated. Some examples are two dimensional convection-diffusion problems and the incompressible driven cavity flow problem. The construction and analysis of efficient preconditioners for the interface operator to be used in the iterative solution of the interface solution is described. For the convection-diffusion problems, the effect of the convection term and its discretization on the performance of some of the preconditioners is discussed. For the driven cavity problem, the effectiveness of a class of boundary probe preconditioners is discussed.

S{sub 2}SA preconditioning for the S{sub n} equations with strictly non negative spatial discretization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bruss, D. E.; Morel, J. E.; Ragusa, J. C.

2013-07-01

Preconditioners based upon sweeps and diffusion-synthetic acceleration have been constructed and applied to the zeroth and first spatial moments of the 1-D S{sub n} transport equation using a strictly non negative nonlinear spatial closure. Linear and nonlinear preconditioners have been analyzed. The effectiveness of various combinations of these preconditioners are compared. In one dimension, nonlinear sweep preconditioning is shown to be superior to linear sweep preconditioning, and DSA preconditioning using nonlinear sweeps in conjunction with a linear diffusion equation is found to be essentially equivalent to nonlinear sweeps in conjunction with a nonlinear diffusion equation. The ability to use amore » linear diffusion equation has important implications for preconditioning the S{sub n} equations with a strictly non negative spatial discretization in multiple dimensions. (authors)« less

Udzawa-type iterative method with parareal preconditioner for a parabolic optimal control problem

NASA Astrophysics Data System (ADS)

Lapin, A.; Romanenko, A.

2016-11-01

The article deals with the optimal control problem with the parabolic equation as state problem. There are point-wise constraints on the state and control functions. The objective functional involves the observation given in the domain at each moment. The conditions for convergence Udzawa's type iterative method are given. The parareal method to inverse preconditioner is given. The results of calculations are presented.

Tensor-product preconditioners for a space-time discontinuous Galerkin method

NASA Astrophysics Data System (ADS)

Diosady, Laslo T.; Murman, Scott M.

2014-10-01

A space-time discontinuous Galerkin spectral element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equations. An efficient solution technique based on a matrix-free Newton-Krylov method is presented. A diagonalized alternating direction implicit preconditioner is extended to a space-time formulation using entropy variables. The effectiveness of this technique is demonstrated for the direct numerical simulation of turbulent flow in a channel.

Using Perturbed QR Factorizations To Solve Linear Least-Squares Problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Avron, Haim; Ng, Esmond G.; Toledo, Sivan

2008-03-21

We propose and analyze a new tool to help solve sparse linear least-squares problems min{sub x} {parallel}Ax-b{parallel}{sub 2}. Our method is based on a sparse QR factorization of a low-rank perturbation {cflx A} of A. More precisely, we show that the R factor of {cflx A} is an effective preconditioner for the least-squares problem min{sub x} {parallel}Ax-b{parallel}{sub 2}, when solved using LSQR. We propose applications for the new technique. When A is rank deficient we can add rows to ensure that the preconditioner is well-conditioned without column pivoting. When A is sparse except for a few dense rows we canmore » drop these dense rows from A to obtain {cflx A}. Another application is solving an updated or downdated problem. If R is a good preconditioner for the original problem A, it is a good preconditioner for the updated/downdated problem {cflx A}. We can also solve what-if scenarios, where we want to find the solution if a column of the original matrix is changed/removed. We present a spectral theory that analyzes the generalized spectrum of the pencil (A*A,R*R) and analyze the applications.« less

Multigrid Methods for the Computation of Propagators in Gauge Fields

NASA Astrophysics Data System (ADS)

Kalkreuter, Thomas

Multigrid methods were invented for the solution of discretized partial differential equations in order to overcome the slowness of traditional algorithms by updates on various length scales. In the present work generalizations of multigrid methods for propagators in gauge fields are investigated. Gauge fields are incorporated in algorithms in a covariant way. The kernel C of the restriction operator which averages from one grid to the next coarser grid is defined by projection on the ground-state of a local Hamiltonian. The idea behind this definition is that the appropriate notion of smoothness depends on the dynamics. The ground-state projection choice of C can be used in arbitrary dimension and for arbitrary gauge group. We discuss proper averaging operations for bosons and for staggered fermions. The kernels C can also be used in multigrid Monte Carlo simulations, and for the definition of block spins and blocked gauge fields in Monte Carlo renormalization group studies. Actual numerical computations are performed in four-dimensional SU(2) gauge fields. We prove that our proposals for block spins are “good”, using renormalization group arguments. A central result is that the multigrid method works in arbitrarily disordered gauge fields, in principle. It is proved that computations of propagators in gauge fields without critical slowing down are possible when one uses an ideal interpolation kernel. Unfortunately, the idealized algorithm is not practical, but it was important to answer questions of principle. Practical methods are able to outperform the conjugate gradient algorithm in case of bosons. The case of staggered fermions is harder. Multigrid methods give considerable speed-ups compared to conventional relaxation algorithms, but on lattices up to 184 conjugate gradient is superior.

Multigrid Methods in Electronic Structure Calculations

NASA Astrophysics Data System (ADS)

Briggs, Emil

1996-03-01

Multigrid techniques have become the method of choice for a broad range of computational problems. Their use in electronic structure calculations introduces a new set of issues when compared to traditional plane wave approaches. We have developed a set of techniques that address these issues and permit multigrid algorithms to be applied to the electronic structure problem in an efficient manner. In our approach the Kohn-Sham equations are discretized on a real-space mesh using a compact representation of the Hamiltonian. The resulting equations are solved directly on the mesh using multigrid iterations. This produces rapid convergence rates even for ill-conditioned systems with large length and/or energy scales. The method has been applied to both periodic and non-periodic systems containing over 400 atoms and the results are in very good agreement with both theory and experiment. Example applications include a vacancy in diamond, an isolated C60 molecule, and a 64-atom cell of GaN with the Ga d-electrons in valence which required a 250 Ry cutoff. A particular strength of a real-space multigrid approach is its ready adaptability to massively parallel computer architectures. The compact representation of the Hamiltonian is especially well suited to such machines. Tests on the Cray-T3D have shown nearly linear scaling of the execution time up to the maximum number of processors (512). The MPP implementation has been used for studies of a large Amyloid Beta Peptide (C_146O_45N_42H_210) found in the brains of Alzheimers disease patients. Further applications of the multigrid method will also be described. (in collaboration D. J. Sullivan and J. Bernholc)

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.

Multigrid Acceleration of Time-Accurate DNS of Compressible Turbulent Flow

NASA Technical Reports Server (NTRS)

Broeze, Jan; Geurts, Bernard; Kuerten, Hans; Streng, Martin

1996-01-01

An efficient scheme for the direct numerical simulation of 3D transitional and developed turbulent flow is presented. Explicit and implicit time integration schemes for the compressible Navier-Stokes equations are compared. The nonlinear system resulting from the implicit time discretization is solved with an iterative method and accelerated by the application of a multigrid technique. Since we use central spatial discretizations and no artificial dissipation is added to the equations, the smoothing method is less effective than in the more traditional use of multigrid in steady-state calculations. Therefore, a special prolongation method is needed in order to obtain an effective multigrid method. This simulation scheme was studied in detail for compressible flow over a flat plate. In the laminar regime and in the first stages of turbulent flow the implicit method provides a speed-up of a factor 2 relative to the explicit method on a relatively coarse grid. At increased resolution this speed-up is enhanced correspondingly.

Fast preconditioned multigrid solution of the Euler and Navier-Stokes equations for steady, compressible flows

NASA Astrophysics Data System (ADS)

Caughey, David A.; Jameson, Antony

2003-10-01

New versions of implicit algorithms are developed for the efficient solution of the Euler and Navier-Stokes equations of compressible flow. The methods are based on a preconditioned, lower-upper (LU) implementation of a non-linear, symmetric Gauss-Seidel (SGS) algorithm for use as a smoothing algorithm in a multigrid method. Previously, this method had been implemented for flows in quasi-one-dimensional ducts and for two-dimensional flows past airfoils on boundary-conforming O-type grids for a variety of symmetric limited positive (SLIP) spatial approximations, including the scalar dissipation and convective upwind split pressure (CUSP) schemes. Here results are presented for both inviscid and viscous (laminar) flows past airfoils on boundary-conforming C-type grids. The method is significantly faster than earlier explicit or implicit methods for inviscid problems, allowing solution of these problems to the level of truncation error in three to five multigrid cycles. Viscous solutions still require as many as twenty multigrid cycles.

A multigrid solver for the semiconductor equations

NASA Technical Reports Server (NTRS)

Bachmann, Bernhard

1993-01-01

We present a multigrid solver for the exponential fitting method. The solver is applied to the current continuity equations of semiconductor device simulation in two dimensions. The exponential fitting method is based on a mixed finite element discretization using the lowest-order Raviart-Thomas triangular element. This discretization method yields a good approximation of front layers and guarantees current conservation. The corresponding stiffness matrix is an M-matrix. 'Standard' multigrid solvers, however, cannot be applied to the resulting system, as this is dominated by an unsymmetric part, which is due to the presence of strong convection in part of the domain. To overcome this difficulty, we explore the connection between Raviart-Thomas mixed methods and the nonconforming Crouzeix-Raviart finite element discretization. In this way we can construct nonstandard prolongation and restriction operators using easily computable weighted L(exp 2)-projections based on suitable quadrature rules and the upwind effects of the discretization. The resulting multigrid algorithm shows very good results, even for real-world problems and for locally refined grids.

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 obtained by AMA is always better than the required accuracy; the computational complexity of the AMA algorithm is (nearly) optimal (comparable with the complexity of the FMG algorithm applied to solve the problem on the optimally spaced target grid).

Reducing Communication in Algebraic Multigrid Using Additive Variants

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vassilevski, Panayot S.; Yang, Ulrike Meier

Algebraic multigrid (AMG) has proven to be an effective scalable solver on many high performance computers. However, its increasing communication complexity on coarser levels has shown to seriously impact its performance on computers with high communication cost. Moreover, additive AMG variants provide not only increased parallelism as well as decreased numbers of messages per cycle but also generally exhibit slower convergence. Here we present various new additive variants with convergence rates that are significantly improved compared to the classical additive algebraic multigrid method and investigate their potential for decreased communication, and improved communication-computation overlap, features that are essential for goodmore » performance on future exascale architectures.« less

Reducing Communication in Algebraic Multigrid Using Additive Variants

DOE PAGES

Vassilevski, Panayot S.; Yang, Ulrike Meier

2014-02-12

Algebraic multigrid (AMG) has proven to be an effective scalable solver on many high performance computers. However, its increasing communication complexity on coarser levels has shown to seriously impact its performance on computers with high communication cost. Moreover, additive AMG variants provide not only increased parallelism as well as decreased numbers of messages per cycle but also generally exhibit slower convergence. Here we present various new additive variants with convergence rates that are significantly improved compared to the classical additive algebraic multigrid method and investigate their potential for decreased communication, and improved communication-computation overlap, features that are essential for goodmore » performance on future exascale architectures.« less

Development and Application of Agglomerated Multigrid Methods for Complex Geometries

NASA Technical Reports Server (NTRS)

Nishikawa, Hiroaki; Diskin, Boris; Thomas, James L.

2010-01-01

We report progress in the development of agglomerated multigrid techniques for fully un- structured grids in three dimensions, building upon two previous studies focused on efficiently solving a model diffusion equation. We demonstrate a robust fully-coarsened agglomerated multigrid technique for 3D complex geometries, incorporating the following key developments: consistent and stable coarse-grid discretizations, a hierarchical agglomeration scheme, and line-agglomeration/relaxation using prismatic-cell discretizations in the highly-stretched grid regions. A signi cant speed-up in computer time is demonstrated for a model diffusion problem, the Euler equations, and the Reynolds-averaged Navier-Stokes equations for 3D realistic complex geometries.

Multigrid for Staggered Lattice Fermions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brower, Richard C.; Clark, M. A.; Strelchenko, Alexei

Critical slowing down in Krylov methods for the Dirac operator presents a major obstacle to further advances in lattice field theory as it approaches the continuum solution. Here we formulate a multi-grid algorithm for the Kogut-Susskind (or staggered) fermion discretization which has proven difficult relative to Wilson multigrid due to its first-order anti-Hermitian structure. The solution is to introduce a novel spectral transformation by the K\\"ahler-Dirac spin structure prior to the Galerkin projection. We present numerical results for the two-dimensional, two-flavor Schwinger model, however, the general formalism is agnostic to dimension and is directly applicable to four-dimensional lattice QCD.

A dynamically adaptive multigrid algorithm for the incompressible Navier-Stokes equations: Validation and model problems

NASA Technical Reports Server (NTRS)

Thompson, C. P.; Leaf, G. K.; Vanrosendale, J.

1991-01-01

An algorithm is described for the solution of the laminar, incompressible Navier-Stokes equations. The basic algorithm is a multigrid based on a robust, box-based smoothing step. Its most important feature is the incorporation of automatic, dynamic mesh refinement. This algorithm supports generalized simple domains. The program is based on a standard staggered-grid formulation of the Navier-Stokes equations for robustness and efficiency. Special grid transfer operators were introduced at grid interfaces in the multigrid algorithm to ensure discrete mass conservation. Results are presented for three models: the driven-cavity, a backward-facing step, and a sudden expansion/contraction.

Seventh Copper Mountain Conference on Multigrid Methods. Part 2

NASA Technical Reports Server (NTRS)

Melson, N. Duane (Editor); Manteuffel, Tom A. (Editor); McCormick, Steve F. (Editor); Douglas, Craig C. (Editor)

1996-01-01

The Seventh Copper Mountain Conference on Multigrid Methods was held on April 2-7, 1995 at Copper Mountain, Colorado. This book is a collection of many of the papers presented at the conference and so represents the conference proceedings. NASA Langley graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The vibrancy and diversity in this field are amply expressed in these important papers, and the collection clearly shows the continuing rapid growth of the use of multigrid acceleration techniques.

Thermally induced defluorination during a mer to fac transformation of a blue-green phosphorescent cyclometalated iridium(III) complex.

PubMed

Zheng, Yonghao; Batsanov, Andrei S; Edkins, Robert M; Beeby, Andrew; Bryce, Martin R

2012-01-02

The new homoleptic tris-cyclometalated [Ir(C^N)(3)] complexes mer-8, fac-8, and fac-9 incorporating γ-carboline ligands are reported. Reaction of 3-(2,4-difluorophenyl)-5-(2-ethylhexyl)-pyrido[4,3-b]indole 6 with iridium(III) chloride under standard cyclometalating conditions gave the homoleptic complex mer-8 in 63% yield. The X-ray crystal structure of mer-8 is described. The Ir-C and Ir-N bonds show the expected bond length alternations for the differing trans influence of phenyl and pyridyl ligands. mer-8 quantitatively isomerized to fac-8 upon irradiation with UV light. However, heating mer-8 at 290 °C in glycerol led to an unusual regioselective loss of one fluorine atom from each of the ligands, yielding fac-9 in 58% yield. fac-8 is thermally very stable: no decomposition was observed when fac-8 was heated in glycerol at 290 °C for 48 h. The γ-carboline system of fac-8 enhances thermal stability compared to the pyridyl analogue fac-Ir(46dfppy)(3)10, which decomposes extensively upon being heated in glycerol at 290 °C for 2 h. Complexes mer-8, fac-8, and fac-9 are emitters of blue-green light (λ(max)(em) = 477, 476, and 494 nm, respectively). The triplet lifetimes for fac-8 and fac-9 are ~4.5 μs at room temperature; solution Φ(PL) values are 0.31 and 0.22, respectively.

Scalable parallel elastic-plastic finite element analysis using a quasi-Newton method with a balancing domain decomposition preconditioner

NASA Astrophysics Data System (ADS)

Yusa, Yasunori; Okada, Hiroshi; Yamada, Tomonori; Yoshimura, Shinobu

2018-04-01

A domain decomposition method for large-scale elastic-plastic problems is proposed. The proposed method is based on a quasi-Newton method in conjunction with a balancing domain decomposition preconditioner. The use of a quasi-Newton method overcomes two problems associated with the conventional domain decomposition method based on the Newton-Raphson method: (1) avoidance of a double-loop iteration algorithm, which generally has large computational complexity, and (2) consideration of the local concentration of nonlinear deformation, which is observed in elastic-plastic problems with stress concentration. Moreover, the application of a balancing domain decomposition preconditioner ensures scalability. Using the conventional and proposed domain decomposition methods, several numerical tests, including weak scaling tests, were performed. The convergence performance of the proposed method is comparable to that of the conventional method. In particular, in elastic-plastic analysis, the proposed method exhibits better convergence performance than the conventional method.

Newton-Krylov-Schwarz: An implicit solver for CFD

NASA Technical Reports Server (NTRS)

Cai, Xiao-Chuan; Keyes, David E.; Venkatakrishnan, V.

1995-01-01

Newton-Krylov methods and Krylov-Schwarz (domain decomposition) methods have begun to become established in computational fluid dynamics (CFD) over the past decade. The former employ a Krylov method inside of Newton's method in a Jacobian-free manner, through directional differencing. The latter employ an overlapping Schwarz domain decomposition to derive a preconditioner for the Krylov accelerator that relies primarily on local information, for data-parallel concurrency. They may be composed as Newton-Krylov-Schwarz (NKS) methods, which seem particularly well suited for solving nonlinear elliptic systems in high-latency, distributed-memory environments. We give a brief description of this family of algorithms, with an emphasis on domain decomposition iterative aspects. We then describe numerical simulations with Newton-Krylov-Schwarz methods on aerodynamics applications emphasizing comparisons with a standard defect-correction approach, subdomain preconditioner consistency, subdomain preconditioner quality, and the effect of a coarse grid.

Preconditioning strategies for nonlinear conjugate gradient methods, based on quasi-Newton updates

NASA Astrophysics Data System (ADS)

Andrea, Caliciotti; Giovanni, Fasano; Massimo, Roma

2016-10-01

This paper reports two proposals of possible preconditioners for the Nonlinear Conjugate Gradient (NCG) method, in large scale unconstrained optimization. On one hand, the common idea of our preconditioners is inspired to L-BFGS quasi-Newton updates, on the other hand we aim at explicitly approximating in some sense the inverse of the Hessian matrix. Since we deal with large scale optimization problems, we propose matrix-free approaches where the preconditioners are built using symmetric low-rank updating formulae. Our distinctive new contributions rely on using information on the objective function collected as by-product of the NCG, at previous iterations. Broadly speaking, our first approach exploits the secant equation, in order to impose interpolation conditions on the objective function. In the second proposal we adopt and ad hoc modified-secant approach, in order to possibly guarantee some additional theoretical properties.

A Numerical Method for Solving the 3D Unsteady Incompressible Navier-Stokes Equations in Curvilinear Domains with Complex Immersed Boundaries.

PubMed

Ge, Liang; Sotiropoulos, Fotis

2007-08-01

A novel numerical method is developed that integrates boundary-conforming grids with a sharp interface, immersed boundary methodology. The method is intended for simulating internal flows containing complex, moving immersed boundaries such as those encountered in several cardiovascular applications. The background domain (e.g the empty aorta) is discretized efficiently with a curvilinear boundary-fitted mesh while the complex moving immersed boundary (say a prosthetic heart valve) is treated with the sharp-interface, hybrid Cartesian/immersed-boundary approach of Gilmanov and Sotiropoulos [1]. To facilitate the implementation of this novel modeling paradigm in complex flow simulations, an accurate and efficient numerical method is developed for solving the unsteady, incompressible Navier-Stokes equations in generalized curvilinear coordinates. The method employs a novel, fully-curvilinear staggered grid discretization approach, which does not require either the explicit evaluation of the Christoffel symbols or the discretization of all three momentum equations at cell interfaces as done in previous formulations. The equations are integrated in time using an efficient, second-order accurate fractional step methodology coupled with a Jacobian-free, Newton-Krylov solver for the momentum equations and a GMRES solver enhanced with multigrid as preconditioner for the Poisson equation. Several numerical experiments are carried out on fine computational meshes to demonstrate the accuracy and efficiency of the proposed method for standard benchmark problems as well as for unsteady, pulsatile flow through a curved, pipe bend. To demonstrate the ability of the method to simulate flows with complex, moving immersed boundaries we apply it to calculate pulsatile, physiological flow through a mechanical, bileaflet heart valve mounted in a model straight aorta with an anatomical-like triple sinus.

A Numerical Method for Solving the 3D Unsteady Incompressible Navier-Stokes Equations in Curvilinear Domains with Complex Immersed Boundaries

PubMed Central

Ge, Liang; Sotiropoulos, Fotis

2008-01-01

A novel numerical method is developed that integrates boundary-conforming grids with a sharp interface, immersed boundary methodology. The method is intended for simulating internal flows containing complex, moving immersed boundaries such as those encountered in several cardiovascular applications. The background domain (e.g the empty aorta) is discretized efficiently with a curvilinear boundary-fitted mesh while the complex moving immersed boundary (say a prosthetic heart valve) is treated with the sharp-interface, hybrid Cartesian/immersed-boundary approach of Gilmanov and Sotiropoulos [1]. To facilitate the implementation of this novel modeling paradigm in complex flow simulations, an accurate and efficient numerical method is developed for solving the unsteady, incompressible Navier-Stokes equations in generalized curvilinear coordinates. The method employs a novel, fully-curvilinear staggered grid discretization approach, which does not require either the explicit evaluation of the Christoffel symbols or the discretization of all three momentum equations at cell interfaces as done in previous formulations. The equations are integrated in time using an efficient, second-order accurate fractional step methodology coupled with a Jacobian-free, Newton-Krylov solver for the momentum equations and a GMRES solver enhanced with multigrid as preconditioner for the Poisson equation. Several numerical experiments are carried out on fine computational meshes to demonstrate the accuracy and efficiency of the proposed method for standard benchmark problems as well as for unsteady, pulsatile flow through a curved, pipe bend. To demonstrate the ability of the method to simulate flows with complex, moving immersed boundaries we apply it to calculate pulsatile, physiological flow through a mechanical, bileaflet heart valve mounted in a model straight aorta with an anatomical-like triple sinus. PMID:19194533

Lecture Notes on Multigrid Methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vassilevski, P S

The Lecture Notes are primarily based on a sequence of lectures given by the author while been a Fulbright scholar at 'St. Kliment Ohridski' University of Sofia, Sofia, Bulgaria during the winter semester of 2009-2010 academic year. The notes are somewhat expanded version of the actual one semester class he taught there. The material covered is slightly modified and adapted version of similar topics covered in the author's monograph 'Multilevel Block-Factorization Preconditioners' published in 2008 by Springer. The author tried to keep the notes as self-contained as possible. That is why the lecture notes begin with some basic introductory matrix-vectormore » linear algebra, numerical PDEs (finite element) facts emphasizing the relations between functions in finite dimensional spaces and their coefficient vectors and respective norms. Then, some additional facts on the implementation of finite elements based on relation tables using the popular compressed sparse row (CSR) format are given. Also, typical condition number estimates of stiffness and mass matrices, the global matrix assembly from local element matrices are given as well. Finally, some basic introductory facts about stationary iterative methods, such as Gauss-Seidel and its symmetrized version are presented. The introductory material ends up with the smoothing property of the classical iterative methods and the main definition of two-grid iterative methods. From here on, the second part of the notes begins which deals with the various aspects of the principal TG and the numerous versions of the MG cycles. At the end, in part III, we briefly introduce algebraic versions of MG referred to as AMG, focusing on classes of AMG specialized for finite element matrices.« less

Eigensystem analysis of classical relaxation techniques with applications to multigrid analysis

NASA Technical Reports Server (NTRS)

Lomax, Harvard; Maksymiuk, Catherine

1987-01-01

Classical relaxation techniques are related to numerical methods for solution of ordinary differential equations. Eigensystems for Point-Jacobi, Gauss-Seidel, and SOR methods are presented. Solution techniques such as eigenvector annihilation, eigensystem mixing, and multigrid methods are examined with regard to the eigenstructure.

Multidimensional radiative transfer with multilevel atoms. II. The non-linear multigrid method.

NASA Astrophysics Data System (ADS)

Fabiani Bendicho, P.; Trujillo Bueno, J.; Auer, L.

1997-08-01

A new iterative method for solving non-LTE multilevel radiative transfer (RT) problems in 1D, 2D or 3D geometries is presented. The scheme obtains the self-consistent solution of the kinetic and RT equations at the cost of only a few (<10) formal solutions of the RT equation. It combines, for the first time, non-linear multigrid iteration (Brandt, 1977, Math. Comp. 31, 333; Hackbush, 1985, Multi-Grid Methods and Applications, springer-Verlag, Berlin), an efficient multilevel RT scheme based on Gauss-Seidel iterations (cf. Trujillo Bueno & Fabiani Bendicho, 1995ApJ...455..646T), and accurate short-characteristics formal solution techniques. By combining a valid stopping criterion with a nested-grid strategy a converged solution with the desired true error is automatically guaranteed. Contrary to the current operator splitting methods the very high convergence speed of the new RT method does not deteriorate when the grid spatial resolution is increased. With this non-linear multigrid method non-LTE problems discretized on N grid points are solved in O(N) operations. The nested multigrid RT method presented here is, thus, particularly attractive in complicated multilevel transfer problems where small grid-sizes are required. The properties of the method are analyzed both analytically and with illustrative multilevel calculations for Ca II in 1D and 2D schematic model atmospheres.

2 CFR 200.36 - Federal Audit Clearinghouse (FAC).

Code of Federal Regulations, 2014 CFR

2014-01-01

... 2 Grants and Agreements 1 2014-01-01 2014-01-01 false Federal Audit Clearinghouse (FAC). 200.36... Clearinghouse (FAC). FAC means the clearinghouse designated by OMB as the repository of record where non-Federal... part. The mailing address of the FAC is Federal Audit Clearinghouse, Bureau of the Census, 1201 E. 10th...

48 CFR 301.603-72 - FAC-C and HHS SAC certification requirements.

Code of Federal Regulations, 2013 CFR

2013-10-01

... 48 Federal Acquisition Regulations System 4 2013-10-01 2013-10-01 false FAC-C and HHS SAC... Responsibilities 301.603-72 FAC-C and HHS SAC certification requirements. (a) The FAC-C certification program is... thereunder are not required to re-take training courses, but shall follow FAC-C training requirements when...

48 CFR 301.603-72 - FAC-C and HHS SAC certification requirements.

Code of Federal Regulations, 2014 CFR

2014-10-01

... 48 Federal Acquisition Regulations System 4 2014-10-01 2014-10-01 false FAC-C and HHS SAC... Responsibilities 301.603-72 FAC-C and HHS SAC certification requirements. (a) The FAC-C certification program is... thereunder are not required to re-take training courses, but shall follow FAC-C training requirements when...

48 CFR 301.603-72 - FAC-C and HHS SAC certification requirements.

Code of Federal Regulations, 2011 CFR

2011-10-01

... 48 Federal Acquisition Regulations System 4 2011-10-01 2011-10-01 false FAC-C and HHS SAC... Responsibilities 301.603-72 FAC-C and HHS SAC certification requirements. (a) The FAC-C certification program is... thereunder are not required to re-take training courses, but shall follow FAC-C training requirements when...

48 CFR 301.603-72 - FAC-C and HHS SAC certification requirements.

Code of Federal Regulations, 2012 CFR

2012-10-01

... 48 Federal Acquisition Regulations System 4 2012-10-01 2012-10-01 false FAC-C and HHS SAC... Responsibilities 301.603-72 FAC-C and HHS SAC certification requirements. (a) The FAC-C certification program is... thereunder are not required to re-take training courses, but shall follow FAC-C training requirements when...

Multigrid for hypersonic viscous two- and three-dimensional flows

NASA Technical Reports Server (NTRS)

Turkel, E.; Swanson, R. C.; Vatsa, V. N.; White, J. A.

1991-01-01

The use of a multigrid method with central differencing to solve the Navier-Stokes equations for hypersonic flows is considered. The time dependent form of the equations is integrated with an explicit Runge-Kutta scheme accelerated by local time stepping and implicit residual smoothing. Variable coefficients are developed for the implicit process that removes the diffusion limit on the time step, producing significant improvement in convergence. A numerical dissipation formulation that provides good shock capturing capability for hypersonic flows is presented. This formulation is shown to be a crucial aspect of the multigrid method. Solutions are given for two-dimensional viscous flow over a NACA 0012 airfoil and three-dimensional flow over a blunt biconic.

Seventh Copper Mountain Conference on Multigrid Methods. Part 1

NASA Technical Reports Server (NTRS)

Melson, N. Duane; Manteuffel, Tom A.; McCormick, Steve F.; Douglas, Craig C.

1996-01-01

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

The Sixth Copper Mountain Conference on Multigrid Methods, part 2

NASA Technical Reports Server (NTRS)

Melson, N. Duane (Editor); Mccormick, Steve F. (Editor); Manteuffel, Thomas A. (Editor)

1993-01-01

The Sixth Copper Mountain Conference on Multigrid Methods was held on April 4-9, 1993, at Copper Mountain, Colorado. This book is a collection of many of the papers presented at the conference and so represents the conference proceedings. NASA Langley graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The multigrid discipline continues to expand and mature, as is evident from these proceedings. The vibrancy in this field is amply expressed in these important papers, and the collection clearly shows its rapid trend to further diversity and depth.

Mapping implicit spectral methods to distributed memory architectures

NASA Technical Reports Server (NTRS)

Overman, Andrea L.; Vanrosendale, John

1991-01-01

Spectral methods were proven invaluable in numerical simulation of PDEs (Partial Differential Equations), but the frequent global communication required raises a fundamental barrier to their use on highly parallel architectures. To explore this issue, a 3-D implicit spectral method was implemented on an Intel hypercube. Utilization of about 50 percent was achieved on a 32 node iPSC/860 hypercube, for a 64 x 64 x 64 Fourier-spectral grid; finer grids yield higher utilizations. Chebyshev-spectral grids are more problematic, since plane-relaxation based multigrid is required. However, by using a semicoarsening multigrid algorithm, and by relaxing all multigrid levels concurrently, relatively high utilizations were also achieved in this harder case.

Multigrid solutions to quasi-elliptic schemes

NASA Technical Reports Server (NTRS)

Brandt, A.; Taasan, S.

1985-01-01

Quasi-elliptic schemes arise from central differencing or finite element discretization of elliptic systems with odd order derivatives on non-staggered grids. They are somewhat unstable and less accurate then corresponding staggered-grid schemes. When usual multigrid solvers are applied to them, the asymptotic algebraic convergence is necessarily slow. Nevertheless, it is shown by mode analyses and numerical experiments that the usual FMG algorithm is very efficient in solving quasi-elliptic equations to the level of truncation errors. Also, a new type of multigrid algorithm is presented, mode analyzed and tested, for which even the asymptotic algebraic convergence is fast. The essence of that algorithm is applicable to other kinds of problems, including highly indefinite ones.

Multigrid solutions to quasi-elliptic schemes

NASA Technical Reports Server (NTRS)

Brandt, A.; Taasan, S.

1985-01-01

Quasi-elliptic schemes arise from central differencing or finite element discretization of elliptic systems with odd order derivatives on non-staggered grids. They are somewhat unstable and less accurate than corresponding staggered-grid schemes. When usual multigrid solvers are applied to them, the asymptotic algebraic convergence is necessarily slow. Nevertheless, it is shown by mode analyses and numerical experiments that the usual FMG algorithm is very efficient in solving quasi-elliptic equations to the level of truncation errors. Also, a new type of multigrid algorithm is presented, mode analyzed and tested, for which even the asymptotic algebraic convergence is fast. The essence of that algorithm is applicable to other kinds of problems, including highly indefinite ones.

Multigrid techniques for the solution of the passive scalar advection-diffusion equation

NASA Technical Reports Server (NTRS)

Phillips, R. E.; Schmidt, F. W.

1985-01-01

The solution of elliptic passive scalar advection-diffusion equations is required in the analysis of many turbulent flow and convective heat transfer problems. The accuracy of the solution may be affected by the presence of regions containing large gradients of the dependent variables. The multigrid concept of local grid refinement is a method for improving the accuracy of the calculations in these problems. In combination with the multilevel acceleration techniques, an accurate and efficient computational procedure is developed. In addition, a robust implementation of the QUICK finite-difference scheme is described. Calculations of a test problem are presented to quantitatively demonstrate the advantages of the multilevel-multigrid method.

The interplanetary magnetic field B[sub y] effects on large-scale field-aligned currents near local noon: Contributions from cusp part and noncusp part

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yamauchi, M.; Lundin, R.; Woch, J.

1993-04-01

latitudinals develop a model to account for the effect of the interplanetary magnetic field (IMF) B[sub y] component on the dayside field-aligned currents (FACs). As part of the model the FACs are divided into a [open quotes]cusp part[close quotes] and a [open quotes]noncusp part[close quotes]. The authors then propose that the cusp part FACs shift in the longitudinal direction while the noncusplike part FACs shift in both longitudinal and latitudinal directions in response to the y component of the IMF. If combined, it is observed that the noncusp part FAC is found poleward of the cusp part FAC system whenmore » the y component of the IMF is large. These two FAC systems flow in the same direction. They reinforce one another, creating a strong FAC, termed the DPY-FAC. The model also predicts that the polewardmost part of the DPY-FAC flows on closed field lines, even in regions conventionally occupied by the polar cap. Results of the model are successfully compared with particle and magnetic field data from Viking missions.« less

Swarm Observation of Field-Aligned Currents Associated With Multiple Auroral Arc Systems

NASA Astrophysics Data System (ADS)

Wu, J.; Knudsen, D. J.; Gillies, D. M.; Donovan, E. F.; Burchill, J. K.

2017-10-01

Auroral arcs occur in regions of upward field-aligned currents (FACs); however, the relation is not one to one, since kinetic energy of the current-carrying electrons is also important in the production of auroral luminosity. Multiple auroral arc systems provide an opportunity to study the relation between FACs and auroral brightness in detail. In this study, we have identified two types of FAC configurations in multiple parallel arc systems using ground-based optical data from the Time History of Events and Macroscale Interactions during Substorms all-sky imagers, magnetometers and electric field instruments on board the Swarm satellites. In "unipolar FAC" events, each arc is an intensification within a broad, unipolar current sheet and downward return currents occur outside of this broad sheet. In "multipolar FAC" events, multiple arc systems represent a collection of multiple up/down current pairs. By collecting 17 events with unipolar FAC and 12 events with multipolar FACs, we find that (1) unipolar FAC events occur most frequently between 20 and 21 magnetic local time and multipolar FAC events tend to occur around local midnight and within 1 h after substorm onset. (2) Arcs in unipolar FAC systems have a typical width of 10-20 km and a spacing of 25-50 km. Arcs in multipolar FAC systems are wider and more separated. (3) Upward currents with more arcs embedded have larger intensities and widths. (4) Electric fields are strong and highly structured on the edges of multiple arc system with unipolar FAC. The fact that arcs with unipolar FAC are much more highly structured than the associated currents suggests that arc multiplicity is indicative not of a structured generator deep in the magnetosphere, but rather of the magnetosphere-ionosphere coupling process.

Effective matrix-free preconditioning for the augmented immersed interface method

NASA Astrophysics Data System (ADS)

Xia, Jianlin; Li, Zhilin; Ye, Xin

2015-12-01

We present effective and efficient matrix-free preconditioning techniques for the augmented immersed interface method (AIIM). AIIM has been developed recently and is shown to be very effective for interface problems and problems on irregular domains. GMRES is often used to solve for the augmented variable(s) associated with a Schur complement A in AIIM that is defined along the interface or the irregular boundary. The efficiency of AIIM relies on how quickly the system for A can be solved. For some applications, there are substantial difficulties involved, such as the slow convergence of GMRES (particularly for free boundary and moving interface problems), and the inconvenience in finding a preconditioner (due to the situation that only the products of A and vectors are available). Here, we propose matrix-free structured preconditioning techniques for AIIM via adaptive randomized sampling, using only the products of A and vectors to construct a hierarchically semiseparable matrix approximation to A. Several improvements over existing schemes are shown so as to enhance the efficiency and also avoid potential instability. The significance of the preconditioners includes: (1) they do not require the entries of A or the multiplication of AT with vectors; (2) constructing the preconditioners needs only O (log ⁡ N) matrix-vector products and O (N) storage, where N is the size of A; (3) applying the preconditioners needs only O (N) flops; (4) they are very flexible and do not require any a priori knowledge of the structure of A. The preconditioners are observed to significantly accelerate the convergence of GMRES, with heuristical justifications of the effectiveness. Comprehensive tests on several important applications are provided, such as Navier-Stokes equations on irregular domains with traction boundary conditions, interface problems in incompressible flows, mixed boundary problems, and free boundary problems. The preconditioning techniques are also useful for several other problems and methods.

Toward an optimal solver for time-spectral fluid-dynamic and aeroelastic solutions on unstructured meshes

NASA Astrophysics Data System (ADS)

Mundis, Nathan L.; Mavriplis, Dimitri J.

2017-09-01

The time-spectral method applied to the Euler and coupled aeroelastic equations theoretically offers significant computational savings for purely periodic problems when compared to standard time-implicit methods. However, attaining superior efficiency with time-spectral methods over traditional time-implicit methods hinges on the ability rapidly to solve the large non-linear system resulting from time-spectral discretizations which become larger and stiffer as more time instances are employed or the period of the flow becomes especially short (i.e. the maximum resolvable wave-number increases). In order to increase the efficiency of these solvers, and to improve robustness, particularly for large numbers of time instances, the Generalized Minimal Residual Method (GMRES) is used to solve the implicit linear system over all coupled time instances. The use of GMRES as the linear solver makes time-spectral methods more robust, allows them to be applied to a far greater subset of time-accurate problems, including those with a broad range of harmonic content, and vastly improves the efficiency of time-spectral methods. In previous work, a wave-number independent preconditioner that mitigates the increased stiffness of the time-spectral method when applied to problems with large resolvable wave numbers has been developed. This preconditioner, however, directly inverts a large matrix whose size increases in proportion to the number of time instances. As a result, the computational time of this method scales as the cube of the number of time instances. In the present work, this preconditioner has been reworked to take advantage of an approximate-factorization approach that effectively decouples the spatial and temporal systems. Once decoupled, the time-spectral matrix can be inverted in frequency space, where it has entries only on the main diagonal and therefore can be inverted quite efficiently. This new GMRES/preconditioner combination is shown to be over an order of magnitude more efficient than the previous wave-number independent preconditioner for problems with large numbers of time instances and/or large reduced frequencies.

Block-accelerated aggregation multigrid for Markov chains with application to PageRank problems

NASA Astrophysics Data System (ADS)

Shen, Zhao-Li; Huang, Ting-Zhu; Carpentieri, Bruno; Wen, Chun; Gu, Xian-Ming

2018-06-01

Recently, the adaptive algebraic aggregation multigrid method has been proposed for computing stationary distributions of Markov chains. This method updates aggregates on every iterative cycle to keep high accuracies of coarse-level corrections. Accordingly, its fast convergence rate is well guaranteed, but often a large proportion of time is cost by aggregation processes. In this paper, we show that the aggregates on each level in this method can be utilized to transfer the probability equation of that level into a block linear system. Then we propose a Block-Jacobi relaxation that deals with the block system on each level to smooth error. Some theoretical analysis of this technique is presented, meanwhile it is also adapted to solve PageRank problems. The purpose of this technique is to accelerate the adaptive aggregation multigrid method and its variants for solving Markov chains and PageRank problems. It also attempts to shed some light on new solutions for making aggregation processes more cost-effective for aggregation multigrid methods. Numerical experiments are presented to illustrate the effectiveness of this technique.

Functional Activity of the Fanconi Anemia Protein FAA Requires FAC Binding and Nuclear Localization

PubMed Central

Näf, Dieter; Kupfer, Gary M.; Suliman, Ahmed; Lambert, Kathleen; D’Andrea, Alan D.

1998-01-01

Fanconi anemia (FA) is an autosomal recessive disease characterized by genomic instability, cancer susceptibility, and cellular hypersensitivity to DNA-cross-linking agents. Eight complementation groups of FA (FA-A through FA-H) have been identified. Two FA genes, corresponding to complementation groups FA-A and FA-C, have been cloned, but the functions of the encoded FAA and FAC proteins remain unknown. We have recently demonstrated that FAA and FAC interact to form a nuclear complex. In this study, we have analyzed a series of mutant forms of the FAA protein with respect to functional activity, FAC binding, and nuclear localization. Mutation or deletion of the amino-terminal nuclear localization signal (NLS) of FAA results in loss of functional activity, loss of FAC binding, and cytoplasmic retention of FAA. Replacement of the NLS sequence with a heterologous NLS sequence, derived from the simian virus 40 T antigen, results in nuclear localization but does not rescue functional activity or FAC binding. Nuclear localization of the FAA protein is therefore necessary but not sufficient for FAA function. Mutant forms of FAA which fail to bind to FAC also fail to promote the nuclear accumulation of FAC. In addition, wild-type FAC promotes the accumulation of wild-type FAA in the nucleus. Our results suggest that FAA and FAC perform a concerted function in the cell nucleus, required for the maintenance of chromosomal stability. PMID:9742112

Magnetospheric Multiscale Observations of Field-Aligned Currents in the Magnetotail

NASA Astrophysics Data System (ADS)

Strangeway, R. J.; Russell, C. T.; Zhao, C.; Plaschke, F.; Fischer, D.; Anderson, B. J.; Weygand, J. M.; Le, G.; Kepko, L.; Nakamura, R.; Baumjohann, W.; Slavin, J. A.; Paterson, W. R.; Giles, B. L.; Shuster, J. R.; Torbert, R. B.; Burch, J. L.

2017-12-01

Field-aligned currents (FACs) are frequently observed by Magnetospheric Multiscale (MMS) within the Earth's magnetotail. However, unlike the FACs observed by MMS at the dayside magnetopause, which are of the order 100s of nA/m2, the magnetotail FACs are relatively weak, of the order 10s of nA/m2. There appear to be a variety of sources for the FACs. FACs are observed in association with dipolarization fronts that are propagating both earthward and tailward, at the boundary of the current sheet, and in flux-ropes. FACs are also observed to be embedded in regions of high speed flow, both earthward and tailward, and not just at the dipolarization front frequently associated with high speed flows. As is the case for FACs observed at the dayside magnetopause, these observations raise questions as to how or where the FACs close.

A Multigrid NLS-4DVar Data Assimilation Scheme with Advanced Research WRF (ARW)

NASA Astrophysics Data System (ADS)

Zhang, H.; Tian, X.

2017-12-01

The motions of the atmosphere have multiscale properties in space and/or time, and the background error covariance matrix (Β) should thus contain error information at different correlation scales. To obtain an optimal analysis, the multigrid three-dimensional variational data assimilation scheme is used widely when sequentially correcting errors from large to small scales. However, introduction of the multigrid technique into four-dimensional variational data assimilation is not easy, due to its strong dependence on the adjoint model, which has extremely high computational costs in data coding, maintenance, and updating. In this study, the multigrid technique was introduced into the nonlinear least-squares four-dimensional variational assimilation (NLS-4DVar) method, which is an advanced four-dimensional ensemble-variational method that can be applied without invoking the adjoint models. The multigrid NLS-4DVar (MG-NLS-4DVar) scheme uses the number of grid points to control the scale, with doubling of this number when moving from a coarse to a finer grid. Furthermore, the MG-NLS-4DVar scheme not only retains the advantages of NLS-4DVar, but also sufficiently corrects multiscale errors to achieve a highly accurate analysis. The effectiveness and efficiency of the proposed MG-NLS-4DVar scheme were evaluated by several groups of observing system simulation experiments using the Advanced Research Weather Research and Forecasting Model. MG-NLS-4DVar outperformed NLS-4DVar, with a lower computational cost.

Multigrid method based on the transformation-free HOC scheme on nonuniform grids for 2D convection diffusion problems

NASA Astrophysics Data System (ADS)

Ge, Yongbin; Cao, Fujun

2011-05-01

In this paper, a multigrid method based on the high order compact (HOC) difference scheme on nonuniform grids, which has been proposed by Kalita et al. [J.C. Kalita, A.K. Dass, D.C. Dalal, A transformation-free HOC scheme for steady convection-diffusion on non-uniform grids, Int. J. Numer. Methods Fluids 44 (2004) 33-53], is proposed to solve the two-dimensional (2D) convection diffusion equation. The HOC scheme is not involved in any grid transformation to map the nonuniform grids to uniform grids, consequently, the multigrid method is brand-new for solving the discrete system arising from the difference equation on nonuniform grids. The corresponding multigrid projection and interpolation operators are constructed by the area ratio. Some boundary layer and local singularity problems are used to demonstrate the superiority of the present method. Numerical results show that the multigrid method with the HOC scheme on nonuniform grids almost gets as equally efficient convergence rate as on uniform grids and the computed solution on nonuniform grids retains fourth order accuracy while on uniform grids just gets very poor solution for very steep boundary layer or high local singularity problems. The present method is also applied to solve the 2D incompressible Navier-Stokes equations using the stream function-vorticity formulation and the numerical solutions of the lid-driven cavity flow problem are obtained and compared with solutions available in the literature.

77 FR 3751 - Commission Information Collection Activities (FERC-725A); Comment Request; Submitted for OMB Review

Federal Register 2010, 2011, 2012, 2013, 2014

2012-01-25

... Commission, 888 First Street NE., Washington, DC 20426. FOR FURTHER INFORMATION CONTACT: Ellen Brown may be... Additional recordkeeping beyond FAC-008-1 FAC-008-3 Applies to: and FAC-009-1 and FAC-009-1 R1 Generator... Generator owners None, this requirement is derived Retention period increased by 2 years. from R1 of FAC-008...

An adaptive grid algorithm for one-dimensional nonlinear equations

NASA Technical Reports Server (NTRS)

Gutierrez, William E.; Hills, Richard G.

1990-01-01

Richards' equation, which models the flow of liquid through unsaturated porous media, is highly nonlinear and difficult to solve. Step gradients in the field variables require the use of fine grids and small time step sizes. The numerical instabilities caused by the nonlinearities often require the use of iterative methods such as Picard or Newton interation. These difficulties result in large CPU requirements in solving Richards equation. With this in mind, adaptive and multigrid methods are investigated for use with nonlinear equations such as Richards' equation. Attention is focused on one-dimensional transient problems. To investigate the use of multigrid and adaptive grid methods, a series of problems are studied. First, a multigrid program is developed and used to solve an ordinary differential equation, demonstrating the efficiency with which low and high frequency errors are smoothed out. The multigrid algorithm and an adaptive grid algorithm is used to solve one-dimensional transient partial differential equations, such as the diffusive and convective-diffusion equations. The performance of these programs are compared to that of the Gauss-Seidel and tridiagonal methods. The adaptive and multigrid schemes outperformed the Gauss-Seidel algorithm, but were not as fast as the tridiagonal method. The adaptive grid scheme solved the problems slightly faster than the multigrid method. To solve nonlinear problems, Picard iterations are introduced into the adaptive grid and tridiagonal methods. Burgers' equation is used as a test problem for the two algorithms. Both methods obtain solutions of comparable accuracy for similar time increments. For the Burgers' equation, the adaptive grid method finds the solution approximately three times faster than the tridiagonal method. Finally, both schemes are used to solve the water content formulation of the Richards' equation. For this problem, the adaptive grid method obtains a more accurate solution in fewer work units and less computation time than required by the tridiagonal method. The performance of the adaptive grid method tends to degrade as the solution process proceeds in time, but still remains faster than the tridiagonal scheme.

Time-marching multi-grid seismic tomography

NASA Astrophysics Data System (ADS)

Tong, P.; Yang, D.; Liu, Q.

2016-12-01

From the classic ray-based traveltime tomography to the state-of-the-art full waveform inversion, because of the nonlinearity of seismic inverse problems, a good starting model is essential for preventing the convergence of the objective function toward local minima. With a focus on building high-accuracy starting models, we propose the so-called time-marching multi-grid seismic tomography method in this study. The new seismic tomography scheme consists of a temporal time-marching approach and a spatial multi-grid strategy. We first divide the recording period of seismic data into a series of time windows. Sequentially, the subsurface properties in each time window are iteratively updated starting from the final model of the previous time window. There are at least two advantages of the time-marching approach: (1) the information included in the seismic data of previous time windows has been explored to build the starting models of later time windows; (2) seismic data of later time windows could provide extra information to refine the subsurface images. Within each time window, we use a multi-grid method to decompose the scale of the inverse problem. Specifically, the unknowns of the inverse problem are sampled on a coarse mesh to capture the macro-scale structure of the subsurface at the beginning. Because of the low dimensionality, it is much easier to reach the global minimum on a coarse mesh. After that, finer meshes are introduced to recover the micro-scale properties. That is to say, the subsurface model is iteratively updated on multi-grid in every time window. We expect that high-accuracy starting models should be generated for the second and later time windows. We will test this time-marching multi-grid method by using our newly developed eikonal-based traveltime tomography software package tomoQuake. Real application results in the 2016 Kumamoto earthquake (Mw 7.0) region in Japan will be demonstrated.

Matrix-Free Polynomial-Based Nonlinear Least Squares Optimized Preconditioning and its Application to Discontinuous Galerkin Discretizations of the Euler Equations

DTIC Science & Technology

2015-06-01

cient parallel code for applying the operator. Our method constructs a polynomial preconditioner using a nonlinear least squares (NLLS) algorithm. We show...apply the underlying operator. Such a preconditioner can be very attractive in scenarios where one has a highly efficient parallel code for applying...repeatedly solve a large system of linear equations where one has an extremely fast parallel code for applying an underlying fixed linear operator

On multigrid solution of the implicit equations of hydrodynamics. Experiments for the compressible Euler equations in general coordinates

NASA Astrophysics Data System (ADS)

Kifonidis, K.; Müller, E.

2012-08-01

Aims: We describe and study a family of new multigrid iterative solvers for the multidimensional, implicitly discretized equations of hydrodynamics. Schemes of this class are free of the Courant-Friedrichs-Lewy condition. They are intended for simulations in which widely differing wave propagation timescales are present. A preferred solver in this class is identified. Applications to some simple stiff test problems that are governed by the compressible Euler equations, are presented to evaluate the convergence behavior, and the stability properties of this solver. Algorithmic areas are determined where further work is required to make the method sufficiently efficient and robust for future application to difficult astrophysical flow problems. Methods: The basic equations are formulated and discretized on non-orthogonal, structured curvilinear meshes. Roe's approximate Riemann solver and a second-order accurate reconstruction scheme are used for spatial discretization. Implicit Runge-Kutta (ESDIRK) schemes are employed for temporal discretization. The resulting discrete equations are solved with a full-coarsening, non-linear multigrid method. Smoothing is performed with multistage-implicit smoothers. These are applied here to the time-dependent equations by means of dual time stepping. Results: For steady-state problems, our results show that the efficiency of the present approach is comparable to the best implicit solvers for conservative discretizations of the compressible Euler equations that can be found in the literature. The use of red-black as opposed to symmetric Gauss-Seidel iteration in the multistage-smoother is found to have only a minor impact on multigrid convergence. This should enable scalable parallelization without having to seriously compromise the method's algorithmic efficiency. For time-dependent test problems, our results reveal that the multigrid convergence rate degrades with increasing Courant numbers (i.e. time step sizes). Beyond a Courant number of nine thousand, even complete multigrid breakdown is observed. Local Fourier analysis indicates that the degradation of the convergence rate is associated with the coarse-grid correction algorithm. An implicit scheme for the Euler equations that makes use of the present method was, nevertheless, able to outperform a standard explicit scheme on a time-dependent problem with a Courant number of order 1000. Conclusions: For steady-state problems, the described approach enables the construction of parallelizable, efficient, and robust implicit hydrodynamics solvers. The applicability of the method to time-dependent problems is presently restricted to cases with moderately high Courant numbers. This is due to an insufficient coarse-grid correction of the employed multigrid algorithm for large time steps. Further research will be required to help us to understand and overcome the observed multigrid convergence difficulties for time-dependent problems.

The National Wetland Plant List

DTIC Science & Technology

2012-10-01

P. Adams FACW Florida Sands St. John’s-Wort Hypericum fasciculatum Lam. FACW FACW FACW Peel -Bark St. John’s-Wort Hypericum fraseri...Dewflower Musa X paradisiaca L. (pro sp.) UPL FAC FACU Musa acuminata Colla FACW Edible Banana Musa troglodytarum L. FACU Fe’i... Banana Myoporum laetum G. Forst. FACU UPL Ngaio-Tree Myosotis arvensis (L.) Hill FAC FAC UPL FAC FAC FACU FACU Rough Forget-Me-Not

Flow Accelerated Erosion-Corrosion (FAC) considerations for secondary side piping in the AP1000{sup R} nuclear power plant design

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vanderhoff, J. F.; Rao, G. V.; Stein, A.

2012-07-01

The issue of Flow Accelerated Erosion-Corrosion (FAC) in power plant piping is a known phenomenon that has resulted in material replacements and plant accidents in operating power plants. Therefore, it is important for FAC resistance to be considered in the design of new nuclear power plants. This paper describes the design considerations related to FAC that were used to develop a safe and robust AP1000{sup R} plant secondary side piping design. The primary FAC influencing factors include: - Fluid Temperature - Pipe Geometry/layout - Fluid Chemistry - Fluid Velocity - Pipe Material Composition - Moisture Content (in steam lines) Duemore » to the unknowns related to the relative impact of the influencing factors and the complexities of the interactions between these factors, it is difficult to accurately predict the expected wear rate in a given piping segment in a new plant. This paper provides: - a description of FAC and the factors that influence the FAC degradation rate, - an assessment of the level of FAC resistance of AP1000{sup R} secondary side system piping, - an explanation of options to increase FAC resistance and associated benefits/cost, - discussion of development of a tool for predicting FAC degradation rate in new nuclear power plants. (authors)« less

Spectral multigrid methods for elliptic equations 2

NASA Technical Reports Server (NTRS)

Zang, T. A.; Wong, Y. S.; Hussaini, M. Y.

1983-01-01

A detailed description of spectral multigrid methods is provided. This includes the interpolation and coarse-grid operators for both periodic and Dirichlet problems. The spectral methods for periodic problems use Fourier series and those for Dirichlet problems are based upon Chebyshev polynomials. An improved preconditioning for Dirichlet problems is given. Numerical examples and practical advice are included.

Multigrid and Krylov Subspace Methods for the Discrete Stokes Equations

NASA Technical Reports Server (NTRS)

Elman, Howard C.

1996-01-01

Discretization of the Stokes equations produces a symmetric indefinite system of linear equations. For stable discretizations, a variety of numerical methods have been proposed that have rates of convergence independent of the mesh size used in the discretization. In this paper, we compare the performance of four such methods: variants of the Uzawa, preconditioned conjugate gradient, preconditioned conjugate residual, and multigrid methods, for solving several two-dimensional model problems. The results indicate that where it is applicable, multigrid with smoothing based on incomplete factorization is more efficient than the other methods, but typically by no more than a factor of two. The conjugate residual method has the advantage of being both independent of iteration parameters and widely applicable.

Multigrid Solution of the Navier-Stokes Equations at Low Speeds with Large Temperature Variations

NASA Technical Reports Server (NTRS)

Sockol, Peter M.

2002-01-01

Multigrid methods for the Navier-Stokes equations at low speeds and large temperature variations are investigated. The compressible equations with time-derivative preconditioning and preconditioned flux-difference splitting of the inviscid terms are used. Three implicit smoothers have been incorporated into a common multigrid procedure. Both full coarsening and semi-coarsening with directional fine-grid defect correction have been studied. The resulting methods have been tested on four 2D laminar problems over a range of Reynolds numbers on both uniform and highly stretched grids. Two of the three methods show efficient and robust performance over the entire range of conditions. In addition none of the methods have any difficulty with the large temperature variations.

The Sixth Copper Mountain Conference on Multigrid Methods, part 1

NASA Technical Reports Server (NTRS)

Melson, N. Duane (Editor); Manteuffel, T. A. (Editor); Mccormick, S. F. (Editor)

1993-01-01

The Sixth Copper Mountain Conference on Multigrid Methods was held on 4-9 Apr. 1993, at Copper Mountain, CO. This book is a collection of many of the papers presented at the conference and as such represents the conference proceedings. NASA LaRC graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The multigrid discipline continues to expand and mature, as is evident from these proceedings. The vibrancy in this field is amply expressed in these important papers, and the collection clearly shows its rapid trend to further diversity and depth.

Updated users' guide for TAWFIVE with multigrid

NASA Technical Reports Server (NTRS)

Melson, N. Duane; Streett, Craig L.

1989-01-01

A program for the Transonic Analysis of a Wing and Fuselage with Interacted Viscous Effects (TAWFIVE) was improved by the incorporation of multigrid and a method to specify lift coefficient rather than angle-of-attack. A finite volume full potential multigrid method is used to model the outer inviscid flow field. First order viscous effects are modeled by a 3-D integral boundary layer method. Both turbulent and laminar boundary layers are treated. Wake thickness effects are modeled using a 2-D strip method. A brief discussion of the engineering aspects of the program is given. The input, output, and use of the program are covered in detail. Sample results are given showing the effects of boundary layer corrections and the capability of the lift specification method.

Assessment of Fever Advisory Cards (FACs) as an Initiative to Improve Febrile Neutropenia Management in a Regional Cancer Center Emergency Department.

PubMed

Kapil, Priyanka; MacMillan, Meghan; Carvalho, Maritza; Lymburner, Patricia; Fung, Ron; Almeida, Bernadette; Van Dorn, Laurie; Enright, Katherine

2016-09-01

We aimed to improve the time to antibiotics (TTA) for patients treated with chemotherapy who present to the emergency department (ED) with febrile neutropenia (FN) by using standardized fever advisory cards (FACs). Patients treated with chemotherapy who visited the ED at the Peel Regional Cancer Center in Ontario, Canada, with suspected FN were identified, before (April 2012 to March 2013) and after (October 2013 to March 2014) FAC implementation. The primary outcome of interest was TTA. Additional process measures included Canadian Triage and Acuity Scale score, time to physician assessment, and FAC compliance. Outcomes were analyzed with descriptive statistics and control charts to determine whether the change in primary measures were within statistical control over time. Between the pre-FAC cohort (n = 239) and post-FAC cohort (n = 69), TTA did not change significantly post-FACs (195 v 244 min, P = .09), with monthly averages demonstrating normal variation by statistical process control methodology. The introduction of FACs increased the percentage of patients with correctly assigned Canadian Triage and Acuity Scale scores (87% v 100%) but did not affect time to physician assessment. Compliance with FACs among patients was not ideal, with only 62.5% using them as intended. The distribution of FACs was associated with an improved incidence of correct FN triaging but did not demonstrate a meaningful improvement in the quality of FN management. This may be explained by FAC use among patients not being ideal. Next steps in the continued effort toward high-quality FN care include redesign of FACs, reinforcement of provider and patient education, and ED outreach. Copyright © 2016 by American Society of Clinical Oncology.

Functionalized granular activated carbon and surface complexation with chromates and bi-chromates in wastewater.

PubMed

Singha, Somdutta; Sarkar, Ujjaini; Luharuka, Pallavi

2013-03-01

Cr(VI) is present in the aqueous medium as chromate (CrO4(2-)) and bi-chromate (HCrO4(-)). Functionalized granular activated carbons (FACs) are used as adsorbents in the treatment of wastewaters containing hexavalent chromium. The FACs are prepared by chemical modifications of granular activated carbons (GACs) using functionalizing agents like HNO3, HCl and HF. The Brunauer, Emmett and Teller surface areas of FAC-HCl (693.5m(2)/g), FAC-HNO3 (648.8m(2)/g) and FAC-HF (726.2m(2)/g) are comparable to the GAC (777.7m(2)/g). But, the adsorption capacity of each of the FAC-HNO3, FAC-HCl and FAC-HF is found to be higher than the GAC. The functional groups play an important role in the adsorption process and pH has practically no role in this specific case. The FACs have hydrophilic protonated external surfaces in particular, along with the functional surface sites capable to make complexes with the CrO4(2-) and HCrO4(-) present. Surface complex formation is maximized in the order FAC-HNO3>FAC-HF>FAC-HCl, in proportion to the total surface acidity. This is also confirmed by the well-known pseudo second-order kinetic model. Physi-sorption equilibrium isotherms are parameterized by using standard Freundlich and Langmuir models. Langmuir fits better. The formation of surface complexes with the functional groups and hexavalent chromium is also revealed in the images of field emission scanning electron micrograph; energy dispersive X-ray spectroscopy and Fourier transform infrared spectroscopy analysis after adsorption. The intra-particle diffusion is not the only rate-controlling factor. The Boyd's film diffusion model fits very well with R(2) as high as 98.1% for FAC-HNO3. This result demonstrates that the functionalization of the GAC by acid treatments would increase the diffusion rate, predominantly with a boundary layer diffusion effect. Copyright © 2013 Elsevier B.V. All rights reserved.

Fluorouracil, doxorubicin, and cyclophosphamide (FAC) versus FAC followed by weekly paclitaxel as adjuvant therapy for high-risk, node-negative breast cancer: results from the GEICAM/2003-02 study.

PubMed

Martín, Miguel; Ruiz, Amparo; Ruiz Borrego, Manuel; Barnadas, Agustí; González, Sonia; Calvo, Lourdes; Margelí Vila, Mireia; Antón, Antonio; Rodríguez-Lescure, Alvaro; Seguí-Palmer, Miguel Angel; Muñoz-Mateu, Montserrat; Dorca Ribugent, Joan; López-Vega, José Manuel; Jara, Carlos; Espinosa, Enrique; Mendiola Fernández, César; Andrés, Raquel; Ribelles, Nuria; Plazaola, Arrate; Sánchez-Rovira, Pedro; Salvador Bofill, Javier; Crespo, Carmen; Carabantes, Francisco J; Servitja, Sonia; Chacón, José Ignacio; Rodríguez, César A; Hernando, Blanca; Álvarez, Isabel; Carrasco, Eva; Lluch, Ana

2013-07-10

Adding taxanes to anthracycline-based adjuvant therapy improves survival outcomes of patients with node-positive breast cancer (BC). Currently, however, most patients with BC are node negative at diagnosis. The only pure node-negative study (Spanish Breast Cancer Research Group 9805) reported so far showed a docetaxel benefit but significant toxicity. Here we tested the efficacy and safety of weekly paclitaxel (wP) in node-negative patients, which is yet to be established. Patients with BC having T1-T3/N0 tumors and at least one high-risk factor for recurrence (according to St. Gallen 1998 criteria) were eligible. After primary surgery, 1,925 patients were randomly assigned to receive fluorouracil, doxorubicin, and cyclophosphamide (FAC) × 6 or FAC × 4 followed by wP × 8 (FAC-wP). The primary end point was disease-free survival (DFS) after a median follow-up of 5 years. Secondary end points included toxicity and overall survival. After a median follow-up of 63.3 months, 93% and 90.3% of patients receiving FAC-wP or FAC regimens, respectively, remained disease free (hazard ratio [HR], 0.73; 95% CI, 0.54 to 0.99; log-rank P = .04). Thirty-one patients receiving FAC-wP versus 40 patients receiving FAC died (one and seven from cardiovascular diseases, respectively; HR, 0.79; 95% CI, 0.49 to 1.26; log-rank P = .31). The most relevant grade 3 and 4 adverse events in the FAC-wP versus the FAC arm were febrile neutropenia (2.7% v 3.6%), fatigue (7.9% v 3.4%), and sensory neuropathy (5.5% v 0%). For patients with high-risk node-negative BC, the adjuvant FAC-wP regimen was associated with a small but significant improvement in DFS compared with FAC therapy, in addition to manageable toxicity, especially regarding long-term cardiac effects.

Condition number estimation of preconditioned matrices.

PubMed

Kushida, Noriyuki

2015-01-01

The present paper introduces a condition number estimation method for preconditioned matrices. The newly developed method provides reasonable results, while the conventional method which is based on the Lanczos connection gives meaningless results. The Lanczos connection based method provides the condition numbers of coefficient matrices of systems of linear equations with information obtained through the preconditioned conjugate gradient method. Estimating the condition number of preconditioned matrices is sometimes important when describing the effectiveness of new preconditionerers or selecting adequate preconditioners. Operating a preconditioner on a coefficient matrix is the simplest method of estimation. However, this is not possible for large-scale computing, especially if computation is performed on distributed memory parallel computers. This is because, the preconditioned matrices become dense, even if the original matrices are sparse. Although the Lanczos connection method can be used to calculate the condition number of preconditioned matrices, it is not considered to be applicable to large-scale problems because of its weakness with respect to numerical errors. Therefore, we have developed a robust and parallelizable method based on Hager's method. The feasibility studies are curried out for the diagonal scaling preconditioner and the SSOR preconditioner with a diagonal matrix, a tri-daigonal matrix and Pei's matrix. As a result, the Lanczos connection method contains around 10% error in the results even with a simple problem. On the other hand, the new method contains negligible errors. In addition, the newly developed method returns reasonable solutions when the Lanczos connection method fails with Pei's matrix, and matrices generated with the finite element method.

48 CFR 301.607-72 - Applicability.

Code of Federal Regulations, 2012 CFR

2012-10-01

... Applicability. (a) The FAC-P/PM certification prerequisites and continuous learning requirements apply to all HHS employees who seek to obtain a FAC-P/PM certification. Although obtaining a FAC-P/PM certification... construction capital investment acquisitions. Consistent with OFPP guidance, HHS requires FAC-P/PM Level III...

48 CFR 301.607-72 - Applicability.

Code of Federal Regulations, 2013 CFR

2013-10-01

... Applicability. (a) The FAC-P/PM certification prerequisites and continuous learning requirements apply to all HHS employees who seek to obtain a FAC-P/PM certification. Although obtaining a FAC-P/PM certification... construction capital investment acquisitions. Consistent with OFPP guidance, HHS requires FAC-P/PM Level III...

48 CFR 301.607-72 - Applicability.

Code of Federal Regulations, 2014 CFR

2014-10-01

... Applicability. (a) The FAC-P/PM certification prerequisites and continuous learning requirements apply to all HHS employees who seek to obtain a FAC-P/PM certification. Although obtaining a FAC-P/PM certification... construction capital investment acquisitions. Consistent with OFPP guidance, HHS requires FAC-P/PM Level III...

Multi-Grid detector for neutron spectroscopy: results obtained on time-of-flight spectrometer CNCS

NASA Astrophysics Data System (ADS)

Anastasopoulos, M.; Bebb, R.; Berry, K.; Birch, J.; Bryś, T.; Buffet, J.-C.; Clergeau, J.-F.; Deen, P. P.; Ehlers, G.; van Esch, P.; Everett, S. M.; Guerard, B.; Hall-Wilton, R.; Herwig, K.; Hultman, L.; Höglund, C.; Iruretagoiena, I.; Issa, F.; Jensen, J.; Khaplanov, A.; Kirstein, O.; Lopez Higuera, I.; Piscitelli, F.; Robinson, L.; Schmidt, S.; Stefanescu, I.

2017-04-01

The Multi-Grid detector technology has evolved from the proof-of-principle and characterisation stages. Here we report on the performance of the Multi-Grid detector, the MG.CNCS prototype, which has been installed and tested at the Cold Neutron Chopper Spectrometer, CNCS at SNS. This has allowed a side-by-side comparison to the performance of 3He detectors on an operational instrument. The demonstrator has an active area of 0.2 m2. It is specifically tailored to the specifications of CNCS. The detector was installed in June 2016 and has operated since then, collecting neutron scattering data in parallel to the He-3 detectors of CNCS. In this paper, we present a comprehensive analysis of this data, in particular on instrument energy resolution, rate capability, background and relative efficiency. Stability, gamma-ray and fast neutron sensitivity have also been investigated. The effect of scattering in the detector components has been measured and provides input to comparison for Monte Carlo simulations. All data is presented in comparison to that measured by the 3He detectors simultaneously, showing that all features recorded by one detector are also recorded by the other. The energy resolution matches closely. We find that the Multi-Grid is able to match the data collected by 3He, and see an indication of a considerable advantage in the count rate capability. Based on these results, we are confident that the Multi-Grid detector will be capable of producing high quality scientific data on chopper spectrometers utilising the unprecedented neutron flux of the ESS.

Modeling of frequency-domain scalar wave equation with the average-derivative optimal scheme based on a multigrid-preconditioned iterative solver

NASA Astrophysics Data System (ADS)

Cao, Jian; Chen, Jing-Bo; Dai, Meng-Xue

2018-01-01

An efficient finite-difference frequency-domain modeling of seismic wave propagation relies on the discrete schemes and appropriate solving methods. The average-derivative optimal scheme for the scalar wave modeling is advantageous in terms of the storage saving for the system of linear equations and the flexibility for arbitrary directional sampling intervals. However, using a LU-decomposition-based direct solver to solve its resulting system of linear equations is very costly for both memory and computational requirements. To address this issue, we consider establishing a multigrid-preconditioned BI-CGSTAB iterative solver fit for the average-derivative optimal scheme. The choice of preconditioning matrix and its corresponding multigrid components is made with the help of Fourier spectral analysis and local mode analysis, respectively, which is important for the convergence. Furthermore, we find that for the computation with unequal directional sampling interval, the anisotropic smoothing in the multigrid precondition may affect the convergence rate of this iterative solver. Successful numerical applications of this iterative solver for the homogenous and heterogeneous models in 2D and 3D are presented where the significant reduction of computer memory and the improvement of computational efficiency are demonstrated by comparison with the direct solver. In the numerical experiments, we also show that the unequal directional sampling interval will weaken the advantage of this multigrid-preconditioned iterative solver in the computing speed or, even worse, could reduce its accuracy in some cases, which implies the need for a reasonable control of directional sampling interval in the discretization.

A multigrid LU-SSOR scheme for approximate Newton iteration applied to the Euler equations

NASA Technical Reports Server (NTRS)

Yoon, Seokkwan; Jameson, Antony

1986-01-01

A new efficient relaxation scheme in conjunction with a multigrid method is developed for the Euler equations. The LU SSOR scheme is based on a central difference scheme and does not need flux splitting for Newton iteration. Application to transonic flow shows that the new method surpasses the performance of the LU implicit scheme.

On some theoretical and practical aspects of multigrid methods. [to solve finite element systems from elliptic equations

NASA Technical Reports Server (NTRS)

Nicolaides, R. A.

1979-01-01

A description and explanation of a simple multigrid algorithm for solving finite element systems is given. Numerical results for an implementation are reported for a number of elliptic equations, including cases with singular coefficients and indefinite equations. The method shows the high efficiency, essentially independent of the grid spacing, predicted by the theory.

Semiannual Report October 1, 1999 through March 31, 2000

DTIC Science & Technology

2000-04-01

Mark Carpenter (NASA Langley). Textbook Multigrid Efficiency for the Navier-Stokes Equations Boris Diskin A typical modern Reynolds-Averaged...defined as textbook multigrid efficiency (TME), meaning the solutions to the governing system of equations are attained in a computational work...basic elements of the barriers to be overcome in extending textbook efficiencies to the compressible RANS equations, namely entering flows, far wake

On Bi-Grid Local Mode Analysis of Solution Techniques for 3-D Euler and Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Ibraheem, S. O.; Demuren, A. O.

1994-01-01

A procedure is presented for utilizing a bi-grid stability analysis as a practical tool for predicting multigrid performance in a range of numerical methods for solving Euler and Navier-Stokes equations. Model problems based on the convection, diffusion and Burger's equation are used to illustrate the superiority of the bi-grid analysis as a predictive tool for multigrid performance in comparison to the smoothing factor derived from conventional von Neumann analysis. For the Euler equations, bi-grid analysis is presented for three upwind difference based factorizations, namely Spatial, Eigenvalue and Combination splits, and two central difference based factorizations, namely LU and ADI methods. In the former, both the Steger-Warming and van Leer flux-vector splitting methods are considered. For the Navier-Stokes equations, only the Beam-Warming (ADI) central difference scheme is considered. In each case, estimates of multigrid convergence rates from the bi-grid analysis are compared to smoothing factors obtained from single-grid stability analysis. Effects of grid aspect ratio and flow skewness are examined. Both predictions are compared with practical multigrid convergence rates for 2-D Euler and Navier-Stokes solutions based on the Beam-Warming central scheme.

An upwind multigrid method for solving viscous flows on unstructured triangular meshes. M.S. Thesis

NASA Technical Reports Server (NTRS)

Bonhaus, Daryl Lawrence

1993-01-01

A multigrid algorithm is combined with an upwind scheme for solving the two dimensional Reynolds averaged Navier-Stokes equations on triangular meshes resulting in an efficient, accurate code for solving complex flows around multiple bodies. The relaxation scheme uses a backward-Euler time difference and relaxes the resulting linear system using a red-black procedure. Roe's flux-splitting scheme is used to discretize convective and pressure terms, while a central difference is used for the diffusive terms. The multigrid scheme is demonstrated for several flows around single and multi-element airfoils, including inviscid, laminar, and turbulent flows. The results show an appreciable speed up of the scheme for inviscid and laminar flows, and dramatic increases in efficiency for turbulent cases, especially those on increasingly refined grids.

On multigrid methods for the Navier-Stokes Computer

NASA Technical Reports Server (NTRS)

Nosenchuck, D. M.; Krist, S. E.; Zang, T. A.

1988-01-01

The overall architecture of the multipurpose parallel-processing Navier-Stokes Computer (NSC) being developed by Princeton and NASA Langley (Nosenchuck et al., 1986) is described and illustrated with extensive diagrams, and the NSC implementation of an elementary multigrid algorithm for simulating isotropic turbulence (based on solution of the incompressible time-dependent Navier-Stokes equations with constant viscosity) is characterized in detail. The present NSC design concept calls for 64 nodes, each with the performance of a class VI supercomputer, linked together by a fiber-optic hypercube network and joined to a front-end computer by a global bus. In this configuration, the NSC would have a storage capacity of over 32 Gword and a peak speed of over 40 Gflops. The multigrid Navier-Stokes code discussed would give sustained operation rates of about 25 Gflops.

The application of silicalite-1/fly ash cenosphere (S/FAC) zeolite composite for the adsorption of methyl tert-butyl ether (MTBE).

PubMed

Lu, Jia; Xu, Fang; Wang, Deju; Huang, Jue; Cai, Weimin

2009-06-15

Silicalite-1/fly ash cenosphere (S/FAC) zeolite composite has been applied for batch adsorption of methyl tert-butyl ether (MTBE) from water systems. Here the key experimental conditions, including the ratio of initial MTBE concentration to the amount weight of S/FAC, adsorption time and temperature, have been discussed in detail. The results show that approximately 93-95% MTBE could be adsorbed with initial concentration of MTBE solution 1000 microg l(-1). The column flow-through experiments also prove the high capacity of S/FAC composite for MTBE removal. The distinct advantages of S/FAC zeolite composite as adsorbent lie in (1) enhanced adsorption rate and capacity based on hierarchical micro and meso/macroporosity of S/FAC; (2) more easily operation and recycling process by assembly of nano-sized silicalite-1 zeolite on FAC support.

78 FR 13763 - Federal Acquisition Regulation; Federal Acquisition Circular 2005-66; Introduction

Federal Register 2010, 2011, 2012, 2013, 2014

2013-02-28

... Regulations Council (Councils) in this Federal Acquisition Circular (FAC) 2005-66. A companion document, the Small Entity Compliance Guide (SECG), follows this FAC. The FAC, including the SECG, is available via... in relation to each FAR case. Please cite FAC 2005-66 and the specific FAR case numbers. For...

A green emissive amorphous fac-Alq3 solid generated by grinding crystalline blue fac-Alq3 powder.

PubMed

Bi, Hai; Chen, Dong; Li, Di; Yuan, Yang; Xia, Dandan; Zhang, Zuolun; Zhang, Hongyu; Wang, Yue

2011-04-14

A novel green emissive Alq(3) solid with a facial isomeric form has been obtained by grinding the typical blue luminescent fac-Alq(3) crystalline powder. This is the first report, to the best of our knowledge, that a fac-Alq(3) isomer emits green light.

48 CFR 301.607-76 - FAC-P/PM application process.

Code of Federal Regulations, 2010 CFR

2010-10-01

... 48 Federal Acquisition Regulations System 4 2010-10-01 2010-10-01 false FAC-P/PM application... 301.607-76 FAC-P/PM application process. The P/PM Handbook contains application procedures and forms...; recertification; and certification waiver. Applicants for HHS FAC-P/PM certification actions shall comply with the...

48 CFR 301.603-74 - Requirement for retention of FAC-C and HHS SAC certification.

Code of Federal Regulations, 2014 CFR

2014-10-01

... of FAC-C and HHS SAC certification. 301.603-74 Section 301.603-74 Federal Acquisition Regulations..., Contracting Authority, and Responsibilities 301.603-74 Requirement for retention of FAC-C and HHS SAC certification. To maintain FAC-C certification, all warranted Contracting Officers, regardless of series, as...

48 CFR 301.607-76 - FAC-P/PM application process.

Code of Federal Regulations, 2011 CFR

2011-10-01

... 48 Federal Acquisition Regulations System 4 2011-10-01 2011-10-01 false FAC-P/PM application... 301.607-76 FAC-P/PM application process. The P/PM Handbook contains application procedures and forms...; recertification; and certification waiver. Applicants for HHS FAC-P/PM certification actions shall comply with the...

75 FR 39413 - Federal Acquisition Regulation; Federal Acquisition Circular 2005-44; Introduction

Federal Register 2010, 2011, 2012, 2013, 2014

2010-07-08

... Acquisition Council and the Defense Acquisition Regulations Council in this Federal Acquisition Circular (FAC) 2005-44. A companion document, the Small Entity Compliance Guide (SECG), follows this FAC. The FAC.... Please cite FAC 2005-44 and the FAR case number. Interested parties may also visit our Web site at http...

77 FR 69713 - Federal Acquisition Regulation; Federal Acquisition Circular 2005-62; Introduction

Federal Register 2010, 2011, 2012, 2013, 2014

2012-11-20

... Regulations Council (Councils) in this Federal Acquisition Circular (FAC) 2005-62. A companion document, the Small Entity Compliance Guide (SECG), follows this FAC. The FAC, including the SECG, is available via... in relation to each FAR case. Please cite FAC 2005-62 and the specific FAR case numbers. For...

48 CFR 301.607-76 - FAC-P/PM application process.

Code of Federal Regulations, 2014 CFR

2014-10-01

... 48 Federal Acquisition Regulations System 4 2014-10-01 2014-10-01 false FAC-P/PM application... 301.607-76 FAC-P/PM application process. The P/PM Handbook contains application procedures and forms...; recertification; and certification waiver. Applicants for HHS FAC-P/PM certification actions shall comply with the...

48 CFR 301.607-76 - FAC-P/PM application process.

Code of Federal Regulations, 2012 CFR

2012-10-01

... 48 Federal Acquisition Regulations System 4 2012-10-01 2012-10-01 false FAC-P/PM application... 301.607-76 FAC-P/PM application process. The P/PM Handbook contains application procedures and forms...; recertification; and certification waiver. Applicants for HHS FAC-P/PM certification actions shall comply with the...

48 CFR 301.607-76 - FAC-P/PM application process.

Code of Federal Regulations, 2013 CFR

2013-10-01

... 48 Federal Acquisition Regulations System 4 2013-10-01 2013-10-01 false FAC-P/PM application... 301.607-76 FAC-P/PM application process. The P/PM Handbook contains application procedures and forms...; recertification; and certification waiver. Applicants for HHS FAC-P/PM certification actions shall comply with the...

48 CFR 301.603-74 - Requirement for retention of FAC-C and HHS SAC certification.

Code of Federal Regulations, 2013 CFR

2013-10-01

... of FAC-C and HHS SAC certification. 301.603-74 Section 301.603-74 Federal Acquisition Regulations..., Contracting Authority, and Responsibilities 301.603-74 Requirement for retention of FAC-C and HHS SAC certification. To maintain FAC-C certification, all warranted Contracting Officers, regardless of series, as...

76 FR 4187 - Federal Acquisition Regulation; Federal Acquisition Circular 2005-49; Introduction

Federal Register 2010, 2011, 2012, 2013, 2014

2011-01-24

..., GSA, and NASA in this Federal Acquisition Circular (FAC) 2005-49. A companion document, the Small Entity Compliance Guide (SECG), follows this FAC. The FAC, including the SECG, is available via the... FAR case. Please cite FAC 2005-49 and the specific FAR case number. For information pertaining to...

77 FR 75765 - Federal Acquisition Regulation; Federal Acquisition Circular 2005-64; Introduction

Federal Register 2010, 2011, 2012, 2013, 2014

2012-12-21

... (Councils) in this Federal Acquisition Circular (FAC) 2005-64. A companion document, the Small Entity Compliance Guide (SECG), follows this FAC. The FAC, including the SECG, is available via the Internet at http... cite FAC 2005-64 and the specific FAR case number. For information pertaining to status or publication...

48 CFR 301.603-74 - Requirement for retention of FAC-C and HHS SAC certification.

Code of Federal Regulations, 2012 CFR

2012-10-01

... of FAC-C and HHS SAC certification. 301.603-74 Section 301.603-74 Federal Acquisition Regulations..., Contracting Authority, and Responsibilities 301.603-74 Requirement for retention of FAC-C and HHS SAC certification. To maintain FAC-C certification, all warranted Contracting Officers, regardless of series, as...

48 CFR 301.603-74 - Requirement for retention of FAC-C and HHS SAC certification.

Code of Federal Regulations, 2011 CFR

2011-10-01

... of FAC-C and HHS SAC certification. 301.603-74 Section 301.603-74 Federal Acquisition Regulations..., Contracting Authority, and Responsibilities 301.603-74 Requirement for retention of FAC-C and HHS SAC certification. To maintain FAC-C certification, all warranted Contracting Officers, regardless of series, as...

77 FR 23363 - Federal Acquisition Regulation; Federal Acquisition Circular 2005-58; Introduction

Federal Register 2010, 2011, 2012, 2013, 2014

2012-04-18

...) in this Federal Acquisition Circular (FAC) 2005-58. A companion document, the Small Entity Compliance Guide (SECG), follows this FAC. The FAC, including the SECG, is available via the Internet at http://www... case. Please cite FAC 2005-58 and the specific FAR case numbers. For information pertaining to status...

Properties and behaviour of FAC currents in the inner magnetosphere

NASA Astrophysics Data System (ADS)

Yang, Junying; Dunlop, Malcolm; Yang, Yanyan; Xiong, Chao; Lühr, Hermann; Cao, Jinbin; Li, Liuyuan; Ma, Yuduan; Shen, Chao

2017-04-01

Cusp, region 1 and 2, and other large scale field-aligned currents (FACs), are sampled in situ by both the four Cluster spacecraft and by the three Swarm spacecraft at different altitudes, separated by a few to several Earth radii, and sometimes simultaneously. Here, the capability of Swarm-Cluster coordination for probing the behaviour of the field aligned currents (FACs) at medium and low orbits is explored. Joint signatures of R1 and R2 FACs (as well as cusp, R0 and NBZ currents) can be found and compared in terms of the magnetic signatures, using multi-spacecraft analysis where possible. Using the Swarm configuration, statistical correlation analysis of the local time variation of R1/R2 FACs can be shown and compared to standard MVA analysis. For context, we identify the associated auroral boundaries through application of a method to determine the FAC intensity gradients in order to interpret and resolve the R1 and R2 FACs. We also explore the relation of R2 FACs to the ring current properties measured in situ.

Individualized FAC on bottom tab subassemblies to minimize adhesive gap between emitter and optics

NASA Astrophysics Data System (ADS)

Sauer, Sebastian; Müller, Tobias; Haag, Sebastian; Beleke, Andreas; Zontar, Daniel; Baum, Christoph; Brecher, Christian

2017-02-01

High Power Diode Laser (HPDL) systems with short focal length fast-axis collimators (FAC) require submicron assembly precision. Conventional FAC-Lens assembly processes require adhesive gaps of 50 microns or more in order to compensate for component tolerances (e.g. deviation of back focal length) and previous assembly steps. In order to control volumetric shrinkage of fast-curing UV-adhesives shrinkage compensation is mandatory. The novel approach described in this paper aims to minimize the impact of volumetric shrinkage due to the adhesive gap between HPDL edge emitters and FAC-Lens. Firstly, the FAC is actively aligned to the edge emitter without adhesives or bottom tab. The relative position and orientation of FAC to emitter are measured and stored. Consecutively, an individual subassembly of FAC and bottom tab is assembled on Fraunhofer IPT's mounting station with a precision of +/-1 micron. Translational and lateral offsets can be compensated, so that a narrow and uniform glue gap for the consecutive bonding process of bottom tab to heatsink applies (Figure 4). Accordingly, FAC and bottom tab are mounted to the heatsink without major shrinkage compensation. Fraunhofer IPT's department assembly of optical systems and automation has made several publications regarding active alignment of FAC lenses [SPIE LASE 8241-12], volumetric shrinkage compensation [SPIE LASE 9730-28] and FAC on bottom tab assembly [SPIE LASE 9727-31] in automated production environments. The approach described in this paper combines these and is the logical continuation of that work towards higher quality of HPDLs.

Evaluation of a 30-gene paclitaxel, fluorouracil, doxorubicin and cyclophosphamide chemotherapy response predictor in a multicenter randomized trial in breast cancer

PubMed Central

Tabchy, Adel; Valero, Vicente; Vidaurre, Tatiana; Lluch, Ana; Gomez, Henry; Martin, Miguel; Qi, Yuan; Barajas-Figueroa, Luis Javier; Souchon, Eduardo; Coutant, Charles; Doimi, Franco D; Ibrahim, Nuhad K; Gong, Yun; Hortobagyi, Gabriel N; Hess, Kenneth R; Symmans, W Fraser; Pusztai, Lajos

2010-01-01

Purpose We examined in a prospective, randomized, international clinical trial the performance of a previously defined 30-gene predictor (DLDA-30) of pathologic complete response (pCR) to preoperative weekly paclitaxel and fluorouracil, doxorubicin, cyclophosphamide (T/FAC) chemotherapy, and assessed if DLDA-30 also predicts increased sensitivity to FAC-only chemotherapy. We compared the pCR rates after T/FAC versus FAC×6 preoperative chemotherapy. We also performed an exploratory analysis to identify novel candidate genes that differentially predict response in the two treatment arms. Experimental Design 273 patients were randomly assigned to receive either weekly paclitaxel × 12 followed by FAC × 4 (T/FAC, n=138), or FAC × 6 (n=135) neoadjuvant chemotherapy. All patients underwent a pretreatment FNA biopsy of the tumor for gene expression profiling and treatment response prediction. Results The pCR rates were 19% and 9% in the T/FAC and FAC arms, respectively (p<0.05). In the T/FAC arm, the positive predictive value (PPV) of the genomic predictor was 38% (95%CI:21–56%), the negative predictive value (NPV) 88% (CI:77–95%) and the AUC 0.711. In the FAC arm, the PPV was 9% (CI:1–29%) and the AUC 0.584. This suggests that the genomic predictor may have regimen-specificity. Its performance was similar to a clinical variable-based predictor nomogram. Conclusions Gene expression profiling for prospective response prediction was feasible in this international trial. The 30-gene predictor can identify patients with greater than average sensitivity to T/FAC chemotherapy. However, it captured molecular equivalents of clinical phenotype. Next generation predictive markers will need to be developed separately for different molecular subsets of breast cancers. PMID:20829329

Parallel Element Agglomeration Algebraic Multigrid and Upscaling Library

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barker, Andrew T.; Benson, Thomas R.; Lee, Chak Shing

ParELAG is a parallel C++ library for numerical upscaling of finite element discretizations and element-based algebraic multigrid solvers. It provides optimal complexity algorithms to build multilevel hierarchies and solvers that can be used for solving a wide class of partial differential equations (elliptic, hyperbolic, saddle point problems) on general unstructured meshes. Additionally, a novel multilevel solver for saddle point problems with divergence constraint is implemented.

Multigrid time-accurate integration of Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Arnone, Andrea; Liou, Meng-Sing; Povinelli, Louis A.

1993-01-01

Efficient acceleration techniques typical of explicit steady-state solvers are extended to time-accurate calculations. Stability restrictions are greatly reduced by means of a fully implicit time discretization. A four-stage Runge-Kutta scheme with local time stepping, residual smoothing, and multigridding is used instead of traditional time-expensive factorizations. Some applications to natural and forced unsteady viscous flows show the capability of the procedure.

Condition Number Estimation of Preconditioned Matrices

PubMed Central

Kushida, Noriyuki

2015-01-01

The present paper introduces a condition number estimation method for preconditioned matrices. The newly developed method provides reasonable results, while the conventional method which is based on the Lanczos connection gives meaningless results. The Lanczos connection based method provides the condition numbers of coefficient matrices of systems of linear equations with information obtained through the preconditioned conjugate gradient method. Estimating the condition number of preconditioned matrices is sometimes important when describing the effectiveness of new preconditionerers or selecting adequate preconditioners. Operating a preconditioner on a coefficient matrix is the simplest method of estimation. However, this is not possible for large-scale computing, especially if computation is performed on distributed memory parallel computers. This is because, the preconditioned matrices become dense, even if the original matrices are sparse. Although the Lanczos connection method can be used to calculate the condition number of preconditioned matrices, it is not considered to be applicable to large-scale problems because of its weakness with respect to numerical errors. Therefore, we have developed a robust and parallelizable method based on Hager’s method. The feasibility studies are curried out for the diagonal scaling preconditioner and the SSOR preconditioner with a diagonal matrix, a tri-daigonal matrix and Pei’s matrix. As a result, the Lanczos connection method contains around 10% error in the results even with a simple problem. On the other hand, the new method contains negligible errors. In addition, the newly developed method returns reasonable solutions when the Lanczos connection method fails with Pei’s matrix, and matrices generated with the finite element method. PMID:25816331

Algebraic multigrid domain and range decomposition (AMG-DD / AMG-RD)*

DOE PAGES

Bank, R.; Falgout, R. D.; Jones, T.; ...

2015-10-29

In modern large-scale supercomputing applications, algebraic multigrid (AMG) is a leading choice for solving matrix equations. However, the high cost of communication relative to that of computation is a concern for the scalability of traditional implementations of AMG on emerging architectures. This paper introduces two new algebraic multilevel algorithms, algebraic multigrid domain decomposition (AMG-DD) and algebraic multigrid range decomposition (AMG-RD), that replace traditional AMG V-cycles with a fully overlapping domain decomposition approach. While the methods introduced here are similar in spirit to the geometric methods developed by Brandt and Diskin [Multigrid solvers on decomposed domains, in Domain Decomposition Methods inmore » Science and Engineering, Contemp. Math. 157, AMS, Providence, RI, 1994, pp. 135--155], Mitchell [Electron. Trans. Numer. Anal., 6 (1997), pp. 224--233], and Bank and Holst [SIAM J. Sci. Comput., 22 (2000), pp. 1411--1443], they differ primarily in that they are purely algebraic: AMG-RD and AMG-DD trade communication for computation by forming global composite “grids” based only on the matrix, not the geometry. (As is the usual AMG convention, “grids” here should be taken only in the algebraic sense, regardless of whether or not it corresponds to any geometry.) Another important distinguishing feature of AMG-RD and AMG-DD is their novel residual communication process that enables effective parallel computation on composite grids, avoiding the all-to-all communication costs of the geometric methods. The main purpose of this paper is to study the potential of these two algebraic methods as possible alternatives to existing AMG approaches for future parallel machines. As a result, this paper develops some theoretical properties of these methods and reports on serial numerical tests of their convergence properties over a spectrum of problem parameters.« less

Influence of the IMF Cone Angle on Invariant Latitudes of Polar Region Footprints of FACs in the Magnetotail: Cluster Observation

NASA Astrophysics Data System (ADS)

Cheng, Z. W.; Shi, J. K.; Zhang, J. C.; Torkar, K.; Kistler, L. M.; Dunlop, M.; Carr, C.; Rème, H.; Dandouras, I.; Fazakerley, A.

2018-04-01

The influence of the interplanetary magnetic field (IMF) cone angle θ (the angle between the IMF direction and the Sun-Earth line) on the invariant latitudes of the footprints of the field-aligned currents (FACs) in the magnetotail has been investigated. We performed a statistical study of 542 FAC cases observed by the four Cluster spacecraft in the Northern Hemisphere. The results show that there are almost no FACs when the IMF cone angle is less than 10°, and there are indications of the FACs in the plasma sheet boundary layers being weak under the radial IMF conditions. The footprints of the large FAC (>10 nA/m2) cases are within invariant latitudes <71° and mainly within IMF cone angles θ > 60°, which implies that the footprints of the large FACs mainly expand equatorward with large IMF cone angle. The equatorward boundary of the FAC footprints in the polar region decreases with increasing IMF cone angle (and has a better correlation for northward IMF), which shows that the IMF cone angle plays an important controlling role in FAC distributions in the magnetosphere-ionosphere coupling system. There is almost no correlation between the poleward boundary and the IMF cone angle for both northward and southward IMF. This is because the poleward boundary movement is limited by an enhanced lobe magnetic flux. This is the first time a correlation between FAC footprints in the polar region and IMF cone angles has been determined.

A Comprehensive Analysis of Multiscale Field-Aligned Currents: Characteristics, Controlling Parameters, and Relationships

NASA Astrophysics Data System (ADS)

McGranaghan, Ryan M.; Mannucci, Anthony J.; Forsyth, Colin

2017-12-01

We explore the characteristics, controlling parameters, and relationships of multiscale field-aligned currents (FACs) using a rigorous, comprehensive, and cross-platform analysis. Our unique approach combines FAC data from the Swarm satellites and the Advanced Magnetosphere and Planetary Electrodynamics Response Experiment (AMPERE) to create a database of small-scale (˜10-150 km, <1° latitudinal width), mesoscale (˜150-250 km, 1-2° latitudinal width), and large-scale (>250 km) FACs. We examine these data for the repeatable behavior of FACs across scales (i.e., the characteristics), the dependence on the interplanetary magnetic field orientation, and the degree to which each scale "departs" from nominal large-scale specification. We retrieve new information by utilizing magnetic latitude and local time dependence, correlation analyses, and quantification of the departure of smaller from larger scales. We find that (1) FACs characteristics and dependence on controlling parameters do not map between scales in a straight forward manner, (2) relationships between FAC scales exhibit local time dependence, and (3) the dayside high-latitude region is characterized by remarkably distinct FAC behavior when analyzed at different scales, and the locations of distinction correspond to "anomalous" ionosphere-thermosphere behavior. Comparing with nominal large-scale FACs, we find that differences are characterized by a horseshoe shape, maximizing across dayside local times, and that difference magnitudes increase when smaller-scale observed FACs are considered. We suggest that both new physics and increased resolution of models are required to address the multiscale complexities. We include a summary table of our findings to provide a quick reference for differences between multiscale FACs.

Swarm observation of field-aligned current and electric field in multiple arc systems

NASA Astrophysics Data System (ADS)

Wu, J.; Knudsen, D. J.; Gillies, M.; Donovan, E.; Burchill, J. K.

2017-12-01

It is often thought that auroral arcs are a direct consequence of upward field-aligned currents. In fact, the relation between currents and brightness is more complicated. Multiple auroral arc systems provide and opportunity to study this relation in detail. In this study, we have identified two types of FAC configurations in multiple parallel arc systems using ground-based optical data from the THEMIS all-sky imagers (ASIs), magnetometers and electric field instruments onboard the Swarm satellites during the period from December 2013 to March 2015. In type 1 events, each arc is an intensification within a broad, unipolar current sheet and downward currents only exist outside the upward current sheet. These types of events are termed "unipolar FAC" events. In type 2 events, multiple arc systems represent a collection of multiple up/down current pairs, which are termed as "multipolar FAC" events. Comparisons of these two types of FAC events are presented with 17 "unipolar FAC" events and 12 "multipolar FAC" events. The results show that "unipolar FAC" and "multipolar FAC" events have systematic differences in terms of MLT, arc width and separation, and dependence on substorm onset time. For "unipolar FAC" events, significant electric field enhancements are shown on the edges of the broad upward current sheet. Electric field fluctuations inside the multiple arc system can be large or small. For "multipolar FAC" events, a strong correlation between magnetic and electric field indicate uniform conductance within each upward current sheet. The electrodynamical structures of multiple arc systems presented in this paper represents a step toward understanding arc generation.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lipnikov, Konstantin; Moulton, David; Svyatskiy, Daniil

2016-04-29

We develop a new approach for solving the nonlinear Richards’ equation arising in variably saturated flow modeling. The growing complexity of geometric models for simulation of subsurface flows leads to the necessity of using unstructured meshes and advanced discretization methods. Typically, a numerical solution is obtained by first discretizing PDEs and then solving the resulting system of nonlinear discrete equations with a Newton-Raphson-type method. Efficiency and robustness of the existing solvers rely on many factors, including an empiric quality control of intermediate iterates, complexity of the employed discretization method and a customized preconditioner. We propose and analyze a new preconditioningmore » strategy that is based on a stable discretization of the continuum Jacobian. We will show with numerical experiments for challenging problems in subsurface hydrology that this new preconditioner improves convergence of the existing Jacobian-free solvers 3-20 times. Furthermore, we show that the Picard method with this preconditioner becomes a more efficient nonlinear solver than a few widely used Jacobian-free solvers.« less

An extended GS method for dense linear systems

NASA Astrophysics Data System (ADS)

Niki, Hiroshi; Kohno, Toshiyuki; Abe, Kuniyoshi

2009-09-01

Davey and Rosindale [K. Davey, I. Rosindale, An iterative solution scheme for systems of boundary element equations, Internat. J. Numer. Methods Engrg. 37 (1994) 1399-1411] derived the GSOR method, which uses an upper triangular matrix [Omega] in order to solve dense linear systems. By applying functional analysis, the authors presented an expression for the optimum [Omega]. Moreover, Davey and Bounds [K. Davey, S. Bounds, A generalized SOR method for dense linear systems of boundary element equations, SIAM J. Comput. 19 (1998) 953-967] also introduced further interesting results. In this note, we employ a matrix analysis approach to investigate these schemes, and derive theorems that compare these schemes with existing preconditioners for dense linear systems. We show that the convergence rate of the Gauss-Seidel method with preconditioner PG is superior to that of the GSOR method. Moreover, we define some splittings associated with the iterative schemes. Some numerical examples are reported to confirm the theoretical analysis. We show that the EGS method with preconditioner produces an extremely small spectral radius in comparison with the other schemes considered.

Directed Laplacians For Fuzzy Autocatalytic Set Of Fuzzy Graph Type-3 Of An Incineration Process

NASA Astrophysics Data System (ADS)

Ahmad, Tahir; Baharun, Sabariah; Bakar, Sumarni Abu

2010-11-01

Fuzzy Autocatalytic Set (FACS) of Fuzzy Graph Type-3 was used in the modeling of a clinical waste incineration process in Malacca. FACS provided more accurate explanations of the incineration process than using crisp graph. In this paper we explore further FACS. Directed and combinatorial Laplacian of FACS are developed and their basic properties are presented.

48 CFR 301.607-78 - Contracting Officer designation of a Program/Project Manager as the Contracting Officer's...

Code of Federal Regulations, 2013 CFR

2013-10-01

... Representative. Personnel who are FAC-P/PM certified, at any level, meet the requirements for FAC-COTR certification and are, therefore, not required to obtain FAC-COTR certification to serve as a COTR for an HHS acquisition. However, for those individuals serving as a Program or Project Manager under a FAC-P/PM...

48 CFR 301.607-78 - Contracting Officer designation of a Program/Project Manager as the Contracting Officer's...

Code of Federal Regulations, 2012 CFR

2012-10-01

... Representative. Personnel who are FAC-P/PM certified, at any level, meet the requirements for FAC-COTR certification and are, therefore, not required to obtain FAC-COTR certification to serve as a COTR for an HHS acquisition. However, for those individuals serving as a Program or Project Manager under a FAC-P/PM...

48 CFR 301.607-78 - Contracting Officer designation of a Program/Project Manager as the Contracting Officer's...

Code of Federal Regulations, 2011 CFR

2011-10-01

... Representative. Personnel who are FAC-P/PM certified, at any level, meet the requirements for FAC-COTR certification and are, therefore, not required to obtain FAC-COTR certification to serve as a COTR for an HHS acquisition. However, for those individuals serving as a Program or Project Manager under a FAC-P/PM...

48 CFR 301.607-78 - Contracting Officer designation of a Program/Project Manager as the Contracting Officer's...

Code of Federal Regulations, 2014 CFR

2014-10-01

... Representative. Personnel who are FAC-P/PM certified, at any level, meet the requirements for FAC-COTR certification and are, therefore, not required to obtain FAC-COTR certification to serve as a COTR for an HHS acquisition. However, for those individuals serving as a Program or Project Manager under a FAC-P/PM...

Three-dimensional multigrid algorithms for the flux-split Euler equations

NASA Technical Reports Server (NTRS)

Anderson, W. Kyle; Thomas, James L.; Whitfield, David L.

1988-01-01

The Full Approximation Scheme (FAS) multigrid method is applied to several implicit flux-split algorithms for solving the three-dimensional Euler equations in a body fitted coordinate system. Each of the splitting algorithms uses a variation of approximate factorization and is implemented in a finite volume formulation. The algorithms are all vectorizable with little or no scalar computation required. The flux vectors are split into upwind components using both the splittings of Steger-Warming and Van Leer. The stability and smoothing rate of each of the schemes are examined using a Fourier analysis of the complete system of equations. Results are presented for three-dimensional subsonic, transonic, and supersonic flows which demonstrate substantially improved convergence rates with the multigrid algorithm. The influence of using both a V-cycle and a W-cycle on the convergence is examined.

Iterative and multigrid methods in the finite element solution of incompressible and turbulent fluid flow

NASA Astrophysics Data System (ADS)

Lavery, N.; Taylor, C.

1999-07-01

Multigrid and iterative methods are used to reduce the solution time of the matrix equations which arise from the finite element (FE) discretisation of the time-independent equations of motion of the incompressible fluid in turbulent motion. Incompressible flow is solved by using the method of reduce interpolation for the pressure to satisfy the Brezzi-Babuska condition. The k-l model is used to complete the turbulence closure problem. The non-symmetric iterative matrix methods examined are the methods of least squares conjugate gradient (LSCG), biconjugate gradient (BCG), conjugate gradient squared (CGS), and the biconjugate gradient squared stabilised (BCGSTAB). The multigrid algorithm applied is based on the FAS algorithm of Brandt, and uses two and three levels of grids with a V-cycling schedule. These methods are all compared to the non-symmetric frontal solver. Copyright

A multiple-block multigrid method for the solution of the three-dimensional Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Atkins, Harold

1991-01-01

A multiple block multigrid method for the solution of the three dimensional Euler and Navier-Stokes equations is presented. The basic flow solver is a cell vertex method which employs central difference spatial approximations and Runge-Kutta time stepping. The use of local time stepping, implicit residual smoothing, multigrid techniques and variable coefficient numerical dissipation results in an efficient and robust scheme is discussed. The multiblock strategy places the block loop within the Runge-Kutta Loop such that accuracy and convergence are not affected by block boundaries. This has been verified by comparing the results of one and two block calculations in which the two block grid is generated by splitting the one block grid. Results are presented for both Euler and Navier-Stokes computations of wing/fuselage combinations.

On the solution of evolution equations based on multigrid and explicit iterative methods

NASA Astrophysics Data System (ADS)

Zhukov, V. T.; Novikova, N. D.; Feodoritova, O. B.

2015-08-01

Two schemes for solving initial-boundary value problems for three-dimensional parabolic equations are studied. One is implicit and is solved using the multigrid method, while the other is explicit iterative and is based on optimal properties of the Chebyshev polynomials. In the explicit iterative scheme, the number of iteration steps and the iteration parameters are chosen as based on the approximation and stability conditions, rather than on the optimization of iteration convergence to the solution of the implicit scheme. The features of the multigrid scheme include the implementation of the intergrid transfer operators for the case of discontinuous coefficients in the equation and the adaptation of the smoothing procedure to the spectrum of the difference operators. The results produced by these schemes as applied to model problems with anisotropic discontinuous coefficients are compared.

Multigrid method for stability problems

NASA Technical Reports Server (NTRS)

Ta'asan, Shlomo

1988-01-01

The problem of calculating the stability of steady state solutions of differential equations is addressed. Leading eigenvalues of large matrices that arise from discretization are calculated, and an efficient multigrid method for solving these problems is presented. The resulting grid functions are used as initial approximations for appropriate eigenvalue problems. The method employs local relaxation on all levels together with a global change on the coarsest level only, which is designed to separate the different eigenfunctions as well as to update their corresponding eigenvalues. Coarsening is done using the FAS formulation in a nonstandard way in which the right-hand side of the coarse grid equations involves unknown parameters to be solved on the coarse grid. This leads to a new multigrid method for calculating the eigenvalues of symmetric problems. Numerical experiments with a model problem are presented which demonstrate the effectiveness of the method.

Multi-grid finite element method used for enhancing the reconstruction accuracy in Cerenkov luminescence tomography

NASA Astrophysics Data System (ADS)

Guo, Hongbo; He, Xiaowei; Liu, Muhan; Zhang, Zeyu; Hu, Zhenhua; Tian, Jie

2017-03-01

Cerenkov luminescence tomography (CLT), as a promising optical molecular imaging modality, can be applied to cancer diagnostic and therapeutic. Most researches about CLT reconstruction are based on the finite element method (FEM) framework. However, the quality of FEM mesh grid is still a vital factor to restrict the accuracy of the CLT reconstruction result. In this paper, we proposed a multi-grid finite element method framework, which was able to improve the accuracy of reconstruction. Meanwhile, the multilevel scheme adaptive algebraic reconstruction technique (MLS-AART) based on a modified iterative algorithm was applied to improve the reconstruction accuracy. In numerical simulation experiments, the feasibility of our proposed method were evaluated. Results showed that the multi-grid strategy could obtain 3D spatial information of Cerenkov source more accurately compared with the traditional single-grid FEM.

48 CFR 1401.603-2 - Selection.

Code of Federal Regulations, 2012 CFR

2012-10-01

... Acquisition Certification in Contracting (FAC-C) Program Manual. Director, PAM, is the approving authority for all new and reinstated FAC-C certifications. BPCs are authorized to approve renewal FAC-C...

48 CFR 1401.603-2 - Selection.

Code of Federal Regulations, 2013 CFR

2013-10-01

... Acquisition Certification in Contracting (FAC-C) Program Manual. Director, PAM, is the approving authority for all new and reinstated FAC-C certifications. BPCs are authorized to approve renewal FAC-C...

48 CFR 1401.603-2 - Selection.

Code of Federal Regulations, 2014 CFR

2014-10-01

... Acquisition Certification in Contracting (FAC-C) Program Manual. Director, PAM, is the approving authority for all new and reinstated FAC-C certifications. BPCs are authorized to approve renewal FAC-C...

48 CFR 1401.603-2 - Selection.

Code of Federal Regulations, 2011 CFR

2011-10-01

... Acquisition Certification in Contracting (FAC-C) Program Manual. Director, PAM, is the approving authority for all new and reinstated FAC-C certifications. BPCs are authorized to approve renewal FAC-C...

A NetCDF version of the two-dimensional energy balance model based on the full multigrid algorithm

NASA Astrophysics Data System (ADS)

Zhuang, Kelin; North, Gerald R.; Stevens, Mark J.

A NetCDF version of the two-dimensional energy balance model based on the full multigrid method in Fortran is introduced for both pedagogical and research purposes. Based on the land-sea-ice distribution, orbital elements, greenhouse gases concentration, and albedo, the code calculates the global seasonal surface temperature. A step-by-step guide with examples is provided for practice.

Study of field-aligned current (FAC), interplanetary electric field component (Ey), interplanetary magnetic field component (Bz), and northward (x) and eastward (y) components of geomagnetic field during supersubstorm

NASA Astrophysics Data System (ADS)

Adhikari, Binod; Dahal, Subodh; Chapagain, Narayan P.

2017-05-01

A dominant process by which energy and momentum are transported from the magnetosphere to the ionosphere is known as field-aligned current (FAC). It is enhanced during magnetic reconnection and explosive energy release at a substorm. In this paper, we studied FAC, interplanetary electric field component (Ey), interplanetary magnetic field component (Bz), and northward (x) and eastward (y) components of geomagnetic field during three events of supersubstorm occurred on 24 November 2001, 21 January 2005, and 24 August 2005. Large-scale FAC, supposed to be produced during supersubstorm (SSS), has potentiality to cause blackout on Earth. We examined temporal variations of the x and y components of high-latitude geomagnetic field during SSS, which is attributed to the FACs. We shall report the characteristics of high-latitude northward and eastward components of geomagnetic field variation during the growth phase of SSS by the implementation of discrete wavelet transform (DWT) and cross-correlation analysis. Among three examples of SSS events, the highest peak value of FAC was estimated to be 19 μAm-2. This is shore up with the prediction made by Parks (1991) and Stasiewicz et al. (1998) that the FACs may vary from a few tens to several hundred μAm-2. Although this peak value of FACs for SSS event is much higher than the average FACs associated with regular substorms or magnetic storms, it is expedient and can be expect for SSS events which might be due to very high density solar wind plasma parcels (PPs) triggering the SSS events. In all events, during growth phase, the FAC increases to extremely high level and the geomagnetic northward component decreases to extremely low level. This represents a strong positive correlation between FAC and geomagnetic northward component. The DWT analysis accounts that the highest amplitude of the wavelet coefficients indicates singularities present in FAC during SSS event. But the amplitude of squared wavelet coefficient is found to be different from each other, which might be due to the solar wind PPs of different density triggering the SSS events. The cross-correlation analysis suggests that the perturbation on geomagnetic northward component at high latitude during SSS strongly correlates with the fluctuation pattern of FAC density. Hence, the FAC is the primary sources for the eastward-westward magnetic field perturbations at high latitude.

Highly Efficient Parallel Multigrid Solver For Large-Scale Simulation of Grain Growth Using the Structural Phase Field Crystal Model

NASA Astrophysics Data System (ADS)

Guan, Zhen; Pekurovsky, Dmitry; Luce, Jason; Thornton, Katsuyo; Lowengrub, John

The structural phase field crystal (XPFC) model can be used to model grain growth in polycrystalline materials at diffusive time-scales while maintaining atomic scale resolution. However, the governing equation of the XPFC model is an integral-partial-differential-equation (IPDE), which poses challenges in implementation onto high performance computing (HPC) platforms. In collaboration with the XSEDE Extended Collaborative Support Service, we developed a distributed memory HPC solver for the XPFC model, which combines parallel multigrid and P3DFFT. The performance benchmarking on the Stampede supercomputer indicates near linear strong and weak scaling for both multigrid and transfer time between multigrid and FFT modules up to 1024 cores. Scalability of the FFT module begins to decline at 128 cores, but it is sufficient for the type of problem we will be examining. We have demonstrated simulations using 1024 cores, and we expect to achieve 4096 cores and beyond. Ongoing work involves optimization of MPI/OpenMP-based codes for the Intel KNL Many-Core Architecture. This optimizes the code for coming pre-exascale systems, in particular many-core systems such as Stampede 2.0 and Cori 2 at NERSC, without sacrificing efficiency on other general HPC systems.

Application of p-Multigrid to Discontinuous Galerkin Formulations of the Poisson Equation

NASA Technical Reports Server (NTRS)

Helenbrook, B. T.; Atkins, H. L.

2006-01-01

We investigate p-multigrid as a solution method for several different discontinuous Galerkin (DG) formulations of the Poisson equation. Different combinations of relaxation schemes and basis sets have been combined with the DG formulations to find the best performing combination. The damping factors of the schemes have been determined using Fourier analysis for both one and two-dimensional problems. One important finding is that when using DG formulations, the standard approach of forming the coarse p matrices separately for each level of multigrid is often unstable. To ensure stability the coarse p matrices must be constructed from the fine grid matrices using algebraic multigrid techniques. Of the relaxation schemes, we find that the combination of Jacobi relaxation with the spectral element basis is fairly effective. The results using this combination are p sensitive in both one and two dimensions, but reasonable convergence rates can still be achieved for moderate values of p and isotropic meshes. A competitive alternative is a block Gauss-Seidel relaxation. This actually out performs a more expensive line relaxation when the mesh is isotropic. When the mesh becomes highly anisotropic, the implicit line method and the Gauss-Seidel implicit line method are the only effective schemes. Adding the Gauss-Seidel terms to the implicit line method gives a significant improvement over the line relaxation method.

Multigrid treatment of implicit continuum diffusion

NASA Astrophysics Data System (ADS)

Francisquez, Manaure; Zhu, Ben; Rogers, Barrett

2017-10-01

Implicit treatment of diffusive terms of various differential orders common in continuum mechanics modeling, such as computational fluid dynamics, is investigated with spectral and multigrid algorithms in non-periodic 2D domains. In doubly periodic time dependent problems these terms can be efficiently and implicitly handled by spectral methods, but in non-periodic systems solved with distributed memory parallel computing and 2D domain decomposition, this efficiency is lost for large numbers of processors. We built and present here a multigrid algorithm for these types of problems which outperforms a spectral solution that employs the highly optimized FFTW library. This multigrid algorithm is not only suitable for high performance computing but may also be able to efficiently treat implicit diffusion of arbitrary order by introducing auxiliary equations of lower order. We test these solvers for fourth and sixth order diffusion with idealized harmonic test functions as well as a turbulent 2D magnetohydrodynamic simulation. It is also shown that an anisotropic operator without cross-terms can improve model accuracy and speed, and we examine the impact that the various diffusion operators have on the energy, the enstrophy, and the qualitative aspect of a simulation. This work was supported by DOE-SC-0010508. This research used resources of the National Energy Research Scientific Computing Center (NERSC).

fac-[Re(CO)3(dmso-O)3](CF3SO3): a new versatile and efficient Re(I) precursor for the preparation of mono and polynuclear compounds containing fac-[Re(CO)3]+ fragments.

PubMed

Casanova, Massimo; Zangrando, Ennio; Munini, Fabio; Iengo, Elisabetta; Alessio, Enzo

2006-11-14

We show here that the new complex fac-[Re(CO)3(dmso-O)3](CF3SO3) (1), efficiently prepared in one step from [ReBr(CO)5] and featuring a broad range of solubility, is, in general, a better precursor for the one-step synthesis of mono- and polynuclear inorganic compounds containing fac-[Re(CO)3]+ fragments compared to the commonly used (NEt4)2fac-[ReBr3(CO)3] and fac-[Re(CO)3(CH3CN)3](Y) (Y = PF6, BF4, ClO4) species. Compound 1 is the first example of a Re(I)-dmso complex structurally characterized and confirms the rule that dmso is always O-bonded when trans to CO. The reactivity of 1 was tested in the one-step preparation of several new and known complexes. The O-bonded sulfoxides of 1 are replaced under mild conditions by tri- (L3) and bidentate ligands (L2) to produce fac-[Re(CO)3(L3)]+ and fac-[Re(CO)3(L2)(dmso-O)]+ compounds, respectively. An excess of monodentate ligands (L) and more forcing conditions are needed to prepare fac-[Re(CO)3(L)3]+ compounds. The new compounds include fac-[Re(CO)3(bipy)(dmso-O)](CF3SO3) (4), that turned out to be an excellent precursor for binding the luminescent fac-[Re(CO)3(bipy)]+ fragment to polytopic ligands for the construction of more elaborate assemblies. One example reported here is the two-step preparation of fac-[{Re(CO)3(bipy)}(mu-4,4'-bipy){Ru(TPP)(CO)}](CF3SO3) (8) (TPP = tetraphenylporphyrin). The X-ray structures of the new compounds 1, 4, of the bis-porphyrin complex fac-[Re(CO)3Cl(4'MPyP)2] (13) (4'MPyP = 5-(4'pyridyl)-10,15,20-triphenylporphyrin), and of the rhenium-cyclophane [{(CO)3Re(mu-OH)2Re(CO)3}2(micro-4,4'-bipy)2] (15), among others, are described. Compound 1 might find useful applications in supramolecular chemistry (metal-mediated assembly of large architectures), in the in situ preparation of stable Re compounds to be used in nuclear medicine, and for the labeling of biomolecules.

Possibility of Ionospheric Cause of FACs and Convection Field in the Magnetosphere-Ionosphere System: The Harang Reversal, Premidnight Upward-FAC, and the Ionospheric Hall Polarization Field

NASA Astrophysics Data System (ADS)

Nakamizo, A.; Yoshikawa, A.

2016-12-01

Whereas it is generally thought that Birkeland Currents (FACs) are generated in the magnetosphere and that the ionospheric convection reflects the magnetospheric convection, we present a possibility that the ionosphere drives FACs and the convection field in the M-I system. We apply this idea to the Harang Reversal (HR) for demonstration. By using an ionospheric potential solver we calculate the electrostatic field for given distributions of FACs and conductance. The result shows that a conspicuous structure resembling HR is generated even for a symmetric distribution of the R1-type FACs and that the Hall polarization field is produced at the equatorward boundary of the auroral region as the primary currents diverge/converge at the conductance gradient there, which causes the potential deformation (HR). Conventionally HR has been considered to be of the magnetospheric origin, and a ring current model actually produces the corresponding structure in the magnetosphere [e.g., Erickson et al., 1991]. Observationally the divE equivalent to HR is consistent with the premidnight upward-FAC seen in Iijima and Potemra's diagram. A recent theoretical study [Ohtani et al., 2016] proposes that HR is a required structure for the interchange stability of the magnetotail in the presence of the R1 and R2-FAC systems including a premidnight upward-FAC. Returning to our result, the important point is that HR is reproduced at the conductance edge by the ionospheric polarization field, for which the primary field originates from the R1-FACs distributed far from that region. We also suggest: (i) In a more realistic finite ΣA, the total ionospheric polarization is partly released by a FAC, which may be a part of the premidnight upward-FAC. (ii) However, existing simulation models do not allow this type of current closure, and accordingly they may enhance the HR structure in the magnetosphere. This discussion should hold generally and would promote the global M-I coupling studies to the next step.

Structure and Properties of fac-[Re(I)(CO)3(NTA)](2-) (NTA(3-) = Trianion of Nitrilotriacetic Acid) and fac-[Re(I)(CO)3(L)](n-) Analogues Useful for Assessing the Excellent Renal Clearance of the fac-[(99m)Tc(I)(CO)3(NTA)](2-) Diagnostic Renal Agent.

PubMed

Klenc, Jeffrey; Lipowska, Malgorzata; Abhayawardhana, Pramuditha L; Taylor, Andrew T; Marzilli, Luigi G

2015-07-06

We previously identified two new agents based on the [(99m)Tc(V)O](3+) core with renal clearances in human volunteers 30% higher than that of the widely used clinical tracer (99m)Tc-MAG3 (MAG3(5-) = penta-anion of mercaptoacetyltriglycine). However, renal agents with even higher clearances are needed. More recently, we changed our focus from the [(99m)Tc(V)O](3+) core to the discovery of superior tracers based on the fac-[(99m)Tc(I)(CO)3](+) core. Compared to (99m)Tc-MAG3, fac-[(99m)Tc(I)(CO)3(NTA)](2-) (NTA(3-) = trianion of nitrilotriacetic acid) holds great promise by virtue of its efficient renal clearance via tubular secretion and the absence of hepatobiliary elimination, even in patients with severely reduced renal function. We report here NMR, molecular (X-ray) structure, and solution data on fac-[Re(I)(CO)3(NTA)](2-) with a -CH2CO2(-) dangling monoanionic chain and on two fac-[Re(I)(CO)3(L)](-) analogues with either a -CH2CONH2 or a -CH2CH2OH dangling neutral chain. In these three fac-[Re(I)(CO)3(L)](n-) complexes, the fac-[Re(I)(CO)3(N(CH2CO2)2)](-) moiety is structurally similar and has similar electronic properties (as assessed by NMR data). In reported and ongoing studies, the two fac-[(99m)Tc(I)(CO)3(L)](-) analogues with these neutral dangling chains were found to have pharmacokinetic properties very similar to those of fac-[(99m)Tc(I)(CO)3(NTA)](2-). Therefore, we reach the unexpected conclusion that in fac-[(99m)Tc(I)(CO)3(L)](n-) agents, renal clearance is affected much more than anticipated by features of the core plus the chelate rings (the [(99m)Tc(I)(CO)3(N(CH2CO2)2)](-) moiety) than by the presence of a negatively charged dangling carboxylate chain.

A Polynomial-Based Nonlinear Least Squares Optimized Preconditioner for Continuous and Discontinuous Element-Based Discretizations of the Euler Equations

DTIC Science & Technology

2014-01-01

system (here using left- preconditioning ) (KÃ)x = Kb̃, (3.1) where K is a low-order polynomial in à given by K = s(Ã) = m∑ i=0 kià i, (3.2) and has a... system with a complex spectrum, region E in the complex plane must be some convex form (e.g., an ellipse or polygon) that approximately encloses the...preconditioners with p = 2 and p = 20 on the spectrum of the preconditioned system matrices Kà and KH̃ for both CG Schur-complement form and DG form cases

Higher Order, Hybrid BEM/FEM Methods Applied to Antenna Modeling

NASA Technical Reports Server (NTRS)

Fink, P. W.; Wilton, D. R.; Dobbins, J. A.

2002-01-01

In this presentation, the authors address topics relevant to higher order modeling using hybrid BEM/FEM formulations. The first of these is the limitation on convergence rates imposed by geometric modeling errors in the analysis of scattering by a dielectric sphere. The second topic is the application of an Incomplete LU Threshold (ILUT) preconditioner to solve the linear system resulting from the BEM/FEM formulation. The final tOpic is the application of the higher order BEM/FEM formulation to antenna modeling problems. The authors have previously presented work on the benefits of higher order modeling. To achieve these benefits, special attention is required in the integration of singular and near-singular terms arising in the surface integral equation. Several methods for handling these terms have been presented. It is also well known that achieving he high rates of convergence afforded by higher order bases may als'o require the employment of higher order geometry models. A number of publications have described the use of quadratic elements to model curved surfaces. The authors have shown in an EFIE formulation, applied to scattering by a PEC .sphere, that quadratic order elements may be insufficient to prevent the domination of modeling errors. In fact, on a PEC sphere with radius r = 0.58 Lambda(sub 0), a quartic order geometry representation was required to obtain a convergence benefi.t from quadratic bases when compared to the convergence rate achieved with linear bases. Initial trials indicate that, for a dielectric sphere of the same radius, - requirements on the geometry model are not as severe as for the PEC sphere. The authors will present convergence results for higher order bases as a function of the geometry model order in the hybrid BEM/FEM formulation applied to dielectric spheres. It is well known that the system matrix resulting from the hybrid BEM/FEM formulation is ill -conditioned. For many real applications, a good preconditioner is required to obtain usable convergence from an iterative solver. The authors have examined the use of an Incomplete LU Threshold (ILUT) preconditioner . to solver linear systems stemming from higher order BEM/FEM formulations in 2D scattering problems. Although the resulting preconditioner provided aD excellent approximation to the system inverse, its size in terms of non-zero entries represented only a modest improvement when compared with the fill-in associated with a sparse direct solver. Furthermore, the fill-in of the preconditioner could not be substantially reduced without the occurrence of instabilities. In addition to the results for these 2D problems, the authors will present iterative solution data from the application of the ILUT preconditioner to 3D problems.

Antinociceptive and anti-edema properties of the ethyl acetate fraction obtained from extracts of Coriandrum sativum Linn. leaves.

PubMed

Begnami, Andreza Fabiana; Spindola, Humberto M; Ruiz, Ana Lucia T Gois; de Carvalho, João Ernesto; Groppo, Francisco Carlos; Rehder, Vera L Garcia

2018-07-01

This study evaluated the antinociceptive and anti-edema properties of fractions of Coriandrum sativum Linn. (Apiaceae/Umbelliferae) leaves in mice. Ethyl acetate fractions (FAc) were obtained from dichloromethane extracts prepared from dried C. sativum (CS) leaves and stems. The effects of different concentrations of FAc on mice were observed using the open-field test, formalin-, capsaicin-, and carrageenan-induced paw edema tests, and the acetic acid-induced abdominal writhing test. Results from the carrageenan-induced paw edema test were subjected to a linear regression analysis and data from other assays were subjected to the Kruskal-Wallis test (followed by the SNK post hoc test). Dihydrocoriandrin (34.5%), coriandrin (14.4%), vitamin E (4.6%), and stigmasterol (7.9%) were identified in FAc. The number of squares the mice crossed in the open field test was decreased by 100 mg/kg and 300 mg/kg FAc (i.p.). The administration of 30, 100, and 300 mg/kg FAc induced fewer abdominal writhes than the control. In the formalin test, neurogenic pain was reduced by 20 mg/kg morphine and 30 and 100 mg/kg FAc, but not 5 mg/kg dexamethasone or 10 mg/kg FAc. Formalin-induced inflammatory pain was decreased by morphine, dexamethasone, and 30 and 100 mg/kg FAc. Morphine and 30, 100, and 300 mg/kg FAc significantly decreased the reaction time during the capsaicin test. Dexamethasone reduced both early and later phases of carrageenan-induced edema. Both 30 and 300 mg/kg FAc induced less edema than the control throughout the experiment. FAc showed antinociceptive, anti-edema and anti-inflammatory properties and it may be considered as a potential phytotherapeutic agent in the future. Copyright © 2018 Elsevier Masson SAS. All rights reserved.

In Vitro and In Vivo Comparison of Gemcitabine and the Gemcitabine Analog 1-(2'-deoxy-2'-fluoroarabinofuranosyl) Cytosine (FAC) in Human Orthotopic and Genetically Modified Mouse Pancreatic Cancer Models.

PubMed

Russell, James; Pillarsetty, Nagavarakishore; Kramer, Robin M; Romesser, Paul B; Desai, Pooja; Haimovitz-Friedman, Adriana; Lowery, Maeve A; Humm, John L

2017-12-01

Although gemcitabine is a mainstay of pancreatic cancer therapy, it is only moderately effective, and it would be desirable to measure drug uptake in patients. 1-(2'-deoxy-2'-fluoroarabinofuranosyl) cytosine (FAC), is an analog of gemcitabine, and when labeled with F-18, it may be a potential surrogate PET tracer for the drug. [ 18 F]FAC was synthesized to a radiochemical purity of >96 %. The human tumor lines AsPC1, BxPC3, Capan-1, Panc1, and MiaPaca2 were grown orthotopically in nude mice. KPC mice that conditionally express oncogenic K-ras and p53 mutations in pancreatic tissue were also used. The intra-tumoral distributions of [ 14 C]gemcitabine and [ 18 F]FAC were mapped with autoradiography. The inter-tumor correlation between [ 14 C]gemcitabine and [ 18 F]FAC was established in the orthotopic tumors. Expression of the equilibrative and concentrative nucleoside transporters (ENT, CNT) in vitro was detected by western blotting. Drug uptake was characterized in vitro using [ 3 H]gemcitabine and the effect of transporter inhibition on gemcitabine and FAC uptake was investigated. The relative affinity of cells for gemcitabine and FAC was tested in competition assays. The cell lines differed in sensitivity to transport inhibitors and in competition studies. There was a good in vivo correlation between the total uptake of [ 18 F]FAC and [ 14 C]gemcitabine, measured across all orthotopic tumors. Using the KPC and BxPC3 models, we found that [ 14 C]gemcitabine and [ 18 F]FAC were largely co-localized. In the lines examined here, [ 18 F]FAC uptake correlates well with gemcitabine in vivo, supporting the notion that [ 18 F]FAC can serve as a PET radiotracer surrogate to determine the uptake and distribution of gemcitabine within pancreatic tumors.

In Vitro and In Vivo Comparison of Gemcitabine and the Gemcitabine Analog 1-(2′-deoxy-2′-fluoroarabinofuranosyl) Cytosine (FAC) in Human Orthotopic and Genetically Modified Mouse Pancreatic Cancer Models

PubMed Central

Russell, James; Pillarsetty, Nagavarakishore; Kramer, Robin M; Romesser, Paul B; Desai, Pooja; Haimovitz-Friedman, Adriana; Lowery, Maeve A; Humm, John L

2017-01-01

Purpose Although gemcitabine is a mainstay of pancreatic cancer therapy, it is only moderately effective, and it would be desirable to measure drug uptake in patients. 1-(2′-deoxy-2′-fluoroarabinofuranosyl) cytosine (FAC), is an analog of gemcitabine, and when labeled with F-18, it may be a potential surrogate PET tracer for the drug. Procedures [18F]FAC was synthesized to a radiochemical purity of >96 %. The human tumor lines AsPC1, BxPC3, Capan-1, Panc1, and MiaPaca2 were grown orthotopically in nude mice. KPC mice that conditionally express oncogenic K-ras and p53 mutations in pancreatic tissue were also used. The intra-tumoral distributions of [14C]gemcitabine and [18F]FAC were mapped with autoradiography. The inter-tumor correlation between [14C]gemcitabine and [18F]FAC was established in the orthotopic tumors. Expression of the equilibrative and concentrative nucleoside transporters (ENT, CNT) in vitro was detected by western blotting. Drug uptake was characterized in vitro using [3H]gemcitabine and the effect of transporter inhibition on gemcitabine and FAC uptake was investigated. The relative affinity of cells for gemcitabine and FAC was tested in competition assays. The cell lines differed in sensitivity to transport inhibitors and in competition studies. There was a good in vivo correlation between the total uptake of [18F]FAC and [14C]gemcitabine, measured across all orthotopic tumors. Using the KPC and BxPC3 models, we found that [14C]gemcitabine and [18F]FAC were largely co-localized. Conclusions In the lines examined here, [18F]FAC uptake correlates well with gemcitabine in vivo, supporting the notion that [18F]FAC can serve as a PET radiotracer surrogate to determine the uptake and distribution of gemcitabine within pancreatic tumors. PMID:28349292

Flow-accelerated corrosion in power plants. Revision 1

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chexal, B.; Horowitz, J.; Dooley, B.

1998-07-01

Flow-Accelerated Corrosion (FAC) is a phenomenon that results in metal loss from piping, vessels, and equipment made of carbon steel. FAC occurs only under certain conditions of flow, chemistry, geometry, and material. Unfortunately, those conditions are common in much of the high-energy piping in nuclear and fossil-fueled power plants. Undetected, FAC will cause leaks and ruptures. Consequently, FAC has become a major issue, particularly for nuclear plants. Although major failures are rare, the consequences can be severe. In 1986, four men in the area of an FAC-induced pipe rupture were killed. Fossil plants too, are subject to FAC. In 1995,more » a failure at a fossil-fired plant caused two fatalities. In addition to concerns about personnel safety, FAC failures can pose challenges to plant safety. Regulatory agencies have therefore required nuclear utilities to institute formal programs to address FAC. Finally, a major FAC failure (like the one that happened in 1997 at a US nuclear power plant) can force a plant to shutdown and purchase replacement power at a price approaching a million dollars per day depending upon the MWe rating of the plant. A great deal of time and money has been spent to develop the technology to predict, detect, and mitigate FAC in order to prevent catastrophic failures. Over time, substantial progress has been made towards understanding and preventing FAC. The results of these efforts include dozens of papers, reports, calculations, and manuals, as well as computer programs and other tools. This book is written to provide a detailed treatment of the entire subject in a single document. Any complex issue requires balancing know-how, the risk of decision making, and a pragmatic engineering solution. This book addresses these by carrying out the necessary R and D and engineering along with plant knowledge to cover all quadrants of Chexal`s four quadrant known-unknown diagram, as seen in Figure i.« less

Free Active Chlorine in Sodium Hypochlorite Solutions Admixed with Octenidine, SmearOFF, Chlorhexidine, and EDTA.

PubMed

Krishnan, Unni; Saji, Sreeja; Clarkson, Roger; Lalloo, Ratilal; Moule, Alex J

2017-08-01

The therapeutic effects of sodium hypochlorite (NaOCl) solutions are dependent on the levels of free available chlorine (FAC). Mixing these solutions with irrigants can result in significant reductions in FAC. Although the effect of some irrigants on FAC is known, the effect of other commonly used irrigants is not. Thus, the therapeutic ramifications of the concurrent use of these on the efficiency of NaOCl solutions is not known. Aliquots of 5.2% (w/v) NaOCl solutions were admixed in proportions of 90:10, 80:20, and 50:50 with the following irrigants: octenidine dihydrochloride (OCT); SmearOFF (Vista Dental Products, Racine, WI), 17% EDTA; and 0.2%, 2%, and 5% chlorhexidine (CHX) solutions. Changes in FAC were measured by iodometric titration. Statistical differences between means were determined using a post hoc Tukey analysis test after an analysis of variance. OCT appeared not to affect FAC and was significantly different than all other irrigants, except for 90:10 and 80:20 mixtures of low concentration (0.2%) CHX. CHX solutions showed a marked concentration- and mixture proportion-dependent detrimental effect on FAC. The reduction of FAC between different concentrations of CHX was statistically significant in 80:20 and 50:50 proportions, with 50:50 mixtures of 5% CHX having the greatest influence. Mixtures containing even small proportions of SmearOFF or EDTA exhibited significant losses in FAC. OCT has little effect on FAC and can be used concurrently with NaOCl solutions. Higher concentrations of CHX significantly affect FAC. Their combined use with NaOCl solutions should be avoided. EDTA and SmearOFF should not be mixed with NaOCl solutions. Copyright © 2017 American Association of Endodontists. All rights reserved.

Substorm Birkeland currents and Cowling channels in the ionosphere

NASA Astrophysics Data System (ADS)

Fujii, R.

2016-12-01

Field-aligned current (FAC) connects electromagnetically the ionosphere with the magnetosphere and plays important roles on dynamics and energetics in the magnetosphere and the ionosphere. In particular, connections between FACs in the ionosphere give important information on various current sources in the magnetosphere and the linkage between them, although the connection between FACs in the ionosphere does not straightforwardly give that in the magnetosphere. FACs in the ionosphere are closed to each other through ionospheric currents determined with the electric field and the Hall and Pedersen conductivities. The electric field and the conductivities are not independently distributed, but rather they are harmonized with each other spatially and temporarily in a physically consistent manner to give a certain FAC. In particular, the divergence of the Hall current due to the inhomogeneity of the Hall conductivity either flows in/out to the magnetosphere as a secondary FAC or accumulates excess charges that produce a secondary electric field. This electric field drives a current circuit connecting the Hall current with the Pedersen current; a Cowling channel current circuit. The FAC (the electric field) we observe is the sum of the primary and secondary FACs (electric fields). The talk will present characteristics of FACs and associated electric field and auroras during substorms, and the ionospheric current closures between the FACs. A statistical study has shown that the majority of region 1 currents are connected to their adjacent region 2 or region 0 currents, indicating the Pedersen current closure rather than the Hall current closure is dominant. On the other hand, the Pedersen currents associated with surge and substorm-related auroras often are connected to the Hall currents, forming a Cowling channel current circuit within the ionosphere.

Fluorescent aromatic hydrocarbons in bile as a biomarker of exposure of brown bullheads (Ameiurus nebulosus) to contaminated sediments

DOE Office of Scientific and Technical Information (OSTI.GOV)

Leadly, T.A.; Haffner, G.D.; Arcand-Hoy, L.D.

1999-04-01

Analysis of fluorescent aromatic compounds (FACs) in the bile of fish has been widely used as a biomarker of exposure to polynuclear aromatic hydrocarbon (PAH) contamination. However, bile FAC data for feral fish populations are typically highly variable, and in a few cases, elevation of FACs has not been observed in fish from contaminated areas. In this study, the bile FACs and hepatic ethoxyresorufin-O-deethylase activity in brown bullheads (Ameiurus nebulosus) exposed in the laboratory to contaminated sediments from Hamilton Harbour, Ontario, Canada, increased by 173-fold within 72 h of initial exposure and rapidly declined thereafter. In bullheads caged in themore » contaminated Trenton Channel area of the Detroit River, bile FACs also increased rapidly within 4 d of initial exposure to mean levels >3,000 ng of benzo[a]pyrene equivalents per milliliter of bile. Surprisingly, there was no difference in the mean-levels of bile FACs in fish caged above the sediment versus fish caged in direct contact with the sediment, indicating that water may be the major vector for uptake of PAHs. The lower bile FACs in bullheads caged in other regions of the Detroit River were consistent with the lower concentrations of PAHs in the sediments from these areas. These data indicate that bile FAC levels are a biomarker of recent exposure to aromatic hydrocarbons in sediments. However, FAC data were highly variable even in these studies, in which fish were relatively homogenous in size, feeding status, and exposure history. Therefore, Even higher variability in bile FAC data are expected in biomarker studies as a result of differences in reproductive status, size, diet, and mobility of the fish.« less

Ocular Pharmacokinetics of Fluocinolone Acetonide Following Iluvien Implantation in the Vitreous Humor of Rabbits

PubMed Central

Kane, Frances E.

2015-01-01

Abstract Purpose: The purpose of this study was to evaluate the systemic and ocular pharmacokinetics (PK) of fluocinolone acetonide (FAc) following administration of Iluvien® intravitreal implants. Methods: The FAc intravitreal implant was administered to rabbits in 3 doses (0.2, 0.5, and 1.0 μg/day). The concentration of FAc was measured by a validated liquid chromatography-mass spectrometry/mass spectrometry (LC-MS/MS) method in plasma and ocular tissues at various time points through month 24. Results: Following administration of the 0.2 μg/day implant, FAc levels peaked in most tissues at day 2 or 8, reached approximate steady state levels by month 3 and very gradually decreased over the duration of the study. The FAc level in the aqueous humor was not measurable at most time points in the rabbit. FAc was still present in most ocular tissues at 2 years. The 0.5 and 1.0 μg/day dose groups followed the same pattern through month 9. The elimination half lives in the tissues for which it was measurable were greater than 83 days. Exposure to FAc was highest in the choroid/retinal pigment epithelium for all doses, followed by lens and retina. Conclusions: The results of this study demonstrate sustained delivery of FAc from the Iluvien intravitreal implant in the ocular tissue of rabbits. Retina and lens FAc levels with the Iluvien implant were approximately 1/10 those reported with the Retisert® implant. FAc levels in the aqueous were not measureable with Iluvien where they were measured for 12 months with Retisert. PMID:25562126

The interplanetary magnetic field B sub y -dependent field-aligned current in the dayside polar cap under quiet conditions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yamauchi, M.; Araki, T.

1989-03-01

Spatial distribution and temporal variation of the interplanetary magnetic field (IMF) B{sub y}-dependent cusp region field-aligned currents (FACs) during quiet periods were studied by use of magnetic data observed by Magsat. The analysis was made for 11 events (each event lasts more than one and a half days) when the IMF B{sub y} component was steadily large and B{sub x} was relatively small ({vert bar}B{sub z}{vert bar} < {vert bar}B{sub y}{vert bar}). Results of the analysis of total 62 half-day periods for the IMF B{sub y}-dependent cusp region FAC are summarized as follows: (1) the IMF B{sub y}-dependent cusp regionmore » FAC is located at around 86{degree}-87{degree} invariant latitude local noon, which is more poleward than the location of the IMF B{sub z}-dependent cusp region FAC; (2) the current density of this FAC is greater than previous studies ({ge} 4 {mu}A/m{sup 2} for IMF B{sub y} = 6 nT); (3) there are two time scales for the IMF B{sub y}-dependent cusp region FAC to appear: the initial rise of the current is on a short time scale, {approximately} 10 min, and it is followed by a gradual increase on a time scale of several hours to a half day; (4) the seasonal change of this FAC is greater than that of the nightside region 1 or region 2 FACs; (5) the IMF B{sub z}-dependent cusp region FAC is not well observed around the cusp when the IMF B{sub y}-dependent cusp region FAC is intense.« less

Field-Aligned Current at Plasma Sheet Boundary Layers During Storm Time: Cluster Observation

NASA Astrophysics Data System (ADS)

Shi, J.; Cheng, Z.; Zhang, T.; Dunlop, M.; Liu, Z.

2007-05-01

The magnetic field data from the FGM instruments on board the four Cluster spacecrafts were used to study Field Aligned Current (FAC) at the Plasma Sheet Boundary Layers (PSBLs) with the so called "curlometer technique". We analyzed the date obtained in 2001 in the magnetotail and only two cases were found in the storm time. One (August 17, 2001) occurred from sudden commencement to main phase, and the other (October 1, 2001) lay in the main phase and recovery phase. The relationship between the FAC density and the AE index was studied and the results are shown as follows. (1) In the sudden commencement and the main phase the density of the FAC increases obviously, in the recovery phase the density of the FAC increases slightly. (2) From the sudden commencement to the initial stage of the main phase the FAC increases with decreasing AE index and decreases with increasing AE index. From the late stage of the main phase to initial stage of the recovery phase, the FAC increases with increasing AE index and decreases with decreasing AE index. In the late stage of the recovery phase the disturbance of the FAC is not so violent, so that the FAC varying with the AE index is not very obvious.

The influence of IMF cone angle on invariant latitudes of polar region footprints of FACs in the magnetotail: Cluster observatio

NASA Astrophysics Data System (ADS)

Cheng, Z.; Shi, J.; Zhang, J.; Kistler, L. M.

2017-12-01

The influence of the interplanetary magnetic field (IMF) cone angle θ (the angle between the IMF direction and the Sun-Earth line) on the invariant latitudes (ILATs) of the footprints of the field-aligned currents (FACs) in the magnetotail has been investigated. We performed a statistic study of 542 FAC cases observed by the four Cluster spacecraft in the northern hemisphere. The results show that the large FAC (>10 nA/m2) cases occur at the low ILATs (<71 º) and mainly occur when the IMF cone angle θ>60º, which implies the footprints of the large FACs mainly expand equatorward with large IMF cone angle. The equatorward boundary of the FAC footprints in the polar region decreases with the IMF cone angle especially when IMF Bz is positive. There is almost no correlation or a weak positive correlation of the poleward boundary and IMF cone angle no matter IMF is northward or southward. The equatorward boundary is more responsive to the IMF cone angle. Compared to the equatorward boundary, the center of the FAC projected location changes very little. This is the first time a correlation between FAC projected location and IMF cone angle has been determined.

Utilization of operating experience to prevent piping failures at steam plants

DOE Office of Scientific and Technical Information (OSTI.GOV)

Adams, T.S.; Dietrich, E.B.

1999-11-01

The key to preventing flow-accelerated corrosion (FAC) induced piping failures in steam plants is the development and implementation of a methodical program for assessing plant susceptibility to FAC and managing the effects of FAC. One of the key elements of an effective FAC program is the accurate and comprehensive utilization of plant-specific and industry-wide operating experience. Operating experience should be used to develop the program to identify specific areas for inspection or replacement, and to maintain an effective program. This paper discusses the utilization of operating experience in FAC programs at nuclear power plants, fossil plants and other steam plants.

Pipe degradation investigations for optimization of flow-accelerated corrosion inspection location selection

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chandra, S.; Habicht, P.; Chexal, B.

1995-12-01

A large amount of piping in a typical nuclear power plant is susceptible to Flow-Accelerated Corrosion (FAC) wall thinning to varying degrees. A typical PAC monitoring program includes the wall thickness measurement of a select number of components in order to judge the structural integrity of entire systems. In order to appropriately allocate resources and maintain an adequate FAC program, it is necessary to optimize the selection of components for inspection by focusing on those components which provide the best indication of system susceptibility to FAC. A better understanding of system FAC predictability and the types of FAC damage encounteredmore » can provide some of the insight needed to better focus and optimize the inspection plan for an upcoming refueling outage. Laboratory examination of FAC damaged components removed from service at Northeast Utilities` (NU) nuclear power plants provides a better understanding of the damage mechanisms involved and contributing causes. Selected results of this ongoing study are presented with specific conclusions which will help NU to better focus inspections and thus optimize the ongoing FAC inspection program.« less

An Optimal Order Nonnested Mixed Multigrid Method for Generalized Stokes Problems

NASA Technical Reports Server (NTRS)

Deng, Qingping

1996-01-01

A multigrid algorithm is developed and analyzed for generalized Stokes problems discretized by various nonnested mixed finite elements within a unified framework. It is abstractly proved by an element-independent analysis that the multigrid algorithm converges with an optimal order if there exists a 'good' prolongation operator. A technique to construct a 'good' prolongation operator for nonnested multilevel finite element spaces is proposed. Its basic idea is to introduce a sequence of auxiliary nested multilevel finite element spaces and define a prolongation operator as a composite operator of two single grid level operators. This makes not only the construction of a prolongation operator much easier (the final explicit forms of such prolongation operators are fairly simple), but the verification of the approximate properties for prolongation operators is also simplified. Finally, as an application, the framework and technique is applied to seven typical nonnested mixed finite elements.

On Efficient Multigrid Methods for Materials Processing Flows with Small Particles

NASA Technical Reports Server (NTRS)

Thomas, James (Technical Monitor); Diskin, Boris; Harik, VasylMichael

2004-01-01

Multiscale modeling of materials requires simulations of multiple levels of structural hierarchy. The computational efficiency of numerical methods becomes a critical factor for simulating large physical systems with highly desperate length scales. Multigrid methods are known for their superior efficiency in representing/resolving different levels of physical details. The efficiency is achieved by employing interactively different discretizations on different scales (grids). To assist optimization of manufacturing conditions for materials processing with numerous particles (e.g., dispersion of particles, controlling flow viscosity and clusters), a new multigrid algorithm has been developed for a case of multiscale modeling of flows with small particles that have various length scales. The optimal efficiency of the algorithm is crucial for accurate predictions of the effect of processing conditions (e.g., pressure and velocity gradients) on the local flow fields that control the formation of various microstructures or clusters.

Investigation of upwind, multigrid, multiblock numerical schemes for three dimensional flows. Volume 1: Runge-Kutta methods for a thin layer Navier-Stokes solver

NASA Technical Reports Server (NTRS)

Cannizzaro, Frank E.; Ash, Robert L.

1992-01-01

A state-of-the-art computer code has been developed that incorporates a modified Runge-Kutta time integration scheme, upwind numerical techniques, multigrid acceleration, and multi-block capabilities (RUMM). A three-dimensional thin-layer formulation of the Navier-Stokes equations is employed. For turbulent flow cases, the Baldwin-Lomax algebraic turbulence model is used. Two different upwind techniques are available: van Leer's flux-vector splitting and Roe's flux-difference splitting. Full approximation multi-grid plus implicit residual and corrector smoothing were implemented to enhance the rate of convergence. Multi-block capabilities were developed to provide geometric flexibility. This feature allows the developed computer code to accommodate any grid topology or grid configuration with multiple topologies. The results shown in this dissertation were chosen to validate the computer code and display its geometric flexibility, which is provided by the multi-block structure.

Multigrid methods for numerical simulation of laminar diffusion flames

NASA Technical Reports Server (NTRS)

Liu, C.; Liu, Z.; Mccormick, S.

1993-01-01

This paper documents the result of a computational study of multigrid methods for numerical simulation of 2D diffusion flames. The focus is on a simplified combustion model, which is assumed to be a single step, infinitely fast and irreversible chemical reaction with five species (C3H8, O2, N2, CO2 and H2O). A fully-implicit second-order hybrid scheme is developed on a staggered grid, which is stretched in the streamwise coordinate direction. A full approximation multigrid scheme (FAS) based on line distributive relaxation is developed as a fast solver for the algebraic equations arising at each time step. Convergence of the process for the simplified model problem is more than two-orders of magnitude faster than other iterative methods, and the computational results show good grid convergence, with second-order accuracy, as well as qualitatively agreement with the results of other researchers.

Numerical methods in laminar and turbulent flow; Proceedings of the 7th International Conference, Stanford Univ., CA, July 15-19, 1991. Vol. 7, pts. 1 & 2

NASA Technical Reports Server (NTRS)

Taylor, C. (Editor); Chin, J. H. (Editor); Homsy, G. M. (Editor)

1991-01-01

Consideration is given to the impulse response of a laminar boundary layer and receptivity; numerical transition to turbulence in plane Poiseuille flow; large eddy simulation of turbulent wake flow; a viscous model and loss calculation of a multisplitter cascade; vortex initiation during dynamic stall of an airfoil; a numerical analysis of isothermal flow in a combustion chamber; and compressible flow calculations with a two-equation turbulence model and unstructured grids. Attention is also given to a 2D calculation of a buoyant flow around a burning sphere, a fast multigrid method for 3D turbulent incompressible flows, a streaming flow induced by an oscillating cascade of circular cylinders, an algebraic multigrid scheme for solving the Navier-Stokes equations on unstructured meshes; and nonlinear coupled multigrid solutions to thermal problems employing different nodal grid arrangements and convective transport approximations.

Segmented Domain Decomposition Multigrid For 3-D Turbomachinery Flows

NASA Technical Reports Server (NTRS)

Celestina, M. L.; Adamczyk, J. J.; Rubin, S. G.

2001-01-01

A Segmented Domain Decomposition Multigrid (SDDMG) procedure was developed for three-dimensional viscous flow problems as they apply to turbomachinery flows. The procedure divides the computational domain into a coarse mesh comprised of uniformly spaced cells. To resolve smaller length scales such as the viscous layer near a surface, segments of the coarse mesh are subdivided into a finer mesh. This is repeated until adequate resolution of the smallest relevant length scale is obtained. Multigrid is used to communicate information between the different grid levels. To test the procedure, simulation results will be presented for a compressor and turbine cascade. These simulations are intended to show the ability of the present method to generate grid independent solutions. Comparisons with data will also be presented. These comparisons will further demonstrate the usefulness of the present work for they allow an estimate of the accuracy of the flow modeling equations independent of error attributed to numerical discretization.

Efficient relaxed-Jacobi smoothers for multigrid on parallel computers

NASA Astrophysics Data System (ADS)

Yang, Xiang; Mittal, Rajat

2017-03-01

In this Technical Note, we present a family of Jacobi-based multigrid smoothers suitable for the solution of discretized elliptic equations. These smoothers are based on the idea of scheduled-relaxation Jacobi proposed recently by Yang & Mittal (2014) [18] and employ two or three successive relaxed Jacobi iterations with relaxation factors derived so as to maximize the smoothing property of these iterations. The performance of these new smoothers measured in terms of convergence acceleration and computational workload, is assessed for multi-domain implementations typical of parallelized solvers, and compared to the lexicographic point Gauss-Seidel smoother. The tests include the geometric multigrid method on structured grids as well as the algebraic grid method on unstructured grids. The tests demonstrate that unlike Gauss-Seidel, the convergence of these Jacobi-based smoothers is unaffected by domain decomposition, and furthermore, they outperform the lexicographic Gauss-Seidel by factors that increase with domain partition count.

A Parallel Multigrid Solver for Viscous Flows on Anisotropic Structured Grids

NASA Technical Reports Server (NTRS)

Prieto, Manuel; Montero, Ruben S.; Llorente, Ignacio M.; Bushnell, Dennis M. (Technical Monitor)

2001-01-01

This paper presents an efficient parallel multigrid solver for speeding up the computation of a 3-D model that treats the flow of a viscous fluid over a flat plate. The main interest of this simulation lies in exhibiting some basic difficulties that prevent optimal multigrid efficiencies from being achieved. As the computing platform, we have used Coral, a Beowulf-class system based on Intel Pentium processors and equipped with GigaNet cLAN and switched Fast Ethernet networks. Our study not only examines the scalability of the solver but also includes a performance evaluation of Coral where the investigated solver has been used to compare several of its design choices, namely, the interconnection network (GigaNet versus switched Fast-Ethernet) and the node configuration (dual nodes versus single nodes). As a reference, the performance results have been compared with those obtained with the NAS-MG benchmark.

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.

A matrix-free implicit unstructured multigrid finite volume method for simulating structural dynamics and fluid structure interaction

NASA Astrophysics Data System (ADS)

Lv, X.; Zhao, Y.; Huang, X. Y.; Xia, G. H.; Su, X. H.

2007-07-01

A new three-dimensional (3D) matrix-free implicit unstructured multigrid finite volume (FV) solver for structural dynamics is presented in this paper. The solver is first validated using classical 2D and 3D cantilever problems. It is shown that very accurate predictions of the fundamental natural frequencies of the problems can be obtained by the solver with fast convergence rates. This method has been integrated into our existing FV compressible solver [X. Lv, Y. Zhao, et al., An efficient parallel/unstructured-multigrid preconditioned implicit method for simulating 3d unsteady compressible flows with moving objects, Journal of Computational Physics 215(2) (2006) 661-690] based on the immersed membrane method (IMM) [X. Lv, Y. Zhao, et al., as mentioned above]. Results for the interaction between the fluid and an immersed fixed-free cantilever are also presented to demonstrate the potential of this integrated fluid-structure interaction approach.

Two variants of minimum discarded fill ordering

DOE Office of Scientific and Technical Information (OSTI.GOV)

D'Azevedo, E.F.; Forsyth, P.A.; Tang, Wei-Pai

1991-01-01

It is well known that the ordering of the unknowns can have a significant effect on the convergence of Preconditioned Conjugate Gradient (PCG) methods. There has been considerable experimental work on the effects of ordering for regular finite difference problems. In many cases, good results have been obtained with preconditioners based on diagonal, spiral or natural row orderings. However, for finite element problems having unstructured grids or grids generated by a local refinement approach, it is difficult to define many of the orderings for more regular problems. A recently proposed Minimum Discarded Fill (MDF) ordering technique is effective in findingmore » high quality Incomplete LU (ILU) preconditioners, especially for problems arising from unstructured finite element grids. Testing indicates this algorithm can identify a rather complicated physical structure in an anisotropic problem and orders the unknowns in the preferred'' direction. The MDF technique may be viewed as the numerical analogue of the minimum deficiency algorithm in sparse matrix technology. At any stage of the partial elimination, the MDF technique chooses the next pivot node so as to minimize the amount of discarded fill. In this work, two efficient variants of the MDF technique are explored to produce cost-effective high-order ILU preconditioners. The Threshold MDF orderings combine MDF ideas with drop tolerance techniques to identify the sparsity pattern in the ILU preconditioners. These techniques identify an ordering that encourages fast decay of the entries in the ILU factorization. The Minimum Update Matrix (MUM) ordering technique is a simplification of the MDF ordering and is closely related to the minimum degree algorithm. The MUM ordering is especially for large problems arising from Navier-Stokes problems. Some interesting pictures of the orderings are presented using a visualization tool. 22 refs., 4 figs., 7 tabs.« less

Long Range Transport of War-Related Burn Casualties

DTIC Science & Technology

2008-02-01

Long Range Transport of War-Related Burn Casualties Evan M. Renz, MD, FACS, Leopoldo C . Cancio, MD, FACS, David J. Barillo, MD, FACS, Christopher E...White, MD, FACS, Michael C . Albrecht, MD, Charles K. Thompson, PA- C , Jody L. Ennis, RN, BSN, Sandra M. Wanek, MD, James A. King, MD, FACEP, Kevin K...sched- Submitted for publication October 29, 2007. Accepted for publication October 30, 2007. Copyright © 2008 by Lippincott Williams & Wilkins From the

A FPGA Implementation of the CAR-FAC Cochlear Model.

PubMed

Xu, Ying; Thakur, Chetan S; Singh, Ram K; Hamilton, Tara Julia; Wang, Runchun M; van Schaik, André

2018-01-01

This paper presents a digital implementation of the Cascade of Asymmetric Resonators with Fast-Acting Compression (CAR-FAC) cochlear model. The CAR part simulates the basilar membrane's (BM) response to sound. The FAC part models the outer hair cell (OHC), the inner hair cell (IHC), and the medial olivocochlear efferent system functions. The FAC feeds back to the CAR by moving the poles and zeros of the CAR resonators automatically. We have implemented a 70-section, 44.1 kHz sampling rate CAR-FAC system on an Altera Cyclone V Field Programmable Gate Array (FPGA) with 18% ALM utilization by using time-multiplexing and pipeline parallelizing techniques and present measurement results here. The fully digital reconfigurable CAR-FAC system is stable, scalable, easy to use, and provides an excellent input stage to more complex machine hearing tasks such as sound localization, sound segregation, speech recognition, and so on.

Intermolecular interactions and aggregation of fac-tris(2-phenylpyridinato-C2,N)iridium(III) in nonpolar solvents.

PubMed

Takayasu, Satoshi; Suzuki, Takayoshi; Shinozaki, Kazuteru

2013-08-15

The intermolecular interaction and aggregation of the neutral complex fac-tris(2-phenylpyridinato-C(2),N)iridium(III) (fac-Ir(ppy)3) in solution was investigated. Intermolecular interactions were found to effectively decrease the luminescence lifetime via self-quenching with increasing fac-Ir(ppy)3 concentrations. A Stern-Volmer plot for quenching in acetonitrile was linear, due to bimolecular self-quenching, but curved in toluene as the result of excimer formation. (1)H NMR spectra demonstrated a monomer-aggregate equilibrium which resulted in spectral shifts depending on solvent polarity. X-ray crystallography provided structural information concerning the aggregate, which is based on a tetramer consisting of two Δ-fac-Ir(ppy)3-Λ-fac-Ir(ppy)3 pairs. Offset π-π stacking of ppy ligands and electrostatic dipole-dipole interactions between complex molecules play an important role in the formation of these molecular pairs.

A FPGA Implementation of the CAR-FAC Cochlear Model

PubMed Central

Xu, Ying; Thakur, Chetan S.; Singh, Ram K.; Hamilton, Tara Julia; Wang, Runchun M.; van Schaik, André

2018-01-01

This paper presents a digital implementation of the Cascade of Asymmetric Resonators with Fast-Acting Compression (CAR-FAC) cochlear model. The CAR part simulates the basilar membrane's (BM) response to sound. The FAC part models the outer hair cell (OHC), the inner hair cell (IHC), and the medial olivocochlear efferent system functions. The FAC feeds back to the CAR by moving the poles and zeros of the CAR resonators automatically. We have implemented a 70-section, 44.1 kHz sampling rate CAR-FAC system on an Altera Cyclone V Field Programmable Gate Array (FPGA) with 18% ALM utilization by using time-multiplexing and pipeline parallelizing techniques and present measurement results here. The fully digital reconfigurable CAR-FAC system is stable, scalable, easy to use, and provides an excellent input stage to more complex machine hearing tasks such as sound localization, sound segregation, speech recognition, and so on. PMID:29692700

Field-aligned currents' scale analysis performed with the Swarm constellation

NASA Astrophysics Data System (ADS)

Lühr, Hermann; Park, Jaeheung; Gjerloev, Jesper W.; Rauberg, Jan; Michaelis, Ingo; Merayo, Jose M. G.; Brauer, Peter

2015-01-01

We present a statistical study of the temporal- and spatial-scale characteristics of different field-aligned current (FAC) types derived with the Swarm satellite formation. We divide FACs into two classes: small-scale, up to some 10 km, which are carried predominantly by kinetic Alfvén waves, and large-scale FACs with sizes of more than 150 km. For determining temporal variability we consider measurements at the same point, the orbital crossovers near the poles, but at different times. From correlation analysis we obtain a persistent period of small-scale FACs of order 10 s, while large-scale FACs can be regarded stationary for more than 60 s. For the first time we investigate the longitudinal scales. Large-scale FACs are different on dayside and nightside. On the nightside the longitudinal extension is on average 4 times the latitudinal width, while on the dayside, particularly in the cusp region, latitudinal and longitudinal scales are comparable.

High order spectral volume and spectral difference methods on unstructured grids

NASA Astrophysics Data System (ADS)

Kannan, Ravishekar

The spectral volume (SV) and the spectral difference (SD) methods were developed by Wang and Liu and their collaborators for conservation laws on unstructured grids. They were introduced to achieve high-order accuracy in an efficient manner. Recently, these methods were extended to three-dimensional systems and to the Navier Stokes equations. The simplicity and robustness of these methods have made them competitive against other higher order methods such as the discontinuous Galerkin and residual distribution methods. Although explicit TVD Runge-Kutta schemes for the temporal advancement are easy to implement, they suffer from small time step limited by the Courant-Friedrichs-Lewy (CFL) condition. When the polynomial order is high or when the grid is stretched due to complex geometries or boundary layers, the convergence rate of explicit schemes slows down rapidly. Solution strategies to remedy this problem include implicit methods and multigrid methods. A novel implicit lower-upper symmetric Gauss-Seidel (LU-SGS) relaxation method is employed as an iterative smoother. It is compared to the explicit TVD Runge-Kutta smoothers. For some p-multigrid calculations, combining implicit and explicit smoothers for different p-levels is also studied. The multigrid method considered is nonlinear and uses Full Approximation Scheme (FAS). An overall speed-up factor of up to 150 is obtained using a three-level p-multigrid LU-SGS approach in comparison with the single level explicit method for the Euler equations for the 3rd order SD method. A study of viscous flux formulations was carried out for the SV method. Three formulations were used to discretize the viscous fluxes: local discontinuous Galerkin (LDG), a penalty method and the 2nd method of Bassi and Rebay. Fourier analysis revealed some interesting advantages for the penalty method. These were implemented in the Navier Stokes solver. An implicit and p-multigrid method was also implemented for the above. An overall speed-up factor of up to 1500 is obtained using a three-level p-multigrid LU-SGS approach in comparison with the single level explicit method for the Navier-Stokes equations. The SV method was also extended to turbulent flows. The RANS based SA model was used to close the Reynolds stresses. The numerical results are very promising and indicate that the approaches have great potentials for 3D flow problems.

Field-aligned currents and large-scale magnetospheric electric fields

NASA Technical Reports Server (NTRS)

Dangelo, N.

1979-01-01

The existence of field-aligned currents (FAC) at northern and southern high latitudes was confirmed by a number of observations, most clearly by experiments on the TRIAD and ISIS 2 satellites. The high-latitude FAC system is used to relate what is presently known about the large-scale pattern of high-latitude ionospheric electric fields and their relation to solar wind parameters. Recently a simplified model was presented for polar cap electric fields. The model is of considerable help in visualizing the large-scale features of FAC systems. A summary of the FAC observations is given. The simplified model is used to visualize how the FAC systems are driven by their generators.

Active role of fatty acid amino acid conjugates in nitrogen metabolism in Spodoptera litura larvae

PubMed Central

Yoshinaga, Naoko; Aboshi, Takako; Abe, Hiroaki; Nishida, Ritsuo; Alborn, Hans T.; Tumlinson, James H.; Mori, Naoki

2008-01-01

Since the first fatty acid amino acid conjugate (FAC) was isolated from regurgitant of Spodoptera exigua larvae in 1997 [volicitin: N-(17-hydroxylinolenoyl)-l-glutamine], their role as elicitors of induced responses in plants has been well documented. However, studies of the biosyntheses and the physiological role of FACs in the insect have been minimal. By using 14C-labeled glutamine, glutamic acid, and linolenic acid in feeding studies of Spodoptera litura larvae, combined with tissue analyses, we found glutamine in the midgut cells to be a major source for biosynthesis of FACs. Furthermore, 20% of the glutamine moiety of FACs was derived from glutamic acid and ammonia through enzymatic reaction of glutamine synthetase (GS). To determine whether FACs improve GS productivity, we studied nitrogen assimilation efficiency of S. litura larvae fed on artificial diets containing 15NH4Cl and glutamic acid. When the diet was enriched with linolenic acid, the nitrogen assimilation efficiency improved from 40% to >60%. In the lumen, the biosynthesized FACs are hydrolyzed to fatty acids and glutamine, which are reabsorbed into tissues and hemolymph. These results strongly suggested that FACs play an active role in nitrogen assimilation in Lepidoptera larva and that glutamine containing FACs in the gut lumen may function as a form of storage of glutamine, a key compound of nitrogen metabolism. PMID:18997016

Multigrid Techniques for Highly Indefinite Equations

NASA Technical Reports Server (NTRS)

Shapira, Yair

1996-01-01

A multigrid method for the solution of finite difference approximations of elliptic PDE's is introduced. A parallelizable version of it, suitable for two and multi level analysis, is also defined, and serves as a theoretical tool for deriving a suitable implementation for the main version. For indefinite Helmholtz equations, this analysis provides a suitable mesh size for the coarsest grid used. Numerical experiments show that the method is applicable to diffusion equations with discontinuous coefficients and highly indefinite Helmholtz equations.

Convergence of Defect-Correction and Multigrid Iterations for Inviscid Flows

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.

2011-01-01

Convergence of multigrid and defect-correction iterations is comprehensively studied within different incompressible and compressible inviscid regimes on high-density grids. Good smoothing properties of the defect-correction relaxation have been shown using both a modified Fourier analysis and a more general idealized-coarse-grid analysis. Single-grid defect correction alone has some slowly converging iterations on grids of medium density. The convergence is especially slow for near-sonic flows and for very low compressible Mach numbers. Additionally, the fast asymptotic convergence seen on medium density grids deteriorates on high-density grids. Certain downstream-boundary modes are very slowly damped on high-density grids. Multigrid scheme accelerates convergence of the slow defect-correction iterations to the extent determined by the coarse-grid correction. The two-level asymptotic convergence rates are stable and significantly below one in most of the regions but slow convergence is noted for near-sonic and very low-Mach compressible flows. Multigrid solver has been applied to the NACA 0012 airfoil and to different flow regimes, such as near-tangency and stagnation. Certain convergence difficulties have been encountered within stagnation regions. Nonetheless, for the airfoil flow, with a sharp trailing-edge, residuals were fast converging for a subcritical flow on a sequence of grids. For supercritical flow, residuals converged slower on some intermediate grids than on the finest grid or the two coarsest grids.

78 FR 58449 - Generator Requirements at the Transmission Interface

Federal Register 2010, 2011, 2012, 2013, 2014

2013-09-24

... Connection Requirements), FAC-003-3 (Transmission Vegetation Management), PRC-004- 2.1a (Analysis and... and Generation Protection System Maintenance and Testing). The modifications improve reliability... Standards FAC-001-1 (Facility Connection Requirements), FAC-003-3 (Transmission Vegetation Management), PRC...

Iterative methods for mixed finite element equations

NASA Technical Reports Server (NTRS)

Nakazawa, S.; Nagtegaal, J. C.; Zienkiewicz, O. C.

1985-01-01

Iterative strategies for the solution of indefinite system of equations arising from the mixed finite element method are investigated in this paper with application to linear and nonlinear problems in solid and structural mechanics. The augmented Hu-Washizu form is derived, which is then utilized to construct a family of iterative algorithms using the displacement method as the preconditioner. Two types of iterative algorithms are implemented. Those are: constant metric iterations which does not involve the update of preconditioner; variable metric iterations, in which the inverse of the preconditioning matrix is updated. A series of numerical experiments is conducted to evaluate the numerical performance with application to linear and nonlinear model problems.

Implicit solvers for unstructured meshes

NASA Technical Reports Server (NTRS)

Venkatakrishnan, V.; Mavriplis, Dimitri J.

1991-01-01

Implicit methods for unstructured mesh computations are developed and tested. The approximate system which arises from the Newton-linearization of the nonlinear evolution operator is solved by using the preconditioned generalized minimum residual technique. These different preconditioners are investigated: the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over-relaxation (SSOR). The preconditioners have been optimized to have good vectorization properties. 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 investigated. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.

Analysis of Preconditioning and Relaxation Operators for the Discontinuous Galerkin Method Applied to Diffusion

NASA Technical Reports Server (NTRS)

Atkins, H. L.; Shu, Chi-Wang

2001-01-01

The explicit stability constraint of the discontinuous Galerkin method applied to the diffusion operator decreases dramatically as the order of the method is increased. Block Jacobi and block Gauss-Seidel preconditioner operators are examined for their effectiveness at accelerating convergence. A Fourier analysis for methods of order 2 through 6 reveals that both preconditioner operators bound the eigenvalues of the discrete spatial operator. Additionally, in one dimension, the eigenvalues are grouped into two or three regions that are invariant with order of the method. Local relaxation methods are constructed that rapidly damp high frequencies for arbitrarily large time step.

Parallel conjugate gradient algorithms for manipulator dynamic simulation

NASA Technical Reports Server (NTRS)

Fijany, Amir; Scheld, Robert E.

1989-01-01

Parallel conjugate gradient algorithms for the computation of multibody dynamics are developed for the specialized case of a robot manipulator. For an n-dimensional positive-definite linear system, the Classical Conjugate Gradient (CCG) algorithms are guaranteed to converge in n iterations, each with a computation cost of O(n); this leads to a total computational cost of O(n sq) on a serial processor. A conjugate gradient algorithms is presented that provide greater efficiency using a preconditioner, which reduces the number of iterations required, and by exploiting parallelism, which reduces the cost of each iteration. Two Preconditioned Conjugate Gradient (PCG) algorithms are proposed which respectively use a diagonal and a tridiagonal matrix, composed of the diagonal and tridiagonal elements of the mass matrix, as preconditioners. Parallel algorithms are developed to compute the preconditioners and their inversions in O(log sub 2 n) steps using n processors. A parallel algorithm is also presented which, on the same architecture, achieves the computational time of O(log sub 2 n) for each iteration. Simulation results for a seven degree-of-freedom manipulator are presented. Variants of the proposed algorithms are also developed which can be efficiently implemented on the Robot Mathematics Processor (RMP).

A new preconditioner update strategy for the solution of sequences of linear systems in structural mechanics: application to saddle point problems in elasticity

NASA Astrophysics Data System (ADS)

Mercier, Sylvain; Gratton, Serge; Tardieu, Nicolas; Vasseur, Xavier

2017-12-01

Many applications in structural mechanics require the numerical solution of sequences of linear systems typically issued from a finite element discretization of the governing equations on fine meshes. The method of Lagrange multipliers is often used to take into account mechanical constraints. The resulting matrices then exhibit a saddle point structure and the iterative solution of such preconditioned linear systems is considered as challenging. A popular strategy is then to combine preconditioning and deflation to yield an efficient method. We propose an alternative that is applicable to the general case and not only to matrices with a saddle point structure. In this approach, we consider to update an existing algebraic or application-based preconditioner, using specific available information exploiting the knowledge of an approximate invariant subspace or of matrix-vector products. The resulting preconditioner has the form of a limited memory quasi-Newton matrix and requires a small number of linearly independent vectors. Numerical experiments performed on three large-scale applications in elasticity highlight the relevance of the new approach. We show that the proposed method outperforms the deflation method when considering sequences of linear systems with varying matrices.

A Performance Comparison of the Parallel Preconditioners for Iterative Methods for Large Sparse Linear Systems Arising from Partial Differential Equations on Structured Grids

NASA Astrophysics Data System (ADS)

Ma, Sangback

In this paper we compare various parallel preconditioners such as Point-SSOR (Symmetric Successive OverRelaxation), ILU(0) (Incomplete LU) in the Wavefront ordering, ILU(0) in the Multi-color ordering, Multi-Color Block SOR (Successive OverRelaxation), SPAI (SParse Approximate Inverse) and pARMS (Parallel Algebraic Recursive Multilevel Solver) for solving large sparse linear systems arising from two-dimensional PDE (Partial Differential Equation)s on structured grids. Point-SSOR is well-known, and ILU(0) is one of the most popular preconditioner, but it is inherently serial. ILU(0) in the Wavefront ordering maximizes the parallelism in the natural order, but the lengths of the wave-fronts are often nonuniform. ILU(0) in the Multi-color ordering is a simple way of achieving a parallelism of the order N, where N is the order of the matrix, but its convergence rate often deteriorates as compared to that of natural ordering. We have chosen the Multi-Color Block SOR preconditioner combined with direct sparse matrix solver, since for the Laplacian matrix the SOR method is known to have a nondeteriorating rate of convergence when used with the Multi-Color ordering. By using block version we expect to minimize the interprocessor communications. SPAI computes the sparse approximate inverse directly by least squares method. Finally, ARMS is a preconditioner recursively exploiting the concept of independent sets and pARMS is the parallel version of ARMS. Experiments were conducted for the Finite Difference and Finite Element discretizations of five two-dimensional PDEs with large meshsizes up to a million on an IBM p595 machine with distributed memory. Our matrices are real positive, i. e., their real parts of the eigenvalues are positive. We have used GMRES(m) as our outer iterative method, so that the convergence of GMRES(m) for our test matrices are mathematically guaranteed. Interprocessor communications were done using MPI (Message Passing Interface) primitives. The results show that in general ILU(0) in the Multi-Color ordering ahd ILU(0) in the Wavefront ordering outperform the other methods but for symmetric and nearly symmetric 5-point matrices Multi-Color Block SOR gives the best performance, except for a few cases with a small number of processors.

Comparison of flow cytometry and immunohistochemistry in non-radioisotopic murine lymph node assay using bromodeoxyuridine.

PubMed

Jung, Kyoung-Mi; Bae, Il-Hong; Kim, Bae-Hwan; Kim, Wang-Ki; Chung, Jin-Ho; Park, Young-Ho; Lim, Kyung-Min

2010-02-01

Non-radioisotopic local lymph node assay (LLNA) employing 5-bromo-2'-deoxyuridine (BrdU) with flow cytometry (FACS) or immunohistochemistry (IHC) is gaining attention due to a regulatory issue of using radioisotope, (3)H-thymidine, in vivo in traditional LLNA. In this study, to compare the performance of these non-radioisotopic endpoints, 7 chemicals with known sensitizing potencies were examined in LLNA. Mice were topically treated with chemicals or vehicle on both ears for 3 days. After intraperitoneal injection of BrdU, bilateral lymph nodes were isolated separately and undergone respectively, FACS or IHC to determine BrdU incorporated lymph node cells (LNCs). Weight and histology of treated ears were also examined to evaluate chemical-induced edema and irritation. Both FACS and IHC could successively identify the skin sensitizers from non-sensitizers. Comparison of FACS and IHC with traditional LLNA revealed that FACS has a higher sensitivity although both assays produced comparable sensitivity and performance to traditional LLNA. In conclusion, non-radioisotopic LLNA using FACS and IHC can successfully detect sensitizers with a good correlation to traditional LLNA. Notably, FACS showed almost equivalent sensitivity and accuracy to traditional LLNA. 2009 Elsevier Ireland Ltd. All rights reserved.

Filamentary field-aligned currents at the polar cap region during northward interplanetary magnetic field derived with the Swarm constellation

PubMed Central

Lühr, Hermann; Huang, Tao; Wing, Simon; Kervalishvili, Guram; Rauberg, Jan; Korth, Haje

2017-01-01

ESA’s Swarm constellation mission makes it possible for the first time to determine field-aligned currents (FACs) in the ionosphere uniquely. In particular at high latitudes, the dual-satellite approach can reliably detect some FAC structures which are missed by the traditional single-satellite technique. These FAC events occur preferentially poleward of the auroral oval and during times of northward interplanetary magnetic field (IMF) orientation. Most events appear on the nightside. They are not related to the typical FAC structures poleward of the cusp, commonly termed NBZ. Simultaneously observed precipitating particle spectrograms and auroral images from Defense Meteorological Satellite Program (DMSP) satellites are consistent with the detected FACs and indicate that they occur on closed field lines mostly adjacent to the auroral oval. We suggest that the FACs are associated with Sun-aligned filamentary auroral arcs. Here we introduce in an initial study features of the high-latitude FAC structures which have been observed during the early phase of the Swarm mission. A more systematic survey over longer times is required to fully characterize the so far undetected field aligned currents. PMID:29056833

Computational Challenges of 3D Radiative Transfer in Atmospheric Models

NASA Astrophysics Data System (ADS)

Jakub, Fabian; Bernhard, Mayer

2017-04-01

The computation of radiative heating and cooling rates is one of the most expensive components in todays atmospheric models. The high computational cost stems not only from the laborious integration over a wide range of the electromagnetic spectrum but also from the fact that solving the integro-differential radiative transfer equation for monochromatic light is already rather involved. This lead to the advent of numerous approximations and parameterizations to reduce the cost of the solver. One of the most prominent one is the so called independent pixel approximations (IPA) where horizontal energy transfer is neglected whatsoever and radiation may only propagate in the vertical direction (1D). Recent studies implicate that the IPA introduces significant errors in high resolution simulations and affects the evolution and development of convective systems. However, using fully 3D solvers such as for example MonteCarlo methods is not even on state of the art supercomputers feasible. The parallelization of atmospheric models is often realized by a horizontal domain decomposition, and hence, horizontal transfer of energy necessitates communication. E.g. a cloud's shadow at a low zenith angle will cast a long shadow and potentially needs to communication through a multitude of processors. Especially light in the solar spectral range may travel long distances through the atmosphere. Concerning highly parallel simulations, it is vital that 3D radiative transfer solvers put a special emphasis on parallel scalability. We will present an introduction to intricacies computing 3D radiative heating and cooling rates as well as report on the parallel performance of the TenStream solver. The TenStream is a 3D radiative transfer solver using the PETSc framework to iteratively solve a set of partial differential equation. We investigate two matrix preconditioners, (a) geometric algebraic multigrid preconditioning(MG+GAMG) and (b) block Jacobi incomplete LU (ILU) factorization. The TenStream solver is tested for up to 4096 cores and shows a parallel scaling efficiency of 80-90% on various supercomputers.

Deflation as a method of variance reduction for estimating the trace of a matrix inverse

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gambhir, Arjun Singh; Stathopoulos, Andreas; Orginos, Kostas

Many fields require computing the trace of the inverse of a large, sparse matrix. The typical method used for such computations is the Hutchinson method which is a Monte Carlo (MC) averaging over matrix quadratures. To improve its convergence, several variance reductions techniques have been proposed. In this paper, we study the effects of deflating the near null singular value space. We make two main contributions. First, we analyze the variance of the Hutchinson method as a function of the deflated singular values and vectors. Although this provides good intuition in general, by assuming additionally that the singular vectors aremore » random unitary matrices, we arrive at concise formulas for the deflated variance that include only the variance and mean of the singular values. We make the remarkable observation that deflation may increase variance for Hermitian matrices but not for non-Hermitian ones. This is a rare, if not unique, property where non-Hermitian matrices outperform Hermitian ones. The theory can be used as a model for predicting the benefits of deflation. Second, we use deflation in the context of a large scale application of "disconnected diagrams" in Lattice QCD. On lattices, Hierarchical Probing (HP) has previously provided an order of magnitude of variance reduction over MC by removing "error" from neighboring nodes of increasing distance in the lattice. Although deflation used directly on MC yields a limited improvement of 30% in our problem, when combined with HP they reduce variance by a factor of over 150 compared to MC. For this, we pre-computated 1000 smallest singular values of an ill-conditioned matrix of size 25 million. Furthermore, using PRIMME and a domain-specific Algebraic Multigrid preconditioner, we perform one of the largest eigenvalue computations in Lattice QCD at a fraction of the cost of our trace computation.« less

Deflation as a method of variance reduction for estimating the trace of a matrix inverse

DOE PAGES

Gambhir, Arjun Singh; Stathopoulos, Andreas; Orginos, Kostas

2017-04-06

Many fields require computing the trace of the inverse of a large, sparse matrix. The typical method used for such computations is the Hutchinson method which is a Monte Carlo (MC) averaging over matrix quadratures. To improve its convergence, several variance reductions techniques have been proposed. In this paper, we study the effects of deflating the near null singular value space. We make two main contributions. First, we analyze the variance of the Hutchinson method as a function of the deflated singular values and vectors. Although this provides good intuition in general, by assuming additionally that the singular vectors aremore » random unitary matrices, we arrive at concise formulas for the deflated variance that include only the variance and mean of the singular values. We make the remarkable observation that deflation may increase variance for Hermitian matrices but not for non-Hermitian ones. This is a rare, if not unique, property where non-Hermitian matrices outperform Hermitian ones. The theory can be used as a model for predicting the benefits of deflation. Second, we use deflation in the context of a large scale application of "disconnected diagrams" in Lattice QCD. On lattices, Hierarchical Probing (HP) has previously provided an order of magnitude of variance reduction over MC by removing "error" from neighboring nodes of increasing distance in the lattice. Although deflation used directly on MC yields a limited improvement of 30% in our problem, when combined with HP they reduce variance by a factor of over 150 compared to MC. For this, we pre-computated 1000 smallest singular values of an ill-conditioned matrix of size 25 million. Furthermore, using PRIMME and a domain-specific Algebraic Multigrid preconditioner, we perform one of the largest eigenvalue computations in Lattice QCD at a fraction of the cost of our trace computation.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Weston, Brian T.

This dissertation focuses on the development of a fully-implicit, high-order compressible ow solver with phase change. The work is motivated by laser-induced phase change applications, particularly by the need to develop large-scale multi-physics simulations of the selective laser melting (SLM) process in metal additive manufacturing (3D printing). Simulations of the SLM process require precise tracking of multi-material solid-liquid-gas interfaces, due to laser-induced melting/ solidi cation and evaporation/condensation of metal powder in an ambient gas. These rapid density variations and phase change processes tightly couple the governing equations, requiring a fully compressible framework to robustly capture the rapid density variations ofmore » the ambient gas and the melting/evaporation of the metal powder. For non-isothermal phase change, the velocity is gradually suppressed through the mushy region by a variable viscosity and Darcy source term model. The governing equations are discretized up to 4th-order accuracy with our reconstructed Discontinuous Galerkin spatial discretization scheme and up to 5th-order accuracy with L-stable fully implicit time discretization schemes (BDF2 and ESDIRK3-5). The resulting set of non-linear equations is solved using a robust Newton-Krylov method, with the Jacobian-free version of the GMRES solver for linear iterations. Due to the sti nes associated with the acoustic waves and thermal and viscous/material strength e ects, preconditioning the GMRES solver is essential. A robust and scalable approximate block factorization preconditioner was developed, which utilizes the velocity-pressure (vP) and velocity-temperature (vT) Schur complement systems. This multigrid block reduction preconditioning technique converges for high CFL/Fourier numbers and exhibits excellent parallel and algorithmic scalability on classic benchmark problems in uid dynamics (lid-driven cavity ow and natural convection heat transfer) as well as for laser-induced phase change problems in 2D and 3D.« less

A numerical method for solving the 3D unsteady incompressible Navier Stokes equations in curvilinear domains with complex immersed boundaries

NASA Astrophysics Data System (ADS)

Ge, Liang; Sotiropoulos, Fotis

2007-08-01

A novel numerical method is developed that integrates boundary-conforming grids with a sharp interface, immersed boundary methodology. The method is intended for simulating internal flows containing complex, moving immersed boundaries such as those encountered in several cardiovascular applications. The background domain (e.g. the empty aorta) is discretized efficiently with a curvilinear boundary-fitted mesh while the complex moving immersed boundary (say a prosthetic heart valve) is treated with the sharp-interface, hybrid Cartesian/immersed-boundary approach of Gilmanov and Sotiropoulos [A. Gilmanov, F. Sotiropoulos, A hybrid cartesian/immersed boundary method for simulating flows with 3d, geometrically complex, moving bodies, Journal of Computational Physics 207 (2005) 457-492.]. To facilitate the implementation of this novel modeling paradigm in complex flow simulations, an accurate and efficient numerical method is developed for solving the unsteady, incompressible Navier-Stokes equations in generalized curvilinear coordinates. The method employs a novel, fully-curvilinear staggered grid discretization approach, which does not require either the explicit evaluation of the Christoffel symbols or the discretization of all three momentum equations at cell interfaces as done in previous formulations. The equations are integrated in time using an efficient, second-order accurate fractional step methodology coupled with a Jacobian-free, Newton-Krylov solver for the momentum equations and a GMRES solver enhanced with multigrid as preconditioner for the Poisson equation. Several numerical experiments are carried out on fine computational meshes to demonstrate the accuracy and efficiency of the proposed method for standard benchmark problems as well as for unsteady, pulsatile flow through a curved, pipe bend. To demonstrate the ability of the method to simulate flows with complex, moving immersed boundaries we apply it to calculate pulsatile, physiological flow through a mechanical, bileaflet heart valve mounted in a model straight aorta with an anatomical-like triple sinus.

The Fear-Avoidance Components Scale (FACS): Responsiveness to Functional Restoration Treatment in a Chronic Musculoskeletal Pain Disorder (CMPD) Population.

PubMed

Neblett, Randy; Mayer, Tom G; Williams, Mark J; Asih, Sali; Cuesta-Vargas, Antonio I; Hartzell, Meredith M; Gatchel, Robert J

2017-12-01

To assess the clinical validity and factor structure of the Fear-Avoidance Components Scale (FACS), a new fear-avoidance measure. In this study, 426 chronic musculoskeletal pain disorder patients were admitted to a Functional Restoration Program (FRP). They were categorized into 5 FACS severity levels, from subclinical to extreme, at admission, and again at discharge. Associations with objective lifting performance and other patient-reported psychosocial measures were determined at admission and discharge, and objective work outcomes for this predominantly disabled cohort, were assessed 1 year later. Those patients in the severe and extreme FACS severity groups at admission were more likely to "drop out" of treatment than those in the lower severity groups (P=0.05). At both admission and discharge, the FACS severity groups were highly and inversely correlated with objective lifting performance and patient-reported fear-avoidance-related psychosocial variables, including kinesiophobia, pain intensity, depressive symptoms, perceived disability, perceived injustice, and insomnia (Ps<0.001). All variables showed improvement at FRP discharge. Patients in the extreme FACS severity group at discharge were less likely to return to, or retain, work 1 year later (P≤0.02). A factor analysis identified a 2-factor solution. Strong associations were found among FACS scores and other patient-reported psychosocial and objective lifting performance variables at both admission and discharge. High discharge-FACS scores were associated with worse work outcomes 1 year after discharge. The FACS seems to be a valid and clinically useful measure for predicting attendance, physical performance, distress, and relevant work outcomes in FRP treatment of chronic musculoskeletal pain disorder patients.

Comparison of cosmetic outcomes of absorbable versus nonabsorbable sutures in pediatric facial lacerations.

PubMed

Luck, Raemma; Tredway, Trevor; Gerard, James; Eyal, Dalit; Krug, Lauren; Flood, Robert

2013-06-01

We sought to compare cosmetic outcomes, complication rates, and patient/caregiver satisfaction of absorbable versus nonabsorbable sutures in children. Healthy patients, 1 to 18 years old, with facial lacerations 1 to 5 cm, were randomized to repair with fast-absorbing catgut (FAC) or nylon (NYL) sutures. Patients returned in 4 to 7 days and in 3 to 4 months, at which time photographs and caregiver surveys were completed. Unlike part I, all FAC sutures were permitted to absorb rather than be removed. Using a 100-mm visual analog scale (VAS), a noninferiority (NI) design was applied, with a difference of less than 15 mm considered clinically equivalent. Caregivers and 3 blinded physicians independently rated the scars via photographs. Ninety-eight patients were enrolled, 76 caregiver surveys were completed, and 61 (29 FAC, 32 NYL) had photographs scored by physicians. The mean physician VAS scores for FAC and NYL were 57.6 and 67.6, respectively (difference, -10.0; 95% confidence interval, -19.1 to -0.4); thus, NI could not be established. The mean caregiver VAS scores for the FAC and NYL groups were 93.8 and 86.6, respectively (difference, 7.2; 95% confidence interval, -4.9 to 13.9); thus, NI of FAC was established. There were no significant differences in rates of infection, wound dehiscence, or keloid formation. In terms of future preference, caregivers favored FAC (33/33) over NYL (26/36) (P < 0.01). Caregiver VAS scores showed NI of FAC, which were also preferred by the caregivers. However, NI for FAC could not be demonstrated by blinded physicians with respect to cosmetic outcomes.

The Fanconi anemia pathway requires FAA phosphorylation and FAA/FAC nuclear accumulation

PubMed Central

Yamashita, Takayuki; Kupfer, Gary M.; Naf, Dieter; Suliman, Ahmed; Joenje, Hans; Asano, Shigetaka; D’Andrea, Alan D.

1998-01-01

Fanconi anemia (FA) is an autosomal recessive cancer susceptibility syndrome with at least eight complementation groups (A–H). Two FA genes, corresponding to complementation groups A and C, have been cloned, but the function of the FAA and FAC proteins remains unknown. We have recently shown that the FAA and FAC proteins bind and form a nuclear complex. In the current study, we analyzed the FAA and FAC proteins in normal lymphoblasts and lymphoblasts from multiple FA complementation groups. In contrast to normal controls, FA cells derived from groups A, B, C, E, F, G, and H were defective in the formation of the FAA/FAC protein complex, the phosphorylation of the FAA protein, and the accumulation of the FAA/FAC protein complex in the nucleus. These biochemical events seem to define a signaling pathway required for the maintenance of genomic stability and normal hematopoiesis. Our results support the idea that multiple gene products cooperate in the FA Pathway. PMID:9789045

Observation of a Unipolar Field-aligned Current System Associated With IMF By-triggered Theta Auroras

NASA Astrophysics Data System (ADS)

Hairston, M. R.; Watanabe, M.

2016-12-01

We investigate the existence of a specific field-aligned current (FAC) system predicted by numerical magnetohydrodynamic simulations in a past study. The FAC system is expected to occur when a drifting theta aurora is formed in response to a stepwise transition of interplanetary magnetic field (IMF) By during strongly northward IMF periods. When the IMF By changes from positive to negative, a crossbar forms in the Northern Hemisphere that moves dawnward, while in the Southern Hemisphere the crossbar moves in the opposite direction. The crossbar motion reverses when the IMF By changes from negative to positive. The FAC system appears on the trailing side of the drifting crossbar of the theta aurora as it moves either dawnward or duskward. When the theta aurora is drifting dawnward, the FACs flow into the ionosphere. The FAC polarity reverses when the theta aurora is drifting duskward. Using low-altitude satellite data, we confirmed the real existence of the above model-predicted FAC system.

Tuning the reactivity in classic low-spin d6 rhenium(I) tricarbonyl radiopharmaceutical synthon by selective bidentate ligand variation (L,L'-Bid; L,L'= N,N', N,O, and O,O' donor atom sets) in fac-[Re(CO)3(L,L'-Bid)(MeOH)]n complexes.

PubMed

Schutte, Marietjie; Kemp, Gerdus; Visser, Hendrik G; Roodt, Andreas

2011-12-19

A range of fac-[Re(CO)(3)(L,L'-Bid)(H(2)O)](n) (L,L'-Bid = neutral or monoanionic bidentate ligands with varied L,L' donor atoms, N,N', N,O, or O,O': 1,10-phenanthroline, 2,2'-bipydine, 2-picolinate, 2-quinolinate, 2,4-dipicolinate, 2,4-diquinolinate, tribromotropolonate, and hydroxyflavonate; n = 0, +1) has been synthesized and the aqua/methanol substitution has been investigated. The complexes were characterized by UV-vis, IR and NMR spectroscopy and X-ray crystallographic studies of the compounds fac-[Re(CO)(3)(Phen)(H(2)O)]NO(3)·0.5Phen, fac-[Re(CO)(3)(2,4-dQuinH)(H(2)O)]·H(2)O, fac-[Re(CO)(3)(2,4-dQuinH)Py]Py, and fac-[Re(CO)(3)(Flav)(CH(3)OH)]·CH(3)OH are reported. A four order-of-magnitude of activation for the methanol substitution is induced as manifested by the second order rate constants with (N,N'-Bid) < (N,O-Bid) < (O,O'-Bid). Forward and reverse rate and stability constants from slow and stopped-flow UV/vis measurements (k(1), M(-1) s(-1); k(-1), s(-1); K(1), M(-1)) for bromide anions as entering nucleophile are as follows: fac-[Re(CO)(3)(Phen)(MeOH)](+) (50 ± 3) × 10(-3), (5.9 ± 0.3) × 10(-4), 84 ± 7; fac-[Re(CO)(3)(2,4-dPicoH)(MeOH)] (15.7 ± 0.2) × 10(-3), (6.3 ± 0.8) × 10(-4), 25 ± 3; fac-[Re(CO)(3)(TropBr(3))(MeOH)] (7.06 ± 0.04) × 10(-2), (4 ± 1) × 10(-3), 18 ± 4; fac-[Re(CO)(3)(Flav)(MeOH)] 7.2 ± 0.3, 3.17 ± 0.09, 2.5 ± 2. Activation parameters (ΔH(k1)(++), kJmol(-1); ΔS(k1)(), J K(-1) mol(-1)) from Eyring plots for entering nucleophiles as indicated are as follows: fac-[Re(CO)(3)(Phen)(MeOH)](+) iodide 70 ± 1, -35 ± 3; fac-[Re(CO)(3)(2,4-dPico)(MeOH)] bromide 80.8 ± 6, -8 ± 2; fac-[Re(CO)(3)(Flav)(MeOH)] bromide 52 ± 5, -52 ± 15. A dissociative interchange mechanism is proposed. © 2011 American Chemical Society

General relaxation schemes in multigrid algorithms for higher order singularity methods

NASA Technical Reports Server (NTRS)

Oskam, B.; Fray, J. M. J.

1981-01-01

Relaxation schemes based on approximate and incomplete factorization technique (AF) are described. The AF schemes allow construction of a fast multigrid method for solving integral equations of the second and first kind. The smoothing factors for integral equations of the first kind, and comparison with similar results from the second kind of equations are a novel item. Application of the MD algorithm shows convergence to the level of truncation error of a second order accurate panel method.

Numerical solution of a coupled pair of elliptic equations from solid state electronics

NASA Technical Reports Server (NTRS)

Phillips, T. N.

1983-01-01

Iterative methods are considered for the solution of a coupled pair of second order elliptic partial differential equations which arise in the field of solid state electronics. A finite difference scheme is used which retains the conservative form of the differential equations. Numerical solutions are obtained in two ways, by multigrid and dynamic alternating direction implicit methods. Numerical results are presented which show the multigrid method to be an efficient way of solving this problem.

Spectral multigrid methods for the solution of homogeneous turbulence problems

NASA Technical Reports Server (NTRS)

Erlebacher, G.; Zang, T. A.; Hussaini, M. Y.

1987-01-01

New three-dimensional spectral multigrid algorithms are analyzed and implemented to solve the variable coefficient Helmholtz equation. Periodicity is assumed in all three directions which leads to a Fourier collocation representation. Convergence rates are theoretically predicted and confirmed through numerical tests. Residual averaging results in a spectral radius of 0.2 for the variable coefficient Poisson equation. In general, non-stationary Richardson must be used for the Helmholtz equation. The algorithms developed are applied to the large-eddy simulation of incompressible isotropic turbulence.

Multigrid solution strategies for adaptive meshing problems

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.

1995-01-01

This paper discusses the issues which arise when combining multigrid strategies with adaptive meshing techniques for solving steady-state problems on unstructured meshes. A basic strategy is described, and demonstrated by solving several inviscid and viscous flow cases. Potential inefficiencies in this basic strategy are exposed, and various alternate approaches are discussed, some of which are demonstrated with an example. Although each particular approach exhibits certain advantages, all methods have particular drawbacks, and the formulation of a completely optimal strategy is considered to be an open problem.

A new multigrid formulation for high order finite difference methods on summation-by-parts form

NASA Astrophysics Data System (ADS)

Ruggiu, Andrea A.; Weinerfelt, Per; Nordström, Jan

2018-04-01

Multigrid schemes for high order finite difference methods on summation-by-parts form are studied by comparing the effect of different interpolation operators. By using the standard linear prolongation and restriction operators, the Galerkin condition leads to inaccurate coarse grid discretizations. In this paper, an alternative class of interpolation operators that bypass this issue and preserve the summation-by-parts property on each grid level is considered. Clear improvements of the convergence rate for relevant model problems are achieved.

Parameter estimation problems for distributed systems using a multigrid method

NASA Technical Reports Server (NTRS)

Ta'asan, Shlomo; Dutt, Pravir

1990-01-01

The problem of estimating spatially varying coefficients of partial differential equations is considered from observation of the solution and of the right hand side of the equation. It is assumed that the observations are distributed in the domain and that enough observations are given. A method of discretization and an efficient multigrid method for solving the resulting discrete systems are described. Numerical results are presented for estimation of coefficients in an elliptic and a parabolic partial differential equation.

Multiscale field-aligned current analyzer

NASA Astrophysics Data System (ADS)

Bunescu, C.; Marghitu, O.; Constantinescu, D.; Narita, Y.; Vogt, J.; Blǎgǎu, A.

2015-11-01

The magnetosphere-ionosphere coupling is achieved, essentially, by a superposition of quasi-stationary and time-dependent field-aligned currents (FACs), over a broad range of spatial and temporal scales. The planarity of the FAC structures observed by satellite data and the orientation of the planar FAC sheets can be investigated by the well-established minimum variance analysis (MVA) of the magnetic perturbation. However, such investigations are often constrained to a predefined time window, i.e., to a specific scale of the FAC. The multiscale field-aligned current analyzer, introduced here, relies on performing MVA continuously and over a range of scales by varying the width of the analyzing window, appropriate for the complexity of the magnetic field signatures above the auroral oval. The proposed technique provides multiscale information on the planarity and orientation of the observed FACs. A new approach, based on the derivative of the largest eigenvalue of the magnetic variance matrix with respect to the length of the analysis window, makes possible the inference of the current structures' location (center) and scale (thickness). The capabilities of the FAC analyzer are explored analytically for the magnetic field profile of the Harris sheet and tested on synthetic FAC structures with uniform current density and infinite or finite geometry in the cross-section plane of the FAC. The method is illustrated with data observed by the Cluster spacecraft on crossing the nightside auroral region, and the results are cross checked with the optical observations from the Time History of Events and Macroscale Interactions during Substorms ground network.

Effect of sleep deprivation on driving safety in housestaff.

PubMed

Marcus, C L; Loughlin, G M

1996-12-01

Sleep deprivation is known to affect driving safety. Housestaff (HS) are routinely sleep-deprived when on call. We hypothesized that this would affect their driving. We therefore administered questionnaires regarding driving to 70 pediatric HS, who were on call every fourth night, and to 85 faculty members (FAC), who were rarely disturbed at night. HS were questioned about events during their residency, and FAC were questioned about events during the preceding three years. There was an 87% response rate for each group. HS slept 2.7 +/- 0.9 (SD) hours when on call vs 7.2 +/- 0.8 hours when not on call (p < 0.001). 44% of HS had fallen asleep when stopped at a light, vs 12.5% FAC (p < 0.001). 23% of HS had fallen asleep while driving vs. 8% FAC (ns). A total of 49% of HS had fallen asleep at the wheel; 90% of these events occurred post-call. In contrast, only 13% of FAC had fallen asleep at the wheel (p < 0.001). HS had received a total of 25 traffic citations for moving violations vs. 15 for FAC and were involved in 20 motor vehicle accidents vs. 11 for FAC. One traffic citation clearly resulted from HS falling asleep at the wheel vs. none for FAC. We conclude that HS frequently fall asleep when driving post-call. We speculate that current HS work schedules may place some HS at risk for injury to themselves and others. Further study, using prospectively objective measures is indicated.

High-latitude Pi2 pulsations associated with kink-like neutral sheet oscillations

NASA Astrophysics Data System (ADS)

Wang, G. Q.; Volwerk, M.; Zhang, T. L.; Schmid, D.; Yoshikawa, A.

2017-03-01

A kink-like neutral sheet oscillation event observed by Cluster between 1436 and 1445 UT on 15 October 2004 has been investigated. The oscillations with periods between 40 and 60 s, observed at (-13.1, 8.7, -0.5) RE, are dominant in BX and BY. And they propagate mainly duskward with a velocity of (86, 147, 46) km/s. Their periods and velocity can be explained by the magnetic double-gradient instability. These oscillations are accompanied by strong field-aligned currents (FACs), which prefer to occur near the strongly tilted current sheet, and local maximum FAC tends to occur near the neutral sheet. The FACs show one-to-one correlated with a high-latitude Pi2 pulsation event recorded by KTN and TIK stations with a delay time of 60 and 90 s, respectively. Both the Pi2 and oscillations propagate westward with a comparative conjunctive speed. These findings suggest a strong relation between the FACs and Pi2, and we infer that the Pi2 is caused by the FACs. The periods of the FACs are modulated by the oscillations but not exactly equal, which is one possible reason that the period of the Pi2 caused by the FACs could be different from the oscillations. We speculate that a current circuit between the plasma sheet and ionosphere can be formed during strongly tilted current sheet, and successive tilted current sheet could generate quasiperiodic multiple FAC systems, which can generate high-latitude Pi2 pulsations and control their periods.

Interim Regional Supplement to the Corps of Engineers Wetland Delineation Manual: Great Plans Region

DTIC Science & Technology

2008-03-01

artemisiifolia Iva annua Cardiospermum halicacabum Xanthium strumarium FACW FACU− FAC FAC FAC− 40 15 15 8 6 Yes Yes Yes No No Total...virgatum 50 40 90 2 180 FAC species Iva annua Celtis laevigata Cardiospermum halicacabum Xanthium strumarium Toxicodendron radicans3 15 12

48 CFR 301.603-72 - FAC-C and HHS SAC certification requirements.

Code of Federal Regulations, 2010 CFR

2010-10-01

... HUMAN SERVICES GENERAL HHS ACQUISITION REGULATION SYSTEM Career Development, Contracting Authority, and... retention of certification, including the requirement to earn continuous learning points (CLPs). FAC-C... to employees for the first time at a department or agency.) (c) The FAC-C certification is based on...

48 CFR 301.607-74 - Certification transfers.

Code of Federal Regulations, 2012 CFR

2012-10-01

....607-74 Certification transfers. (a) HHS recognizes and accepts FAC-P/PM certifications issued by other... under FAC-P/PM. See FAI's Web site, and Chapter 3, Federal Acquisition Certification—Program and Project... certification transfer should not be initiated when an individual, who holds a current FAC-P/PM certification...

48 CFR 301.607-74 - Certification transfers.

Code of Federal Regulations, 2013 CFR

2013-10-01

....607-74 Certification transfers. (a) HHS recognizes and accepts FAC-P/PM certifications issued by other... under FAC-P/PM. See FAI's Web site, and Chapter 3, Federal Acquisition Certification—Program and Project... certification transfer should not be initiated when an individual, who holds a current FAC-P/PM certification...

48 CFR 301.607-74 - Certification transfers.

Code of Federal Regulations, 2014 CFR

2014-10-01

....607-74 Certification transfers. (a) HHS recognizes and accepts FAC-P/PM certifications issued by other... under FAC-P/PM. See FAI's Web site, and Chapter 3, Federal Acquisition Certification—Program and Project... certification transfer should not be initiated when an individual, who holds a current FAC-P/PM certification...

48 CFR 301.607-74 - Certification transfers.

Code of Federal Regulations, 2011 CFR

2011-10-01

....607-74 Certification transfers. (a) HHS recognizes and accepts FAC-P/PM certifications issued by other... under FAC-P/PM. See FAI's Web site, and Chapter 3, Federal Acquisition Certification—Program and Project... certification transfer should not be initiated when an individual, who holds a current FAC-P/PM certification...

Predicting, examining, and evaluating FAC in US power plants

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cohn, M.J.; Garud, Y.S.; Raad, J. de

1999-11-01

There have been many pipe failures in fossil and nuclear power plant piping systems caused by flow-accelerated corrosion (FAC). In some piping systems, this failure mechanism maybe the most important type of damage to mitigate because FAC damage has led to catastrophic failures and fatalities. Detecting the damage and mitigating the problem can significantly reduce future forced outages and increase personnel safety. This article discusses the implementation of recent developments to select FAC inspection locations, perform cost-effective examinations, evaluate results, and mitigate FAC failures. These advances include implementing the combination of software to assist in selecting examination locations and anmore » improved pulsed eddy current technique to scan for wall thinning without removing insulation. The use of statistical evaluation methodology and possible mitigation strategies also are discussed.« less

Antifungal Susceptibility Testing of Fluconazole by Flow Cytometry Correlates with Clinical Outcome

PubMed Central

Wenisch, Christoph; Moore, Caroline B.; Krause, Robert; Presterl, Elisabeth; Pichna, Peter; Denning, David W.

2001-01-01

Susceptibility testing of fungi by flow cytometry (also called fluorescence-activated cell sorting [FACS]) using vital staining with FUN-1 showed a good correlation with the standard M27-A procedure for assessing MICs. In this study we determined MICs for blood culture isolates from patients with candidemia by NCCLS M27-A and FACS methods and correlated the clinical outcome of these patients with in vitro antifungal resistance test results. A total of 24 patients with candidemia for whom one or more blood cultures were positive for a Candida sp. were included. Susceptibility testing was performed by NCCLS M27-A and FACS methods. The correlation of MICs (NCCLS M27-A and FACS) and clinical outcome was calculated. In 83% of the cases, the MICs of fluconazole determined by FACS were within 1 dilution of the MICs determined by the NCCLS M27-A method. For proposed susceptibility breakpoints, there was 100% agreement between the M27-A and FACS methods. In the FACS assay, a fluconazole MIC of <1 μg/ml was associated with cure (P < 0.001) whereas an MIC of ≥1 μg/ml was associated with death (P < 0.001). The M27-A-derived fluconazole MICs did not correlate with outcome (P = 1 and P = 0.133). PMID:11427554

Chexal-Horowitz flow-accelerated corrosion model -- Parameters and influences

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chexal, V.K.; Horowitz, J.S.

1995-12-01

Flow-accelerated corrosion (FAC) continues to cause problems in nuclear and fossil power plants. Thinning caused by FAC has lead to many leaks and complete ruptures. These failures have required costly repairs and occasionally have caused lengthy shutdowns. To deal with FAC, utilities have instituted costly inspection and piping replacement programs. Typically, a nuclear unit will inspect about 100 large bore piping components plus additional small bore components during every refueling outage. To cope with FAC, there has been a great deal of research and development performed to obtain a greater understanding of the phenomenon. Currently, there is general agreement onmore » the mechanism of FAC. This understanding has lead to the development of computer based tools to assist utility engineers in dealing with this issue. In the United States, the most commonly used computer program to predict and control is CHECWORKS{trademark}. This paper presents a description of the mechanism of FAC, and introduces the predictive algorithms used in CHECWORKS{trademark}. The parametric effects of water chemistry, materials, flow and geometry as predicted by CHECWORKS{trademark} will then be discussed. These trends will be described and explained by reference to the corrosion mechanism. The remedial actions possible to reduce the rate of damage caused by FAC will also be discussed.« less

Defense Meteorological Satellite Program Data in Dynamic Auroral Boundary Coordinates: New insights into Polar Cap and Auroral Dynamics

NASA Astrophysics Data System (ADS)

Knipp, D.

2016-12-01

Using reprocessed (Level-2) data from the Defense Meteorology Satellite Program magnetometer (SSM) and particle precipitation (SSJ) instruments we determine the boundaries of the central plasma sheet auroral oval, and then consider the relative locations and intensities of field aligned currents. Large-scale field-aligned currents (FAC) are determined using the Minimum Variance Analysis technique, and their influence is then removed from the magnetic perturbations allowing us to estimate intensity and scale-size of the smaller-scale currents. When sorted by dynamic auroral boundary coordinates we find that large- scale Region 1 (R1) FAC are often within the polar cap and Region 2 (R2) FAC show a strong dawn-dusk asymmetry (as in Ohtani et al., 2010). We find that mesoscale FAC are stronger in the summer and are most consistently present in the vicinity of dawnside (downward) R1 FAC. Further, mesoscale FAC are confined to auroral latitudes and above on the dawnside, but can be subaroural on the dusk side. Hotspots of mesoscale FAC occur in pre-midnight regions especially during summer. Finally, we show how this information can be combined with measurements from above and below the ionosphere-thermosphere to help explain significant perturbations in polar cap dynamics.

Multigrid methods with space–time concurrency

DOE PAGES

Falgout, R. D.; Friedhoff, S.; Kolev, Tz. V.; ...

2017-10-06

Here, we consider the comparison of multigrid methods for parabolic partial differential equations that allow space–time concurrency. With current trends in computer architectures leading towards systems with more, but not faster, processors, space–time concurrency is crucial for speeding up time-integration simulations. In contrast, traditional time-integration techniques impose serious limitations on parallel performance due to the sequential nature of the time-stepping approach, allowing spatial concurrency only. This paper considers the three basic options of multigrid algorithms on space–time grids that allow parallelism in space and time: coarsening in space and time, semicoarsening in the spatial dimensions, and semicoarsening in the temporalmore » dimension. We develop parallel software and performance models to study the three methods at scales of up to 16K cores and introduce an extension of one of them for handling multistep time integration. We then discuss advantages and disadvantages of the different approaches and their benefit compared to traditional space-parallel algorithms with sequential time stepping on modern architectures.« less

Topology-Aware Performance Optimization and Modeling of Adaptive Mesh Refinement Codes for Exascale

DOE PAGES

Chan, Cy P.; Bachan, John D.; Kenny, Joseph P.; ...

2017-01-26

Here, we introduce a topology-aware performance optimization and modeling workflow for AMR simulation that includes two new modeling tools, ProgrAMR and Mota Mapper, which interface with the BoxLib AMR framework and the SSTmacro network simulator. ProgrAMR allows us to generate and model the execution of task dependency graphs from high-level specifications of AMR-based applications, which we demonstrate by analyzing two example AMR-based multigrid solvers with varying degrees of asynchrony. Mota Mapper generates multiobjective, network topology-aware box mappings, which we apply to optimize the data layout for the example multigrid solvers. While the sensitivity of these solvers to layout and executionmore » strategy appears to be modest for balanced scenarios, the impact of better mapping algorithms can be significant when performance is highly constrained by network hop latency. Furthermore, we show that network latency in the multigrid bottom solve is the main contributing factor preventing good scaling on exascale-class machines.« less

Application of multi-grid method on the simulation of incremental forging processes

NASA Astrophysics Data System (ADS)

Ramadan, Mohamad; Khaled, Mahmoud; Fourment, Lionel

2016-10-01

Numerical simulation becomes essential in manufacturing large part by incremental forging processes. It is a splendid tool allowing to show physical phenomena however behind the scenes, an expensive bill should be paid, that is the computational time. That is why many techniques are developed to decrease the computational time of numerical simulation. Multi-Grid method is a numerical procedure that permits to reduce computational time of numerical calculation by performing the resolution of the system of equations on several mesh of decreasing size which allows to smooth faster the low frequency of the solution as well as its high frequency. In this paper a Multi-Grid method is applied to cogging process in the software Forge 3. The study is carried out using increasing number of degrees of freedom. The results shows that calculation time is divide by two for a mesh of 39,000 nodes. The method is promising especially if coupled with Multi-Mesh method.

Topology-Aware Performance Optimization and Modeling of Adaptive Mesh Refinement Codes for Exascale

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chan, Cy P.; Bachan, John D.; Kenny, Joseph P.

Here, we introduce a topology-aware performance optimization and modeling workflow for AMR simulation that includes two new modeling tools, ProgrAMR and Mota Mapper, which interface with the BoxLib AMR framework and the SSTmacro network simulator. ProgrAMR allows us to generate and model the execution of task dependency graphs from high-level specifications of AMR-based applications, which we demonstrate by analyzing two example AMR-based multigrid solvers with varying degrees of asynchrony. Mota Mapper generates multiobjective, network topology-aware box mappings, which we apply to optimize the data layout for the example multigrid solvers. While the sensitivity of these solvers to layout and executionmore » strategy appears to be modest for balanced scenarios, the impact of better mapping algorithms can be significant when performance is highly constrained by network hop latency. Furthermore, we show that network latency in the multigrid bottom solve is the main contributing factor preventing good scaling on exascale-class machines.« less

Multigrid methods with space–time concurrency

DOE Office of Scientific and Technical Information (OSTI.GOV)

Falgout, R. D.; Friedhoff, S.; Kolev, Tz. V.

Here, we consider the comparison of multigrid methods for parabolic partial differential equations that allow space–time concurrency. With current trends in computer architectures leading towards systems with more, but not faster, processors, space–time concurrency is crucial for speeding up time-integration simulations. In contrast, traditional time-integration techniques impose serious limitations on parallel performance due to the sequential nature of the time-stepping approach, allowing spatial concurrency only. This paper considers the three basic options of multigrid algorithms on space–time grids that allow parallelism in space and time: coarsening in space and time, semicoarsening in the spatial dimensions, and semicoarsening in the temporalmore » dimension. We develop parallel software and performance models to study the three methods at scales of up to 16K cores and introduce an extension of one of them for handling multistep time integration. We then discuss advantages and disadvantages of the different approaches and their benefit compared to traditional space-parallel algorithms with sequential time stepping on modern architectures.« less

αAMG based on Weighted Matching for Systems of Elliptic PDEs Arising From Displacement and Mixed Methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

D'Ambra, P.; Vassilevski, P. S.

2014-05-30

Adaptive Algebraic Multigrid (or Multilevel) Methods (αAMG) are introduced to improve robustness and efficiency of classical algebraic multigrid methods in dealing with problems where no a-priori knowledge or assumptions on the near-null kernel of the underlined matrix are available. Recently we proposed an adaptive (bootstrap) AMG method, αAMG, aimed to obtain a composite solver with a desired convergence rate. Each new multigrid component relies on a current (general) smooth vector and exploits pairwise aggregation based on weighted matching in a matrix graph to define a new automatic, general-purpose coarsening process, which we refer to as “the compatible weighted matching”. Inmore » this work, we present results that broaden the applicability of our method to different finite element discretizations of elliptic PDEs. In particular, we consider systems arising from displacement methods in linear elasticity problems and saddle-point systems that appear in the application of the mixed method to Darcy problems.« less

Three dimensional unstructured multigrid for the Euler equations

NASA Technical Reports Server (NTRS)

Mavriplis, D. J.

1991-01-01

The three dimensional Euler equations are solved on unstructured tetrahedral meshes using a multigrid strategy. The driving algorithm consists of an explicit vertex-based finite element scheme, which employs an edge-based data structure to assemble the residuals. The multigrid approach employs a sequence of independently generated coarse and fine meshes to accelerate the convergence to steady-state of the fine grid solution. Variables, residuals and corrections are passed back and forth between the various grids of the sequence using linear interpolation. The addresses and weights for interpolation are determined in a preprocessing stage using linear interpolation. The addresses and weights for interpolation are determined in a preprocessing stage using an efficient graph traversal algorithm. The preprocessing operation is shown to require a negligible fraction of the CPU time required by the overall solution procedure, while gains in overall solution efficiencies greater than an order of magnitude are demonstrated on meshes containing up to 350,000 vertices. Solutions using globally regenerated fine meshes as well as adaptively refined meshes are given.

Multigrid calculation of internal flows in complex geometries

NASA Technical Reports Server (NTRS)

Smith, K. M.; Vanka, S. P.

1992-01-01

The development, validation, and application of a general purpose multigrid solution algorithm and computer program for the computation of elliptic flows in complex geometries is presented. This computer program combines several desirable features including a curvilinear coordinate system, collocated arrangement of the variables, and Full Multi-Grid/Full Approximation Scheme (FMG/FAS). Provisions are made for the inclusion of embedded obstacles and baffles inside the flow domain. The momentum and continuity equations are solved in a decoupled manner and a pressure corrective equation is used to update the pressures such that the fluxes at the cell faces satisfy local mass continuity. Despite the computational overhead required in the restriction and prolongation phases of the multigrid cycling, the superior convergence results in reduced overall CPU time. The numerical scheme and selected results of several validation flows are presented. Finally, the procedure is applied to study the flowfield in a side-inlet dump combustor and twin jet impingement from a simulated aircraft fuselage.

Final Report: Subcontract B623868 Algebraic Multigrid solvers for coupled PDE systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brannick, J.

The Pennsylvania State University (“Subcontractor”) continued to work on the design of algebraic multigrid solvers for coupled systems of partial differential equations (PDEs) arising in numerical modeling of various applications, with a main focus on solving the Dirac equation arising in Quantum Chromodynamics (QCD). The goal of the proposed work was to develop combined geometric and algebraic multilevel solvers that are robust and lend themselves to efficient implementation on massively parallel heterogeneous computers for these QCD systems. The research in these areas built on previous works, focusing on the following three topics: (1) the development of parallel full-multigrid (PFMG) andmore » non-Galerkin coarsening techniques in this frame work for solving the Wilson Dirac system; (2) the use of these same Wilson MG solvers for preconditioning the Overlap and Domain Wall formulations of the Dirac equation; and (3) the design and analysis of algebraic coarsening algorithms for coupled PDE systems including Stokes equation, Maxwell equation and linear elasticity.« less

An automatic multigrid method for the solution of sparse linear systems

NASA Technical Reports Server (NTRS)

Shapira, Yair; Israeli, Moshe; Sidi, Avram

1993-01-01

An automatic version of the multigrid method for the solution of linear systems arising from the discretization of elliptic PDE's is presented. This version is based on the structure of the algebraic system solely, and does not use the original partial differential operator. Numerical experiments show that for the Poisson equation the rate of convergence of our method is equal to that of classical multigrid methods. Moreover, the method is robust in the sense that its high rate of convergence is conserved for other classes of problems: non-symmetric, hyperbolic (even with closed characteristics) and problems on non-uniform grids. No double discretization or special treatment of sub-domains (e.g. boundaries) is needed. When supplemented with a vector extrapolation method, high rates of convergence are achieved also for anisotropic and discontinuous problems and also for indefinite Helmholtz equations. A new double discretization strategy is proposed for finite and spectral element schemes and is found better than known strategies.

A new extrapolation cascadic multigrid method for three dimensional elliptic boundary value problems

NASA Astrophysics Data System (ADS)

Pan, Kejia; He, Dongdong; Hu, Hongling; Ren, Zhengyong

2017-09-01

In this paper, we develop a new extrapolation cascadic multigrid method, which makes it possible to solve three dimensional elliptic boundary value problems with over 100 million unknowns on a desktop computer in half a minute. First, by combining Richardson extrapolation and quadratic finite element (FE) interpolation for the numerical solutions on two-level of grids (current and previous grids), we provide a quite good initial guess for the iterative solution on the next finer grid, which is a third-order approximation to the FE solution. And the resulting large linear system from the FE discretization is then solved by the Jacobi-preconditioned conjugate gradient (JCG) method with the obtained initial guess. Additionally, instead of performing a fixed number of iterations as used in existing cascadic multigrid methods, a relative residual tolerance is introduced in the JCG solver, which enables us to obtain conveniently the numerical solution with the desired accuracy. Moreover, a simple method based on the midpoint extrapolation formula is proposed to achieve higher-order accuracy on the finest grid cheaply and directly. Test results from four examples including two smooth problems with both constant and variable coefficients, an H3-regular problem as well as an anisotropic problem are reported to show that the proposed method has much better efficiency compared to the classical V-cycle and W-cycle multigrid methods. Finally, we present the reason why our method is highly efficient for solving these elliptic problems.

Activation of rhenium(I) toward substitution in fac-[Re(N,O'-Bid)(CO)3(HOCH3)] by Schiff-base bidentate ligands (N,O'-Bid).

PubMed

Brink, Alice; Visser, Hendrik G; Roodt, Andreas

2013-08-05

A series of fac-[Re(N,O'-Bid)(CO)3(L)] (N,O'-Bid = monoanionic bidentate Schiff-base ligands with N,O donor atoms; L = neutral monodentate ligand) has been synthesized, and the methanol substitution reactions have been investigated. The complexes were characterized by NMR, IR, and UV-vis spectroscopy. X-ray crystal structures of the compounds fac-[Re(Sal-mTol)(CO)3(HOCH3)], fac-[Re(Sal-pTol)(CO)3(HOCH3)], fac-[Re(Sal-Ph)(CO)3(HOCH3)], and fac-[Re(Sal-Ph)(CO)3(Py)] (Sal-mTol = 2-(m-tolyliminomethyl)phenolato; Sal-pTol = 2-(p-tolyliminomethyl)phenolato; Sal-Ph = 2-(phenyliminomethyl)phenolato; Py = pyridine) are reported. Significant activation for the methanol substitution is induced by the use of the N,O bidentate ligand as manifested by the second order rate constants, with limiting kinetics being observed for the first time. Rate constants (25 °C) (k1 or k3) and activation parameters (ΔHk‡, kJ mol(-1); ΔSk‡, J K(-1) mol(-1)) from Eyring plots for entering nucleophiles as indicated are as follows: fac-[Re(Sal-mTol)(CO)3(HOCH3)] 3-chloropyridine: (k1) 2.33 ± 0.01 M(-1) s(-1); 85.1 ± 0.6, 48 ± 2; fac-[Re(Sal-mTol)(CO)3(HOCH3)] pyridine: (k1) 1.29 ± 0.02 M(-1) s(-1); 92 ± 2, 66 ± 7; fac-[Re(Sal-mTol)(CO)3(HOCH3)] 4-picoline: (k1) 1.27 ± 0.05 M(-1) s(-1); 88 ± 2, 53 ± 6; (k3) 3.9 ± 0.03 s(-1); 78 ± 8, 30 ± 27; (kf) 1.7 ± 0.02 M(-1) s(-1); 86 ± 2, 49 ± 6; fac-[Re(Sal-mTol)(CO)3(HOCH3)] DMAP (k3) 1.15 ± 0.02 s(-1); 88 ± 2, 52 ± 7. An interchange dissociative mechanism is proposed.

Several novel N-donor tridentate ligands formed in chemical studies of new fac-Re(CO)3 complexes relevant to fac-99mTc(CO)3 radiopharmaceuticals: attack of a terminal amine on coordinated acetonitrile.

PubMed

Perera, Theshini; Marzilli, Patricia A; Fronczek, Frank R; Marzilli, Luigi G

2010-03-01

To evaluate syntheses of fac-[Re(CO)(3)L](+) complexes in organic solvents, we treated fac-[Re(CO)(3)(CH(3)CN)(3)]PF(6)/BF(4) in acetonitrile with triamine ligands (L). When L had two primary or two tertiary terminal amine groups, the expected fac-[Re(CO)(3)L](+) complexes formed. In contrast, N,N-dimethyldiethylenetriamine (N,N-Me(2)dien) formed an unusual compound, fac-[Re(CO)(3)(DAE)]BF(4) {DAE = (Z)-N'-(2-(2-(dimethylamino)ethylamino)ethyl)acetimidamide = (Me(2)NCH(2)CH(2))NH(CH(2)CH(2)N=C(NH(2))Me)}. DAE is formed by addition of acetonitrile to the N,N-Me(2)dien terminal primary amine, converting this sp(3) nitrogen to an sp(2) nitrogen with a double bond to the original acetonitrile sp carbon. The three Ns bound to Re derive from N,N-Me(2)dien. The pathway to fac-[Re(CO)(3)(DAE)]BF(4) is suggested by a second unusual compound, fac-[Re(CO)(3)(MAE)]PF(6) {MAE = N-methyl-N-(2-(methyl-(2-(methylamino)ethyl)amino)ethyl)acetimidamide = MeN(H)-CH(2)CH(2)-N(Me)-CH(2)CH(2)-N(Me)-C(Me)=NH}, isolated after treating fac-[Re(CO)(3)(CH(3)CN)(3)]PF(6) with N,N',N''-trimethyldiethylenetriamine (N,N',N''-Me(3)dien). MAE chelates via a terminal and a central sp(3) N from N,N',N''-Me(3)dien and via one sp(2) NH in a C(Me)=NH group. This group is derived from acetonitrile by addition of the other N,N',N''-Me(3)dien terminal amine to the nitrile carbon. This addition creates an endocyclic NMe group within a seven-membered chelate ring. The structure and other properties of fac-[Re(CO)(3)(MAE)]PF(6) allow us to propose a reaction scheme for the formation of the unprecedented DAE ligand. The new compounds advance our understanding of the spectral and structural properties of Re analogues of (99m)Tc radiopharmaceuticals.

Coordinated aqua vs methanol substitution kinetics in fac-Re(I) tricarbonyl tropolonato complexes.

PubMed

Schutte, Marietjie; Roodt, Andreas; Visser, Hendrik G

2012-11-05

Water-soluble fac-[Re(CO)(3)(L,L'-Bid)(X)] (L,L'-Bid = tropolonato, X = H(2)O, methanol) complexes have been synthesized, and the aqua and methanol substitution reactions were investigated in water (pH range 6.3-10.0) and methanol, respectively, and compared. Thiocyanate ions were used as monodentate entering ligand. The complexes were characterized by UV-vis, IR, and NMR spectroscopy. The crystal structures of the complexes [NEt(4)] fac-[Re(Trop)(CO)(3)(H(2)O)].NO(3).H(2)O (reactant) and fac-[Re(CO)(3)(Trop)(Py)], a substitution product, are reported. Overall it was found that the aqua substitution of fac-[Re(CO)(3)(Trop)(H(2)O)] is about 10 times faster than the methanol substitution reaction for fac-[Re(CO)(3)(Trop)(MeOH)], with forward and reverse rate and stability constants [k(1) (M(-1) s(-1)), k(-1) (s(-1)), K(1), (M(-1))] for thiocyanate as monodentate entering ligand as follows: fac-[Re(CO)(3)(Trop)(H(2)O)] = 2.54 ± 0.03, 0.0077 ± 0.0005, 330 ± 22/207 ± 14 and fac-[Re(CO)(3)(Trop)(MeOH)] = 0.268 ± 0.002, 0.0044 ± 0.0002, (61 ± 3)/(52 ± 4). The activation parameters [ΔH(‡)(k1) (kJ mol(-1)), ΔS(‡)(k1) (J K(-1) mol(-1))] for the aqua and methanol complex respectively are 56.1 ± 0.7, -49 ± 2 and 64 ± 1, -43 ± 5.

Field-aligned Currents' Scale Analysis Performed by the Swarm Constellation

NASA Astrophysics Data System (ADS)

Luhr, H.; Park, J.; Gjerloev, J. W.; Rauberg, J.; Michaelis, I.; Le, G.; Merayo, J. M. G.; Brauer, P.

2014-12-01

We present a statistical study of the temporal and spatial scale characteristics of different field-aligned current (FAC) types. Very suitable for this purpose is the closely spaced Swarm satellite formation, which existed shortly after launch during the commissioning phase. As dataset we use the standard Level 2 product, Single Satellite FAC, which comes at a data rate of 1 Hz, corresponding to an along-track distance of 7.5 km. FACs are known to cover a wide range of scales from 1km to several hundred kilometres, the smaller the scale the larger the amplitude. We like to divide the FACs into two classes. Those of intermediate scale, some tens of kilometres, which are carried predominantly by kinetic Alfvén waves, while the large-scale FACs are assumed to be stationary current structures on the timescales of a satellite crossing. For distinguishing between the two we first look how the temporal variability changes with scale. For that we consider subsequent measurements at the same point, the orbital cross-over near the geographic poles, and interpret the temporal current changes. Here we focus on observations in the southern hemisphere at locations where the geographic pole lies within the auroral region. In a next step the latitudinal and longitudinal scales of the larger-scale FAC structures are investigated. FACs related to Alfvén waves cannot be studied in this way because we have no simultaneous measurements at the same latitude and longitude. The results from this analysis are different for dayside and nightside. Implications for the FAC characteristics resulting from these observations are interpreted in the end.

National Standards for Family and Consumer Sciences Education.

ERIC Educational Resources Information Center

National Association of State Administrators for Family and Consumer Sciences.

The document presents a new set of standards for family and consumer sciences (FACS) education. Section 1 is a three-chapter overview. Chapter 1 addresses the rationale for change and the FACS vision and mission. Chapter 2 describes the approach to develop the national standards, FACS format, and components of the standards. Chapter 3 provides…

Increased universality of Lepidopteran elicitor compounds across insects: Identification of fatty acid amino acid conjugates (FACs)

USDA-ARS?s Scientific Manuscript database

Fatty acid amino acid conjugates (FACs) are known elicitors of induced release of volatile compounds in plants that, in turn, attract foraging parasitoids. Since the discovery of volicitin [N-(17-hydroxylinolenoyl)-L-glutamine] in the regurgitant of larval Spodoptera exigua1, a series of related FAC...

75 FR 39420 - Federal Acquisition Regulation; Federal Acquisition Circular 2005-44; Small Entity Compliance Guide

Federal Register 2010, 2011, 2012, 2013, 2014

2010-07-08

... Federal Acquisition Circular (FAC) 2005-44 which amends the Federal Acquisition Regulation (FAR). Interested parties may obtain further information regarding this rule by referring to FAC 2005-44 which... . FOR FURTHER INFORMATION CONTACT: The analyst whose name appears in the table below. Please cite FAC...

2 CFR 200.513 - Responsibilities.

Code of Federal Regulations, 2014 CFR

2014-01-01

... notice of the change to the FAC, the auditee, and, if known, the auditor. The cognizant agency for audit... agency for audit must provide notice of the change to the FAC, the auditee, and, if known, the auditor...; providing input on single audit and follow-up policy; enhancing the utility of the FAC; and studying ways to...

76 FR 4191 - Federal Acquisition Regulation; Federal Acquisition Circular 2005-49; Small Entity Compliance Guide

Federal Register 2010, 2011, 2012, 2013, 2014

2011-01-24

... Federal Acquisition Circular (FAC) 2005-49, which amend the Federal Acquisition Regulation (FAR). Interested parties may obtain further information regarding these rules by referring to FAC 2005-49, which... analyst whose name appears in the table below. Please cite FAC 2005-49 and the specific FAR case number...

F-Area Acid/Caustic Basin groundwater monitoring report: Third quarter 1994

DOE Office of Scientific and Technical Information (OSTI.GOV)

Not Available

1994-12-01

During third quarter 1994, samples from the FAC monitoring wells at the F-Area Acid/Caustic Basin were collected and analyzed for herbicides/pesticides, indicator parameters, metals, nitrate, radionuclide indicators, volatile organic compounds, and other constituents. Piezometer FAC 5P and monitoring well FAC 6 were dry and could not be sampled. New monitoring wells FAC 9C, 10C, 11C, and 12C were sampled for the first time during third quarter. Analytical results that exceeded final Primary Drinking Water Standards (PDWS), other Savannah River Site (SRS) Flag 2 criteria, or the SRS turbidity standard of 50 NTU during the quarter were as follows: gross alphamore » exceeded the final PDWS and aluminum, iron, manganese, and total alpha-emitting radium exceeded the SRS Flag 2 criteria in one or more of the FAC wells. Turbidity exceeded the SRS standard in wells FAC 3 and 10C. Groundwater flow direction and rate in the water table beneath the F-Area Acid/Caustic Basin were similar to past quarters.« less

Crystal structures of fac-tri-chlorido-tris-(tri-methyl-phosphane-κP)rhodium(III) monohydrate and fac-tri-chlorido-tris-(tri-methyl-phosphane-κP)rhodium(III) methanol hemisolvate: rhodium structures that are isotypic with their iridium analogs.

PubMed

Merola, Joseph S; Franks, Marion A

2015-02-01

The crystal structures of two solvates of fac-tri-chlorido-tris-(tri-methyl-phosphane-κP)rhodium(III) are reported, i.e. one with water in the crystal lattice, fac-[RhCl3(Me3P)3]·H2O, and one with methanol in the crystal lattice, fac-[RhCl3(Me3P)3]·0.5CH3OH. These rhodium compounds exhibit distorted octahedral coordination spheres at the metal and are isotypic with the analogous iridium compounds previously reported by us [Merola et al. (2013 ▶). Polyhedron, 54, 67-73]. Comparison is made between the rhodium and iridium compounds, highlighting their isostructural relationships.

Flow Accelerated Corrosion of Carbon Steel in the Feedwater System of PWR Plants - Behaviour of Welds and Weld Assemblies

NASA Astrophysics Data System (ADS)

Mansour, C.; Pavageau, E. M.; Faucher, A.; Inada, F.; Yoneda, K.; Miller, C.; Bretelle, J.-L.

Flow Accelerated Corrosion (FAC) of carbon steel is a phenomenon that has been studied for many years. However, to date, the specific behavior of welds and weld assemblies of carbon steel towards this phenomenon has been scarcely examined. An experimental program of FAC of welds and weld assemblies is being conducted by EDF and CRIEPI. This paper describes the results obtained on the behavior of weld metal independently of its behavior in a weld assembly as well as the sensitivity to FAC of various weld assembly configurations. Tests are performed, at EDF, in the CIROCO loop which permits to follow the FAC rate by gammametry measurements, and at CRIEPI, in the PRINTEMPS loop where FAC is measured by laser displacement sensor. Welds are performed by two different methods: Submerged Arc Welding (SAW) and Gas Tungsten Arc Welding (GTAW). The influence of several parameters on FAC of welds is examined: welding method, chromium content and temperature. For weld assemblies, only the impact of chromium content is studied. All the tests are conducted in ammonia medium at pH 9.0 and oxygen concentration lower then 1 ppb. Chemical parameters, as the pH, the conductivity and oxygen concentration, are measured in situ during the test and surface characterizations are performed after the test. The results show that, with more than 0.15% chromium, no FAC is detected on the weld metal, which is similar to the base metal behaviour. For the same and lower chromium content, the two types of metal have the same FAC rate. Concerning the temperature effect, for both metals FAC rate decreases with temperature increase above 150°C. Below 150 °C, their behaviour seems to be different. For weld assemblies, the study of different configurations shows that the chromium content is the main parameter affecting the behaviour of the specimens. Additional tests and modeling studies will be conducted in order to complete the results.

fac-[Re(CO)(3)L](+) complexes with N-CH(2)-CH(2)-X-CH(2)-CH(2)-N tridentate ligands. synthetic, X-ray crystallographic, and NMR spectroscopic investigations.

PubMed

Christoforou, Anna Maria; Marzilli, Patricia A; Fronczek, Frank R; Marzilli, Luigi G

2007-12-24

Polyamine ligands (L) have excellent binding characteristics for the formation of fac-99mTc(CO)3-based radiopharmaceuticals. Normally, these L are elaborated so as to leave pendant groups designed to impart useful biodistribution characteristics to the fac-[99mTc(CO)3L] imaging agent. Our goal is to lay a foundation for understanding the features of the bound elaborated ligands by using the fac-[Re(CO)3L]-analogue approach with the minimal prototypical ligands, diethylenetriamine (dien) or simple dien-related derivatives. Treatment of the fac-[Re(CO)3(H2O)3]+ cation with such triamine (NNN) ligands afforded fac-[Re(CO)3L]+ complexes. Ligand variations included having a central amine thioether donor, thus allowing X-ray crystallographic and NMR spectroscopic comparisons of fac-[Re(CO)3L]+ complexes with NNN and NSN ligands. fac-[Re(CO)3L]+ complexes with two terminal exo-NH groups exhibit unusually far upfield exo-NH NMR signals in DMSO-d6. Upon the addition of Cl-, these exo-NH signals move downfield, while the signals of any endo-NH or central NH groups move very little. This behavior is attributed to the formation of 1:1 ion pairs having selective Cl- hydrogen bonding to both exo-NH groups. Base addition to a DMSO-d6 solution of meso-exo-[Re(CO)3(N,N',N''-Me3dien)]PF6 led to isomerization of only one NHMe group, producing the chiral isomer. The meso isomer did not form. The [Re(CO)3(N,N,N',N'',N''-pentamethyldiethylenetriamine)]triflate.[Re(CO)3(mu3-OH)]4.3.35H2O crystal, the first structure with a fac-[Re(CO)3L] complex cocrystallized with this well-known cluster, provided parameters for a bulky NNN ligand and also reveals CO-CO interlocking intermolecular interactions that could stabilize the crystal.

Solving groundwater flow problems by conjugate-gradient methods and the strongly implicit procedure

USGS Publications Warehouse

Hill, Mary C.

1990-01-01

The performance of the preconditioned conjugate-gradient method with three preconditioners is compared with the strongly implicit procedure (SIP) using a scalar computer. The preconditioners considered are the incomplete Cholesky (ICCG) and the modified incomplete Cholesky (MICCG), which require the same computer storage as SIP as programmed for a problem with a symmetric matrix, and a polynomial preconditioner (POLCG), which requires less computer storage than SIP. Although POLCG is usually used on vector computers, it is included here because of its small storage requirements. In this paper, published comparisons of the solvers are evaluated, all four solvers are compared for the first time, and new test cases are presented to provide a more complete basis by which the solvers can be judged for typical groundwater flow problems. Based on nine test cases, the following conclusions are reached: (1) SIP is actually as efficient as ICCG for some of the published, linear, two-dimensional test cases that were reportedly solved much more efficiently by ICCG; (2) SIP is more efficient than other published comparisons would indicate when common convergence criteria are used; and (3) for problems that are three-dimensional, nonlinear, or both, and for which common convergence criteria are used, SIP is often more efficient than ICCG, and is sometimes more efficient than MICCG.

A SEMI-LAGRANGIAN TWO-LEVEL PRECONDITIONED NEWTON-KRYLOV SOLVER FOR CONSTRAINED DIFFEOMORPHIC IMAGE REGISTRATION.

PubMed

Mang, Andreas; Biros, George

2017-01-01

We propose an efficient numerical algorithm for the solution of diffeomorphic image registration problems. We use a variational formulation constrained by a partial differential equation (PDE), where the constraints are a scalar transport equation. We use a pseudospectral discretization in space and second-order accurate semi-Lagrangian time stepping scheme for the transport equations. We solve for a stationary velocity field using a preconditioned, globalized, matrix-free Newton-Krylov scheme. We propose and test a two-level Hessian preconditioner. We consider two strategies for inverting the preconditioner on the coarse grid: a nested preconditioned conjugate gradient method (exact solve) and a nested Chebyshev iterative method (inexact solve) with a fixed number of iterations. We test the performance of our solver in different synthetic and real-world two-dimensional application scenarios. We study grid convergence and computational efficiency of our new scheme. We compare the performance of our solver against our initial implementation that uses the same spatial discretization but a standard, explicit, second-order Runge-Kutta scheme for the numerical time integration of the transport equations and a single-level preconditioner. Our improved scheme delivers significant speedups over our original implementation. As a highlight, we observe a 20 × speedup for a two dimensional, real world multi-subject medical image registration problem.

Right Ventricular Function in Preterm and Term Neonates: Reference Values for Right Ventricle Areas and Fractional Area of Change

PubMed Central

Levy, Philip T.; Diodena, Brittney; Holland, Mark R.; Sekarski, Timothy J.; Lee, Caroline K.; Mathur, Amit; Cade, W. Todd; Cahill, Alison G.; Hamvas, Aaron; Singh, Gautam K.

2015-01-01

Background Right Ventricle fractional area of change (RV FAC) is a quantitative two- dimensional echocardiographic measurement of RV function. RV FAC expresses the percentage change in the RV chamber area between end-diastole (RVEDA) to end-systole (RVESA). The objectives of this study were to determine the maturational (age- and weight- related) changes of RV FAC and RV areas and to establish reference values in healthy preterm and term neonates. Methods A prospective longitudinal study was conducted in 115 preterm infants (23-28 weeks gestational age at birth, 500-1500 gram). RV FAC was measured at 24 hours of age, 72 hours of age, 32 weeks and 36 weeks postmenstrual age (PMA). The maturational patterns of RVEDA, RVESA, and RV FAC were compared to 60 healthy full term infants in a cross sectional study (> 37 weeks, 3.5 +/− 1 kg), who received echocardiograms at birth (n=25) and one month of age (n=35). RVEDA and RVESA were traced in the RV focused apical 4-chamber view, and FAC was calculated using the formula: 100 * [(RVEDA – RVESA)/RVEDA)]. Premature infants that developed chronic lung disease or had a clinically and hemodynamically significant PDA were excluded (n=55) from the reference values. Intra- and inter- observer reproducibility analysis was performed. Results RV FAC ranged from 26% at birth to 35% by 36 weeks PMA in preterm infants (n=60) and increased almost two times faster in the first month of age as compared to healthy term infants (n=60). Similarly, RVEDA and RVESA increased throughout maturation in both term and preterm infants. RV FAC and RV areas correlated with weight (r=0.81, p<0.001), but were independent of gestational age at birth (r=0.3, p=0.45). RVEDA and RVESA correlated with PMA in weeks (r=0.81, p<0.001). RV FAC trended lower in preterm infants with bronchopulmonary dysplasia (p=0.04), but did not correlate to size of PDA (p=0.56). There was no difference in RV FAC based on gender or need for mechanical ventilation. Conclusions This study establishes reference values of RV areas (RVEDA and RVESA) and RV fractional area of change (RV FAC) in healthy term and preterm infants and tracks their maturational changes during postnatal development. These measures increase from birth to 36 weeks PMA, and this is reflective of the postnatal cardiac growth as a contributor to the maturation of cardiac function These measures are also linearly associated with increasing weight throughout maturation. This study suggests that two-dimensional RV FAC can be used as a complementary modality to assess global RV systolic function in neonates and facilitates its incorporation into clinical pediatric and neonatal guidelines. PMID:25753503

Generation of field-aligned current (FAC) and convection through the formation of pressure regimes: Correction for the concept of Dungey's convection

NASA Astrophysics Data System (ADS)

Tanaka, T.; Watanabe, M.; Den, M.; Fujita, S.; Ebihara, Y.; Kikuchi, T.; Hashimoto, K. K.; Kataoka, R.

2016-09-01

In this paper, we try to elucidate the generation mechanism of the field-aligned current (FAC) and coexisting convection. From the comparison between the theoretical prediction and the state of numerical solution from the high-resolution global simulation, we obtain the following conclusions about the distribution of dynamo, the magnetic field structure along the flow path that diverges Poynting flux, and energy conversion promoting the generation of electromagnetic energy. The dynamo for the region 1 FAC, which is in the high-latitude-side cusp-mantle region, has a structure in which magnetic field is compressed along the convection path by the slow mode motion. The dynamo for the region 2 FAC is in the ring current region at the inner edge of the plasma sheet, and has a structure in which magnetic field is curved outward along the convection path. Under these structures, electromagnetic energy is generated from the work done by pressure gradient force, in both dynamos for the region 1 and region 2 FACs. In these generation processes of the FACs, the excitation of convection and the formation of pressure regimes occur as interdependent processes. This structure leads to a modification in the way of understanding the Dungey's convection. Generation of the FAC through the formation of pressure regimes is essential even for the case of substorm onset.

Convergent validity evidence for the Pain and Discomfort Scale (PADS) for pain assessment among adults with intellectual disability

PubMed Central

Shinde, Satomi K.; Danov, Stacy; Chen, Chin-Chih; Clary, Jamie; Harper, Vicki; Bodfish, James W.; Symons, Frank J.

2014-01-01

Objectives The main aim of the study was to generate initial convergent validity evidence for the Pain and Discomfort Scale (PADS) for use with non-verbal adults with intellectual disabilities (ID). Methods Forty-four adults with intellectual disability (mean age = 46, 52 % male) were evaluated using a standardized sham-controlled and blinded sensory testing protocol, from which FACS and PADS scores were tested for (1) sensitivity to an array of calibrated sensory stimuli, (2) specificity (active vs. sham trials), and (3) concordance. Results The primary findings were that participants were reliably coded using both FACS and PADS approaches as being reactive to the sensory stimuli (FACS: F[2, 86] = 4.71, P < .05, PADS: F[2, 86] = 21.49, P < .05) (sensitivity evidence), not reactive during the sham stimulus trials (FACS: F[1, 43]= 3.77, p = .06, PADS: F[1, 43] = 5.87, p = .02) (specificity evidence), and there were significant (r = .41 – .51, p < .01) correlations between PADS and FACS (convergent validity evidence). Discussion FACS is an objective coding platform for facial expression. It requires intensive training and resources for scoring. As such it may be limited for clinical application. PADS was designed for clinical application. PADS scores were comparable to FACS scores under controlled evaluation conditions providing partial convergent validity evidence for its use. PMID:24135902

Synthesis and characterization of fac-Re(CO)3-aspartic-N-monoacetic acid, a structural analogue of a potential new renal tracer, fac-99mTc(CO)3(ASMA).

PubMed

Klenc, Jeffrey; Lipowska, Malgorzata; Taylor, Andrew T; Marzilli, Luigi G

2012-09-01

The reaction of an aminopolycarboxylate ligand, as partic- N - m onoacetic a cid (ASMA), with [Re(CO) 3 (H 2 O) 3 ] + was examined. The tridentate coordination of ASMA to this Re I tricarbonyl precursor yielded fac -Re(CO) 3 (ASMA) as a mixture of diastereomers. The chemistry is analogous to that of the Tc I tricarbonyl complex, which yields fac - 99m Tc(CO) 3 (ASMA) under similar conditions. The formation, structure, and isomerization of fac -Re(CO) 3 (ASMA) products were characterized by HPLC, 1 H NMR spectroscopy, and X-ray crystallography. The two major fac -Re(CO) 3 (ASMA) diastereomeric products each have a linear ONO coordination mode with two adjacent five-membered chelate rings, but they differ in the endo or exo orientation of the uncoordinated acetate group, in agreement with expectations based on previous studies. Conditions have been identified for the expedient isomerization of fac -Re(CO) 3 (ASMA) to a mixture consisting primarily of one major product. Because different isomeric species typically have different pharmacokinetic characteristics, these conditions may provide for the practical isolation of a single 99m Tc(CO) 3 (ASMA) species, thus allowing the isolation of the isomer that has optimal imaging and pharmacokinetic characteristics. This information will aid in the design of future 99m Tc radiopharmaceuticals.

Synthesis and characterization of fac-Re(CO)3-aspartic-N-monoacetic acid, a structural analogue of a potential new renal tracer, fac-99mTc(CO)3(ASMA)

PubMed Central

Klenc, Jeffrey; Lipowska, Malgorzata; Taylor, Andrew T.; Marzilli, Luigi G.

2013-01-01

The reaction of an aminopolycarboxylate ligand, aspartic-N-monoacetic acid (ASMA), with [Re(CO)3(H2O)3]+ was examined. The tridentate coordination of ASMA to this ReI tricarbonyl precursor yielded fac-Re(CO)3(ASMA) as a mixture of diastereomers. The chemistry is analogous to that of the TcI tricarbonyl complex, which yields fac-99mTc(CO)3(ASMA) under similar conditions. The formation, structure, and isomerization of fac-Re(CO)3(ASMA) products were characterized by HPLC, 1H NMR spectroscopy, and X-ray crystallography. The two major fac-Re(CO)3(ASMA) diastereomeric products each have a linear ONO coordination mode with two adjacent five-membered chelate rings, but they differ in the endo or exo orientation of the uncoordinated acetate group, in agreement with expectations based on previous studies. Conditions have been identified for the expedient isomerization of fac-Re(CO)3(ASMA) to a mixture consisting primarily of one major product. Because different isomeric species typically have different pharmacokinetic characteristics, these conditions may provide for the practical isolation of a single 99mTc(CO)3(ASMA) species, thus allowing the isolation of the isomer that has optimal imaging and pharmacokinetic characteristics. This information will aid in the design of future 99mTc radiopharmaceuticals. PMID:24273448

Multigrid Computations of 3-D Incompressible Internal and External Viscous Rotating Flows

NASA Technical Reports Server (NTRS)

Sheng, Chunhua; Taylor, Lafayette K.; Chen, Jen-Ping; Jiang, Min-Yee; Whitfield, David L.

1996-01-01

This report presents multigrid methods for solving the 3-D incompressible viscous rotating flows in a NASA low-speed centrifugal compressor and a marine propeller 4119. Numerical formulations are given in both the rotating reference frame and the absolute frame. Comparisons are made for the accuracy, efficiency, and robustness between the steady-state scheme and the time-accurate scheme for simulating viscous rotating flows for complex internal and external flow applications. Prospects for further increase in efficiency and accuracy of unsteady time-accurate computations are discussed.

Multigrid Algorithms for the Solution of Linear Complementarity Problems Arising from Free Boundary Problems.

DTIC Science & Technology

1980-10-01

faster than previous algorithms. Indeed, with only minor modifications, the standard multigrid programs solve the LCP with essentially the same efficiency... Lemna 2.2. Let Uk be the solution of the LCP (2.3), and let uk > 0 be an approximate solu- tion obtained after one or more Gk projected sweeps. Let...in Figure 3.2, Ivu IIG decreased from .293 10 to .110 10 with the expenditure of (99.039-94.400) = 4.639 work units. While minor variations do arise, a

48 CFR 301.605 - Contracting Officer designation of Contracting Officer Technical Representative.

Code of Federal Regulations, 2014 CFR

2014-10-01

... under HHS' FAC-COTR program before delegating authority to that individual to act as a COTR. Even if an individual is FAC-COTR-certified, a candidate becomes a COTR only when a Contracting Officer provides in... order file the individual's active FAC-COTR certificate. In the event that the HCA has granted an...

48 CFR 301.605 - Contracting Officer designation of Contracting Officer Technical Representative.

Code of Federal Regulations, 2013 CFR

2013-10-01

... under HHS' FAC-COTR program before delegating authority to that individual to act as a COTR. Even if an individual is FAC-COTR-certified, a candidate becomes a COTR only when a Contracting Officer provides in... order file the individual's active FAC-COTR certificate. In the event that the HCA has granted an...

75 FR 14067 - Federal Acquisition Regulation; Federal Acquisition Circular 2005-40; Small Entity Compliance Guide

Federal Register 2010, 2011, 2012, 2013, 2014

2010-03-23

... of the rule appearing in Federal Acquisition Circular (FAC) 2005-40 which amends the Federal... referring to FAC 2005-40 which precedes this document. These documents are also available via the Internet... the table below. Please cite FAC 2005-40 and the specific FAR case number. For information pertaining...

77 FR 23371 - Federal Acquisition Regulation; Federal Acquisition Circular 2005-58; Small Entity Compliance Guide

Federal Register 2010, 2011, 2012, 2013, 2014

2012-04-18

... Federal Acquisition Circular (FAC) 2005-58, which amends the Federal Acquisition Regulation (FAR). An... parties may obtain further information regarding this rule by referring to FAC 2005-58, which precedes... analyst whose name appears in the table below. Please cite FAC 2005-58 and the FAR case number. For...

48 CFR 301.605 - Contracting Officer designation of Contracting Officer Technical Representative.

Code of Federal Regulations, 2010 CFR

2010-10-01

... under HHS' FAC-COTR program before delegating authority to that individual to act as a COTR. Even if an individual is FAC-COTR-certified, a candidate becomes a COTR only when a Contracting Officer provides in... order file the individual's active FAC-COTR certificate. In the event that the HCA has granted an...

78 FR 13769 - Federal Acquisition Regulation; Federal Acquisition Circular 2005-66; Small Entity Compliance Guide

Federal Register 2010, 2011, 2012, 2013, 2014

2013-02-28

... Federal Acquisition Circular (FAC) 2005-66, which amends the Federal Acquisition Regulation (FAR). An... parties may obtain further information regarding this rule by referring to FAC 2005-66, which precedes... analyst whose name appears in the table below. Please cite FAC 2005-66 and the FAR case number. For...

48 CFR 301.605 - Contracting Officer designation of Contracting Officer Technical Representative.

Code of Federal Regulations, 2011 CFR

2011-10-01

... under HHS' FAC-COTR program before delegating authority to that individual to act as a COTR. Even if an individual is FAC-COTR-certified, a candidate becomes a COTR only when a Contracting Officer provides in... order file the individual's active FAC-COTR certificate. In the event that the HCA has granted an...

48 CFR 301.605 - Contracting Officer designation of Contracting Officer Technical Representative.

Code of Federal Regulations, 2012 CFR

2012-10-01

... under HHS' FAC-COTR program before delegating authority to that individual to act as a COTR. Even if an individual is FAC-COTR-certified, a candidate becomes a COTR only when a Contracting Officer provides in... order file the individual's active FAC-COTR certificate. In the event that the HCA has granted an...

A comparative analysis of single cell and droplet-based FACS for improving production phenotypes: Riboflavin overproduction in Yarrowia lipolytica.

PubMed

Wagner, James M; Liu, Leqian; Yuan, Shuo-Fu; Venkataraman, Maya V; Abate, Adam R; Alper, Hal S

2018-04-23

Evolutionary approaches to strain engineering inherently require the identification of suitable selection techniques for the product and phenotype of interest. In this work, we undertake a comparative analysis of two related but functionally distinct methods of high-throughput screening: traditional single cell fluorescence activated cell sorting (single cell FACS) and microdroplet-enabled FACS (droplet FACS) using water/oil/water (w/o/w) emulsions. To do so, we first engineer and evolve the non-conventional yeast Yarrowia lipolytica for high extracellular production of riboflavin (vitamin B2), an innately fluorescent product. Following mutagenesis and adaptive evolution, a direct parity-matched comparison of these two selection strategies was conducted. Both single cell FACS and droplet FACS led to significant increases in total riboflavin titer (32 and 54 fold relative to the parental PO1f strain, respectively). However, single cell FACS favored intracellular riboflavin accumulation (with only 70% of total riboflavin secreted) compared with droplet FACS that favored extracellular product accumulation (with 90% of total riboflavin secreted). We find that for the test case of riboflavin, the extent of secretion and total production were highly correlated. The resulting differences in production modes and levels clearly demonstrate the significant impact that selection approaches can exert on final evolutionary outcomes in strain engineering. Moreover, we note that these results provide a cautionary tale when intracellular read-outs of product concentration (including signals from biosensors) are used as surrogates for total production of potentially secreted products. In this regard, these results demonstrate that extracellular production is best assayed through an encapsulation technique when performing high throughput screening. Copyright © 2018 International Metabolic Engineering Society. Published by Elsevier Inc. All rights reserved.

Comparison of tricuspid annular plane systolic excursion with fractional area change for the evaluation of right ventricular systolic function: a meta-analysis

PubMed Central

Low, See-Wei; Pasha, Ahmed K; Howe, Carol L; Lee, Kwan S; Suryanarayana, Prakash G

2018-01-01

Background Accurate determination of right ventricular ejection fraction (RVEF) is challenging because of the unique geometry of the right ventricle. Tricuspidannular plane systolic excursion (TAPSE) and fractional area change (FAC) are commonly used echocardiographic quantitative estimates of RV function. Cardiac MRI (CMRI) has emerged as the gold standard for assessment of RVEF. We sought to summarise the available data on correlation of TAPSE and FAC with CMRI-derived RVEF and to compare their accuracy. Methods We searched PubMed, EMBASE, Web of Science, CINAHL, ClinicalTrials.gov and the Cochrane Library databases for studies that assessed the correlation of TAPSE or FAC with CMRI-derived RVEF. Data from each study selected were pooled and analysed to compare the correlation coefficient of TAPSE and FAC with CMRI-derived RVEF. Subgroup analysis was performed on patients with pulmonary hypertension. Results Analysis of data from 17 studies with a total of 1280 patients revealed that FAC had a higher correlation with CMRI-derived RVEF compared with TAPSE (0.56vs0.40, P=0.018). In patients with pulmonary hypertension, there was no statistical difference in the mean correlation coefficient of FAC and TAPSE to CMR (0.57vs0.46, P=0.16). Conclusions FAC provides a more accurate estimate of RV systolic function (RVSF) compared with TAPSE. Adoption of FAC as a routine tool for the assessment of RVSF should be considered, especially since it is also an independent predictor of morbidity and mortality. Further studies will be needed to compare other methods of echocardiographic measurement of RV function. PMID:29387425

Quantitative Evaluation of the Fetal Right and Left Ventricular Fractional Area Change Using Speckle Tracking Technology.

PubMed

DeVore, Greggory R; Klas, Berthold; Satou, Gary; Sklansky, Mark

2018-03-14

The purpose of this study was to measure the fractional area change (FAC) of the right and left ventricles in normal fetal hearts between 20 and 40 weeks of gestation using speckle-tracking software. The 4-chamber view of the fetal heart was obtained in 200 control fetuses between 20 and 40 weeks of gestation. The FAC was computed from the ventricular areas [((end-diastolic area) - (end-systolic area)/(end-diastolic area)) x 100] for the right and left ventricles and regressed against 7 independent biometric and age variables. The FAC was correlated with longitudinal fractional shortening (LFS) [((end-diastolic longitudinal length) - (end-systolic longitudinal length) /(end-diastolic longitudinal length)) x 100] obtained from the mid ventricular basal-apical lengths of the right and left ventricular chambers and the transverse fractional shortening (TFS) [((end-diastolic transverse length) - (end-systolic transverse length)/(end-diastolic transverse length)) x 100] from three transverse positions (base, mid, apical) located within each ventricular chamber. To evaluate potential clinical utility, the FAC, LFS, and TFS results were examined in 9 fetuses with congenital heart defects (CHD). Regression analysis demonstrated significant associations between the FAC and the biometric and age independent variables (R 2 = 0.13 - 0.15). The FAC was significantly correlated with the LFS (R 2 =0.18 to 0.28) and TFS (R 2 = 0.13 to 0.33). The 9 fetuses with CHD illustrated the interrelationship between the FAC, LFS, and TFS when identifying abnormal ventricular function. This study reports results from measuring the FAC of the right and left ventricles, and demonstrates a correlation with longitudinal fractional shortening (LFS) and transverse fractional shortening (TFS). This article is protected by copyright. All rights reserved.

Design of the free-air ionization chamber, FAC-IR-150, for X-ray dosimetry

NASA Astrophysics Data System (ADS)

Mohammadi, Seyed Mostafa; Tavakoli-Anbaran, Hossein

2018-03-01

The primary standard for X-ray dosimetry is based on the free-air ionization chamber (FAC). Therefore, the Atomic Energy Organization of Iran (AEOI) designed the free-air ionization chamber, FAC-IR-150, for low and medium energy X-ray dosimetry. The purpose of this work is the study of the free-air ionization chamber characteristics and the design of the FAC-IR-150. The FAC-IR-150 dosimeter has two parallel plates, a high voltage plate and a collector plate. A guard electrode surrounds the collector and is separated by an air gap. A group of guard strips is used between up and down electrodes to produce a uniform electric field in all the ion chamber volume. This design involves introducing the correction factors and determining the exact dimensions of the ionization chamber by using Monte Carlo simulation.

Free-air ionization chamber, FAC-IR-300, designed for medium energy X-ray dosimetry

NASA Astrophysics Data System (ADS)

Mohammadi, S. M.; Tavakoli-Anbaran, H.; Zeinali, H. Z.

2017-01-01

The primary standard for X-ray photons is based on parallel-plate free-air ionization chamber (FAC). Therefore, the Atomic Energy Organization of Iran (AEOI) is tried to design and build the free-air ionization chamber, FAC-IR-300, for low and medium energy X-ray dosimetry. The main aim of the present work is to investigate specification of the FAC-IR-300 ionization chamber and design it. FAC-IR-300 dosimeter is composed of two parallel plates, a high voltage (HV) plate and a collector plate, along with a guard electrode that surrounds the collector plate. The guard plate and the collector were separated by an air gap. For obtaining uniformity in the electric field distribution, a group of guard strips was used around the ionization chamber. These characterizations involve determining the exact dimensions of the ionization chamber by using Monte Carlo simulation and introducing correction factors.

TMSOTf assisted synthesis of 2'-deoxy-2'-[18F]fluoro-β-D-arabinofuranosylcytosine ([18F]FAC).

PubMed

Gangangari, Kishore K; Humm, John L; Larson, Steven M; Pillarsetty, Naga Vara Kishore

2018-01-01

[18F]FAC (2'-deoxy-2'-[18F]fluoro-β-D-arabinofuranosylcytosine, 1) is a versatile probe for imaging deoxycytidine kinase (dCK) expression levels in vivo. dCK is responsible for phosphorylation of deoxycytidine (dC, 2) and other nucleoside analogs, plays a key role in immune activation and has demonstrated to be one of the key enzymes in activating nucleoside based drugs including gemcitabine. Reported synthesis of [18F]FAC is high yielding but is quite challenging requiring bromination using HBr and careful drying of excess HBr which is critical for successful synthesis. Here in we report a simplified trimethylsilyl trifluoromethanesulfonate (TMSOTf) assisted synthesis of [18F]FAC eliminating the need of bromination and drying. [18F]FAC (β-anomer) was synthesized with average isolated decay corrected yield of 10.59 + 4.2% (n = 6) with radiochemical purity of >98% and total synthesis time of 158 + 19 min.

Effect of HNT on the Microstructure, Thermal and Mechanical Properties of Al/FACS-HNT Composites Produced by GPI

NASA Astrophysics Data System (ADS)

Siewiorek, A.; Malczyk, P.; Sobczak, N.; Sobczak, J. J.; Czulak, A.; Kozera, R.; Gude, M.; Boczkowska, A.; Homa, M.

2016-08-01

To develop an optimised manufacturing method of fly ash-reinforced metal matrix composites, the preliminary tests were performed on the cenospheres selected from fly ash (FACS) with halloysite nanotubes (HNTs) addition. The preform made out of FACS with and without the addition of HNT (with 5 and 10 wt.%) has been infiltrated by the pure aluminium (Al) via adapted gas pressure infiltration process. This paper reveals the influence of HNT addition on the microstructure (analysis was done by computed tomography and scanning electron microscopy combined with energy-dispersive x-ray spectroscopy), thermal properties (thermal expansion coefficient, thermal conductivity and specific heat) and the mechanical properties (hardness and compression test) of manufactured composites. The analysis of structure-property relationships for Al/FACS-HNT composites produced shows that the addition of 5 wt.% of HNT to FACS preform contributes to receiving of the best mechanical and structural properties of investigated composites.

The Extinction of Home Economics: A Study of Family and Consumer Sciences

ERIC Educational Resources Information Center

Antuna, Amber JoRie

2010-01-01

The purpose of this study was to determine the affects of the No Child Left Behind Act (NCLB) on Family and Consumer Science (FACS) program sustainment in the state of Arizona. FACS programs were not addressed in the NCLB mandates, but are part of the Arizona secondary education programming. FACS programs had seen a decrease in the number of…

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.

Wide-angle full-vector beam propagation method based on an alternating direction implicit preconditioner

NASA Astrophysics Data System (ADS)

Chui, Siu Lit; Lu, Ya Yan

2004-03-01

Wide-angle full-vector beam propagation methods (BPMs) for three-dimensional wave-guiding structures can be derived on the basis of rational approximants of a square root operator or its exponential (i.e., the one-way propagator). While the less accurate BPM based on the slowly varying envelope approximation can be efficiently solved by the alternating direction implicit (ADI) method, the wide-angle variants involve linear systems that are more difficult to handle. We present an efficient solver for these linear systems that is based on a Krylov subspace method with an ADI preconditioner. The resulting wide-angle full-vector BPM is used to simulate the propagation of wave fields in a Y branch and a taper.

Wide-angle full-vector beam propagation method based on an alternating direction implicit preconditioner.

PubMed

Chui, Siu Lit; Lu, Ya Yan

2004-03-01

Wide-angle full-vector beam propagation methods (BPMs) for three-dimensional wave-guiding structures can be derived on the basis of rational approximants of a square root operator or its exponential (i.e., the one-way propagator). While the less accurate BPM based on the slowly varying envelope approximation can be efficiently solved by the alternating direction implicit (ADI) method, the wide-angle variants involve linear systems that are more difficult to handle. We present an efficient solver for these linear systems that is based on a Krylov subspace method with an ADI preconditioner. The resulting wide-angle full-vector BPM is used to simulate the propagation of wave fields in a Y branch and a taper.

Correlations between Geomagnetic Disturbances and Field-Aligned Currents during the 22-29 July 2004 Storm Time Interval

NASA Astrophysics Data System (ADS)

Hood, R.; Woodroffe, J. R.; Morley, S.; Aruliah, A. L.

2017-12-01

Using the CHAMP fluxgate magnetometer to calculate field-aligned current (FAC) densities and magnetic latitudes, with SuperMAG ground magnetometers analogously providing ground geomagnetic disturbances (GMD) magnetic perturbations and latitudes, we probe FAC locations and strengths as predictors of GMD locations and strengths. We also study the relationships between solar wind drivers and global magnetospheric activity, and both FACs and GMDs using IMF Bz and the Sym-H index. We present an event study of the 22-29 July 2004 storm time interval, which had particularly large GMDs given its storm intensity. We find no correlation between FAC and GMD magnitudes, perhaps due to CHAMP orbit limitations or ground magnetometer coverage. There is, however, a correlation between IMF Bz and nightside GMD magnitudes, supportive of their generation via tail reconnection. IMF Bz is also correlated with dayside FAC and GMD magnetic latitudes, indicating solar wind as an initial driver. The ring current influence increases during the final storm, with improved correlations between the Sym-H index and both FAC magnetic latitudes and GMD magnitudes. Sym-H index correlations may only be valid for higher intensity storms; a statistical analysis of many storms is needed to verify this.

Metal-assisted in situ formation of a tridentate acetylacetone ligand for complexation of fac-Re(CO)3+ for radiopharmaceutical applications.

PubMed

Benny, Paul D; Fugate, Glenn A; Barden, Adam O; Morley, Jennifer E; Silva-Lopez, Elsa; Twamley, Brendan

2008-04-07

Reaction of [NEt4]2[ReBr3(CO)3] with 2,4-pentanedione (acac) yields a complex of the type fac-Re(acac)(OH2)(CO)3 (1) under aqueous conditions. 1 was further reacted with a monodentate ligand (pyridine) to yield a fac-Re(acac)(pyridine)(CO)3 complex (2). Complex 1 was found to react with primary amines to generate a Schiff base (imine) in aqueous solutions. When a mixed-nitrogen donor bidentate ligand, 2-(2-aminoethyl)pyridine, that has different coordination affinities for fac-Re(acac)(OH2)(CO)3 was utilized, a unique tridentate ligand was formed in situ utilizing a metal-assisted Schiff base formation to yield a complex fac-Re(CO)3(3[(2-phenylethyl)imino]-2-pentanone) (3). Tridentate ligand formation was found to occur only with the Re-coordinated acac ligand. Reactions of acac with fac-Re(CO)3Br(2-(2-aminoethyl)pyridine) (4) or a mixture of [NEt4]2[ReBr3(CO)3], acac, and 2-(2-aminoethyl)pyridine did not yield the formation of complex 3 in water.

Statistical Comparisons of Meso- and Small-Scale Field-Aligned Currents with Auroral Electron Acceleration Mechanisms from FAST Observations

NASA Astrophysics Data System (ADS)

Dombeck, J. P.; Cattell, C. A.; Prasad, N.; Sakher, A.; Hanson, E.; McFadden, J. P.; Strangeway, R. J.

2016-12-01

Field-aligned currents (FACs) provide a fundamental driver and means of Magnetosphere-Ionosphere (M-I) coupling. These currents need to be supported by local physics along the entire field line generally with quasi-static potential structures, but also supporting the time-evolution of the structures and currents, producing Alfvén waves and Alfvénic electron acceleration. In regions of upward current, precipitating auroral electrons are accelerated earthward. These processes can result in ion outflow, changes in ionospheric conductivity, and affect the particle distributions on the field line, affecting the M-I coupling processes supporting the individual FACs and potentially the entire FAC system. The FAST mission was well suited to study both the FACs and the electron auroral acceleration processes. We present the results of the comparisons between meso- and small-scale FACs determined from FAST using the method of Peria, et al., 2000, and our FAST auroral acceleration mechanism study when such identification is possible for the entire ˜13 year FAST mission. We also present the latest results of the electron energy (and number) flux ionospheric input based on acceleration mechanism (and FAC characteristics) from our FAST auroral acceleration mechanism study.

F-Area Acid/Caustic Basin groundwater monitoring report. First quarter 1995

DOE Office of Scientific and Technical Information (OSTI.GOV)

NONE

1995-06-01

During first quarter 1995, samples from the FAC monitoring wells at the F-Area Acid/Caustic Basin were collected and analyzed for herbicides/pesticides, indicator parameters, metals, nitrate, radionuclide indicators, volatile organic compounds, and other constituents. Piezometer FAC 5P and monitoring well FAC 6 were dry and could not be sampled. New monitoring wells FAC 9C, 10C, 11C, and 12C were completed in the Barnwell/McBean aquifer and were sampled for the first time during third quarter 1994 (first quarter 1995 is the third of four quarters of data required to support the closure of the basin). Analytical results that exceeded final Primary Drinkingmore » Water Standards (PDWS), other Savannah River Site (SRS) Flag 2 criteria, or the SRS turbidity standard of 50 NTU during the quarter were as follows: gross alpha exceeded the final PDWS and aluminum, iron, manganese, and total alpha-emitting radium exceeded the SRS Flag 2 criteria in one or more of the FAC wells. Turbidity exceeded the SRS standard (50 NTU) in wells FAC 3 and 11C. Groundwater flow direction and rate in the water table beneath the F-Area Acid/Caustic Basin were similar to past quarters.« less

Long-Term Prognostic Risk After Neoadjuvant Chemotherapy Associated With Residual Cancer Burden and Breast Cancer Subtype

PubMed Central

Wei, Caimiao; Gould, Rebekah; Yu, Xian; Zhang, Ya; Liu, Mei; Walls, Andrew; Bousamra, Alex; Ramineni, Maheshwari; Sinn, Bruno; Hunt, Kelly; Buchholz, Thomas A.; Valero, Vicente; Buzdar, Aman U.; Yang, Wei; Brewster, Abenaa M.; Moulder, Stacy; Pusztai, Lajos; Hatzis, Christos; Hortobagyi, Gabriel N.

2017-01-01

Purpose To determine the long-term prognosis in each phenotypic subset of breast cancer related to residual cancer burden (RCB) after neoadjuvant chemotherapy alone, or with concurrent human epidermal growth factor receptor 2 (HER2)–targeted treatment. Methods We conducted a pathologic review to measure the continuous RCB index (wherein pathologic complete response has RCB = 0; residual disease is categorized into three predefined classes of RCB index [RCB-I, RCB-II, and RCB-III]), and yp-stage of residual disease. Patients were prospectively observed for survival. Three patient cohorts received paclitaxel (T) followed by fluorouracil, doxorubicin, and cyclophosphamide (T/FAC): original development cohort (T/FAC-1), validation cohort (T/FAC-2), and independent validation cohort (T/FAC-3). Another validation cohort received FAC chemotherapy only, and a fifth cohort received concurrent trastuzumab (H) with sequential paclitaxel and fluorouracil, epirubicin, and cyclophosphamide (FEC; H+T/FEC). Phenotypic subsets were defined by hormone receptor (HR) and HER2 status at diagnosis, classified as HR-positive/HER2-negative, HER2-positive (HR-negative/HER2-positive or HR-positive/HER2-positive), or triple receptor–negative. Relapse-free survival estimates were determined from Kaplan-Meier analysis and compared using the log-rank test. Results Five cohorts (T/FAC-1 [n = 219], T/FAC-2 [n = 262], T/FAC-3 [n = 342], FAC [n = 132], and H+T/FEC [n = 203]) had median event-free follow-up of 13.5, 9.1, 6.8, 16.4, and 7.1 years, respectively. Continuous RCB index was prognostic within each phenotypic subset, independent of other clinical-pathologic variables. RCB classes stratified prognostic risk overall, within each phenotypic subset, and within yp-stage categories. Estimates of 10-year relapse-free survival rates in the four RCB classes (pathologic complete response, RCB-I, RCB-II, and RCB-III) were 86%, 81%, 55%, and 23% for triple receptor–negative; 83%, 97%, 74%, and 52% for HR-positive/HER2-negative in the combined T/FAC cohorts; and 95%, 77%, 47%, and 21% in the H+T/FEC cohort. Conclusion RCB was prognostic for long-term survival after neoadjuvant chemotherapy in all three phenotypic subsets of breast cancer. Our institutional findings should be externally validated. PMID:28135148

Activation requirements and responses to TLR ligands in human CD4+ T cells: comparison of two T cell isolation techniques.

PubMed

Lancioni, Christina L; Thomas, Jeremy J; Rojas, Roxana E

2009-05-15

Direct regulation of T cell function by microbial ligands through Toll-like receptors (TLR) is an emerging area of T cell biology. Currently either immunomagnetic cell sorting (IMACS) or fluorescence-activated cell sorting (FACS), are utilized to isolate T-cell subsets for such studies. However, it is unknown to what extent differences in T cell purity between these isolation techniques influence T cell functional assays. We compared the purity, response to mitogen, activation requirements, and response to TLR ligands between human CD4(+) T cells isolated either by IMACS (IMACS-CD4(+)) or by IMACS followed by FACS (IMACS/FACS-CD4(+)). As expected, IMACS-CD4(+) were less pure than IMACS/FACS-CD4(+) (92.5%+/-1.4% versus 99.7%+/-0.2%, respectively). Consequently, IMACS-CD4(+) proliferated and produced cytokines in response to mitogen alone and had lower activation requirements compared to IMACS/FACS-CD4(+). In addition IMACS-CD4(+) but not IMACS/FACS-CD4(+) responses were upregulated by the TLR-4 ligand lipopolysaccharide (LPS). On the other hand, TLR-2 and TLR-5 engagement induced costimulation in both IMACS-CD4(+) and highly purified IMACS-/FACS-CD4(+). Altogether these results indicate that small differences in cell purity can significantly alter T cell responses to TLR ligands. This study stresses the importance of a stringent purification method when investigating the role of microbial ligands in T cell function.

Optimizing acidified bleach solutions to improve sporicidal efficacy on building materials.

PubMed

Wood, J P; Calfee, M W; Clayton, M; Griffin-Gatchalian, N; Touati, A

2011-12-01

We evaluated whether lowering pH (with acetic acid) and raising free available chlorine (FAC) levels in bleach solutions would improve efficacy in inactivating Bacillus spores on different materials. We also determined how varying pH and FAC levels affected bleach stability. Acidified bleach solutions with pH levels of 4.5, 6 and 7.5 and FAC levels between 5000 and 10,000 ppm were evaluated for decontamination efficacy against Bacillus subtilis spores inoculated onto test coupons made from wood, ceramic and galvanized steel. Lowering the pH or increasing the FAC level improved efficacy in some of the tests, but depended on the material, which significantly affected decontamination efficacy. The acidified bleach at pH of 7.5 was significantly less effective than bleach at a pH of 4.5 or 6. The FAC levels in the bleach were the most stable at pH 4.5, and stability at pH 4.5 was not significantly affected by the initial FAC level. It may be advisable to use bleach solutions with lower pH (rather than high FAC levels) in light of both the decontamination efficacy and bleach stability results. For wood materials, use of sporicides other than acidified bleach may be warranted. These results may be useful in preparing acidified bleach solutions for decontamination of materials contaminated with spores such as Bacillus anthracis. © 2011 The Authors. Letters in Applied Microbiology © 2011 The Society for Applied Microbiology.

A Domain-Decomposed Multilevel Method for Adaptively Refined Cartesian Grids with Embedded Boundaries

NASA Technical Reports Server (NTRS)

Aftosmis, M. J.; Berger, M. J.; Adomavicius, G.

2000-01-01

Preliminary verification and validation of an efficient Euler solver for adaptively refined Cartesian meshes with embedded boundaries is presented. The parallel, multilevel method makes use of a new on-the-fly parallel domain decomposition strategy based upon the use of space-filling curves, and automatically generates a sequence of coarse meshes for processing by the multigrid smoother. The coarse mesh generation algorithm produces grids which completely cover the computational domain at every level in the mesh hierarchy. A series of examples on realistically complex three-dimensional configurations demonstrate that this new coarsening algorithm reliably achieves mesh coarsening ratios in excess of 7 on adaptively refined meshes. Numerical investigations of the scheme's local truncation error demonstrate an achieved order of accuracy between 1.82 and 1.88. Convergence results for the multigrid scheme are presented for both subsonic and transonic test cases and demonstrate W-cycle multigrid convergence rates between 0.84 and 0.94. Preliminary parallel scalability tests on both simple wing and complex complete aircraft geometries shows a computational speedup of 52 on 64 processors using the run-time mesh partitioner.

The Effects of Dissipation and Coarse Grid Resolution for Multigrid in Flow Problems

NASA Technical Reports Server (NTRS)

Eliasson, Peter; Engquist, Bjoern

1996-01-01

The objective of this paper is to investigate the effects of the numerical dissipation and the resolution of the solution on coarser grids for multigrid with the Euler equation approximations. The convergence is accomplished by multi-stage explicit time-stepping to steady state accelerated by FAS multigrid. A theoretical investigation is carried out for linear hyperbolic equations in one and two dimensions. The spectra reveals that for stability and hence robustness of spatial discretizations with a small amount of numerical dissipation the grid transfer operators have to be accurate enough and the smoother of low temporal accuracy. Numerical results give grid independent convergence in one dimension. For two-dimensional problems with a small amount of numerical dissipation, however, only a few grid levels contribute to an increased speed of convergence. This is explained by the small numerical dissipation leading to dispersion. Increasing the mesh density and hence making the problem over resolved increases the number of mesh levels contributing to an increased speed of convergence. If the steady state equations are elliptic, all grid levels contribute to the convergence regardless of the mesh density.

77 FR 1889 - Federal Acquisition Regulation; Set-Asides for Small Business; Extension of Comment Period

Federal Register 2010, 2011, 2012, 2013, 2014

2012-01-12

... ADMINISTRATION 48 CFR Parts 8, 12, 16, 19, 38, and 52 [FAC 2005-54; FAR Case 2011-024; Item VI; Docket 2011-0024... FAC 2005-54, FAR Case 2011- 024, by any of the following methods: Regulations.gov : http://www... comments only and cite FAC 2005-54, FAR Case 2011-024, in all correspondence related to this case. All...

Tetramethylbenzidine method for monitoring the free available chlorine and microbicidal activity of chlorite-based sanitizers under organic-matter-rich environments.

PubMed

Yamaoka, H; Nakayama-Imaohji, H; Horiuchi, I; Yamasaki, H; Nagao, T; Fujita, Y; Maeda, H; Goda, H; Kuwahara, T

2016-01-01

Chlorine is a principal disinfectant for food and environmental sanitation. Monitoring of free available chlorine (FAC) is essential for ensuring the efficacy of food disinfection processes that rely on chlorine. N,N-diethyl-p-phenylenediamine (DPD) is commonly used for FAC monitoring. However, here, we show that upon contact with bovine serum albumin (BSA) or broiler carcasses, chlorite (HClO2 )-based sanitizers acquire a pink colour, which can interfere with measurement of oxidized DPD absorbance at 513-550 nm. Alternatively, the pink colour did not interfere with 3,3',5,5'-tetramethylbenzidine (TMB)-based FAC monitoring. The FAC levels of NaClO and weakly acidified chlorous acid water (WACAW) were first adjusted by the TMB method and the killing activity of these sanitizers towards methicillin-resistant Staphylococcus aureus (MRSA) and feline calicivirus (FCV) was compared in the presence or absence of 0·5% BSA. At 200 ppm FAC, NaClO lost its bactericidal activity against MRSA after 10-min incubation with 0·5% BSA. Meanwhile, under the same conditions WACAW reduced the number of bacteria to below the detection limit. Similar results were obtained with FCV, indicating that the chlorite-based WACAW sanitizer is relatively stable under organic-matter-rich conditions. Moreover, TMB is suitable for in situ FAC monitoring of chlorite-based sanitizers in food and environmental disinfection processes. For practical applications of chlorine in food processing, monitoring of FAC is critical to validate disinfection efficacy. In this study we found that chlorite-based sanitizers acquired a pink colour upon contact with BSA or broiler carcasses. This pink colour interfered with FAC monitoring by methods that measure oxidized N,N-diethyl-p-phenylenediamine absorbance between 513-550 nm. Alternatively, FAC levels of chlorite-based sanitizers could be monitored using the absorbance of 3,3',5,5'-tetramethylbenzidine at 650 nm, which does not overlap with the acquired pink colour. These data provide valuable information for safety management of disinfection processes that use chlorite-based sanitizers. © 2015 The Society for Applied Microbiology.

Prospective randomized trial of 5-fluorouracil, doxorubicin, and cyclophosphamide (FAC) versus paclitaxel and FAC (TFAC) in patients with operable breast cancer: impact of taxane chemotherapy on locoregional control.

PubMed

Albert, Jeffrey M; Buzdar, Aman U; Guzman, Reina; Allen, Pamela K; Strom, Eric A; Perkins, George H; Woodward, Wendy A; Hoffman, Karen E; Tereffe, Welela; Hunt, Kelly K; Buchholz, Thomas A; Oh, Julia L

2011-07-01

A previous randomized trial (CALGB 9344/Intergroup 0148) compared four cycles of adjuvant doxorubicin/cyclophosphamide (AC) to four cycles of AC plus four cycles of paclitaxel (AC + T) and demonstrated that the addition of paclitaxel improved locoregional control (LRC) in patients with node-positive breast cancer. However, it could not be determined whether it was the paclitaxel or the increased duration of chemotherapy that led to this improvement. The present study aimed to analyze whether the addition of paclitaxel to a doxorubicin-based regimen improves LRC in a cohort of patients who all received eight total cycles of chemotherapy. Five hundred eleven women with operable breast cancer were randomized on a single-institution prospective trial to receive 5-fluorouracil, doxorubicin, cyclophosphamide (FAC) × 8 cycles (n = 252) or FAC × 4 cycles plus paclitaxel × 4 cycles (TFAC) (n = 259). Rates of LRC and overall survival (OS) were analyzed. Median follow-up was 124 months (range 5-167 months). The 10-year LRC rate was 92.6 versus 93.1% in the FAC versus TFAC arms, respectively (P = 0.26). The LRC between treatment arms did not differ when analyzed by locoregional treatment group: breast conservation therapy (BCT), mastectomy alone (M), and mastectomy + radiation (M + RT). The 10-year LRC rates were 95.1% (FAC) versus 91.2% (TFAC) after BCT (P = 0.98), 89.5% (FAC) versus 93.4% (TFAC) after M (P = 0.24), and 94.7% (FAC) versus 96.5% (TFAC) after M + RT (P = 0.59). Additionally, there was no difference in OS between the treatment arms, with 10-year OS rates of 78.4% (FAC) versus 81.7% (TFAC) (P = 0.93). The addition of paclitaxel to a doxorubicin-based regimen had no impact on LRC, regardless of the type of local therapy received. Historically inferior LRC with AC chemotherapy alone versus AC + T may have been due to an inadequate duration of systemic therapy and not due to the absence of paclitaxel.

Probing the mer- to fac-isomerization of tris-cyclometallated homo- and heteroleptic (C,N)3 iridium(III) complexes.

PubMed

McDonald, Aidan R; Lutz, Martin; von Chrzanowski, Lars S; van Klink, Gerard P M; Spek, Anthony L; van Koten, Gerard

2008-08-04

We have developed techniques which allow for covalent tethering, via a "hetero" cyclometallating ligand, of heteroleptic tris-cyclometallated iridium(III) complexes to polymeric supports (for application in light-emitting diode technologies). This involved the selective synthesis and thorough characterization of heteroleptic [Ir(C,N) 2(C',N')] tris-cyclometallated iridium(III) complexes. Furthermore, the synthesis and characterization of heteroleptic [Ir(C,N) 2OR] complexes is presented. Under standard thermal conditions for the synthesis of the facial ( fac) isomer of tris-cyclometallated complexes, it was not possible to synthesize pure heteroleptic complexes of the form [Ir(C,N) 2(C',N')]. Instead, a mixture of homo- and heteroleptic complexes was acquired. It was found that a stepwise procedure involving the synthesis of a pure meridonial ( mer) isomer followed by photochemical isomerization of this mer to the fac isomer was necessary to synthesize pure fac-[Ir(C,N) 2(C',N')] complexes. Under thermal isomerization conditions, the conversion of mer-[Ir(C,N) 2(C',N')] to fac-[Ir(C,N) 2(C',N')] was also not a clean reaction, with again a mixture of homo- and heteroleptic complexes acquired. An investigation into the thermal mer to fac isomerization of both homo- and heteroleptic tris-cyclometallated complexes is presented. It was found that the process is an alcohol-catalyzed reaction with the formation of an iridium alkoxide [Ir(C,N) 2OR] intermediate in the isomerization process. This catalyzed reaction can be carried out between 50 and 100 degrees C, the first such example of low-temperature mer-fac thermal isomerization. We have synthesized analogous complexes and have shown that they do indeed react so as to give fac-tris-cyclometallated products. A detailed explanation of the intermediates (and all of their stereoisomers, in particular when systems of the generic formula [M(a,b) 2(a',b')] are synthesized) formed in the mer to fac isomerization process is presented, including how the formed intermediates react further, and the stereoisomeric products they yield.

Flow-accelerated corrosion 2016 international conference

NASA Astrophysics Data System (ADS)

Tomarov, G. V.; Shipkov, A. A.

2017-05-01

The paper discusses materials and results of the most representative world forum on the problems of flow-accelerated metal corrosion in power engineering—Flow-Accelerated Corrosion (FAC) 2016, the international conference, which was held in Lille (France) from May 23 through May 27, 2016, sponsored by EdF-DTG with the support of the International Atomic Energy Agency (IAEA) and the World Association of Nuclear Operators (WANO). The information on major themes of reports and materials of the exhibition arranged within the framework of the congress is presented. The statistics on operation time and intensity of FAC wall thinning of NPP pipelines and equipment in the world is set out. The paper describes typical examples of flow-accelerated corrosion damage of condensate-feed and wet-steam pipeline components of nuclear and thermal power plants that caused forced shutdowns or accidents. The importance of research projects on the problem of flow-accelerated metal corrosion of nuclear power units coordinated by the IAEA with the participation of leading experts in this field from around the world is considered. The reports presented at the conference considered issues of implementation of an FAC mechanism in single- and two-phase flows, the impact of hydrodynamic and water-chemical factors, the chemical composition of the metal, and other parameters on the intensity and location of FAC wall thinning localized areas in pipeline components and power equipment. Features and patterns of local and general FAC leading to local metal thinning and contamination of the working environment with ferriferous compounds are considered. Main trends of modern practices preventing FAC wear of NPP pipelines and equipment are defined. An increasing role of computer codes for the assessment and prediction of FAC rate, as well as software systems of support of the NPP personnel for the inspection planning and prevention of FAC wall thinning of equipment operating in singleand two-phase flows, is accepted. Different lines of attack on the problem of FAC of pipelines and equipment components of existing and future nuclear power units are reviewed. Promising methods of nondestructive inspection of pipelines and equipment are presented.

Multigrid preconditioned conjugate-gradient method for large-scale wave-front reconstruction.

PubMed

Gilles, Luc; Vogel, Curtis R; Ellerbroek, Brent L

2002-09-01

We introduce a multigrid preconditioned conjugate-gradient (MGCG) iterative scheme for computing open-loop wave-front reconstructors for extreme adaptive optics systems. We present numerical simulations for a 17-m class telescope with n = 48756 sensor measurement grid points within the aperture, which indicate that our MGCG method has a rapid convergence rate for a wide range of subaperture average slope measurement signal-to-noise ratios. The total computational cost is of order n log n. Hence our scheme provides for fast wave-front simulation and control in large-scale adaptive optics systems.

Algebraic multigrid methods applied to problems in computational structural mechanics

NASA Technical Reports Server (NTRS)

Mccormick, Steve; Ruge, John

1989-01-01

The development of algebraic multigrid (AMG) methods and their application to certain problems in structural mechanics are described with emphasis on two- and three-dimensional linear elasticity equations and the 'jacket problems' (three-dimensional beam structures). Various possible extensions of AMG are also described. The basic idea of AMG is to develop the discretization sequence based on the target matrix and not the differential equation. Therefore, the matrix is analyzed for certain dependencies that permit the proper construction of coarser matrices and attendant transfer operators. In this manner, AMG appears to be adaptable to structural analysis applications.

Numerical boundary condition procedures and multigrid methods; Proceedings of the Symposium, NASA Ames Research Center, Moffett Field, CA, October 19-22, 1981

NASA Technical Reports Server (NTRS)

1982-01-01

Papers presented in this volume provide an overview of recent work on numerical boundary condition procedures and multigrid methods. The topics discussed include implicit boundary conditions for the solution of the parabolized Navier-Stokes equations for supersonic flows; far field boundary conditions for compressible flows; and influence of boundary approximations and conditions on finite-difference solutions. Papers are also presented on fully implicit shock tracking and on the stability of two-dimensional hyperbolic initial boundary value problems for explicit and implicit schemes.

A three dimensional multigrid multiblock multistage time stepping scheme for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Elmiligui, Alaa; Cannizzaro, Frank; Melson, N. D.

1991-01-01

A general multiblock method for the solution of the three-dimensional, unsteady, compressible, thin-layer Navier-Stokes equations has been developed. The convective and pressure terms are spatially discretized using Roe's flux differencing technique while the viscous terms are centrally differenced. An explicit Runge-Kutta method is used to advance the solution in time. Local time stepping, adaptive implicit residual smoothing, and the Full Approximation Storage (FAS) multigrid scheme are added to the explicit time stepping scheme to accelerate convergence to steady state. Results for three-dimensional test cases are presented and discussed.

An Overview of the Formation and Attitude Control System for the Terrestrial Planet Finder Formation Flying Interferometer

NASA Technical Reports Server (NTRS)

Scharf, Daniel P.; Hadaegh, Fred Y.; Rahman, Zahidul H.; Shields, Joel F.; Singh, Gurkipal

2004-01-01

The Terrestrial Planet Finder formation flying Interferometer (TPF-I) will be a five-spacecraft, precision formation operating near a Sun-Earth Lagrange point. As part of technology development for TPF-I, a formation and attitude control system (FACS) is being developed that achieves the precision and functionality associated with the TPF-I formation. This FACS will be demonstrated in a distributed, real-time simulation environment. In this paper we present an overview of the FACS and discuss in detail its constituent formation estimation, guidance and control architectures and algorithms. Since the FACS is currently being integrated into a high-fidelity simulation environment, component simulations demonstrating algorithm performance are presented.

Preconditioned conjugate gradient methods for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing

1994-01-01

A preconditioned Krylov subspace method (GMRES) is used to solve the linear systems of equations formed at each time-integration step of the unsteady, two-dimensional, compressible Navier-Stokes equations of fluid flow. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux-split formulation. Several preconditioning techniques are investigated to enhance the efficiency and convergence rate of the implicit solver based on the GMRES algorithm. The superiority of the new solver is established by comparisons with a conventional implicit solver, namely line Gauss-Seidel relaxation (LGSR). Computational test results for low-speed (incompressible flow over a backward-facing step at Mach 0.1), transonic flow (trailing edge flow in a transonic turbine cascade), and hypersonic flow (shock-on-shock interactions on a cylindrical leading edge at Mach 6.0) are presented. For the Mach 0.1 case, overall speedup factors of up to 17 (in terms of time-steps) and 15 (in terms of CPU time on a CRAY-YMP/8) are found in favor of the preconditioned GMRES solver, when compared with the LGSR solver. The corresponding speedup factors for the transonic flow case are 17 and 23, respectively. The hypersonic flow case shows slightly lower speedup factors of 9 and 13, respectively. The study of preconditioners conducted in this research reveals that a new LUSGS-type preconditioner is much more efficient than a conventional incomplete LU-type preconditioner.

A High-resolution Model of Field-aligned Currents Through Empirical Orthogonal Functions Analysis (MFACE)

NASA Technical Reports Server (NTRS)

He, Maosheng; Vogt, Joachim; Luehr, Hermann; Sorbalo, Eugen; Blagau, Adrian; Le, Guan; Lu, Gang

2012-01-01

Ten years of CHAMP magnetic field measurements are integrated into MFACE, a model of field-aligned currents (FACs) using empirical orthogonal functions (EOFs). EOF1 gives the basic Region-1/Region-2 pattern varying mainly with the interplanetary magnetic field Bz component. EOF2 captures separately the cusp current signature and By-related variability. Compared to existing models, MFACE yields significantly better spatial resolution, reproduces typically observed FAC thickness and intensity, improves on the magnetic local time (MLT) distribution, and gives the seasonal dependence of FAC latitudes and the NBZ current signature. MFACE further reveals systematic dependences on By, including 1) Region-1/Region-2 topology modifications around noon; 2) imbalance between upward and downward maximum current density; 3) MLT location of the Harang discontinuity. Furthermore, our procedure allows quantifying response times of FACs to solar wind driving at the bow shock nose: we obtain 20 minutes and 35-40 minutes lags for the FAC density and latitude, respectively.

The particle carriers of field-aligned currents in the Earth's magnetotail during a substorm

NASA Astrophysics Data System (ADS)

Cheng, Z. W.; Zhang, J. C.; Shi, J. K.; Kistler, L. M.; Dunlop, M.; Dandouras, I.; Fazakerley, A.

2016-04-01

Although the particle carriers of field-aligned currents (FACs) in the Earth's magnetotail play an important role in the transfer of momentum and energy between the solar wind, magnetosphere, and ionosphere, the characteristics of the FAC carriers have been poorly understood. Taking advantage of multiinstrument magnetic field and plasma data collected by the four spacecraft of the Cluster constellation as they traversed the northern plasma sheet boundary layer in the magnetotail on 14 September 2004, we identified the species type and energy range of the FAC carriers for the first time. The results indicate that part of tailward FACs is carried by energetic keV ions, which are probably originated from the ionosphere through outflow, and they are not too small (~2 nA/m2) to be ignored. The earthward (tailward) FACs are mainly carried by the dominant tailward (earthward) motion of electrons, and higher-energy electrons (from ~0.5 to 26 keV) are the main carriers.

Characterization of Intraocular Pressure Increases and Management Strategies Following Treatment With Fluocinolone Acetonide Intravitreal Implants in the FAME Trials.

PubMed

Parrish, Richard K; Campochiaro, Peter A; Pearson, P Andrew; Green, Ken; Traverso, Carlo E

2016-05-01

To compare elevated intraocular pressure (IOP) management and outcomes among patients with diabetic macular edema who received fluocinolone acetonide (FAc) implants versus sham-control treatment and explore the prior ocular steroid exposure impact on IOP outcomes. Best-corrected visual acuity (BCVA) was measured using Early Treatment Diabetic Retinopathy Study charts or electronic VA testers. Goldmann applanation tonometry was used to measure IOP. Elevated IOP was more common in FAc-versus sham control-treated patients. Medication, and less often trabeculoplasty or surgery, was used to lower IOP without affecting VA outcomes. No patient treated with 0.2 µg/day FAc who received prior ocular steroid required IOP-lowering surgery. Elevated IOP may occur following FAc implant receipt; however, in the present study, it was manageable and did not impact vision outcomes. Patients previously treated with ocular steroid did not require IOP-lowering surgery following 0.2 µg/day FAc implant administration. [Ophthalmic Surg Lasers Imaging Retina. 2016;47:426-435.]. Copyright 2016, SLACK Incorporated.

TMSOTf assisted synthesis of 2’-deoxy-2’-[18F]fluoro-β-D-arabinofuranosylcytosine ([18F]FAC)

PubMed Central

Humm, John L.; Larson, Steven M.; Pillarsetty, Naga Vara Kishore

2018-01-01

[18F]FAC (2’-deoxy-2’-[18F]fluoro-β-D-arabinofuranosylcytosine, 1) is a versatile probe for imaging deoxycytidine kinase (dCK) expression levels in vivo. dCK is responsible for phosphorylation of deoxycytidine (dC, 2) and other nucleoside analogs, plays a key role in immune activation and has demonstrated to be one of the key enzymes in activating nucleoside based drugs including gemcitabine. Reported synthesis of [18F]FAC is high yielding but is quite challenging requiring bromination using HBr and careful drying of excess HBr which is critical for successful synthesis. Here in we report a simplified trimethylsilyl trifluoromethanesulfonate (TMSOTf) assisted synthesis of [18F]FAC eliminating the need of bromination and drying. [18F]FAC (β-anomer) was synthesized with average isolated decay corrected yield of 10.59 + 4.2% (n = 6) with radiochemical purity of >98% and total synthesis time of 158 + 19 min. PMID:29715301

Water-quality trends for selected sites in the Boulder River and Tenmile Creek watersheds, Montana, based on data collected during water years 1997-2013

USGS Publications Warehouse

Sando, Steven K.; Clark, Melanie L.; Cleasby, Thomas E.; Barnhart, Elliott P.

2015-01-01

Trend results for sites in the Tenmile Creek watershed generally are more variable and difficult to interpret than for sites in the Boulder River watershed. Trend results for Tenmile Creek above City Diversion (site 11) and Minnehaha Creek near Rimini (site 12) for water years 2000–13 indicate decreasing trends in FACs of cadmium, copper, and zinc. The magnitudes of the decreasing trends in FACs of copper generally are moderate and statistically significant for sites 11 and 12. The magnitudes of the decreasing trends in FACs of cadmium and zinc for site 11 are minor to small and not statistically significant; however, the magnitudes for site 12 are moderate and statistically significant. In general, patterns in FACs for Tenmile Creek near Rimini (site 13) are not well represented by fitted trends within the short data collection period, which might indicate that the trend-analysis structure of the study is not appropriate for describing trends in FACs for site 13. The large decreasing trend in FACs of suspended sediment is the strongest indication of change in water quality during the short period of record for site 13; however, this trend is not statistically significant.

Cation-Dependent Light-Induced Halide Demixing in Hybrid Organic–Inorganic Perovskites

DOE PAGES

Sutter-Fella, Carolin M.; Ngo, Quynh P.; Cefarin, Nicola; ...

2018-04-30

Mixed cation metal halide perovskites with increased power conversion efficiency, negligible hysteresis, and improved long-term stability under illumination, moisture, and thermal stressing have emerged as promising compounds for photovoltaic and optoelectronic applications. In this paper, we shed light on photoinduced halide demixing using in situ photoluminescence spectroscopy and in situ synchrotron X-ray diffraction (XRD) to directly compare the evolution of composition and phase changes in CH(NH 2) 2CsPb-halide (FACsPb-) and CH 3NH 3Pb-halide (MAPb-) perovskites upon illumination, thereby providing insights into why FACs-perovskites are less prone to halide demixing than MA-perovskites. We find that halide demixing occurs in both materials.more » However, the I-rich domains formed during demixing accumulate strain in FACsPb-perovskites but readily relax in MA-perovskites. The accumulated strain energy is expected to act as a stabilizing force against halide demixing and may explain the higher Br composition threshold for demixing to occur in FACsPb-halides. In addition, we find that while halide demixing leads to a quenching of the high-energy photoluminescence emission from MA-perovskites, the emission is enhanced from FACs-perovskites. This behavior points to a reduction of nonradiative recombination centers in FACs-perovskites arising from the demixing process and buildup of strain. FACsPb-halide perovskites exhibit excellent intrinsic material properties with photoluminescence quantum yields that are comparable to MA-perovskites. Finally, because improved stability is achieved without sacrificing electronic properties, these compositions are better candidates for photovoltaic applications, especially as wide bandgap absorbers in tandem cells.« less

Seasonal and Temporal Variations of Field-Aligned Currents and Ground Magnetic Deflections During Substorms

NASA Astrophysics Data System (ADS)

Forsyth, C.; Shortt, M.; Coxon, J. C.; Rae, I. J.; Freeman, M. P.; Kalmoni, N. M. E.; Jackman, C. M.; Anderson, B. J.; Milan, S. E.; Burrell, A. G.

2018-04-01

Field-aligned currents (FACs), also known as Birkeland currents, are the agents by which energy and momentum are transferred to the ionosphere from the magnetosphere and solar wind. This coupling is enhanced at substorm onset through the formation of the substorm current wedge. Using FAC data from the Active Magnetosphere and Planetary Electrodynamics Response Experiment and substorm expansion phase onsets identified using the Substorm Onsets and Phases from Indices of the Electrojet technique, we examine the Northern Hemisphere FACs in all local time sectors with respect to substorm onset and subdivided by season. Our results show that while there is a strong seasonal dependence on the underlying FACs, the increase in FACs following substorm onset only varies by 10% with season, with substorms increasing the hemispheric FACs by 420 kA on average. Over an hour prior to substorm onset, the dayside currents in the postnoon quadrant increase linearly, whereas the nightside currents show a linear increase starting 20-30 min before onset. After onset, the nightside Region 1, Region 2, and nonlocally closed currents and the SuperMAG AL (SML) index follow the Weimer (1994, https://doi.org/10.1029/93JA02721) model with the same time constants in each season. These results contrast earlier contradictory studies that indicate that substorms are either longer in the summer or decay faster in the summer. Our results imply that, on average, substorm FACs do not change with season but that their relative impact on the coupled magnetosphere-ionosphere system does due to the changes in the underlying currents.

IMF By effects on ground magnetometer response to increased solar wind dynamic pressure derived from global MHD simulations

NASA Astrophysics Data System (ADS)

Ozturk, Dogacan Su; Zou, Shasha; Slavin, James A.

2017-05-01

During sudden solar wind dynamic pressure enhancements, the magnetosphere undergoes rapid compression resulting in a reconfiguration of the global current systems, most notably the field-aligned currents (FACs). Ground-based magnetometers are traditionally used to study such compression events. However, factors affecting the polarity and magnitude of the ground-based magnetic perturbations are still not well understood. In particular, interplanetary magnetic field (IMF) By is known to create significant asymmetries in the FAC patterns. We use the University of Michigan Block Adaptive Tree Roe Upwind Scheme (BATS'R'US) magnetohydrodynamic code to investigate the effects of IMF By on the global variations of ground magnetic perturbations during solar wind dynamic pressure enhancements. Using virtual magnetometers in three idealized simulations with varying IMF By, we find asymmetries in the peak amplitude and magnetic local time of the ground magnetic perturbations during the preliminary impulse (PI) and the main impulse (MI) phases. These asymmetries are especially evident at high-latitude ground magnetometer responses where the peak amplitudes differ by 50 nT at different locations. We show that the FACs related with the PI are due to magnetopause deformation, and the FACs related with the MI are generated by vortical flows within the magnetosphere, consistent with other simulation results. The perturbation FACs due to pressure enhancements and their magnetospheric sources do not differ much under different IMF By polarities. However, the conductance profile affected by the superposition of the preexisting FACs and the perturbation FACs including their closure currents is responsible for the magnitude and location asymmetries in the ground magnetic perturbations.

Cation-Dependent Light-Induced Halide Demixing in Hybrid Organic-Inorganic Perovskites.

PubMed

Sutter-Fella, Carolin M; Ngo, Quynh P; Cefarin, Nicola; Gardner, Kira L; Tamura, Nobumichi; Stan, Camelia V; Drisdell, Walter S; Javey, Ali; Toma, Francesca M; Sharp, Ian D

2018-06-13

Mixed cation metal halide perovskites with increased power conversion efficiency, negligible hysteresis, and improved long-term stability under illumination, moisture, and thermal stressing have emerged as promising compounds for photovoltaic and optoelectronic applications. Here, we shed light on photoinduced halide demixing using in situ photoluminescence spectroscopy and in situ synchrotron X-ray diffraction (XRD) to directly compare the evolution of composition and phase changes in CH(NH 2 ) 2 CsPb-halide (FACsPb-) and CH 3 NH 3 Pb-halide (MAPb-) perovskites upon illumination, thereby providing insights into why FACs-perovskites are less prone to halide demixing than MA-perovskites. We find that halide demixing occurs in both materials. However, the I-rich domains formed during demixing accumulate strain in FACsPb-perovskites but readily relax in MA-perovskites. The accumulated strain energy is expected to act as a stabilizing force against halide demixing and may explain the higher Br composition threshold for demixing to occur in FACsPb-halides. In addition, we find that while halide demixing leads to a quenching of the high-energy photoluminescence emission from MA-perovskites, the emission is enhanced from FACs-perovskites. This behavior points to a reduction of nonradiative recombination centers in FACs-perovskites arising from the demixing process and buildup of strain. FACsPb-halide perovskites exhibit excellent intrinsic material properties with photoluminescence quantum yields that are comparable to MA-perovskites. Because improved stability is achieved without sacrificing electronic properties, these compositions are better candidates for photovoltaic applications, especially as wide bandgap absorbers in tandem cells.

Long-term outcomes of phakic patients with diabetic macular oedema treated with intravitreal fluocinolone acetonide (FAc) implants.

PubMed

Yang, Y; Bailey, C; Holz, F G; Eter, N; Weber, M; Baker, C; Kiss, S; Menchini, U; Ruiz Moreno, J M; Dugel, P; Lotery, A

2015-09-01

Diabetic macular oedema (DMO) is a leading cause of blindness in working-age adults. Slow-release, nonbioerodible fluocinolone acetonide (FAc) implants have shown efficacy in the treatment of DMO; however, the National Institute for Health and Care Excellence recommends that FAc should be used in patients with chronic DMO considered insufficiently responsive to other available therapies only if the eye to be treated is pseudophakic. The goal of this analysis was to examine treatment outcomes in phakic patients who received 0.2 μg/day FAc implant. This analysis of the phase 3 FAME (Fluocinolone Acetonide in Diabetic Macular Edema) data examines the safety and efficacy of FAc implants in patients who underwent cataract extraction before (cataract before implant (CBI) group) or after (cataract after implant (CAI) group) receiving the implant. The data were further examined by DMO duration. Best corrected visual acuity (BCVA) after 36 months was comparable in the CAI and CBI groups. Both the percentage of patients gaining ≥ 3 lines of vision and mean change in BCVA letter score were numerically greater in the CAI group. In addition, most patients who underwent cataract surgery experienced a net gain in BCVA from presurgery baseline as well as from original study baseline. These data support the use of 0.2 μg/day FAc implants in phakic as well as in pseudophakic patients. These findings will serve as a pilot for design of future studies to evaluate the potential protective effect of FAc implants before cataract surgery in patients with DMO and cataract.

Cation-Dependent Light-Induced Halide Demixing in Hybrid Organic–Inorganic Perovskites

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sutter-Fella, Carolin M.; Ngo, Quynh P.; Cefarin, Nicola

Mixed cation metal halide perovskites with increased power conversion efficiency, negligible hysteresis, and improved long-term stability under illumination, moisture, and thermal stressing have emerged as promising compounds for photovoltaic and optoelectronic applications. In this paper, we shed light on photoinduced halide demixing using in situ photoluminescence spectroscopy and in situ synchrotron X-ray diffraction (XRD) to directly compare the evolution of composition and phase changes in CH(NH 2) 2CsPb-halide (FACsPb-) and CH 3NH 3Pb-halide (MAPb-) perovskites upon illumination, thereby providing insights into why FACs-perovskites are less prone to halide demixing than MA-perovskites. We find that halide demixing occurs in both materials.more » However, the I-rich domains formed during demixing accumulate strain in FACsPb-perovskites but readily relax in MA-perovskites. The accumulated strain energy is expected to act as a stabilizing force against halide demixing and may explain the higher Br composition threshold for demixing to occur in FACsPb-halides. In addition, we find that while halide demixing leads to a quenching of the high-energy photoluminescence emission from MA-perovskites, the emission is enhanced from FACs-perovskites. This behavior points to a reduction of nonradiative recombination centers in FACs-perovskites arising from the demixing process and buildup of strain. FACsPb-halide perovskites exhibit excellent intrinsic material properties with photoluminescence quantum yields that are comparable to MA-perovskites. Finally, because improved stability is achieved without sacrificing electronic properties, these compositions are better candidates for photovoltaic applications, especially as wide bandgap absorbers in tandem cells.« less

Spectroscopic Characterization of Aqua [ fac-Tc(CO)3]+ Complexes at High Ionic Strength.

PubMed

Chatterjee, Sayandev; Hall, Gabriel B; Engelhard, Mark H; Du, Yingge; Washton, Nancy M; Lukens, Wayne W; Lee, Sungsik; Pearce, Carolyn I; Levitskaia, Tatiana G

2018-06-18

Understanding fundamental Tc chemistry is important to both the remediation of nuclear waste and the reprocessing of nuclear fuel; however, current knowledge of the electronic structure and spectral signatures of low-valent Tc compounds significantly lags behind the remainder of the d-block elements. In particular, identification and treatment of Tc speciation in legacy nuclear waste is challenging due to the lack of reference data especially for Tc compounds in the less common oxidation states (I-VI). In an effort to establish a spectroscopic library corresponding to the relevant conditions of extremely high ionic strength typical for the legacy nuclear waste, compounds with the general formula of [ fac-Tc(CO) 3 (OH 2 ) 3- n (OH) n ] 1- n (where n = 0-3) were examined by a range of spectroscopic techniques including 99 Tc/ 13 C NMR, IR, XPS, and XAS. In the series of monomeric aqua species, stepwise hydrolysis results in the increase of the Tc metal center electron density and corresponding progressive decrease of the Tc-C bond distances, Tc electron binding energies, and carbonyl stretching frequencies in the order [ fac-Tc(CO) 3 (OH 2 ) 3 ] + > [ fac-Tc(CO) 3 (OH 2 ) 2 (OH)] > [ fac-Tc(CO) 3 (OH 2 )(OH) 2 ] - . These results correlate with established trends of the 99 Tc upfield chemical shift and carbonyl 13 C downfield chemical shift. The lone exception is [ fac-Tc(CO) 3 (OH)] 4 which exhibits a comparatively low electron density at the metal center attributed to the μ 3 -bridging nature of the - OH ligands causing less σ-donation and no π-donation. This work also reports the first observations of these compounds by XPS and [ fac-Tc(CO) 3 Cl 3 ] 2- by XAS. The unique and distinguishable spectral features of the aqua [ fac-Tc(CO) 3 ] + complexes lay the foundation for their identification in the complex aqueous matrixes.

Plant volatile eliciting FACs in lepidopteran caterpillars, fruit flies, and crickets: a convergent evolution or phylogenetic inheritance?

PubMed Central

Yoshinaga, Naoko; Abe, Hiroaki; Morita, Sayo; Yoshida, Tetsuya; Aboshi, Takako; Fukui, Masao; Tumlinson, James H.; Mori, Naoki

2013-01-01

Fatty acid amino acid conjugates (FACs), first identified in lepidopteran caterpillar spit as elicitors of plant volatile emission, also have been reported as major components in gut tracts of Drosophila melanogaster and cricket Teleogryllus taiwanemma. The profile of FAC analogs in these two insects was similar to that of tobacco hornworm Manduca sexta, showing glutamic acid conjugates predominantly over glutamine conjugates. The physiological function of FACs is presumably to enhance nitrogen assimilation in Spodoptera litura larvae, but in other insects it is totally unknown. Whether these insects share a common synthetic mechanism of FACs is also unclear. In this study, the biosynthesis of FACs was examined in vitro in five lepidopteran species (M. sexta, Cephonodes hylas, silkworm, S. litura, and Mythimna separata), fruit fly larvae and T. taiwanemma. The fresh midgut tissues of all of the tested insects showed the ability to synthesize glutamine conjugates in vitro when incubated with glutamine and sodium linolenate. Such direct conjugation was also observed for glutamic acid conjugates in all the insects but the product amount was very small and did not reflect the in vivo FAC patterns in each species. In fruit fly larvae, the predominance of glutamic acid conjugates could be explained by a shortage of substrate glutamine in midgut tissues, and in M. sexta, a rapid hydrolysis of glutamine conjugates has been reported. In crickets, we found an additional unique biosynthetic pathway for glutamic acid conjugates. T. taiwanemma converted glutamine conjugates to glutamic acid conjugates by deaminating the side chain of the glutamine moiety. Considering these findings together with previous results, a possibility that FACs in these insects are results of convergent evolution cannot be ruled out, but it is more likely that the ancestral insects had the glutamine conjugates and crickets and other insects developed glutamic acid conjugates in a different way. PMID:24744735

SuperSAGE analysis of the Nicotiana attenuata transcriptome after fatty acid-amino acid elicitation (FAC): identification of early mediators of insect responses

PubMed Central

2010-01-01

Background Plants trigger and tailor defense responses after perception of the oral secretions (OS) of attacking specialist lepidopteran larvae. Fatty acid-amino acid conjugates (FACs) in the OS of the Manduca sexta larvae are necessary and sufficient to elicit the herbivory-specific responses in Nicotiana attenuata, an annual wild tobacco species. How FACs are perceived and activate signal transduction mechanisms is unknown. Results We used SuperSAGE combined with 454 sequencing to quantify the early transcriptional changes elicited by the FAC N-linolenoyl-glutamic acid (18:3-Glu) and virus induced gene silencing (VIGS) to examine the function of candidate genes in the M. sexta-N. attenuata interaction. The analysis targeted mRNAs encoding regulatory components: rare transcripts with very rapid FAC-elicited kinetics (increases within 60 and declines within 120 min). From 12,744 unique Tag sequences identified (UniTags), 430 and 117 were significantly up- and down-regulated ≥ 2.5-fold, respectively, after 18:3-Glu elicitation compared to wounding. Based on gene ontology classification, more than 25% of the annotated UniTags corresponded to putative regulatory components, including 30 transcriptional regulators and 22 protein kinases. Quantitative PCR analysis was used to analyze the FAC-dependent regulation of a subset of 27 of these UniTags and for most of them a rapid and transient induction was confirmed. Six FAC-regulated genes were functionally characterized by VIGS and two, a putative lipid phosphate phosphatase (LPP) and a protein of unknown function, were identified as important mediators of the M. sexta-N. attenuata interaction. Conclusions The analysis of the early changes in the transcriptome of N. attenuata after FAC elicitation using SuperSAGE/454 has identified regulatory genes involved in insect-specific mediated responses in plants. Moreover, it has provided a foundation for the identification of additional novel regulators associated with this process. PMID:20398280

SuperSAGE analysis of the Nicotiana attenuata transcriptome after fatty acid-amino acid elicitation (FAC): identification of early mediators of insect responses.

PubMed

Gilardoni, Paola A; Schuck, Stefan; Jüngling, Ruth; Rotter, Björn; Baldwin, Ian T; Bonaventure, Gustavo

2010-04-14

Plants trigger and tailor defense responses after perception of the oral secretions (OS) of attacking specialist lepidopteran larvae. Fatty acid-amino acid conjugates (FACs) in the OS of the Manduca sexta larvae are necessary and sufficient to elicit the herbivory-specific responses in Nicotiana attenuata, an annual wild tobacco species. How FACs are perceived and activate signal transduction mechanisms is unknown. We used SuperSAGE combined with 454 sequencing to quantify the early transcriptional changes elicited by the FAC N-linolenoyl-glutamic acid (18:3-Glu) and virus induced gene silencing (VIGS) to examine the function of candidate genes in the M. sexta-N. attenuata interaction. The analysis targeted mRNAs encoding regulatory components: rare transcripts with very rapid FAC-elicited kinetics (increases within 60 and declines within 120 min). From 12,744 unique Tag sequences identified (UniTags), 430 and 117 were significantly up- and down-regulated >or= 2.5-fold, respectively, after 18:3-Glu elicitation compared to wounding. Based on gene ontology classification, more than 25% of the annotated UniTags corresponded to putative regulatory components, including 30 transcriptional regulators and 22 protein kinases. Quantitative PCR analysis was used to analyze the FAC-dependent regulation of a subset of 27 of these UniTags and for most of them a rapid and transient induction was confirmed. Six FAC-regulated genes were functionally characterized by VIGS and two, a putative lipid phosphate phosphatase (LPP) and a protein of unknown function, were identified as important mediators of the M. sexta-N. attenuata interaction. The analysis of the early changes in the transcriptome of N. attenuata after FAC elicitation using SuperSAGE/454 has identified regulatory genes involved in insect-specific mediated responses in plants. Moreover, it has provided a foundation for the identification of additional novel regulators associated with this process.

Activation of the manganese(I) tricarbonyl core by selective variation of bidentate ligands (L,L'-Bid = N,N' and N,O donor atom sets) in fac-[Mn(CO)3(L,L'-Bid)(CH3OH)](n) complexes.

PubMed

Twala, T N; Schutte-Smith, M; Roodt, A; Visser, H G

2015-02-21

A range of fac-[Mn(CO)3(L,L'-Bid)(H2O)](n) (L,L'-Bid = neutral or monoanionic bidentate ligands with varied L,L' donor atoms, N,N' and N,O, 1,10-phenanthroline, 2,2'-bipyridine, 2-picolinate, 2,4-quinolinate; n = 0, +1) has been synthesized and the methanol substitution has been investigated for the first time. The complexes were characterized by UV/vis, IR and NMR spectroscopy and X-ray crystallographic studies of the compounds fac-[Mn(CO)3(Bipy)(H2O)][CF3SO3] () and fac-[Mn(CO)3(Phen)(H2O)][CF3SO3] () are reported. A two order-of-magnitude of activation for the methanol substitution is induced as manifested by the second order rate constants with (N,N'-Bid) < (N,O-Bid). Forward and reverse rate and stability constants from slow and stopped-flow UV/vis measurements (k1, M(-1) s(-1); k-1, s(-1); K1, M(-1)) for pyridine as entering nucleophile are as follows: fac-[Mn(CO)3(Phen)(CH3OH)](+) (2.39 ± 5) × 10(-3), (1.5 ± 0.3) × 10(-5), 159 ± 32; fac-[Mn(CO)3(2,4-QuinH)(CH3OH)] (4.5 ± 0.2), (4 ± 1) × 10(-2), 113 ± 29. Activation parameters (ΔH, kJ mol(-1); ΔS, J K(-1) mol(-1)) from Eyring plots for entering nucleophiles as indicated are as follows: fac-[Mn(CO)3(Phen)(CH3OH)](+) (bromide ions) 66.7 ± 0.6, -27 ± 2; (pyridine) 80 ± 3, -25 ± 11; fac-[Mn(CO)3(Pico)(CH3OH)] (bromide ions) 68 ± 2, -24 ± 5. A dissociative interchange mechanism is proposed.

A Prospective Comparative Study of the Toxicity Profile of 5-Flurouracil, Adriamycin, Cyclophosphamide Regime VS Adriamycin, Paclitaxel Regime in Patients with Locally Advanced Breast Carcinoma

PubMed Central

Pillai, Pradeep Sadasivan; Jayakumar, Krishnan Nair Lalithamma

2015-01-01

Introduction A 5-flurouracil, Adriamycin, Cyclophosphamide (FAC) and Adriamycin, Paclitaxel (AT) are two popular chemotherapeutic regimens for treatment of breast carcinoma. The most time tested and popular regimen is FAC. It is extensively studied for efficacy and toxicity. But data regarding toxicity profile and efficacy of AT regimen is sparse. Aim To study the toxicity profile, severity of toxicities and clinical response rate of FAC and AT regimens in patients with locally advanced breast carcinoma. Materials and Methods A prospective observational study with 50 patients in each treatment arm. Study duration was 12 months from November 2012 to October 2013. Consecutive patients with locally advanced breast carcinoma receiving treatment with either FAC or AT regimen, satisfying inclusion criteria were enrolled into the study after getting informed written consent. Prior to initiation of treatment detailed medical history was taken from all patients. General clinical examination, examination of organ systems and local examination of breast lump were done. After each cycle of chemotherapy and after completion of treatment patients were interviewed and examined for clinical response and toxicities. Toxicities were graded with WHO toxicity grading criteria. All data were entered in a structured proforma. At least 50% reduction in tumour size was taken as adequate clinical response. Statistical Analysis Data was analysed using Chi-square test with help of Excel 2007 and SPSS-16 statistical software. Results Different pattern of toxicities were seen with FAC and AT regimens. Anaemia, thrombocytopenia, stomatitis, hyperpigmentation, photosensitivity and diarrhoea were more common with patients receiving FAC regimen. Leucopenia, peripheral neuropathy, myalgia, arthralgia, vomiting and injection site reactions were more common in AT regimen. Both FAC and AT regimens gave 100% clinical response. Conclusion FAC and AT regimens are equally efficacious but have different toxicity profiles. Patient’s predisposition to toxicities may govern the selection of a particular regime. PMID:26870703

18F-FAC PET selectively images hepatic infiltrating CD4 and CD8 T cells in a mouse model of autoimmune hepatitis.

PubMed

Salas, Jessica R; Chen, Bao Ying; Wong, Alicia; Cheng, Donghui; Van Arnam, John S; Witte, Owen N; Clark, Peter M

2018-04-26

Immune cell-mediated attack on the liver is a defining feature of autoimmune hepatitis and hepatic allograft rejection. Despite an assortment of diagnostic tools, invasive biopsies remain the only method for identifying immune cells in the liver. We evaluated whether PET imaging with radiotracers that quantify immune activation ( 18 F-FDG and 18 F-FAC) and hepatocyte biology ( 18 F-DFA) can visualize and quantify hepatic infiltrating immune cells and hepatocyte inflammation, respectively, in a preclinical model of autoimmune hepatitis. Methods: Mice treated with Concanavalin A (ConA) to induce a model of autoimmune hepatitis or vehicle were imaged with 18 F-FDG, 18 F-FAC, and 18 F-DFA PET. Immunohistochemistry, digital autoradiography, and ex vivo accumulation assays were used to localize areas of altered radiotracer accumulation in the liver. For comparison, mice treated with an adenovirus to induce a viral hepatitis or vehicle were imaged with 18 F-FDG, 18 F-FAC, and 18 F-DFA PET. 18 F-FAC PET was performed on mice treated with ConA, and vehicle or dexamethasone. Biopsy samples of patients suffering from autoimmune hepatitis were immunostained for deoxycytidine kinase (dCK). Results: Hepatic accumulation of 18 F-FDG and 18 F-FAC was 173% and 61% higher, respectively, and hepatic accumulation of 18 F-DFA was 41% lower in a mouse model of autoimmune hepatitis compared to control mice. Increased hepatic 18 F-FDG accumulation was localized to infiltrating leukocytes and inflamed sinusoidal endothelial cells, increased hepatic 18 F-FAC accumulation was concentrated in infiltrating CD4 and CD8 cells, and decreased hepatic 18 F-DFA accumulation was apparent in hepatocytes throughout the liver. In contrast, viral hepatitis increased hepatic 18 F-FDG accumulation by 109% and decreased hepatic 18 F-DFA accumulation by 20% but had no effect on hepatic 18 F-FAC accumulation (non-significant 2% decrease). 18 F-FAC PET provided a non-invasive biomarker of the efficacy of dexamethasone for treating the autoimmune hepatitis model. Infiltrating leukocytes in liver biopsy samples from patients suffering from autoimmune hepatitis express high levels of dCK, a rate-limiting enzyme in the accumulation of 18 F-FAC. Conclusion: Our data suggests that PET can be used to non-invasively visualize activated leukocytes and inflamed hepatocytes in a mouse model of autoimmune hepatitis. Copyright © 2018 by the Society of Nuclear Medicine and Molecular Imaging, Inc.

Electrodynamic parameters in the nighttime sector during auroral substorms

NASA Technical Reports Server (NTRS)

Fujii, R.; Hoffman, R. A.; Anderson, P. C.; Craven, J. D.; Sugiura, M.; Frank, L. A.; Maynard, N. C.

1994-01-01

The characteristics of the large-scale electrodynamic parameters, field-aligned currents (FACs), electric fields, and electron precipitation, which are associated with auroral substorm events in the nighttime sector, have been obtained through a unique analysis which places the ionospheric measurements of these parameters into the context of a generic substorm determined from global auroral images. A generic bulge-type auroral emission region has been deduced from auroral images taken by the Dynamics Explorer 1 (DE 1) satellite during a number of isolated substorms, and the form has been divided into six sectors, based on the peculiar emission characteristics in each sector: west of bulge, surge horn, surge, middle surge, eastern bulge, and east of bulge. By comparing the location of passes of the Dynamics Explorer 2 (DE 2) satellite to the simultaneously obtained auroral images, each pass is placed onto the generic aurora. The organization of DE 2 data in this way has systematically clarified peculiar characteristics in the electrodynamic parameters. An upward net current mainly appears in the surge, with little net current in the surge horn and the west of bulge. The downward net current is distributed over wide longitudinal regions from the eastern bulge to the east of bulge. Near the poleward boundary of the expanding auroral bulge, a pair of oppositely directed FAC sheets is observed, with the downward FAC on the poleward side. This downward FAC and most of the upward FAC in the surge and the middle surge are assoc iated with narrow, intense antisunwqard convection, corresponding to an equatorward directed spikelike electric field. This pair of currents decreases in amplitude and latitudinal width toward dusk in the surge and the west of bulge, and the region 1 and 2 FACs become embedded in the sunward convection region. The upward FAC region associated with the spikelike field on the poleward edge of the bulge coincides well with intense electron precipitation and aurora appearing in this western and poleward protion of the bulge. The convection reversal is sharp in the west of bulge and surge horn sectors, and near the high-latitude boundary of the upward region 1, with a near stagnation region often extending over a large interval of latitude. In the eastern bulge and east of bulge sectors, the region 1 and 2 FACs are located in the sunward convection region, while a spikelike electric field occasionally appears poleward of the aurora but usually not associated with a pair of FAC sheets. In the eastern bulge, magnetic field data show complicated FAC distributions which correspond to current segments and filamentary currents.