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.
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.
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.
Unstructured multigrid through agglomeration
NASA Technical Reports Server (NTRS)
Venkatakrishnan, V.; Mavriplis, D. J.; Berger, M. J.
1993-01-01
In this work the compressible Euler equations are solved using finite volume techniques on unstructured grids. The spatial discretization employs a central difference approximation augmented by dissipative terms. Temporal discretization is done using a multistage Runge-Kutta scheme. A multigrid technique is used to accelerate convergence to steady state. The coarse grids are derived directly from the given fine grid through agglomeration of the control volumes. This agglomeration is accomplished by using a greedy-type algorithm and is done in such a way that the load, which is proportional to the number of edges, goes down by nearly a factor of 4 when moving from a fine to a coarse grid. The agglomeration algorithm has been implemented and the grids have been tested in a multigrid code. An area-weighted restriction is applied when moving from fine to coarse grids while a trivial injection is used for prolongation. Across a range of geometries and flows, it is shown that the agglomeration multigrid scheme compares very favorably with an unstructured multigrid algorithm that makes use of independent coarse meshes, both in terms of convergence and elapsed times.
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.
NASA Astrophysics Data System (ADS)
Langer, Stefan
2014-11-01
For unstructured finite volume methods an agglomeration multigrid with an implicit multistage Runge-Kutta method as a smoother is developed for solving the compressible Reynolds averaged Navier-Stokes (RANS) equations. The implicit Runge-Kutta method is interpreted as a preconditioned explicit Runge-Kutta method. The construction of the preconditioner is based on an approximate derivative. The linear systems are solved approximately with a symmetric Gauss-Seidel method. To significantly improve this solution method grid anisotropy is treated within the Gauss-Seidel iteration in such a way that the strong couplings in the linear system are resolved by tridiagonal systems constructed along these directions of strong coupling. The agglomeration strategy is adapted to this procedure by taking into account exactly these anisotropies in such a way that a directional coarsening is applied along these directions of strong coupling. Turbulence effects are included by a Spalart-Allmaras model, and the additional transport-type equation is approximately solved in a loosely coupled manner with the same method. For two-dimensional and three-dimensional numerical examples and a variety of differently generated meshes we show the wide range of applicability of the solution method. Finally, we exploit the GMRES method to determine approximate spectral information of the linearized RANS equations. This approximate spectral information is used to discuss and compare characteristics of multistage Runge-Kutta methods.
Agglomeration multigrid for viscous turbulent flows
NASA Technical Reports Server (NTRS)
Mavriplis, D. J.; Venkatakrishnan, V.
1994-01-01
Agglomeration multigrid, which has been demonstrated as an efficient and automatic technique for the solution of the Euler equations on unstructured meshes, is extended to viscous turbulent flows. For diffusion terms, coarse grid discretizations are not possible, and more accurate grid transfer operators are required as well. A Galerkin coarse grid operator construction and an implicit prolongation operator are proposed. Their suitability is evaluated by examining their effect on the solution of Laplace's equation. The resulting strategy is employed to solve the Reynolds-averaged Navier-Stokes equations for aerodynamic flows. Convergence rates comparable to those obtained by a previously developed non-nested mesh multigrid approach are demonstrated, and suggestions for further improvements are given.
Agglomeration multigrid for the three-dimensional Euler equations
NASA Technical Reports Server (NTRS)
Venkatakrishnan, V.; Mavriplis, D. J.
1994-01-01
A multigrid procedure that makes use of coarse grids generated by the agglomeration of control volumes is advocated as a practical approach for solving the three dimensional Euler equations on unstructured grids about complex configurations. It is shown that the agglomeration procedure can be tailored to achieve certain coarse grid properties such as the sizes of the coarse grids and aspect ratios of the coarse grid cells. The agglomeration is done as a preprocessing step and runs in linear time. The implications for multigrid of using arbitrary polyhedral coarse grids are discussed. The agglomeration multigrid technique compares very favorably with existing multigrid procedures both in terms of convergence rates and elapsed times. The main advantage of the present approach is the ease with which coarse grids of any desired degree of coarseness may be generated in three dimensions, without being constrained by considerations of geometry. Inviscid flows over a variety of complex configurations are computed using the agglomeration multigrid strategy.
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.
Adaptive Algebraic Multigrid Methods
Brezina, M; Falgout, R; MacLachlan, S; Manteuffel, T; McCormick, S; Ruge, J
2004-04-09
Our ability to simulate physical processes numerically is constrained by our ability to solve the resulting linear systems, prompting substantial research into the development of multiscale iterative methods capable of solving these linear systems with an optimal amount of effort. Overcoming the limitations of geometric multigrid methods to simple geometries and differential equations, algebraic multigrid methods construct the multigrid hierarchy based only on the given matrix. While this allows for efficient black-box solution of the linear systems associated with discretizations of many elliptic differential equations, it also results in a lack of robustness due to assumptions made on the near-null spaces of these matrices. This paper introduces an extension to algebraic multigrid methods that removes the need to make such assumptions by utilizing an adaptive process. The principles which guide the adaptivity are highlighted, as well as their application to algebraic multigrid solution of certain symmetric positive-definite linear systems.
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.
NASA Technical Reports Server (NTRS)
Marvriplis, D. J.; Venkatakrishnan, V.
1995-01-01
An agglomeration multigrid strategy is developed and implemented for the solution of three-dimensional steady viscous flows. The method enables convergence acceleration with minimal additional memory overheads, and is completely automated, in that it can deal with grids of arbitrary construction. The multigrid technique is validated by comparing the delivered convergence rates with those obtained by a previously developed overset-mesh multigrid approach, and by demonstrating grid independent convergence rates for aerodynamic problems on very large grids. Prospects for further increases in multigrid efficiency for high-Reynolds number viscous flows on highly stretched meshes are discussed.
Multigrid contact detection method
NASA Astrophysics Data System (ADS)
He, Kejing; Dong, Shoubin; Zhou, Zhaoyao
2007-03-01
Contact detection is a general problem of many physical simulations. This work presents a O(N) multigrid method for general contact detection problems (MGCD). The multigrid idea is integrated with contact detection problems. Both the time complexity and memory consumption of the MGCD are O(N) . Unlike other methods, whose efficiencies are influenced strongly by the object size distribution, the performance of MGCD is insensitive to the object size distribution. We compare the MGCD with the no binary search (NBS) method and the multilevel boxing method in three dimensions for both time complexity and memory consumption. For objects with similar size, the MGCD is as good as the NBS method, both of which outperform the multilevel boxing method regarding memory consumption. For objects with diverse size, the MGCD outperform both the NBS method and the multilevel boxing method. We use the MGCD to solve the contact detection problem for a granular simulation system based on the discrete element method. From this granular simulation, we get the density property of monosize packing and binary packing with size ratio equal to 10. The packing density for monosize particles is 0.636. For binary packing with size ratio equal to 10, when the number of small particles is 300 times as the number of big particles, the maximal packing density 0.824 is achieved.
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.
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.
Multigrid methods for isogeometric discretization.
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 [Formula: see text], whereas for three dimensions, only the constant coefficient problem in a unit cube is considered. The numerical results are complete up to polynomial order [Formula: see text], and for [Formula: see text] and [Formula: see text] smoothness. PMID:24511168
Multigrid methods for isogeometric discretization
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
Some Aspects of Multigrid Methods on Non-Structured Meshes
NASA Technical Reports Server (NTRS)
Guillard, H.; Marco, N.
1996-01-01
To solve a given fine mesh problem, the design of a multigrid method requires the definition of coarse levels, associated coarse grid operators and inter-grid transfer operators. For non-structured simplified meshes, these definitions can rely on the use of non-nested triangulations. These definitions can also be founded on agglomeration/aggregation techniques in a purely algebraic manner. This paper analyzes these two options, shows the connections of the volume-agglomeration method with algebraic methods and proposes a new definition of prolongation operator suitable for the application of the volume-agglomeration method to elliptic problems.
Parallel Element Agglomeration Algebraic Multigrid and Upscaling Library
2015-02-19
ParFELAG is a parallel distributed memory C++ library for numerical upscaling of finite element discretizations. It provides optimal complesity algorithms ro 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 mesh (under the assumption that the topology of the agglomerated entities is correct). Additionally, a novel multilevel solver for saddle point problems with divergence constraint is implemented.
The multigrid preconditioned conjugate gradient method
NASA Technical Reports Server (NTRS)
Tatebe, Osamu
1993-01-01
A multigrid preconditioned conjugate gradient method (MGCG method), which uses the multigrid method as a preconditioner of the PCG method, is proposed. The multigrid method has inherent high parallelism and improves convergence of long wavelength components, which is important in iterative methods. By using this method as a preconditioner of the PCG method, an efficient method with high parallelism and fast convergence is obtained. First, it is considered a necessary condition of the multigrid preconditioner in order to satisfy requirements of a preconditioner of the PCG method. Next numerical experiments show a behavior of the MGCG method and that the MGCG method is superior to both the ICCG method and the multigrid method in point of fast convergence and high parallelism. This fast convergence is understood in terms of the eigenvalue analysis of the preconditioned matrix. From this observation of the multigrid preconditioner, it is realized that the MGCG method converges in very few iterations and the multigrid preconditioner is a desirable preconditioner of the conjugate gradient method.
Fuel agglomerates and method of agglomeration
Wen, Wu-Wey
1986-01-01
Solid fuel agglomerates are prepared of particulate coal or other carbonaceous material with a binder having a high humic acid or humate salt content. The humic acid is extracted from oxidized carbonaceous material with a mild aqueous alkali solution of, for instance, ammonia. The particulate material is blended with the extract which serves as the binder for the agglomerates. The water-resistant agglomerates are formed such as by pelletizing, followed by drying to remove moisture and solidify the humic acid binder throughout the agglomerate.
A Parallel Multigrid Method for Neutronics Applications
Alcouffe, Raymond E.
2001-01-01
The multigrid method has been shown to be the most effective general method for solving the multi-dimensional diffusion equation encountered in neutronics. This being the method of choice, we develop a strategy for implementing the multigrid method on computers of massively parallel architecture. This leads us to strategies for parallelizing the relaxation, contraction (interpolation), and prolongation operators involved in the method. We then compare the efficiency of our parallel multigrid with other parallel methods for solving the diffusion equation on selected problems encountered in reactor physics.
Report on the Copper Mountain Conference on Multigrid Methods
2001-04-06
OAK B188 Report on the Copper Mountain Conference on Multigrid Methods. The Copper Mountain Conference on Multigrid Methods was held on April 11-16, 1999. Over 100 mathematicians from all over the world attended the meeting. The conference had two major themes: algebraic multigrid and parallel multigrid. During the five day meeting 69 talks on current research topics were presented as well as 3 tutorials. Talks with similar content were organized into sessions. Session topics included: Fluids; Multigrid and Multilevel Methods; Applications; PDE Reformulation; Inverse Problems; Special Methods; Decomposition Methods; Student Paper Winners; Parallel Multigrid; Parallel Algebraic Multigrid; and FOSLS.
Extending the applicability of multigrid methods
Brannick, J; Brezina, M; Falgout, R; Manteuffel, T; McCormick, S; Ruge, J; Sheehan, B; Xu, J; Zikatanov, L
2006-09-25
Multigrid methods are ideal for solving the increasingly large-scale problems that arise in numerical simulations of physical phenomena because of their potential for computational costs and memory requirements that scale linearly with the degrees of freedom. Unfortunately, they have been historically limited by their applicability to elliptic-type problems and the need for special handling in their implementation. In this paper, we present an overview of several recent theoretical and algorithmic advances made by the TOPS multigrid partners and their collaborators in extending applicability of multigrid methods. Specific examples that are presented include quantum chromodynamics, radiation transport, and electromagnetics.
A multigrid method for the Euler equations
NASA Technical Reports Server (NTRS)
Jespersen, D. C.
1983-01-01
A multigrid algorithm has been developed for the numerical solution of the steady two-dimensional Euler equations. Flux vector splitting and one-sided differencing are employed to define the spatial discretization. Newton's method is used to solve the nonlinear equations, and a multigrid solver is used on each linear problem. The relaxation scheme for the linear problems is symmetric Gauss-Seidel. Standard restriction and interpolation operators are employed. Local mode analysis is used to predict the convergence rate of the multigrid process on the linear problems. Computed results for transonic flows over airfoils are presented.
A multigrid method for variational inequalities
Oliveira, S.; Stewart, D.E.; Wu, W.
1996-12-31
Multigrid methods have been used with great success for solving elliptic partial differential equations. Penalty methods have been successful in solving finite-dimensional quadratic programs. In this paper these two techniques are combined to give a fast method for solving obstacle problems. A nonlinear penalized problem is solved using Newton`s method for large values of a penalty parameter. Multigrid methods are used to solve the linear systems in Newton`s method. The overall numerical method developed is based on an exterior penalty function, and numerical results showing the performance of the method have been obtained.
Multigrid methods with applications to reservoir simulation
Xiao, Shengyou
1994-05-01
Multigrid methods are studied for solving elliptic partial differential equations. Focus is on parallel multigrid methods and their use for reservoir simulation. Multicolor Fourier analysis is used to analyze the behavior of standard multigrid methods for problems in one and two dimensions. Relation between multicolor and standard Fourier analysis is established. Multiple coarse grid methods for solving model problems in 1 and 2 dimensions are considered; at each coarse grid level we use more than one coarse grid to improve convergence. For a given Dirichlet problem, a related extended problem is first constructed; a purification procedure can be used to obtain Moore-Penrose solutions of the singular systems encountered. For solving anisotropic equations, semicoarsening and line smoothing techniques are used with multiple coarse grid methods to improve convergence. Two-level convergence factors are estimated using multicolor. In the case where each operator has the same stencil on each grid point on one level, exact multilevel convergence factors can be obtained. For solving partial differential equations with discontinuous coefficients, interpolation and restriction operators should include information about the equation coefficients. Matrix-dependent interpolation and restriction operators based on the Schur complement can be used in nonsymmetric cases. A semicoarsening multigrid solver with these operators is used in UTCOMP, a 3-D, multiphase, multicomponent, compositional reservoir simulator. The numerical experiments are carried out on different computing systems. Results indicate that the multigrid methods are promising.
Spectral multigrid methods for elliptic equations
NASA Technical Reports Server (NTRS)
Zang, T. A.; Wong, Y. S.; Hussaini, M. Y.
1981-01-01
An alternative approach which employs multigrid concepts in the iterative solution of spectral equations was examined. Spectral multigrid methods are described for self adjoint elliptic equations with either periodic or Dirichlet boundary conditions. For realistic fluid calculations the relevant boundary conditions are periodic in at least one (angular) coordinate and Dirichlet (or Neumann) in the remaining coordinates. Spectral methods are always effective for flows in strictly rectangular geometries since corners generally introduce singularities into the solution. If the boundary is smooth, then mapping techniques are used to transform the problem into one with a combination of periodic and Dirichlet boundary conditions. It is suggested that spectral multigrid methods in these geometries can be devised by combining the techniques.
Multigrid Methods for Nonlinear Problems: An Overview
Henson, V E
2002-12-23
Since their early application to elliptic partial differential equations, multigrid methods have been applied successfully to a large and growing class of problems, from elasticity and computational fluid dynamics to geodetics and molecular structures. Classical multigrid begins with a two-grid process. First, iterative relaxation is applied, whose effect is to smooth the error. Then a coarse-grid correction is applied, in which the smooth error is determined on a coarser grid. This error is interpolated to the fine grid and used to correct the fine-grid approximation. Applying this method recursively to solve the coarse-grid problem leads to multigrid. The coarse-grid correction works because the residual equation is linear. But this is not the case for nonlinear problems, and different strategies must be employed. In this presentation we describe how to apply multigrid to nonlinear problems. There are two basic approaches. The first is to apply a linearization scheme, such as the Newton's method, and to employ multigrid for the solution of the Jacobian system in each iteration. The second is to apply multigrid directly to the nonlinear problem by employing the so-called Full Approximation Scheme (FAS). In FAS a nonlinear iteration is applied to smooth the error. The full equation is solved on the coarse grid, after which the coarse-grid error is extracted from the solution. This correction is then interpolated and applied to the fine grid approximation. We describe these methods in detail, and present numerical experiments that indicate the efficacy of them.
Spectral multigrid methods for elliptic equations II
NASA Technical Reports Server (NTRS)
Zang, T. A.; Wong, Y. S.; Hussaini, M. Y.
1984-01-01
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.
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.
Relaxation schemes for Chebyshev spectral multigrid methods
NASA Technical Reports Server (NTRS)
Kang, Yimin; Fulton, Scott R.
1993-01-01
Two relaxation schemes for Chebyshev spectral multigrid methods are presented for elliptic equations with Dirichlet boundary conditions. The first scheme is a pointwise-preconditioned Richardson relaxation scheme and the second is a line relaxation scheme. The line relaxation scheme provides an efficient and relatively simple approach for solving two-dimensional spectral equations. Numerical examples and comparisons with other methods are given.
Acoustic agglomeration methods and apparatus
NASA Technical Reports Server (NTRS)
Barmatz, M. B. (Inventor)
1984-01-01
Methods are described for using acoustic energy to agglomerate fine particles on the order of one micron diameter that are suspended in gas, to provide agglomerates large enough for efficient removal by other techniques. The gas with suspended particles, is passed through the length of a chamber while acoustic energy at a resonant chamber mode is applied to set up one or more acoustic standing wave patterns that vibrate the suspended particles to bring them together so they agglomerate. Several widely different frequencies can be applied to efficiently vibrate particles of widely differing sizes. The standing wave pattern can be applied along directions transversed to the flow of the gas. The particles can be made to move in circles by applying acoustic energy in perpendicular directions with the energy in both directions being of the same wavelength but 90 deg out of phase.
Multigrid Methods for Mesh Relaxation
O'Brien, M J
2006-06-12
When generating a mesh for the initial conditions for a computer simulation, you want the mesh to be as smooth as possible. A common practice is to use equipotential mesh relaxation to smooth out a distorted computational mesh. Typically a Laplace-like equation is set up for the mesh coordinates and then one or more Jacobi iterations are performed to relax the mesh. As the zone count gets really large, the Jacobi iteration becomes less and less effective and we are stuck with our original unrelaxed mesh. This type of iteration can only damp high frequency errors and the smooth errors remain. When the zone count is large, almost everything looks smooth so relaxation cannot solve the problem. In this paper we examine a multigrid technique which effectively smooths out the mesh, independent of the number of zones.
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)
Grandchild of the frequency: Decomposition multigrid method
Dendy, J.E. Jr.; Tazartes, C.C.
1994-12-31
Previously the authors considered the frequency decomposition multigrid method and rejected it because it was not robust for problems with discontinuous coefficients. In this paper they show how to modify the method so as to obtain such robustness while retaining robustness for problems with anisotropic coefficients. They also discuss application of this method to a problem arising in global ocean modeling on the CM-5.
On Some Versions of the Element Agglomeration AMGe Method
Lashuk, I; Vassilevski, P
2007-08-09
The present paper deals with element-based AMG methods that target linear systems of equations coming from finite element discretizations of elliptic PDEs. The individual element information (element matrices and element topology) is the main input to construct the AMG hierarchy. We study a number of variants of the spectral agglomerate element based AMG method. The core of the algorithms relies on element agglomeration utilizing the element topology (built recursively from fine to coarse levels). The actual selection of the coarse degrees of freedom (dofs) is based on solving large number of local eigenvalue problems. Additionally, we investigate strategies for adaptive AMG as well as multigrid cycles that are more expensive than the V-cycle utilizing simple interpolation matrices and nested conjugate gradient (CG) based recursive calls between the levels. The presented algorithms are illustrated with an extensive set of experiments based on a matlab implementation of the methods.
The multigrid method: Fast relaxation
NASA Technical Reports Server (NTRS)
South, J. C., Jr.; Brandt, A.
1976-01-01
A multi-level grid method was studied as a possible means of accelerating convergence in relaxation calculations for transonic flows. The method employs a hierarchy of grids, ranging from very coarse (e.g. 4 x 2 mesh cells) to fine (e.g. 64 x 32); the coarser grids are used to diminish the magnitude of the smooth part of the residuals, hopefully with far less total work than would be required with optimal iterations on the finest grid. To date the method was applied quite successfully to the solution of the transonic small-disturbance equation for the velocity potential in conservation form. Nonlifting transonic flow past a parabolic arc airfoil is the example studied, with meshes of both constant and variable step size.
Implementing abstract multigrid or multilevel methods
NASA Technical Reports Server (NTRS)
Douglas, Craig C.
1993-01-01
Multigrid methods can be formulated as an algorithm for an abstract problem that is independent of the partial differential equation, domain, and discretization method. In such an abstract setting, problems not arising from partial differential equations can be treated. A general theory exists for linear problems. The general theory was motivated by a series of abstract solvers (Madpack). The latest version was motivated by the theory. Madpack now allows for a wide variety of iterative and direct solvers, preconditioners, and interpolation and projection schemes, including user callback ones. It allows for sparse, dense, and stencil matrices. Mildly nonlinear problems can be handled. Also, there is a fast, multigrid Poisson solver (two and three dimensions). The type of solvers and design decisions (including language, data structures, external library support, and callbacks) are discussed. Based on the author's experiences with two versions of Madpack, a better approach is proposed. This is based on a mixed language formulation (C and FORTRAN + preprocessor). Reasons for not using FORTRAN, C, or C++ (individually) are given. Implementing the proposed strategy is not difficult.
Lecture Notes on Multigrid Methods
Vassilevski, P S
2010-06-28
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-vector 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.
Vandewalle, S.
1994-12-31
Time-stepping methods for parabolic partial differential equations are essentially sequential. This prohibits the use of massively parallel computers unless the problem on each time-level is very large. This observation has led to the development of algorithms that operate on more than one time-level simultaneously; that is to say, on grids extending in space and in time. The so-called parabolic multigrid methods solve the time-dependent parabolic PDE as if it were a stationary PDE discretized on a space-time grid. The author has investigated the use of multigrid waveform relaxation, an algorithm developed by Lubich and Ostermann. The algorithm is based on a multigrid acceleration of waveform relaxation, a highly concurrent technique for solving large systems of ordinary differential equations. Another method of this class is the time-parallel multigrid method. This method was developed by Hackbusch and was recently subject of further study by Horton. It extends the elliptic multigrid idea to the set of equations that is derived by discretizing a parabolic problem in space and in time.
Semi-coarsening multigrid methods for parallel computing
Jones, J.E.
1996-12-31
Standard multigrid methods are not well suited for problems with anisotropic coefficients which can occur, for example, on grids that are stretched to resolve a boundary layer. There are several different modifications of the standard multigrid algorithm that yield efficient methods for anisotropic problems. In the paper, we investigate the parallel performance of these multigrid algorithms. Multigrid algorithms which work well for anisotropic problems are based on line relaxation and/or semi-coarsening. In semi-coarsening multigrid algorithms a grid is coarsened in only one of the coordinate directions unlike standard or full-coarsening multigrid algorithms where a grid is coarsened in each of the coordinate directions. When both semi-coarsening and line relaxation are used, the resulting multigrid algorithm is robust and automatic in that it requires no knowledge of the nature of the anisotropy. This is the basic multigrid algorithm whose parallel performance we investigate in the paper. The algorithm is currently being implemented on an IBM SP2 and its performance is being analyzed. In addition to looking at the parallel performance of the basic semi-coarsening algorithm, we present algorithmic modifications with potentially better parallel efficiency. One modification reduces the amount of computational work done in relaxation at the expense of using multiple coarse grids. This modification is also being implemented with the aim of comparing its performance to that of the basic semi-coarsening algorithm.
Preconditioners for the spectral multigrid method
NASA Technical Reports Server (NTRS)
Phillips, T. N.; Zang, T. A.; Hussaini, M. Y.
1983-01-01
The systems of algebraic equations which arise from spectral discretizations of elliptic equations are full and direct solutions of them are rarely feasible. Iterative methods are an attractive alternative because Fourier transform techniques enable the discrete matrix-vector products to be computed with nearly the same efficiency as is possible for corresponding but sparse finite difference discretizations. For realistic Dirichlet problems preconditioning is essential for acceptable convergence rates. A brief description of Chebyshev spectral approximations and spectral multigrid methods for elliptic problems is given. A survey of preconditioners for Dirichlet problems based on second-order finite difference methods is made. New preconditioning techniques based on higher order finite differences and on the spectral matrix itself are presented. The preconditioners are analyzed in terms of their spectra and numerical examples are presented.
Preconditioners for the spectral multigrid method
NASA Technical Reports Server (NTRS)
Phillips, T. N.; Hussaini, M. Y.; Zang, T. A.
1986-01-01
The systems of algebraic equations which arise from spectral discretizations of elliptic equations are full and direct solutions of them are rarely feasible. Iterative methods are an attractive alternative because Fourier transform techniques enable the discrete matrix-vector products to be computed with nearly the same efficiency as is possible for corresponding but sparse finite difference discretizations. For realistic Dirichlet problem preconditioning is essential for acceptable convergence rates. A brief description of Chebyshev spectral approximations and spectral multigrid methods for elliptic problems is given. A survey of preconditioners for Dirichlet problems based on second-order finite difference methods is made. New preconditioning techniques based on higher order finite differences and on the spectral matrix itself are presented. The preconditioners are analyzed in terms of their spectra and numerical examples are presented.
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.
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.
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.
Spectral multigrid methods with applications to transonic potential flow
NASA Technical Reports Server (NTRS)
Streett, C. L.; Zang, T. A.; Hussaini, M. Y.
1983-01-01
Spectral multigrid methods are demonstrated to be a competitive technique for solving the transonic potential flow equation. The spectral discretization, the relaxation scheme, and the multigrid techniques are described in detail. Significant departures from current approaches are first illustrated on several linear problems. The principal applications and examples, however, are for compressible potential flow. These examples include the relatively challenging case of supercritical flow over a lifting airfoil.
Spectral multigrid methods with applications to transonic potential flow
NASA Technical Reports Server (NTRS)
Streett, C. L.; Zang, T. A.; Hussaini, M. Y.
1985-01-01
Spectral multigrid methods are demonstrated to be a competitive technique for solving the transonic potential flow equation. The spectral discretization, the relaxation scheme, and the multigrid techniques are described in detail. Significant departures from current approaches are first illustrated on several linear problems. The principal applications and examples, however, are for compressible potential flow. These examples include the relatively challenging case of supercritical flow over a lifting airfoil.
The mixed finite element multigrid method for stokes equations.
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 Q2-Q1 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
The Mixed Finite Element Multigrid Method for Stokes Equations
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 Q2-Q1 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
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
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.
Final report on the Copper Mountain conference on multigrid methods
1997-10-01
The Copper Mountain Conference on Multigrid Methods was held on April 6-11, 1997. It took the same format used in the previous Copper Mountain Conferences on Multigrid Method conferences. Over 87 mathematicians from all over the world attended the meeting. 56 half-hour talks on current research topics were presented. Talks with similar content were organized into sessions. Session topics included: fluids; domain decomposition; iterative methods; basics; adaptive methods; non-linear filtering; CFD; applications; transport; algebraic solvers; supercomputing; and student paper winners.
Parallel Algebraic Multigrid Methods - High Performance Preconditioners
Yang, U M
2004-11-11
The development of high performance, massively parallel computers and the increasing demands of computationally challenging applications have necessitated the development of scalable solvers and preconditioners. One of the most effective ways to achieve scalability is the use of multigrid or multilevel techniques. Algebraic multigrid (AMG) is a very efficient algorithm for solving large problems on unstructured grids. While much of it can be parallelized in a straightforward way, some components of the classical algorithm, particularly the coarsening process and some of the most efficient smoothers, are highly sequential, and require new parallel approaches. This chapter presents the basic principles of AMG and gives an overview of various parallel implementations of AMG, including descriptions of parallel coarsening schemes and smoothers, some numerical results as well as references to existing software packages.
A multigrid solution method for mixed hybrid finite elements
Schmid, W.
1996-12-31
We consider the multigrid solution of linear equations arising within the discretization of elliptic second order boundary value problems of the form by mixed hybrid finite elements. Using the equivalence of mixed hybrid finite elements and non-conforming nodal finite elements, we construct a multigrid scheme for the corresponding non-conforming finite elements, and, by this equivalence, for the mixed hybrid finite elements, following guidelines from Arbogast/Chen. For a rectangular triangulation of the computational domain, this non-conforming schemes are the so-called nodal finite elements. We explicitly construct prolongation and restriction operators for this type of non-conforming finite elements. We discuss the use of plain multigrid and the multilevel-preconditioned cg-method and compare their efficiency in numerical tests.
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.
Geometric multigrid for an implicit-time immersed boundary method
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 methods 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.
Geometric multigrid for an implicit-time immersed boundary method
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
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.
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.
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 parallel multigrid method for data-driven multiprocessor systems
Lin, C.H.; Gaudiot, J.L.; Proskurowski, W.
1989-12-31
The multigrid algorithm (MG) is recognized as an efficient and rapidly converging method to solve a wide family of partial differential equations (PDE). When this method is implemented on a multiprocessor system, its major drawback is the low utilization of processors. Due to the sequentiality of the standard algorithm, the fine grid levels cannot start relaxation until the coarse grid levels complete their own relaxation. Indeed, of all processors active on the fine two dimensional grid level only one fourth will be active at the coarse grid level, leaving full 75% idle. In this paper, a novel parallel V-cycle multigrid (PVM) algorithm is proposed to cure the idle processors` problem. Highly programmable systems such as data-flow architectures are then applied to support this new algorithm. The experiments based on the proposed architecture show that the convergence rate of the new algorithm is about twice faster than that of the standard method and twice as efficient system utilization is achieved.
Monolithic multigrid methods for two-dimensional resistive magnetohydrodynamics
Adler, James H.; Benson, Thomas R.; Cyr, Eric C.; MacLachlan, Scott P.; Tuminaro, Raymond S.
2016-01-06
Magnetohydrodynamic (MHD) representations are used to model a wide range of plasma physics applications and are characterized by a nonlinear system of partial differential equations that strongly couples a charged fluid with the evolution of electromagnetic fields. The resulting linear systems that arise from discretization and linearization of the nonlinear problem are generally difficult to solve. In this paper, we investigate multigrid preconditioners for this system. We consider two well-known multigrid relaxation methods for incompressible fluid dynamics: Braess--Sarazin relaxation and Vanka relaxation. We first extend these to the context of steady-state one-fluid viscoresistive MHD. Then we compare the two relaxationmore » procedures within a multigrid-preconditioned GMRES method employed within Newton's method. To isolate the effects of the different relaxation methods, we use structured grids, inf-sup stable finite elements, and geometric interpolation. Furthermore, we present convergence and timing results for a two-dimensional, steady-state test problem.« less
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.
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.
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.
Method for providing improved solid fuels from agglomerated subbituminous coal
Janiak, Jerzy S.; Turak, Ali A.; Pawlak, Wanda; Ignasiak, Boleslaw L.
1989-01-01
A method is provided for separating agglomerated subbituminous coal and the heavy bridging liquid used to form the agglomerates. The separation is performed by contacting the agglomerates with inert gas or steam at a temperature in the range of 250.degree. to 350.degree. C. at substantially atmospheric pressure.
Multigrid methods and the surface consistent equations of Geophysics
NASA Astrophysics Data System (ADS)
Millar, John
The surface consistent equations are a large linear system that is frequently used in signal enhancement for land seismic surveys. Different signatures may be consistent with a particular dynamite (or other) source. Each receiver and the conditions around the receiver will have different impact on the signal. Seismic deconvolution operators, amplitude corrections and static shifts of traces are calculated using the surface consistent equations, both in commercial and scientific seismic processing software. The system of equations is singular, making direct methods such as Gaussian elimination impossible to implement. Iterative methods such as Gauss-Seidel and conjugate gradient are frequently used. A limitation in the nature of the methods leave the long wavelengths of the solution poorly resolved. To reduce the limitations of traditional iterative methods, we employ a multigrid method. Multigrid methods re-sample the entire system of equations on a more coarse grid. An iterative method is employed on the coarse grid. The long wavelengths of the solutions that traditional iterative methods were unable to resolve are calculated on the reduced system of equations. The coarse estimate can be interpolated back up to the original sample rate, and refined using a standard iterative procedure. Multigrid methods provide more accurate solutions to the surface consistent equations, with the largest improvement concentrated in the long wavelengths. Synthetic models and tests on field data show that multigrid solutions to the system of equations can significantly increase the resolution of the seismic data, when used to correct both static time shifts and in calculating deconvolution operators. The first chapter of this thesis is a description of the physical model we are addressing. It reviews some of the literature concerning the surface consistent equations, and provides background on the nature of the problem. Chapter 2 contains a review of iterative and multigrid methods
Method for producing ceramic particles and agglomerates
Phillips, Jonathan; Gleiman, Seth S.; Chen, Chun-Ku
2001-01-01
A method for generating spherical and irregularly shaped dense particles of ceramic oxides having a controlled particle size and particle size distribution. An aerosol containing precursor particles of oxide ceramics is directed into a plasma. As the particles flow through the hot zone of the plasma, they melt, collide, and join to form larger particles. If these larger particles remain in the hot zone, they continue melting and acquire a spherical shape that is retained after they exit the hot zone, cool down, and solidify. If they exit the hot zone before melting completely, their irregular shape persists and agglomerates are produced. The size and size distribution of the dense product particles can be controlled by adjusting several parameters, the most important in the case of powder precursors appears to be the density of powder in the aerosol stream that enters the plasma hot zone. This suggests that particle collision rate is responsible for determining ultimate size of the resulting sphere or agglomerate. Other parameters, particularly the gas flow rates and the microwave power, are also adjusted to control the particle size distribution.
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.
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.
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.
A generalized BPX multigrid framework covering nonnested V-cycle methods
NASA Astrophysics Data System (ADS)
Duan, Huo-Yuan; Gao, Shao-Qin; Tan, Roger C. E.; Zhang, Shangyou
2007-03-01
More than a decade ago, Bramble, Pasciak and Xu developed a framework in analyzing the multigrid methods with nonnested spaces or noninherited quadratic forms. It was subsequently known as the BPX multigrid framework, which was widely used in the analysis of multigrid and domain decomposition methods. However, the framework has an apparent limit in the analysis of nonnested V-cycle methods, and it produces a variable V-cycle, or nonuniform convergence rate V-cycle methods, or other nonoptimal results in analysis thus far. This paper completes a long-time effort in extending the BPX multigrid framework so that it truly covers the nonnested V-cycle. We will apply the extended BPX framework to the analysis of many V-cycle nonnested multigrid methods. Some of them were proven previously only for two-level and W-cycle iterations. Some numerical results are presented to support the theoretical analysis of this paper.
A multigrid method for variable coefficient Maxwell's equations
Jones, J E; Lee, B
2004-05-13
This paper presents a multigrid method for solving variable coefficient Maxwell's equations. The novelty in this method is the use of interpolation operators that do not produce multilevel commutativity complexes that lead to multilevel exactness. Rather, the effects of multilevel exactness are built into the level equations themselves--on the finest level using a discrete T-V formulation, and on the coarser grids through the Galerkin coarsening procedure of a T-V formulation. These built-in structures permit the levelwise use of an effective hybrid smoother on the curl-free near-nullspace components, and these structures permit the development of interpolation operators for handling the curl-free and divergence-free error components separately, with the resulting block diagonal interpolation operator not satisfying multilevel commutativity but having good approximation properties for both of these error components. Applying operator-dependent interpolation for each of these error components leads to an effective multigrid scheme for variable coefficient Maxwell's equations, where multilevel commutativity-based methods can degrade. Numerical results are presented to verify the effectiveness of this new scheme.
Constructive interference II: Semi-chaotic multigrid methods
Douglas, C.C.
1994-12-31
Parallel computer vendors have mostly decided to move towards multi-user, multi-tasking per node machines. A number of these machines already exist today. Self load balancing on these machines is not an option to the users except when the user can convince someone to boot the entire machine in single user mode, which may have to be done node by node. Chaotic relaxation schemes were considered for situations like this as far back as the middle 1960`s. However, very little convergence theory exists. Further, what exists indicates that this is not really a good method. Besides chaotic relaxation, chaotic conjugate direction and minimum residual methods are explored as smoothers for symmetric and nonsymmetric problems. While having each processor potentially going off in a different direction from the rest is not what one would strive for in a unigrid situation, the change of grid procedures in multigrid provide a natural way of aiming all of the processors in the right direction. The author presents some new results for multigrid methods in which synchronization of the calculations on one or more levels is not assumed. However, he assumes that he knows how far out of synch neighboring subdomains are with respect to each other. Thus the author can show that the combination of a limited chaotic smoother and coarse level corrections produces a better algorithm than would be expected.
Large-Eddy Simulation and Multigrid Methods
Falgout,R D; Naegle,S; Wittum,G
2001-06-18
A method to simulate turbulent flows with Large-Eddy Simulation on unstructured grids is presented. Two kinds of dynamic models are used to model the unresolved scales of motion and are compared with each other on different grids. Thereby the behavior of the models is shown and additionally the feature of adaptive grid refinement is investigated. Furthermore the parallelization aspect is addressed.
Apparatus and method for compacting, degassing and carbonizing carbonaceous agglomerates
Theodore, F.W.
1980-08-19
An apparatus for compacting, degassing and carbonizing carbonaceous agglomerates is described. The apparatus comprises a rotary kiln having an agglomerate inlet means for introducing green agglomerates into the kiln near the inlet of the kiln and a heating medium inlet for introducing a heating medium comprising a finely divided solid into the kiln at a preselected location intermediate the inlet end of the kiln and the outlet end of the kiln to produce a mixture at a temperature above the carbonizing temperature of the agglomerates and a sieve positioned to receive the products from the rotary kiln and separate the heating medium and the compacted, degassed, carbonized agglomerate product. A method for producing compacted, degassed, carbonized carbonaceous agglomerates by the use of the apparatus is also disclosed.
Method for recovering light hydrocarbons from coal agglomerates
Huettenhain, Horst; Benz, August D.; Getsoian, John
1991-01-01
A method and apparatus for removing light hydrocarbons, such as heptane, from coal agglomerates includes an enclosed chamber having a substantially horizontal perforate surface therein. The coal agglomerates are introduced into a water bath within the chamber. The agglomerates are advanced over the surface while steam is substantially continuously introduced through the surface into the water bath. Steam heats the water and causes volatilization of the light hydrocarbons, which may be collected from the overhead of the chamber. The resulting agglomerates may be collected at the opposite end from the surface and subjected to final draining processes prior to transportation or use.
Multigrid hierarchical simulated annealing method for reconstructing heterogeneous media.
Pant, Lalit M; Mitra, Sushanta K; Secanell, Marc
2015-12-01
A reconstruction methodology based on different-phase-neighbor (DPN) pixel swapping and multigrid hierarchical annealing is presented. The method performs reconstructions by starting at a coarse image and successively refining it. The DPN information is used at each refinement stage to freeze interior pixels of preformed structures. This preserves the large-scale structures in refined images and also reduces the number of pixels to be swapped, thereby resulting in a decrease in the necessary computational time to reach a solution. Compared to conventional single-grid simulated annealing, this method was found to reduce the required computation time to achieve a reconstruction by around a factor of 70-90, with the potential of even higher speedups for larger reconstructions. The method is able to perform medium sized (up to 300(3) voxels) three-dimensional reconstructions with multiple correlation functions in 36-47 h. PMID:26764849
Solving nonlinear heat conduction problems with multigrid preconditioned Newton-Krylov methods
Rider, W.J.; Knoll, D.A.
1997-09-01
Our objective is to investigate the utility of employing multigrid preconditioned Newton-Krylov methods for solving initial value problems. Multigrid based method promise better performance from the linear scaling associated with them. Our model problem is nonlinear heat conduction which can model idealized Marshak waves. Here we will investigate the efficiency of using a linear multigrid method to precondition a Krylov subspace method. In effect we will show that a fixed point nonlinear iterative method provides an effective preconditioner for the nonlinear problem.
NASA Technical Reports Server (NTRS)
Golik, W. L.
1996-01-01
A robust solver for the elliptic grid generation equations is sought via a numerical study. The system of PDEs is discretized with finite differences, and multigrid methods are applied to the resulting nonlinear algebraic equations. Multigrid iterations are compared with respect to the robustness and efficiency. Different smoothers are tried to improve the convergence of iterations. The methods are applied to four 2D grid generation problems over a wide range of grid distortions. The results of the study help to select smoothing schemes and the overall multigrid procedures for elliptic grid generation.
Novel Binders and Methods for Agglomeration of Ore
S. K. Kawatra; T. C. Eisele; K. A. Lewandowski; J. A. Gurtler
2006-09-30
Heap leaching is one of the methods being used to recover metal from low grade ore deposits. The main problem faced during heap leaching is the migration of fine grained particles through the heap, forming impermeable beds which result in poor solution flow. The poor solution flow leads to less contact between the leach solution and the ore, resulting in low recovery rates. Agglomeration of ore into coarse, porous masses prevents fine particles from migrating and clogging the spaces and channels between the larger ore particles. Currently, there is one facility in the United States which uses agglomeration. This operation agglomerates their ore using leach solution (raffinate), but is still experiencing undesirable metal recovery from the heaps due to agglomerate breakdown. The use of a binder, in addition to the leach solution, during agglomeration would help to produce stronger agglomerates that did not break down during processing. However, there are no known binders that will work satisfactorily in the acidic environment of a heap, at a reasonable cost. As a result, operators of many facilities see a large loss of process efficiency due to their inability to take advantage of agglomeration. Increasing copper recovery in heap leaching by the use of binders and agglomeration would result in a significant decrease in the amount of energy consumed. Assuming that 70% of all the leaching heaps would convert to using agglomeration technology, as much as 1.64*10{sup 12} BTU per year would be able to be saved if a 25% increase in copper recovery was experienced, which is equivalent to saving approximately 18% of the energy currently being used in leaching heaps. For every week a leach cycle was decreased, a savings of as much as 1.23*10{sup 11} BTU per week would result. This project has identified several acid-resistant binders and agglomeration procedures. These binders and experimental procedures will be able to be used for use in improving the energy efficiency of
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.
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.
Copper Mountain conference on multigrid methods. Preliminary proceedings -- List of abstracts
1995-12-31
This report contains abstracts of the papers presented at the conference. Papers cover multigrid algorithms and applications of multigrid methods. Applications include the following: solution of elliptical problems; electric power grids; fluid mechanics; atmospheric data assimilation; thermocapillary effects on weld pool shape; boundary-value problems; prediction of hurricane tracks; modeling multi-dimensional combustion and detailed chemistry; black-oil reservoir simulation; image processing; and others.
Application of the multigrid method to grid generation
NASA Technical Reports Server (NTRS)
Ohring, S.
1980-01-01
The multigrid method (MGM), used to numerically solve the pair of nonlinear elliptic equations commonly used to generate two dimensional boundary-fitted coordinate systems is discussed. Two different geometries are considered: one involving a coordinate system fitted about a circle and the other selected for an impinging jet flow problem. Two different relaxation schemes are tried: one is successive point overrelaxation and the other is a four-color scheme vectorizeable to take advantage of a parallel processor computer for greater computational speed. Results using MGM are compared with those using SOR (doing successive overrelaxations with the corresponding relaxation scheme on the fine grid only). It is found that MGM becomes significantly more effective than SOR as more accuracy is demanded and as more corrective grids, or more grid points, are used. For the accuracy required, it is found that MGM is two to three times faster than SOR in computing time. With the four-color relaxation scheme as applied to the impinging jet problem, the advantage of MGM over SOR is not as great. This may be due to the effect of a poor initial guess on MGM for this problem.
Novel Binders and Methods for Agglomeration of Ore
S. K. Kawatra; T. C. Eisele; K. A. Lewandowski; J. A. Gurtler
2006-12-31
Many metal extraction operations, such as leaching of copper, leaching of precious metals, and reduction of metal oxides to metal in high-temperature furnaces, require agglomeration of ore to ensure that reactive liquids or gases are evenly distributed throughout the ore being processed. Agglomeration of ore into coarse, porous masses achieves this even distribution of fluids by preventing fine particles from migrating and clogging the spaces and channels between the larger ore particles. Binders are critically necessary to produce agglomerates that will not break down during processing. However, for many important metal extraction processes there are no binders known that will work satisfactorily. Primary examples of this are copper heap leaching, where there are no binders that will work in the acidic environment encountered in this process, and advanced ironmaking processes, where binders must function satisfactorily over an extraordinarily large range of temperatures (from room temperature up to over 1200 C). As a result, operators of many facilities see a large loss of process efficiency due to their inability to take advantage of agglomeration. The large quantities of ore that must be handled in metal extraction processes also means that the binder must be inexpensive and useful at low dosages to be economical. The acid-resistant binders and agglomeration procedures developed in this project will also be adapted for use in improving the energy efficiency and performance of a broad range of mineral agglomeration applications, particularly heap leaching and advanced primary ironmaking. This project has identified several acid-resistant binders and agglomeration procedures that can be used for improving the energy efficiency of heap leaching, by preventing the ''ponding'' and ''channeling'' effects that currently cause reduced recovery and extended leaching cycle times. Methods have also been developed for iron ore processing which are intended to improve the
Recent developments in multigrid methods for the steady Euler equations
NASA Technical Reports Server (NTRS)
Jespersen, D. C.
1984-01-01
The solution by multigrid techniques of the steady inviscid compressible equations of gas dynamics, the Euler equations is investigated. Steady two dimensional transonic flow over an airfoil section is studied intensively. Most of the material is applicable to three dimensional flow problems of aerodynamic interest.
Continuous air agglomeration method for high carbon fly ash beneficiation
Gray, McMahon L.; Champagne, Kenneth J.; Finseth, Dennis H.
2000-01-01
The carbon and mineral components of fly ash are effectively separated by a continuous air agglomeration method, resulting in a substantially carboree mineral stream and a highly concentrated carbon product. The method involves mixing the fly ash comprised of carbon and inorganic mineral matter with a liquid hydrocarbon to form a slurry, contacting the slurry with an aqueous solution, dispersing the hydrocarbon slurry into small droplets within the aqueous solution by mechanical mixing and/or aeration, concentrating the inorganic mineral matter in the aqueous solution, agglomerating the carbon and hydrocarbon in the form of droplets, collecting the droplets, separating the hydrocarbon from the concentrated carbon product, and recycling the hydrocarbon.
Continuous air Agglomeration Method for high Carbon fly ash Beneficiation
Gray, McMahan L.; Champagne, Kenneth J.; Finseth, Dennis H.
1998-09-29
The carbon and mineral components of fly ash are effectively separated by a continuous air agglomeration method, resulting in a substantially carbon-free mineral stream and a highly concentrated carbon product. The method involves mixing the fly ash comprised of carbon and inorganic mineral matter with a liquid hydrocarbon to form a slurry, contacting the slurry with an aqueous solution, dispersing the hydrocarbon slurry into small droplets within the aqueous solution by mechanical mixing and/or aeration, concentrating the inorganic mineral matter in the aqueous solution, agglomerating the carbon and hydrocarbon in the form of droplets, collecting the droplets, separating the hydrocarbon from the concentrated carbon product, and recycling the hydrocarbon.
Multigrid lattice Boltzmann method for accelerated solution of elliptic equations
NASA Astrophysics Data System (ADS)
Patil, Dhiraj V.; Premnath, Kannan N.; Banerjee, Sanjoy
2014-05-01
A new solver for second-order elliptic partial differential equations (PDEs) based on the lattice Boltzmann method (LBM) and the multigrid (MG) technique is presented. Several benchmark elliptic equations are solved numerically with the inclusion of multiple grid-levels in two-dimensional domains at an optimal computational cost within the LB framework. The results are compared with the corresponding analytical solutions and numerical solutions obtained using the Stone's strongly implicit procedure. The classical PDEs considered in this article include the Laplace and Poisson equations with Dirichlet boundary conditions, with the latter involving both constant and variable coefficients. A detailed analysis of solution accuracy, convergence and computational efficiency of the proposed solver is given. It is observed that the use of a high-order stencil (for smoothing) improves convergence and accuracy for an equivalent number of smoothing sweeps. The effect of the type of scheduling cycle (V- or W-cycle) on the performance of the MG-LBM is analyzed. Next, a parallel algorithm for the MG-LBM solver is presented and then its parallel performance on a multi-core cluster is analyzed. Lastly, a practical example is provided wherein the proposed elliptic PDE solver is used to compute the electro-static potential encountered in an electro-chemical cell, which demonstrates the effectiveness of this new solver in complex coupled systems. Several orders of magnitude gains in convergence and parallel scaling for the canonical problems, and a factor of 5 reduction for the multiphysics problem are achieved using the MG-LBM.
Multiple Vector Preserving Interpolation Mappings in Algebraic Multigrid
Vassilevski, P S; Zikatanov, L T
2004-11-03
We propose algorithms for the construction of AMG (algebraic multigrid) interpolation mappings such that the resulting coarse space to span (locally and globally) any number of a priori given set of vectors. Specific constructions in the case of element agglomeration AMG methods are given. Some numerical illustration is also provided.
Inverse airfoil design procedure using a multigrid Navier-Stokes method
NASA Technical Reports Server (NTRS)
Malone, J. B.; Swanson, R. C.
1991-01-01
The Modified Garabedian McFadden (MGM) design procedure was incorporated into an existing 2-D multigrid Navier-Stokes airfoil analysis method. The resulting design method is an iterative procedure based on a residual correction algorithm and permits the automated design of airfoil sections with prescribed surface pressure distributions. The new design method, Multigrid Modified Garabedian McFadden (MG-MGM), is demonstrated for several different transonic pressure distributions obtained from both symmetric and cambered airfoil shapes. The airfoil profiles generated with the MG-MGM code are compared to the original configurations to assess the capabilities of the inverse design method.
Multigrid for the Galerkin least squares method in linear elasticity: The pure displacement problem
Yoo, Jaechil
1996-12-31
Franca and Stenberg developed several Galerkin least squares methods for the solution of the problem of linear elasticity. That work concerned itself only with the error estimates of the method. It did not address the related problem of finding effective methods for the solution of the associated linear systems. In this work, we prove the convergence of a multigrid (W-cycle) method. This multigrid is robust in that the convergence is uniform as the parameter, v, goes to 1/2 Computational experiments are included.
Advanced discretizations and multigrid methods for liquid crystal configurations
NASA Astrophysics Data System (ADS)
Emerson, David B.
addition, we present two novel, optimally scaling, multigrid approaches for these systems based on Vanka- and Braess-Sarazin-type relaxation. Both approaches outperform direct methods and represent highly efficient and scalable iterative solvers. Finally, a three-dimensional problem considering the effects of geometrically patterned surfaces is presented, which gives rise to a nonlinear anisotropic reaction-diffusion equation. Well-posedness is shown for the intermediate linearization systems of the proposed Newton linearization. The configurations under consideration are part of ongoing physics research seeking new bistable configurations induced by geometric nano-patterning.
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.
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
Simulation of viscous flows using a multigrid-control volume finite element method
Hookey, N.A.
1994-12-31
This paper discusses a multigrid control volume finite element method (MG CVFEM) for the simulation of viscous fluid flows. The CVFEM is an equal-order primitive variables formulation that avoids spurious solution fields by incorporating an appropriate pressure gradient in the velocity interpolation functions. The resulting set of discretized equations is solved using a coupled equation line solver (CELS) that solves the discretized momentum and continuity equations simultaneously along lines in the calculation domain. The CVFEM has been implemented in the context of both FMV- and V-cycle multigrid algorithms, and preliminary results indicate a five to ten fold reduction in execution times.
Method for agglomerating powdered coal by compaction
Byrne, L.D.; Byrne, B.J.
1987-07-21
A method is described for preparing a powdered carboniferous composition and forming this composition into solid product shapes suitable for handling, transporting and burning, comprising the steps of: (a) mixing (1) powdered carboniferous material with (2) an amount of surfactant effective for wetting the powdered carboniferous material with water but for which no appreciable binding occurs between the surfactant and carboniferous material upon compaction and (3) an amount of water effective to bring the moisture content of the resultant mixture within the range of about 32 to 35% by weight; (b) working the mixture to obtain a homogeneous composition comprising a uniform dispersion of the water, surfactant, and powdered carboniferous material; and (c) compacting the resultant homogeneous composition into the desired solid product shape by extruding the homogeneous composition through a ring pelletizing extruder.
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.
A multigrid method for N-component nucleation.
van Putten, Dennis S; Glazenborg, Simon P; Hagmeijer, Rob; Venner, Cornelis H
2011-07-01
A multigrid algorithm has been developed enabling more efficient solution of the cluster size distribution for N-component nucleation from the Becker-Döring equations. The theoretical derivation is valid for an arbitrary number of condensing components, making the simulation of many-component nucleating systems feasible. A steady state ternary nucleation problem is defined to demonstrate its efficiency. The results are used as a validation for existing nucleation theories. The non-steady state ternary problem provides useful insight into the initial stages of the nucleation process. We observe that for the ideal mixture the main nucleation flux bypasses the saddle point. PMID:21744895
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.
A multigrid Newton-Krylov method for flux-limited radiation diffusion
Rider, W.J.; Knoll, D.A.; Olson, G.L.
1998-09-01
The authors focus on the integration of radiation diffusion including flux-limited diffusion coefficients. The nonlinear integration is accomplished with a Newton-Krylov method preconditioned with a multigrid Picard linearization of the governing equations. They investigate the efficiency of the linear and nonlinear iterative techniques.
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.
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.
Development of methods to predict agglomeration and disposition in FBCs
Mann, M.D.; Henderson, A.K.; Swanson, M.K.; Erickson, T.A.
1995-11-01
This 3-year, multiclient program is providing the information needed to determine the behavior of inorganic components in FBC units using advanced methods of analysis coupled with bench-scale combustion experiments. The major objectives of the program are as follows: (1) To develop further our advanced ash and deposit characterization techniques to quantify the effects of the liquid-phase components in terms of agglomerate formation and ash deposits, (2) To determine the mechanisms of inorganic transformations that lead to bed agglomeration and ash deposition in FBC systems, and (3) To develop a better means to predict the behavior of inorganic components as a function of coal composition, bed material characteristics, and combustion conditions.
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.
Multigrid methods for differential equations with highly oscillatory coefficients
NASA Technical Reports Server (NTRS)
Engquist, Bjorn; Luo, Erding
1993-01-01
New coarse grid multigrid operators for problems with highly oscillatory coefficients are developed. These types of operators are necessary when the characters of the differential equations on coarser grids or longer wavelengths are different from that on the fine grid. Elliptic problems for composite materials and different classes of hyperbolic problems are practical examples. The new coarse grid operators can be constructed directly based on the homogenized differential operators or hierarchically computed from the finest grid. Convergence analysis based on the homogenization theory is given for elliptic problems with periodic coefficients and some hyperbolic problems. These are classes of equations for which there exists a fairly complete theory for the interaction between shorter and longer wavelengths in the problems. Numerical examples are presented.
A multigrid method for a model of the implicit immersed boundary equations
Guy, Robert; Philip, Bobby
2012-01-01
Explicit time stepping schemes for the immersed boundary method require very small time steps in order to maintain stability. Solving the equations that arise from an implicit discretization is difficult. Recently, several different approaches have been proposed, but a complete understanding of this problem is still emerging. A multigrid method is developed and explored for solving the equations in an implicit time discretization of a model of the immersed boundary equations. The model problem consists of a scalar Poisson equation with conformation-dependent singular forces on an immersed boundary. This model does not include the inertial terms or the incompressibility constraint. The method is more efficient than an explicit method, but the efficiency gain is limited. The multigrid method alone may not be an effective solver, but when used as a preconditioner for Krylov methods, the speed-up over the explicit time method is substantial. For example, depending on the constitutive law for the boundary force, with a time step 100 times larger than the explicit method, the implicit method is about 15-100 times more efficient than the explicit method. A very attractive feature of this method is that the efficiency of the multigrid preconditioned Krylov solver is shown to be independent of the number of immersed boundary points.
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.
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
Multilevel local refinement and multigrid methods for 3-D turbulent flow
Liao, C.; Liu, C.; Sung, C.H.; Huang, T.T.
1996-12-31
A numerical approach based on multigrid, multilevel local refinement, and preconditioning methods for solving incompressible Reynolds-averaged Navier-Stokes equations is presented. 3-D turbulent flow around an underwater vehicle is computed. 3 multigrid levels and 2 local refinement grid levels are used. The global grid is 24 x 8 x 12. The first patch is 40 x 16 x 20 and the second patch is 72 x 32 x 36. 4th order artificial dissipation are used for numerical stability. The conservative artificial compressibility method are used for further improvement of convergence. To improve the accuracy of coarse/fine grid interface of local refinement, flux interpolation method for refined grid boundary is used. The numerical results are in good agreement with experimental data. The local refinement can improve the prediction accuracy significantly. The flux interpolation method for local refinement can keep conservation for a composite grid, therefore further modify the prediction accuracy.
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.
Parallel Multigrid Equation Solver
2001-09-07
Prometheus is a fully parallel multigrid equation solver for matrices that arise in unstructured grid finite element applications. It includes a geometric and an algebraic multigrid method and has solved problems of up to 76 mullion degrees of feedom, problems in linear elasticity on the ASCI blue pacific and ASCI red machines.
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.
Numerical solution of flame sheet problems with and without multigrid methods
NASA Technical Reports Server (NTRS)
Douglas, Craig C.; Ern, Alexandre
1993-01-01
Flame sheet problems are on the natural route to the numerical solution of multidimensional flames, which, in turn, are important in many engineering applications. In order to model the structure of flames more accurately, we use the vorticity-velocity formulation of the fluid flow equations, as opposed to the streamfunction-vorticity approach. The numerical solution of the resulting nonlinear coupled elliptic partial differential equations involves a pseudo transient process and a steady state Newton iteration. Rather than working with dimensionless variables, we introduce scale factors that can yield significant savings in the execution time. In this context, we also investigate the applicability and performance of several multigrid methods, focusing on nonlinear damped Newton multigrid, using either one way or correction schemes.
A Parallel Multigrid Method for the Finite Element Analysis of Mechanical Contact
Hales, J D; Parsons, I D
2002-03-21
A geometrical multigrid method for solving the linearized matrix equations arising from node-on-face three-dimensional finite element contact is described. The development of an efficient implementation of this combination that minimizes both the memory requirements and the computational cost requires careful construction and storage of the portion of the coarse mesh stiffness matrices that are associated with the contact stiffness on the fine mesh. The multigrid contact algorithm is parallelized in a manner suitable for distributed memory architectures: results are presented that demonstrates the scheme's scalability. The solution of a large contact problem derived from an analysis of the factory joints present in the Space Shuttle reusable solid rocket motor demonstrates the usefulness of the general approach.
Rotor-stator interaction analysis using the Navier-Stokes equations and a multigrid method
Arnone, A.; Pacciani, R.
1996-10-01
A recently developed, time-accurate multigrid viscous solver has been extended to the analysis of unsteady rotor-stator interaction. In the proposed method, a fully implicit discretization is used to remove stability limitations. By means of a dual time-stepping approach, a four-stage Runge-Kutta scheme is used in conjunction with several accelerating techniques typical of steady-state solvers, instead of traditional time-expensive factorizations. The accelerating strategies include local time stepping, residual smoothing, and multigrid. Two-dimensional viscous calculations of unsteady rotor-stator interaction in the first stage of a modern gas turbine are presented. The stage analysis is based on the introduction of several blade passages to approximate the stator:rotor count ratio. Particular attention is dedicated to grid dependency in space and time as well as to the influence of the number of blades included in the calculations.
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.
Agglomerating combustor-gasifier method and apparatus for coal gasification
Chen, Joseph L. P.; Archer, David H.
1976-09-21
A method and apparatus for gasifying coal wherein the gasification takes place in a spout fluid bed at a pressure of about 10 to 30 atmospheres and a temperature of about 1800.degree. to 2200.degree.F and wherein the configuration of the apparatus and the manner of introduction of gases for combustion and fluidization is such that agglomerated ash can be withdrawn from the bottom of the apparatus and gas containing very low dust loading is produced. The gasification reaction is self-sustaining through the burning of a stoichiometric amount of coal with air in the lower part of the apparatus to form the spout within the fluid bed. The method and apparatus are particularly suitable for gasifying coarse coal particles.
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.
AMG by element agglomeration and constrained energy minimization interpolation
Kolev, T V; Vassilevski, P S
2006-02-17
This paper studies AMG (algebraic multigrid) methods that utilize energy minimization construction of the interpolation matrices locally, in the setting of element agglomeration AMG. The coarsening in element agglomeration AMG is done by agglomerating fine-grid elements, with coarse element matrices defined by a local Galerkin procedure applied to the matrix assembled from the individual fine-grid element matrices. This local Galerkin procedure involves only the coarse basis restricted to the agglomerated element. To construct the coarse basis, one exploits previously proposed constraint energy minimization procedures now applied to the local matrix. The constraints are that a given set of vectors should be interpolated exactly, not only globally, but also locally on every agglomerated element. The paper provides algorithmic details, as well as a convergence result based on a ''local-to-global'' energy bound of the resulting multiple-vector fitting AMG interpolation mappings. A particular implementation of the method is illustrated with a set of numerical experiments.
Novel Binders and Methods for Agglomeration of Ore
S. K. Kawatra; T. C. Eisele; J. A. Gurtler; K. Lewandowski
2005-09-30
Many metal extraction operations, such as leaching of copper, leaching of precious metals, and reduction of metal oxides to metal in high-temperature furnaces, require agglomeration of ore to ensure that reactive liquids or gases are evenly distributed throughout the ore being processed. Agglomeration of ore into coarse, porous masses achieves this even distribution of fluids by preventing fine particles from migrating and clogging the spaces and channels between the larger ore particles. Binders are critically necessary to produce agglomerates that will not break down during processing. However, for many important metal extraction processes there are no binders known that will work satisfactorily at a reasonable cost. A primary example of this is copper heap leaching, where there are no binders currently encountered in this acidic environment process. As a result, operators of many facilities see a large loss of process efficiency due to their inability to take advantage of agglomeration. The large quantities of ore that must be handled in metal extraction processes also means that the binder must be inexpensive and useful at low dosages to be economical. The acid-resistant binders and agglomeration procedures developed in this project will also be adapted for use in improving the energy efficiency and performance of a broad range of mineral agglomeration applications, particularly heap leaching. The active involvement of our industrial partners will help to ensure rapid commercialization of any agglomeration technologies developed by this project.
Novel Binders and Methods for Agglomeration of Ore
S. K. Kawatra; T. C. Eisele; K. A. Lewandowski; J. A. Gurtler
2006-03-31
Many metal extraction operations, such as leaching of copper, leaching of precious metals, and reduction of metal oxides to metal in high-temperature furnaces, require agglomeration of ore to ensure that reactive liquids or gases are evenly distributed throughout the ore being processed. Agglomeration of ore into coarse, porous masses achieves this even distribution of fluids by preventing fine particles from migrating and clogging the spaces and channels between the larger ore particles. Binders are critically necessary to produce agglomerates that will not break down during processing. However, for many important metal extraction processes there are no binders known that will work satisfactorily at a reasonable cost. A primary example of this is copper heap leaching, where there are no binders currently encountered in this acidic environment process. As a result, operators of many facilities see a large loss of process efficiency due to their inability to take advantage of agglomeration. The large quantities of ore that must be handled in metal extraction processes also means that the binder must be inexpensive and useful at low dosages to be economical. The acid-resistant binders and agglomeration procedures developed in this project will also be adapted for use in improving the energy efficiency and performance of a broad range of mineral agglomeration applications, particularly heap leaching. The active involvement of our industrial partners will help to ensure rapid commercialization of any agglomeration technologies developed by this project.
Final Report on Subcontract B605152. Multigrid Methods for Systems of PDEs
Brannick, James; Xu, Jinchao
2015-07-07
The project team has continued with work on developing aggressive coarsening techniques for AMG methods. Of particular interest is the idea to use aggressive coarsening with polynomial smoothing. Using local Fourier analysis the optimal values for the parameters involved in defining the polynomial smoothers are determined automatically in a way to achieve fast convergence of cycles with aggressive coarsening. Numerical tests have the sharpness of the theoretical results. The methods are highly parallelizable and efficient multigrid algorithms on structured and semistructured grids in two and three spatial dimensions.
A comparison of locally adaptive multigrid methods: LDC, FAC and FIC
NASA Technical Reports Server (NTRS)
Khadra, Khodor; Angot, Philippe; Caltagirone, Jean-Paul
1993-01-01
This study is devoted to a comparative analysis of three 'Adaptive ZOOM' (ZOom Overlapping Multi-level) methods based on similar concepts of hierarchical multigrid local refinement: LDC (Local Defect Correction), FAC (Fast Adaptive Composite), and FIC (Flux Interface Correction)--which we proposed recently. These methods are tested on two examples of a bidimensional elliptic problem. We compare, for V-cycle procedures, the asymptotic evolution of the global error evaluated by discrete norms, the corresponding local errors, and the convergence rates of these algorithms.
NOVEL BINDERS AND METHODS FOR AGGLOMERATION OF ORE
S.K. Kawatra; T.C. Eisele; J.A. Gurtler; C.A. Hardison; K. Lewandowski
2004-04-01
Many metal extraction operations, such as leaching of copper, leaching of precious metals, and reduction of metal oxides to metal in high-temperature furnaces, require agglomeration of ore to ensure that reactive liquids or gases are evenly distributed throughout the ore being processed. Agglomeration of ore into coarse, porous masses achieves this even distribution of fluids by preventing fine particles from migrating and clogging the spaces and channels between the larger ore particles. Binders are critically necessary to produce agglomerates that will not break down during processing. However, for many important metal extraction processes there are no binders known that will work satisfactorily. Primary examples of this are copper heap leaching, where there are no binders that will work in the acidic environment encountered in this process, and advanced ironmaking processes, where binders must function satisfactorily over an extraordinarily large range of temperatures (from room temperature up to over 1200 C). As a result, operators of many facilities see a large loss of process efficiency due to their inability to take advantage of agglomeration. The large quantities of ore that must be handled in metal extraction processes also means that the binder must be inexpensive and useful at low dosages to be economical. The acid-resistant binders and agglomeration procedures developed in this project will also be adapted for use in improving the energy efficiency and performance of a broad range of mineral agglomeration applications, particularly heap leaching and advanced primary ironmaking.
Novel Binders and Methods for Agglomeration of Ore
S. K. Kawatra; T. C. Eisele; J. A. Gurtler
2004-03-31
Many metal extraction operations, such as leaching of copper, leaching of precious metals, and reduction of metal oxides to metal in high-temperature furnaces, require agglomeration of ore to ensure that reactive liquids or gases are evenly distributed throughout the ore being processed. Agglomeration of ore into coarse, porous masses achieves this even distribution of fluids by preventing fine particles from migrating and clogging the spaces and channels between the larger ore particles. Binders are critically necessary to produce agglomerates that will not break down during processing. However, for many important metal extraction processes there are no binders known that will work satisfactorily. A primary example of this is copper heap leaching, where there are no binders that will work in the acidic environment encountered in this process. As a result, operators of acidic heap-leach facilities see a large loss of process efficiency due to their inability to take advantage of agglomeration. The large quantities of ore that must be handled in metal extraction processes also means that the binder must be inexpensive and useful at low dosages to be economical. The acid-resistant binders and agglomeration procedures developed in this project will also be adapted for use in improving the energy efficiency and performance of other agglomeration applications, particularly advanced primary ironmaking.
NOVEL BINDERS AND METHODS FOR AGGLOMERATION OF ORE
S.K. Kawatra; T.C. Eisele; J.A. Gurtler; K. Lewandowski
2005-04-01
Many metal extraction operations, such as leaching of copper, leaching of precious metals, and reduction of metal oxides to metal in high-temperature furnaces, require agglomeration of ore to ensure that reactive liquids or gases are evenly distributed throughout the ore being processed. Agglomeration of ore into coarse, porous masses achieves this even distribution of fluids by preventing fine particles from migrating and clogging the spaces and channels between the larger ore particles. Binders are critically necessary to produce agglomerates that will not breakdown during processing. However, for many important metal extraction processes there are no binders known that will work satisfactorily. Primary examples of this are copper heap leaching, where there are no binders that will work in the acidic environment encountered in this process. As a result, operators of many facilities see large loss of process efficiency due to their inability to take advantage of agglomeration. The large quantities of ore that must be handled in metal extraction processes also means that the binder must be inexpensive and useful at low dosages to be economical. The acid-resistant binders and agglomeration procedures developed in this project will also be adapted for use in improving the energy efficiency and performance of a broad range of mineral agglomeration applications, particularly heap leaching.
Multigrid methods for a semilinear PDE in the theory of pseudoplastic fluids
NASA Technical Reports Server (NTRS)
Henson, Van Emden; Shaker, A. W.
1993-01-01
We show that by certain transformations the boundary layer equations for the class of non-Newtonian fluids named pseudoplastic can be generalized in the form the vector differential operator(u) + p(x)u(exp -lambda) = 0, where x is a member of the set Omega and Omega is a subset of R(exp n), n is greater than or equal to 1 under the classical conditions for steady flow over a semi-infinite flat plate. We provide a survey of the existence, uniqueness, and analyticity of the solutions for this problem. We also establish numerical solutions in one- and two-dimensional regions using multigrid methods.
NASA Technical Reports Server (NTRS)
Liu, C.; Liu, Z.
1993-01-01
The fourth-order finite-difference scheme with fully implicit time-marching presently used to computationally study the spatial instability of planar Poiseuille flow incorporates a novel treatment for outflow boundary conditions that renders the buffer area as short as one wavelength. A semicoarsening multigrid method accelerates convergence for the implicit scheme at each time step; a line-distributive relaxation is developed as a robust fast solver that is efficient for anisotropic grids. Computational cost is no greater than that of explicit schemes, and excellent agreement with linear theory is obtained.
A multigrid integral equation method for large-scale models with inhomogeneous backgrounds
NASA Astrophysics Data System (ADS)
Endo, Masashi; Čuma, Martin; Zhdanov, Michael S.
2008-12-01
We present a multigrid integral equation (IE) method for three-dimensional (3D) electromagnetic (EM) field computations in large-scale models with inhomogeneous background conductivity (IBC). This method combines the advantages of the iterative IBC IE method and the multigrid quasi-linear (MGQL) approximation. The new EM modelling method solves the corresponding systems of linear equations within the domains of anomalous conductivity, Da, and inhomogeneous background conductivity, Db, separately on coarse grids. The observed EM fields in the receivers are computed using grids with fine discretization. The developed MGQL IBC IE method can also be applied iteratively by taking into account the return effect of the anomalous field inside the domain of the background inhomogeneity Db, and vice versa. The iterative process described above is continued until we reach the required accuracy of the EM field calculations in both domains, Da and Db. The method was tested for modelling the marine controlled-source electromagnetic field for complex geoelectrical structures with hydrocarbon petroleum reservoirs and a rough sea-bottom bathymetry.
Quasi-Newton and multigrid methods for semiconductor device simulation
Slamet, S.
1983-12-01
A finite difference approximation to the semiconductor device equations using the Bernoulli function approximation to the exponential function is described, and the robustness of this approximation is demonstrated. Sheikh's convergence analysis of Gummel's method and quasi-Newton methods is extended to a nonuniform mesh and the Bernoulli function discretization. It is proved that Gummel's method and the quasi-Newton methods for the scaled carrier densities and carrier densities converge locally for sufficiently smooth problems.
Sixth Copper Mountain Conference on Multigrid Methods. Final report
Not Available
1994-07-01
During the 5-day meeting, 112 half-hour talks on current research topics were presented. Session topics included: fluids, domain decomposition, iterative methods, Basics I and II, adaptive methods, nonlinear filtering, CFD I, II, and III, applications, transport, algebraic solvers, supercomputing, and student paper winners.
Ku, Bon Ki; Kulkarni, Pramod
2015-01-01
We compare different approaches to measure surface area of aerosol agglomerates. The objective was to compare field methods, such as mobility and diffusion charging based approaches, with laboratory approach, such as Brunauer, Emmett, Teller (BET) method used for bulk powder samples. To allow intercomparison of various surface area measurements, we defined ‘geometric surface area’ of agglomerates (assuming agglomerates are made up of ideal spheres), and compared various surface area measurements to the geometric surface area. Four different approaches for measuring surface area of agglomerate particles in the size range of 60–350 nm were compared using (i) diffusion charging-based sensors from three different manufacturers, (ii) mobility diameter of an agglomerate, (iii) mobility diameter of an agglomerate assuming a linear chain morphology with uniform primary particle size, and (iv) surface area estimation based on tandem mobility–mass measurement and microscopy. Our results indicate that the tandem mobility–mass measurement, which can be applied directly to airborne particles unlike the BET method, agrees well with the BET method. It was also shown that the three diffusion charging-based surface area measurements of silver agglomerates were similar within a factor of 2 and were lower than those obtained from the tandem mobility–mass and microscopy method by a factor of 3–10 in the size range studied. Surface area estimated using the mobility diameter depended on the structure or morphology of the agglomerate with significant underestimation at high fractal dimensions approaching 3. PMID:26692585
An angular multigrid method for computing mono-energetic particle beams in Flatland
Boergers, Christoph MacLachlan, Scott
2010-04-20
Beams of microscopic particles penetrating scattering background matter play an important role in several applications. The parameter choices made here are motivated by the problem of electron-beam cancer therapy planning. Mathematically, a steady particle beam penetrating matter, or a configuration of several such beams, is modeled by a boundary value problem for a Boltzmann equation. Grid-based discretization of such a problem leads to a system of algebraic equations. This system is typically very large because of the large number of independent variables in the Boltzmann equation-six if no dimension-reducing assumptions other than time independence are made. If grid-based methods are to be practical for these problems, it is therefore necessary to develop very fast solvers for the discretized problems. For beams of mono-energetic particles interacting with a passive background, but not with each other, in two space dimensions, the first author proposed such a solver, based on angular domain decomposition, some time ago. Here, we propose and test an angular multigrid algorithm for the same model problem. Our numerical experiments show rapid, grid-independent convergence. For high-resolution calculations, our method is substantially more efficient than the angular domain decomposition method. In addition, unlike angular domain decomposition, the angular multigrid method works well even when the angular diffusion coefficient is fairly large.
Multigrid methods for flow transition in three-dimensional boundary layers with surface roughness
NASA Technical Reports Server (NTRS)
Liu, Chaoqun; Liu, Zhining; Mccormick, Steve
1993-01-01
The efficient multilevel adaptive method has been successfully applied to perform direct numerical simulations (DNS) of flow transition in 3-D channels and 3-D boundary layers with 2-D and 3-D isolated and distributed roughness in a curvilinear coordinate system. A fourth-order finite difference technique on stretched and staggered grids, a fully-implicit time marching scheme, a semi-coarsening multigrid method associated with line distributive relaxation scheme, and an improved outflow boundary-condition treatment, which needs only a very short buffer domain to damp all order-one wave reflections, are developed. These approaches make the multigrid DNS code very accurate and efficient. This allows us not only to be able to do spatial DNS for the 3-D channel and flat plate at low computational costs, but also to do spatial DNS for transition in the 3-D boundary layer with 3-D single and multiple roughness elements, which would have extremely high computational costs with conventional methods. Numerical results show good agreement with the linear stability theory, the secondary instability theory, and a number of laboratory experiments. The contribution of isolated and distributed roughness to transition is analyzed.
Adaptive multi-grid method for a periodic heterogeneous medium in 1-D
Fish, J.; Belsky, V.
1995-12-31
A multi-grid method for a periodic heterogeneous medium in 1-D is presented. Based on the homogenization theory special intergrid connection operators have been developed to imitate a low frequency response of the differential equations with oscillatory coefficients. The proposed multi-grid method has been proved to have a fast rate of convergence governed by the ratio q/(4-q), where o
Combustor flow computations in general coordinates with a multigrid method
NASA Astrophysics Data System (ADS)
Shyy, Wei; Braaten, Mark E.
The computational approach presented for single-phase combusting turbulent flowfields balances the requirements of complex physical and chemical flow interactions with those of resolving the three-dimensional geometrical constraints of the combustor contours, film cooling slots, and circular dilution holes. Attention is given to the three-dimensional grid-generation algorithm, the two-dimensional adaptive grid method applied to recirculating turbulent reacting flows, and theory/data assessments for three-dimensional combusting flows in an annular gas turbine combustor.
On multigrid methods for image reconstruction from projections
Henson, V.E.; Robinson, B.T.; Limber, M.
1994-12-31
The sampled Radon transform of a 2D function can be represented as a continuous linear map R : L{sup 1} {yields} R{sup N}. The image reconstruction problem is: given a vector b {element_of} R{sup N}, find an image (or density function) u(x, y) such that Ru = b. Since in general there are infinitely many solutions, the authors pick the solution with minimal 2-norm. Numerous proposals have been made regarding how best to discretize this problem. One can, for example, select a set of functions {phi}{sub j} that span a particular subspace {Omega} {contained_in} L{sup 1}, and model R : {Omega} {yields} R{sup N}. The subspace {Omega} may be chosen as a member of a sequence of subspaces whose limit is dense in L{sup 1}. One approach to the choice of {Omega} gives rise to a natural pixel discretization of the image space. Two possible choices of the set {phi}{sub j} are the set of characteristic functions of finite-width `strips` representing energy transmission paths and the set of intersections of such strips. The authors have studied the eigenstructure of the matrices B resulting from these choices and the effect of applying a Gauss-Seidel iteration to the problem Bw = b. There exists a near null space into which the error vectors migrate with iteration, after which Gauss-Seidel iteration stalls. The authors attempt to accelerate convergence via a multilevel scheme, based on the principles of McCormick`s Multilevel Projection Method (PML). Coarsening is achieved by thickening the rays which results in a much smaller discretization of an optimal grid, and a halving of the number of variables. This approach satisfies all the requirements of the PML scheme. They have observed that a multilevel approach based on this idea accelerates convergence at least to the point where noise in the data dominates.
NASA Technical Reports Server (NTRS)
1981-01-01
Developments in numerical solution of certain types of partial differential equations by rapidly converging sequences of operations on supporting grids that range from very fine to very coarse are presented.
Multigrid on massively parallel architectures
Falgout, R D; Jones, J E
1999-09-17
The scalable implementation of multigrid methods for machines with several thousands of processors is investigated. Parallel performance models are presented for three different structured-grid multigrid algorithms, and a description is given of how these models can be used to guide implementation. Potential pitfalls are illustrated when moving from moderate-sized parallelism to large-scale parallelism, and results are given from existing multigrid codes to support the discussion. Finally, the use of mixed programming models is investigated for multigrid codes on clusters of SMPs.
Multigrid one shot methods for optimal control problems: Infinite dimensional control
NASA Technical Reports Server (NTRS)
Arian, Eyal; Taasan, Shlomo
1994-01-01
The multigrid one shot method for optimal control problems, governed by elliptic systems, is introduced for the infinite dimensional control space. ln this case, the control variable is a function whose discrete representation involves_an increasing number of variables with grid refinement. The minimization algorithm uses Lagrange multipliers to calculate sensitivity gradients. A preconditioned gradient descent algorithm is accelerated by a set of coarse grids. It optimizes for different scales in the representation of the control variable on different discretization levels. An analysis which reduces the problem to the boundary is introduced. It is used to approximate the two level asymptotic convergence rate, to determine the amplitude of the minimization steps, and the choice of a high pass filter to be used when necessary. The effectiveness of the method is demonstrated on a series of test problems. The new method enables the solutions of optimal control problems at the same cost of solving the corresponding analysis problems just a few times.
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.
Multigrid Method for Modeling Multi-Dimensional Combustion with Detailed Chemistry
NASA Technical Reports Server (NTRS)
Zheng, Xiaoqing; Liu, Chaoqun; Liao, Changming; Liu, Zhining; McCormick, Steve
1996-01-01
A highly accurate and efficient numerical method is developed for modeling 3-D reacting flows with detailed chemistry. A contravariant velocity-based governing system is developed for general curvilinear coordinates to maintain simplicity of the continuity equation and compactness of the discretization stencil. A fully-implicit backward Euler technique and a third-order monotone upwind-biased scheme on a staggered grid are used for the respective temporal and spatial terms. An efficient semi-coarsening multigrid method based on line-distributive relaxation is used as the flow solver. The species equations are solved in a fully coupled way and the chemical reaction source terms are treated implicitly. Example results are shown for a 3-D gas turbine combustor with strong swirling inflows.
A Full Multi-Grid Method for the Solution of the Cell Vertex Finite Volume Cauchy-Riemann Equations
NASA Technical Reports Server (NTRS)
Borzi, A.; Morton, K. W.; Sueli, E.; Vanmaele, M.
1996-01-01
The system of inhomogeneous Cauchy-Riemann equations defined on a square domain and subject to Dirichlet boundary conditions is considered. This problem is discretised by using the cell vertex finite volume method on quadrilateral meshes. The resulting algebraic problem is overdetermined and the solution is defined in a least squares sense. By this approach a consistent algebraic problem is obtained which differs from the original one by O(h(exp 2)) perturbations of the right-hand side. A suitable cell-based convergent smoothing iteration is presented which is naturally linked to the least squares formulation. Hence, a standard multi-grid algorithm is reported which combines the given smoother and cell-based transfer operators. Some remarkable reduction properties of these operators are shown. A full multi-grid method is discussed which solves the discrete problem to the level of truncation error by employing one multi-grid cycle at each current level of discretisation. Experiments and applications of the full multi-grid scheme are presented.
Magnetic agglomeration method for size control in the synthesis of magnetic nanoparticles
Huber, Dale L.
2011-07-05
A method for controlling the size of chemically synthesized magnetic nanoparticles that employs magnetic interaction between particles to control particle size and does not rely on conventional kinetic control of the reaction to control particle size. The particles are caused to reversibly agglomerate and precipitate from solution; the size at which this occurs can be well controlled to provide a very narrow particle size distribution. The size of particles is controllable by the size of the surfactant employed in the process; controlling the size of the surfactant allows magnetic control of the agglomeration and precipitation processes. Agglomeration is used to effectively stop particle growth to provide a very narrow range of particle sizes.
A cell-vertex multigrid method for the Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Radespiel, R.
1989-01-01
A cell-vertex scheme for the Navier-Stokes equations, which is based on central difference approximations and Runge-Kutta time stepping, is described. Using local time stepping, implicit residual smoothing, a multigrid method, and carefully controlled artificial dissipative terms, very good convergence rates are obtained for a wide range of two- and three-dimensional flows over airfoils and wings. The accuracy of the code is examined by grid refinement studies and comparison with experimental data. For an accurate prediction of turbulent flows with strong separations, a modified version of the nonequilibrium turbulence model of Johnson and King is introduced, which is well suited for an implementation into three-dimensional Navier-Stokes codes. It is shown that the solutions for three-dimensional flows with strong separations can be dramatically improved, when a nonequilibrium model of turbulence is used.
Practical improvements of multi-grid iteration for adaptive mesh refinement method
NASA Astrophysics Data System (ADS)
Miyashita, Hisashi; Yamada, Yoshiyuki
2005-03-01
Adaptive mesh refinement(AMR) is a powerful tool to efficiently solve multi-scaled problems. However, the vanilla AMR method has a well-known critical demerit, i.e., it cannot be applied to non-local problems. Although multi-grid iteration (MGI) can be regarded as a good remedy for a non-local problem such as the Poisson equation, we observed fundamental difficulties in applying the MGI technique in AMR to realistic problems under complicated mesh layouts because it does not converge or it requires too many iterations even if it does converge. To cope with the problem, when updating the next approximation in the MGI process, we calculate the precise total corrections that are relatively accurate to the current residual by introducing a new iteration for such a total correction. This procedure greatly accelerates the MGI convergence speed especially under complicated mesh layouts.
NASA Technical Reports Server (NTRS)
Zeng, S.; Wesseling, P.
1993-01-01
The performance of a linear multigrid method using four smoothing methods, called SCGS (Symmetrical Coupled GauBeta-Seidel), CLGS (Collective Line GauBeta-Seidel), SILU (Scalar ILU), and CILU (Collective ILU), is investigated for the incompressible Navier-Stokes equations in general coordinates, in association with Galerkin coarse grid approximation. Robustness and efficiency are measured and compared by application to test problems. The numerical results show that CILU is the most robust, SILU the least, with CLGS and SCGS in between. CLGS is the best in efficiency, SCGS and CILU follow, and SILU is the worst.
An Introduction to Algebraic Multigrid
Falgout, R D
2006-04-25
Algebraic multigrid (AMG) solves linear systems based on multigrid principles, but in a way that only depends on the coefficients in the underlying matrix. The author begins with a basic introduction to AMG methods, and then describes some more recent advances and theoretical developments
A parallel geometric multigrid method for finite elements on octree meshes
Sampath, Rahul S; Biros, George
2010-01-01
In this article, we present a parallel geometric multigrid algorithm for solving variable-coefficient elliptic partial differential equations on the unit box (with Dirichlet or Neumann boundary conditions) using highly nonuniform, octree-based, conforming finite element discretizations. Our octrees are 2:1 balanced, that is, we allow no more than one octree-level difference between octants that share a face, edge, or vertex. We describe a parallel algorithm whose input is an arbitrary 2:1 balanced fine-grid octree and whose output is a set of coarser 2:1 balanced octrees that are used in the multigrid scheme. Also, we derive matrix-free schemes for the discretized finite element operators and the intergrid transfer operations. The overall scheme is second-order accurate for sufficiently smooth right-hand sides and material properties; its complexity for nearly uniform trees is {Omicron}(N/n{sub p} log N/n{sub p}) + {Omicron}(n{sub p} log n{sub p}), where N is the number of octree nodes and n{sub p} is the number of processors. Our implementation uses the Message Passing Interface standard. We present numerical experiments for the Laplace and Navier (linear elasticity) operators that demonstrate the scalability of our method. Our largest run was a highly nonuniform, 8-billion-unknown, elasticity calculation using 32,000 processors on the Teragrid system, 'Ranger,' at the Texas Advanced Computing Center. Our implementation is publically available in the Dendro library, which is built on top of the PETSc library from Argonne National Laboratory.
Toward robust scalable algebraic multigrid solvers.
Waisman, Haim; Schroder, Jacob; Olson, Luke; Hiriyur, Badri; Gaidamour, Jeremie; Siefert, Christopher; Hu, Jonathan Joseph; Tuminaro, Raymond Stephen
2010-10-01
This talk highlights some multigrid challenges that arise from several application areas including structural dynamics, fluid flow, and electromagnetics. A general framework is presented to help introduce and understand algebraic multigrid methods based on energy minimization concepts. Connections between algebraic multigrid prolongators and finite element basis functions are made to explored. It is shown how the general algebraic multigrid framework allows one to adapt multigrid ideas to a number of different situations. Examples are given corresponding to linear elasticity and specifically in the solution of linear systems associated with extended finite elements for fracture problems.
NASA Astrophysics Data System (ADS)
Jönsthövel, T. B.; van Gijzen, M. B.; MacLachlan, S.; Vuik, C.; Scarpas, A.
2012-09-01
Many applications in computational science and engineering concern composite materials, which are characterized by large discontinuities in the material properties. Such applications require fine-scale finite-element meshes, which lead to large linear systems that are challenging to solve with current direct and iterative solutions algorithms. In this paper, we consider the simulation of asphalt concrete, which is a mixture of components with large differences in material stiffness. The discontinuities in material stiffness give rise to many small eigenvalues that negatively affect the convergence of iterative solution algorithms such as the preconditioned conjugate gradient (PCG) method. This paper considers the deflated preconditioned conjugate gradient (DPCG) method in which the rigid body modes of sets of elements with homogeneous material properties are used as deflation vectors. As preconditioner we consider several variants of the algebraic multigrid smoothed aggregation method. We evaluate the performance of the DPCG method on a parallel computer using up to 64 processors. Our test problems are derived from real asphalt core samples, obtained using CT scans. We show that the DPCG method is an efficient and robust technique for solving these challenging linear systems.
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.
NASA Astrophysics Data System (ADS)
Zhu, Yu; Cangellaris, Andreas C.
2002-05-01
A new finite element methodology is presented for fast and robust numerical simulation of three-dimensional electromagnetic wave phenomena. The new methodology combines nested multigrid techniques with the ungauged vector and scalar potential formulation of the finite element method. The finite element modeling is performed on nested meshes over the computational domain of interest. The iterative solution of the finite element matrix on the finest mesh is performed using the conjugate gradient method, while the nested multigrid vector and scalar potential algorithm acts as the preconditioner for the iterative solver. Numerical experiments from the application of the new methodology to three-dimensional electromagnetic scattering are used to demonstrate its superior numerical convergence and efficient memory usage.
Development of a pressure based multigrid solution method for complex fluid flows
NASA Technical Reports Server (NTRS)
Shyy, Wei
1991-01-01
In order to reduce the computational difficulty associated with a single grid (SG) solution procedure, the multigrid (MG) technique was identified as a useful means for improving the convergence rate of iterative methods. A full MG full approximation storage (FMG/FAS) algorithm is used to solve the incompressible recirculating flow problems in complex geometries. The algorithm is implemented in conjunction with a pressure correction staggered grid type of technique using the curvilinear coordinates. In order to show the performance of the method, two flow configurations, one a square cavity and the other a channel, are used as test problems. Comparisons are made between the iterations, equivalent work units, and CPU time. Besides showing that the MG method can yield substantial speed-up with wide variations in Reynolds number, grid distributions, and geometry, issues such as the convergence characteristics of different grid levels, the choice of convection schemes, and the effectiveness of the basic iteration smoothers are studied. An adaptive grid scheme is also combined with the MG procedure to explore the effects of grid resolution on the MG convergence rate as well as the numerical accuracy.
Peláez, Daniel; Meyer, Hans-Dieter
2013-01-01
In this article, a new method, multigrid POTFIT (MGPF), is presented. MGPF is a grid-based algorithm which transforms a general potential energy surface into product form, that is, a sum of products of one-dimensional functions. This form is necessary to profit from the computationally advantageous multiconfiguration time-dependent Hartree method for quantum dynamics. MGPF circumvents the dimensionality related issues present in POTFIT [A. Jäckle and H.-D. Meyer, J. Chem. Phys. 104, 7974 (1996)], allowing quantum dynamical studies of systems up to about 12 dimensions. MGPF requires the definition of a fine grid and a coarse grid, the latter being a subset of the former. The MGPF approximation relies on a series of underlying POTFIT calculations on grids which are smaller than the fine one and larger than or equal to the coarse one. This aspect makes MGPF a bit less accurate than POTFIT but orders of magnitude faster and orders of magnitude less memory demanding than POTFIT. Moreover, like POTFIT, MGPF is variational and provides an efficient error control. PMID:23298029
NASA Technical Reports Server (NTRS)
Liu, C.; Liu, Z.
1993-01-01
The high order finite difference and multigrid methods have been successfully applied to direct numerical simulation (DNS) for flow transition in 3D channels and 3D boundary layers with 2D and 3D isolated and distributed roughness in a curvilinear coordinate system. A fourth-order finite difference technique on stretched and staggered grids, a fully-implicit time marching scheme, a semicoarsening multigrid method associated with line distributive relaxation scheme, and a new treatment of the outflow boundary condition, which needs only a very short buffer domain to damp all wave reflection, are developed. These approaches make the multigrid DNS code very accurate and efficient. This makes us not only able to do spatial DNS for the 3D channel and flat plate at low computational costs, but also able to do spatial DNS for transition in the 3D boundary layer with 3D single and multiple roughness elements. Numerical results show good agreement with the linear stability theory, the secondary instability theory, and a number of laboratory experiments.
Filtering Algebraic Multigrid and Adaptive Strategies
Nagel, A; Falgout, R D; Wittum, G
2006-01-31
Solving linear systems arising from systems of partial differential equations, multigrid and multilevel methods have proven optimal complexity and efficiency properties. Due to shortcomings of geometric approaches, algebraic multigrid methods have been developed. One example is the filtering algebraic multigrid method introduced by C. Wagner. This paper proposes a variant of Wagner's method with substantially improved robustness properties. The method is used in an adaptive, self-correcting framework and tested numerically.
Final Report on Subcontract B591217: Multigrid Methods for Systems of PDEs
Xu, J; Brannick, J J; Zikatanov, L
2011-10-25
Progress is summarized in the following areas of study: (1) Compatible relaxation; (2) Improving aggregation-based MG solver performance - variable cycle; (3) First Order System Least Squares (FOSLS) for LQCD; (4) Auxiliary space preconditioners; (5) Bootstrap algebraic multigrid; and (6) Practical applications of AMG and fast auxiliary space preconditioners.
Element Agglomeration Algebraic Multigrid and Upscaling Library
2015-02-11
ELAG is a serial C++ library for numerical upscaling of finite element discretizations. It provides optimal complexity algorithms to build multilevel hierarchies and solvers that can be used for solving a wide class of partial differential equation (elliptic, hyperbolic, saddle point problems) on general unstructured mesh. Additionally, a novel multilevel solver for saddle point problems with divergence constraint is implemented.
Another look at neural multigrid
Baeker, M.
1997-04-01
We present a new multigrid method called neural multigrid which is based on joining multigrid ideas with concepts from neural nets. The main idea is to use the Greenbaum criterion as a cost functional for the neural net. The algorithm is able to learn efficient interpolation operators in the case of the ordered Laplace equation with only a very small critical slowing down and with a surprisingly small amount of work comparable to that of a Conjugate Gradient solver. In the case of the two-dimensional Laplace equation with SU(2) gauge fields at {beta}=0 the learning exhibits critical slowing down with an exponent of about z {approx} 0.4. The algorithm is able to find quite good interpolation operators in this case as well. Thereby it is proven that a practical true multigrid algorithm exists even for a gauge theory. An improved algorithm using dynamical blocks that will hopefully overcome the critical slowing down completely is sketched.
Lignite pellets and methods of agglomerating or pelletizing
Baker, Albert F.; Blaustein, Eric W.; Deurbrouck, Albert W.; Garvin, John P.; McKeever, Robert E.
1981-01-01
The specification discloses lignite pellets which are relatively hard, dust resistant, of generally uniform size and free from spontaneous ignition and general degradation. Also disclosed are methods for making such pellets which involve crushing as mined lignite, mixing said lignite with a binder such as asphalt, forming the lignite binder mixture into pellets, and drying the pellets.
New convergence estimates for multigrid algorithms
Bramble, J.H.; Pasciak, J.E.
1987-10-01
In this paper, new convergence estimates are proved for both symmetric and nonsymmetric multigrid algorithms applied to symmetric positive definite problems. Our theory relates the convergence of multigrid algorithms to a ''regularity and approximation'' parameter ..cap alpha.. epsilon (0, 1) and the number of relaxations m. We show that for the symmetric and nonsymmetric ..nu.. cycles, the multigrid iteration converges for any positive m at a rate which deteriorates no worse than 1-cj/sup -(1-//sup ..cap alpha..//sup )///sup ..cap alpha../, where j is the number of grid levels. We then define a generalized ..nu.. cycle algorithm which involves exponentially increasing (for example, doubling) the number of smoothings on successively coarser grids. We show that the resulting symmetric and nonsymmetric multigrid iterations converge for any ..cap alpha.. with rates that are independent of the mesh size. The theory is presented in an abstract setting which can be applied to finite element multigrid and finite difference multigrid methods.
NASA Technical Reports Server (NTRS)
Demuren, A. O.
1990-01-01
A multigrid method is presented for calculating turbulent jets in crossflow. Fairly rapid convergence is obtained with the k-epsilon turbulence model, but computations with a full Reynolds stress turbulence model (RSM) are not yet very efficient. Grid dependency tests show that there are slight differences between results obtained on the two finest grid levels. Computations using the RSM are significantly different from those with k-epsilon model and compare better to experimental data. Some work is still required to improve the efficiency of the computations with the RSM.
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.
Lee, Barry
2010-05-01
This paper presents a new multigrid method applied to the most common Sn discretizations (Petrov-Galerkin, diamond-differenced, corner-balanced, and discontinuous Galerkin) of the mono-energetic Boltzmann transport equation in the optically thick and thin regimes, and with strong anisotropic scattering. Unlike methods that use scalar DSA diffusion preconditioners for the source iteration, this multigrid method is applied directly to an integral equation for the scalar flux. Thus, unlike the former methods that apply a multigrid strategy to the scalar DSA diffusion operator, this method applies a multigrid strategy to the integral source iteration operator, which is an operator for 5 independent variables in spatial 3-d (3 in space and 2 in angle) and 4 independent variables in spatial 2-d (2 in space and 2 in angle). The core smoother of this multigrid method involves applications of the integral operator. Since the kernel of this integral operator involves the transport sweeps, applying this integral operator requires a transport sweep (an inversion of an upper triagular matrix) for each of the angles used. As the equation is in 5-space or 4-space, the multigrid approach in this paper coarsens in both angle and space, effecting efficient applications of the coarse integral operators. Although each V-cycle of this method is more expensive than a V-cycle for the DSA preconditioner, since the DSA equation does not have angular dependence, the overall computational efficiency is about the same for problems where DSA preconditioning {\\it is} effective. This new method also appears to be more robust over all parameter regimes than DSA approaches. Moreover, this new method is applicable to a variety of Sn spatial discretizations, to problems involving a combination of optically thick and thin regimes, and more importantly, to problems with anisotropic scattering cross-sections, all of which DSA approaches perform poorly or not applicable at all. This multigrid approach
Multicloud: Multigrid convergence with a meshless operator
Katz, Aaron Jameson, Antony
2009-08-01
The primary objective of this work is to develop and test a new convergence acceleration technique we call multicloud. Multicloud is well-founded in the mathematical basis of multigrid, but relies on a meshless operator on coarse levels. The meshless operator enables extremely simple and automatic coarsening procedures for arbitrary meshes using arbitrary fine level discretization schemes. The performance of multicloud is compared with established multigrid techniques for structured and unstructured meshes for the Euler equations on two-dimensional test cases. Results indicate comparable convergence rates per unit work for multicloud and multigrid. However, because of its mesh and scheme transparency, multicloud may be applied to a wide array of problems with no modification of fine level schemes as is often required with agglomeration techniques. The implication is that multicloud can be implemented in a completely modular fashion, allowing researchers to develop fine level algorithms independent of the convergence accelerator for complex three-dimensional problems.
Self-correcting Multigrid Solver
Jerome L.V. Lewandowski
2004-06-29
A new multigrid algorithm based on the method of self-correction for the solution of elliptic problems is described. The method exploits information contained in the residual to dynamically modify the source term (right-hand side) of the elliptic problem. It is shown that the self-correcting solver is more efficient at damping the short wavelength modes of the algebraic error than its standard equivalent. When used in conjunction with a multigrid method, the resulting solver displays an improved convergence rate with no additional computational work.
NASA Astrophysics Data System (ADS)
Chern, R. L.; Chang, C. Chung; Chang, Chien C.; Hwang, R. R.
2003-08-01
In this study, two fast and accurate methods of inverse iteration with multigrid acceleration are developed to compute band structures of photonic crystals of general shape. In particular, we report two-dimensional photonic crystals of silicon air with an optimal full band gap of gap-midgap ratio Δω/ωmid=0.2421, which is 30% larger than ever reported in the literature. The crystals consist of a hexagonal array of circular columns, each connected to its nearest neighbors by slender rectangular rods. A systematic study with respect to the geometric parameters of the photonic crystals was made possible with the present method in drawing a three-dimensional band-gap diagram with reasonable computing time.
Chern, R L; Chang, C Chung; Chang, Chien C; Hwang, R R
2003-08-01
In this study, two fast and accurate methods of inverse iteration with multigrid acceleration are developed to compute band structures of photonic crystals of general shape. In particular, we report two-dimensional photonic crystals of silicon air with an optimal full band gap of gap-midgap ratio Deltaomega/omega(mid)=0.2421, which is 30% larger than ever reported in the literature. The crystals consist of a hexagonal array of circular columns, each connected to its nearest neighbors by slender rectangular rods. A systematic study with respect to the geometric parameters of the photonic crystals was made possible with the present method in drawing a three-dimensional band-gap diagram with reasonable computing time. PMID:14525145
Multigrid for locally refined meshes
Shapira, Y.
1999-12-01
A multilevel method for the solution of finite element schemes on locally refined meshes is introduced. For isotropic diffusion problems, the condition number of the two-level method is bounded independently of the mesh size and the discontinuities in the diffusion coefficient. The curves of discontinuity need not be aligned with the coarse mesh. Indeed, numerical applications with 10 levels of local refinement yield a rapid convergence of the corresponding 10-level, multigrid V-cycle and other multigrid cycles which are more suitable for parallelism even when the discontinuities are invisible on most of the coarse meshes.
Canonical-variables multigrid method for steady-state Euler equations
NASA Technical Reports Server (NTRS)
Taasan, Shlomo
1994-01-01
A novel approach for the solution of inviscid flow problems for subsonic compressible flows is described. The approach is based on canonical forms of the equations, in which subsystems governed by hyperbolic operators are separated from those governed by elliptic ones. The discretizations used as well as the iterative techniques for the different subsystems are inherently different. Hyperbolic parts, which describe, in general, propagation phenomena, are discretized using upwind schemes and are solved by marching techniques. Elliptic parts, which are directionally unbiased, are discretized using h-elliptic central discretizations, and are solved by pointwise relaxations together with coarse grid acceleration. The resulting discretization schemes introduce artificial viscosity only for the hyperbolic parts of the system; thus a smaller total artificial viscosity is used, while the multigrid solvers used are much more efficient. Solutions of the subsonic compressible Euler equations are achieved at the same efficiency as the full potential equation.
MGLab: An Interactive Multigrid Environment
NASA Technical Reports Server (NTRS)
Bordner, James; Saied, Faisal
1996-01-01
MGLab is a set of Matlab functions that defines an interactive environment for experimenting with multigrid algorithms. The package solves two-dimensional elliptic partial differential equations discretized using either finite differences or finite volumes, depending on the problem. Built-in problems include the Poisson equation, the Helmholtz equation, a convection-diffusion problem, and a discontinuous coefficient problem. A number of parameters controlling the multigrid V-cycle can be set using a point-and-click mechanism. The menu-based user interface also allows a choice of several Krylov subspace methods, including CG, GMRES(k), and Bi-CGSTAB, which can be used either as stand-alone solvers or as multigrid acceleration schemes. The package exploits Matlab's visualization and sparse matrix features and has been structured to be easily extensible.
NASA Technical Reports Server (NTRS)
Yang, Cheng I.; Guo, Yan-Hu; Liu, C.- H.
1996-01-01
The analysis and design of a submarine propulsor requires the ability to predict the characteristics of both laminar and turbulent flows to a higher degree of accuracy. This report presents results of certain benchmark computations based on an upwind, high-resolution, finite-differencing Navier-Stokes solver. The purpose of the computations is to evaluate the ability, the accuracy and the performance of the solver in the simulation of detailed features of viscous flows. Features of interest include flow separation and reattachment, surface pressure and skin friction distributions. Those features are particularly relevant to the propulsor analysis. Test cases with a wide range of Reynolds numbers are selected; therefore, the effects of the convective and the diffusive terms of the solver can be evaluated separately. Test cases include flows over bluff bodies, such as circular cylinders and spheres, at various low Reynolds numbers, flows over a flat plate with and without turbulence effects, and turbulent flows over axisymmetric bodies with and without propulsor effects. Finally, to enhance the iterative solution procedure, a full approximation scheme V-cycle multigrid method is implemented. Preliminary results indicate that the method significantly reduces the computational effort.
NASA Astrophysics Data System (ADS)
Debreu, Laurent; Neveu, Emilie; Simon, Ehouarn; Le Dimet, Francois Xavier; Vidard, Arthur
2014-05-01
In order to lower the computational cost of the variational data assimilation process, we investigate the use of multigrid methods to solve the associated optimal control system. On a linear advection equation, we study the impact of the regularization term on the optimal control and the impact of discretization errors on the efficiency of the coarse grid correction step. We show that even if the optimal control problem leads to the solution of an elliptic system, numerical errors introduced by the discretization can alter the success of the multigrid methods. The view of the multigrid iteration as a preconditioner for a Krylov optimization method leads to a more robust algorithm. A scale dependent weighting of the multigrid preconditioner and the usual background error covariance matrix based preconditioner is proposed and brings significant improvements. [1] Laurent Debreu, Emilie Neveu, Ehouarn Simon, François-Xavier Le Dimet and Arthur Vidard, 2014: Multigrid solvers and multigrid preconditioners for the solution of variational data assimilation problems, submitted to QJRMS, http://hal.inria.fr/hal-00874643 [2] Emilie Neveu, Laurent Debreu and François-Xavier Le Dimet, 2011: Multigrid methods and data assimilation - Convergence study and first experiments on non-linear equations, ARIMA, 14, 63-80, http://intranet.inria.fr/international/arima/014/014005.html
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.
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.
Tsujita, K.; Endo, T.; Yamamoto, A.
2013-07-01
An efficient numerical method for time-dependent transport equation, the mutigrid amplitude function (MAF) method, is proposed. The method of characteristics (MOC) is being widely used for reactor analysis thanks to the advances of numerical algorithms and computer hardware. However, efficient kinetic calculation method for MOC is still desirable since it requires significant computation time. Various efficient numerical methods for solving the space-dependent kinetic equation, e.g., the improved quasi-static (IQS) and the frequency transform methods, have been developed so far mainly for diffusion calculation. These calculation methods are known as effective numerical methods and they offer a way for faster computation. However, they have not been applied to the kinetic calculation method using MOC as the authors' knowledge. Thus, the MAF method is applied to the kinetic calculation using MOC aiming to reduce computation time. The MAF method is a unified numerical framework of conventional kinetic calculation methods, e.g., the IQS, the frequency transform, and the theta methods. Although the MAF method is originally developed for the space-dependent kinetic calculation based on the diffusion theory, it is extended to transport theory in the present study. The accuracy and computational time are evaluated though the TWIGL benchmark problem. The calculation results show the effectiveness of the MAF method. (authors)
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.
Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics
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, 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.
Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics
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
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, 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.
Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics
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, 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.
NASA Astrophysics Data System (ADS)
Li, Gang; Zhang, Lili; Hao, Tianyao
2016-02-01
An effective solver for the large complex system of linear equations is critical for improving the accuracy of numerical solutions in three-dimensional (3D) magnetotelluric (MT) modeling using the staggered finite-difference (SFD) method. In electromagnetic modeling, the formed system of linear equations is commonly solved using preconditioned iterative relaxation methods. We present 3D MT modeling using the SFD method, based on former work. The multigrid solver and three solvers preconditioned by incomplete Cholesky decomposition—the minimum residual method, the generalized product bi-conjugate gradient method and the bi-conjugate gradient stabilized method—are used to solve the formed system of linear equations. Divergence correction for the magnetic field is applied. We also present a comparison of the stability and convergence of these iterative solvers if divergence correction is used. Model tests show that divergence correction improves the convergence of iterative solvers and the accuracy of numerical results. Divergence correction can also decrease the number of iterations for fast convergence without changing the stability of linear solvers. For consideration of the computation time and memory requirements, the multigrid solver combined with divergence correction is preferred for 3D MT field simulation.
Multigrid method applied to the solution of an elliptic, generalized eigenvalue problem
Alchalabi, R.M.; Turinsky, P.J.
1996-12-31
The work presented in this paper is concerned with the development of an efficient MG algorithm for the solution of an elliptic, generalized eigenvalue problem. The application is specifically applied to the multigroup neutron diffusion equation which is discretized by utilizing the Nodal Expansion Method (NEM). The underlying relaxation method is the Power Method, also known as the (Outer-Inner Method). The inner iterations are completed using Multi-color Line SOR, and the outer iterations are accelerated using Chebyshev Semi-iterative Method. Furthermore, the MG algorithm utilizes the consistent homogenization concept to construct the restriction operator, and a form function as a prolongation operator. The MG algorithm was integrated into the reactor neutronic analysis code NESTLE, and numerical results were obtained from solving production type benchmark problems.
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]).
MueLu Multigrid Preconditioning Package
2012-09-11
MueLu is intended for the research and development of multigrid algorithms used in the solution of sparse linear systems arising from systems of partial differential equations. The software provides multigrid source code, test programs, and short example programs to demonstrate the various interfaces for creating, accessing, and applying the solvers. MueLu currently provides an implementation of smoothed aggregation algebraic multigrid method and interfaces to many commonly used smoothers. However, the software is intended to be extensible, and new methods can be incorporated easily. MueLu also allows for advanced usage, such as combining multiple methods and segregated solves. The library supports point and block access to matrix data. All algorithms and methods in MueLu have been or will be published in the open scientific literature.
MueLu Multigrid Preconditioning Package
2012-09-11
MueLu is intended for the research and development of multigrid algorithms used in the solution of sparse linear systems arising from systems of partial differential equations. The software provides multigrid source code, test programs, and short example programs to demonstrate the various interfaces for creating, accessing, and applying the solvers. MueLu currently provides an implementation of smoothed aggregation algebraic multigrid method and interfaces to many commonly used smoothers. However, the software is intended to bemore » extensible, and new methods can be incorporated easily. MueLu also allows for advanced usage, such as combining multiple methods and segregated solves. The library supports point and block access to matrix data. All algorithms and methods in MueLu have been or will be published in the open scientific literature.« less
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
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
Selective oil agglomeration of lignite
Halime Abakay Temel; Volkan Bozkurt; Arun Kumar Majumder
2009-01-15
In this study, desulfurization and deashing of Adiyaman-Glbai lignite by the agglomeration method were studied. For this purpose, three groups of agglomeration experiments were made. The effects of solid concentration, bridging liquid type and dosage, pH, and screen size on the agglomeration after desliming were investigated in the first group of experiments. The effects of lake water and sea water (the Mediterranean Sea water, the Aegean Sea water, and the Black Sea water) on the agglomeration were investigated in the second group of experiments. The effects of different salts (NaCl, MgCl{sub 2}, and FeCl{sub 3}) on the agglomeration were investigated in the third group of experiments. Agglomeration results showed that the usage of sea waters and soda lake water in the agglomeration medium had a positive effect on the reduction of total sulfur content of agglomerates. In addition, the usage of NaCl, MgCl{sub 2}, and FeCl{sub 3} in the agglomeration medium had a positive effect on the ash content reduction of the agglomerates. 27 refs., 10 figs., 6 tabs.
3D magnetospheric parallel hybrid multi-grid method applied to planet-plasma interactions
NASA Astrophysics Data System (ADS)
Leclercq, L.; Modolo, R.; Leblanc, F.; Hess, S.; Mancini, M.
2016-03-01
We present a new method to exploit multiple refinement levels within a 3D parallel hybrid model, developed to study planet-plasma interactions. This model is based on the hybrid formalism: ions are kinetically treated whereas electrons are considered as a inertia-less fluid. Generally, ions are represented by numerical particles whose size equals the volume of the cells. Particles that leave a coarse grid subsequently entering a refined region are split into particles whose volume corresponds to the volume of the refined cells. The number of refined particles created from a coarse particle depends on the grid refinement rate. In order to conserve velocity distribution functions and to avoid calculations of average velocities, particles are not coalesced. Moreover, to ensure the constancy of particles' shape function sizes, the hybrid method is adapted to allow refined particles to move within a coarse region. Another innovation of this approach is the method developed to compute grid moments at interfaces between two refinement levels. Indeed, the hybrid method is adapted to accurately account for the special grid structure at the interfaces, avoiding any overlapping grid considerations. Some fundamental test runs were performed to validate our approach (e.g. quiet plasma flow, Alfven wave propagation). Lastly, we also show a planetary application of the model, simulating the interaction between Jupiter's moon Ganymede and the Jovian plasma.
New Multigrid Solver Advances in TOPS
Falgout, R D; Brannick, J; Brezina, M; Manteuffel, T; McCormick, S
2005-06-27
In this paper, we highlight new multigrid solver advances in the Terascale Optimal PDE Simulations (TOPS) project in the Scientific Discovery Through Advanced Computing (SciDAC) program. We discuss two new algebraic multigrid (AMG) developments in TOPS: the adaptive smoothed aggregation method ({alpha}SA) and a coarse-grid selection algorithm based on compatible relaxation (CR). The {alpha}SA method is showing promising results in initial studies for Quantum Chromodynamics (QCD) applications. The CR method has the potential to greatly improve the applicability of AMG.
Some multigrid algorithms for SIMD machines
Dendy, J.E. Jr.
1996-12-31
Previously a semicoarsening multigrid algorithm suitable for use on SIMD architectures was investigated. Through the use of new software tools, the performance of this algorithm has been considerably improved. The method has also been extended to three space dimensions. The method performs well for strongly anisotropic problems and for problems with coefficients jumping by orders of magnitude across internal interfaces. The parallel efficiency of this method is analyzed, and its actual performance on the CM-5 is compared with its performance on the CRAY-YMP. A standard coarsening multigrid algorithm is also considered, and we compare its performance on these two platforms as well.
Application of multigrid methods to the solution of liquid crystal equations on a SIMD computer
NASA Technical Reports Server (NTRS)
Farrell, Paul A.; Ruttan, Arden; Zeller, Reinhardt R.
1993-01-01
We will describe a finite difference code for computing the equilibrium configurations of the order-parameter tensor field for nematic liquid crystals in rectangular regions by minimization of the Landau-de Gennes Free Energy functional. The implementation of the free energy functional described here includes magnetic fields, quadratic gradient terms, and scalar bulk terms through the fourth order. Boundary conditions include the effects of strong surface anchoring. The target architectures for our implementation are SIMD machines, with interconnection networks which can be configured as 2 or 3 dimensional grids, such as the Wavetracer DTC. We also discuss the relative efficiency of a number of iterative methods for the solution of the linear systems arising from this discretization on such architectures.
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.
Spectral element multigrid. Part 2: Theoretical justification
NASA Technical Reports Server (NTRS)
Maday, Yvon; Munoz, Rafael
1988-01-01
A multigrid algorithm is analyzed which is used for solving iteratively the algebraic system resulting from tha approximation of a second order problem by spectral or spectral element methods. The analysis, performed here in the one dimensional case, justifies the good smoothing properties of the Jacobi preconditioner that was presented in Part 1 of this paper.
Unsteady Analysis of Separated Aerodynamic Flows Using an Unstructured Multigrid Algorithm
NASA Technical Reports Server (NTRS)
Pelaez, Juan; Mavriplis, Dimitri J.; Kandil, Osama
2001-01-01
An implicit method for the computation of unsteady flows on unstructured grids is presented. The resulting nonlinear system of equations is solved at each time step using an agglomeration multigrid procedure. The method allows for arbitrarily large time steps and is efficient in terms of computational effort and storage. Validation of the code using a one-equation turbulence model is performed for the well-known case of flow over a cylinder. A Detached Eddy Simulation model is also implemented and its performance compared to the one equation Spalart-Allmaras Reynolds Averaged Navier-Stokes (RANS) turbulence model. Validation cases using DES and RANS include flow over a sphere and flow over a NACA 0012 wing including massive stall regimes. The project was driven by the ultimate goal of computing separated flows of aerodynamic interest, such as massive stall or flows over complex non-streamlined geometries.
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.
Matrix-dependent multigrid-homogenization for diffusion problems
Knapek, S.
1996-12-31
We present a method to approximately determine the effective diffusion coefficient on the coarse scale level of problems with strongly varying or discontinuous diffusion coefficients. It is based on techniques used also in multigrid, like Dendy`s matrix-dependent prolongations and the construction of coarse grid operators by means of the Galerkin approximation. In numerical experiments, we compare our multigrid-homogenization method with homogenization, renormalization and averaging approaches.
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.
Multigrid techniques for the numerical solution of the diffusion equation
NASA Technical Reports Server (NTRS)
Phillips, R. E.; Schmidt, F. W.
1984-01-01
An accurate numerical solution of diffusion problems containing large local gradients can be obtained with a significant reduction in computational time by using a multigrid computational scheme. The spatial domain is covered with sets of uniform square grids of different sizes. The finer grid patterns overlap the coarse grid patterns. The finite-difference expressions for each grid pattern are solved independently by iterative techniques. Two interpolation methods were used to establish the values of the potential function on the fine grid boundaries with information obtained from the coarse grid solution. The accuracy and computational requirements for solving a test problem by a simple multigrid and a multilevel-multigrid method were compared. The multilevel-multigrid method combined with a Taylor series interpolation scheme was found to be best.
2013-05-06
AMG2013 is a parallel algebraic multigrid solver for linear systems arising from problems on unstructured grids. It has been derived directly from the Boomer AMG solver in the hypre library, a large linear solvers library that is being developed in the Center for Applied Scientific Computing (CASC) at LLNL. The driver provided in the benchmark can build various test problems. The default problem is a Laplace type problem on an unstructured domain with various jumps and an anisotropy in one part.
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.
Element Agglomeration Algebraic Multilevel Monte-Carlo Library
2015-02-19
ElagMC is a parallel C++ library for Multilevel Monte Carlo simulations with algebraically constructed coarse spaces. ElagMC enables Multilevel variance reduction techniques in the context of general unstructured meshes by using the specialized element-based agglomeration techniques implemented in ELAG (the Element-Agglomeration Algebraic Multigrid and Upscaling Library developed by U. Villa and P. Vassilevski and currently under review for public release). The ElabMC library can support different type of deterministic problems, including mixed finite element discretizations of subsurface flow problems.
Element Agglomeration Algebraic Multilevel Monte-Carlo Library
2015-02-19
ElagMC is a parallel C++ library for Multilevel Monte Carlo simulations with algebraically constructed coarse spaces. ElagMC enables Multilevel variance reduction techniques in the context of general unstructured meshes by using the specialized element-based agglomeration techniques implemented in ELAG (the Element-Agglomeration Algebraic Multigrid and Upscaling Library developed by U. Villa and P. Vassilevski and currently under review for public release). The ElabMC library can support different type of deterministic problems, including mixed finite element discretizationsmore » of subsurface flow problems.« less
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.
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.
Progress with multigrid schemes for hypersonic flow problems
Radespiel, R.; Swanson, R.C.
1995-01-01
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 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{sup 6} and Mach numbers up to 25. 32 refs., 31 figs., 1 tab.
Coal Cleaning by Gas Agglomeration
Meiyu Shen; Royce Abbott; T. D. Wheelock
1998-03-01
The gas agglomeration method of coal cleaning was demonstrated with laboratory scale mixing equipment which made it possible to generate microscopic gas bubbles in aqueous suspensions of coal particles. A small amount of i-octane was introduced to enhance the hydrophobicity of the coal. Between 1.0 and 2.5 v/w% i-octane was sufficient based on coal weight. Coal agglomerates or aggregates were produced which were bound together by small gas bubbles.
2013-05-06
AMG2013 is a parallel algebraic multigrid solver for linear systems arising from problems on unstructured grids. It has been derived directly from the Boomer AMG solver in the hypre library, a large linear solvers library that is being developed in the Center for Applied Scientific Computing (CASC) at LLNL. The driver provided in the benchmark can build various test problems. The default problem is a Laplace type problem on an unstructured domain with various jumpsmore » and an anisotropy in one part.« less
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.
NASA Technical Reports Server (NTRS)
Mineck, Raymond E.; Thomas, James L.; Biedron, Robert T.; Diskin, Boris
2005-01-01
FMG3D (full multigrid 3 dimensions) is a pilot computer program that solves equations of fluid flow using a finite difference representation on a structured grid. Infrastructure exists for three dimensions but the current implementation treats only two dimensions. Written in Fortran 90, FMG3D takes advantage of the recursive subroutine feature, dynamic memory allocation, and structured-programming constructs of that language. FMG3D supports multi-block grids with three types of block-to-block interfaces: periodic, C-zero, and C-infinity. For all three types, grid points must match at interfaces. For periodic and C-infinity types, derivatives of grid metrics must be continuous at interfaces. The available equation sets are as follows: scalar elliptic equations, scalar convection equations, and the pressure-Poisson formulation of the Navier-Stokes equations for an incompressible fluid. All the equation sets are implemented with nonzero forcing functions to enable the use of user-specified solutions to assist in verification and validation. The equations are solved with a full multigrid scheme using a full approximation scheme to converge the solution on each succeeding grid level. Restriction to the next coarser mesh uses direct injection for variables and full weighting for residual quantities; prolongation of the coarse grid correction from the coarse mesh to the fine mesh uses bilinear interpolation; and prolongation of the coarse grid solution uses bicubic interpolation.
Choi, Young Joon; Jorshari, Razzi Movassaghi; Djilali, Ned
2015-03-10
Direct numerical simulations of the flow-nanoparticle interaction in a colloidal suspension are presented using an extended finite element method (XFEM) in which the dynamics of the nanoparticles is solved in a fully-coupled manner with the flow. The method is capable of accurately describing solid-fluid interfaces without the need of boundary-fitted meshes to investigate the dynamics of particles in complex flows. In order to accurately compute the high interparticle shear stresses and pressures while minimizing computing costs, an adaptive meshing technique is incorporated with the fluid-structure interaction algorithm. The particle-particle interaction at the microscopic level is modeled using the Lennard-Jones (LJ) potential and the corresponding potential parameters are determined by a scaling procedure. The study is relevant to the preparation of inks used in the fabrication of catalyst layers for fuel cells. In this paper, we are particularly interested in investigating agglomeration of the nanoparticles under external shear flow in a sliding bi-periodic Lees-Edwards frame. The results indicate that the external shear has a crucial impact on the structure formation of colloidal particles in a suspension.
Mechanisms for selective agglomeration of coals
Wheelock, T.D.; Drzymala, J.; Allen, R.W.; Hu, Y.-C.; Tyson, D.; Xiaoping, Qiu; Lessa, A.
1989-05-01
Work continued on the basic mechanisms which underlie various processes for beneficiating aqueous suspensions of coal by selective agglomeration with oil. A new method was demonstrated for characterizing the agglomerability of coal suspensions. This method utilizes a photometric dispersion analyzer to monitor changes in the turbidity of a particle suspension as increasing amounts of oil are added to the suspension in a batch agglomeration test. Agglomeration of the particles leads to a marked decrease in the turbidity of the suspension. Another experimental technique was also demonstrated for characterizing oil agglomeration. This technique involves measuring the rate of growth of agglomerates in a continuous flow system operating under stead-state conditions. The data are analyzed by means of a population balance. The results of a preliminary set of experiments in which Indiana V seam coal was agglomerated with tetralin seemed to fit a particular growth model very well. Equipment was also constructed for studying the kinetics of agglomeration in a batch process. While earlier work showed that quebracho (a commercially available dispersant) is a strong agglomeration depressant for pyrite, recent experiments with mixtures of Upper Freeport coal and mineral pyrite showed that quebracho does not appear to be sufficiently selective. Further consideration was given to the separation of mixtures of coal and pyrite agglomeration with heptane. 2 refs., 17 figs., 1 tab.
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.
Spectral Element Agglomerate AMGe
Chartier, T; Falgout, R; Henson, V E; Jones, J E; Vassilevski, P S; Manteuffel, T A; McCormick, S F; Ruge, J W
2005-05-20
The purpose of this note is to describe an algorithm resulting from the uniting of two ideas introduced and applied elsewhere. For many problems, AMG has always been difficult due to complexities whose natures are difficult to discern from the entries of matrix A alone. Element-based interpolation has been shown to be an effective method for some of these problems, but it requires access to the element matrices on all levels. One way to obtain these has been to perform element agglomeration to form coarse elements, but in complicated situations defining the coarse degrees of freedom (dofs) is not easy. The spectral approach to coarse dof selection is very attractive due to its elegance and simplicity. The algorithm presented here combines the robustness of element interpolation, the ease of coarsening by element agglomeration, and the simplicity of defining coarse dofs through the spectral approach. As demonstrated in the numerical results, the method does yield a reasonable solver for the problems described. It can, however, be an expensive method due to the number and cost of the local, small dense linear algebra problems; making it a generally competitive method remains an area for further research.
NASA Astrophysics Data System (ADS)
Ai, Xiaolan
Surface topography has long been recognized to have a significant influence on lubricated contacts. This thesis deals with the subject of elastohydrodynamic lubricated line and point contacts with rough surfaces (rough EHL contacts). As an introduction to this subject, a brief historical review is provided, followed by the mathematical descriptions of the rough EHL contacts for both Newtonian and non-Newtonian lubricants. On the basis of the merits of presently used numerical algorithms, two numerical methods, the semi-system method and the multigrid method, were adopted for developing fast numerical solvers to simulate the rough EHL contact problems. For line contact geometry, numerical simulations were performed for both steady and transient conditions. The surface irregularities examined range from single transverse bump or groove to random surface roughness. Based on the simulation results, an empirical formula for pressure fluctuations was regressed, and a fast pressure calculation model for EHL contact with arbitrary surface profiles was developed. As an extension to the 2-D surface irregularities, the problems of 3-D surface irregularities in line contact geometry were also examined. Parallel simulations were performed for point contact geometry. The types of surface irregularities studied included single asperity, dent, bump, multiple asperities, waviness, and random surface roughness. The orientation of the surface irregularities varies from transverse to striated to longitudinal. The simulation results reveal the fundamental fact that under heavily loaded conditions the domination of pressure flow yields to the unidirectional shear flow in the EHL conjunction. Lubricant passes though the EHL conjunction at approximately the rolling speed. For sliding contact with moving surface roughness, the rolling speed transport behavior leads to an induced transient image. This transient phenomena will be fully developed under steady-state conditions; and, as a
Multigrid solution of the convection-diffusion equation with high-Reynolds number
Zhang, Jun
1996-12-31
A fourth-order compact finite difference scheme is employed with the multigrid technique to solve the variable coefficient convection-diffusion equation with high-Reynolds number. Scaled inter-grid transfer operators and potential on vectorization and parallelization are discussed. The high-order multigrid method is unconditionally stable and produces solution of 4th-order accuracy. Numerical experiments are included.
COAL CLEANING BY GAS AGGLOMERATION
T.D. Wheelock
1999-03-01
The technical feasibility of a gas agglomeration method for cleaning coal was demonstrated by means of bench-scale tests conducted with a mixing system which enabled the treatment of ultra-fine coal particles with a colloidal suspension of microscopic gas bubbles in water. A suitable suspension of microbubbles was prepared by first saturating water with air or carbon dioxide under pressure then reducing the pressure to release the dissolved gas. The formation of microbubbles was facilitated by agitation and a small amount of i-octane. When the suspension of microbubbles and coal particles was mixed, agglomeration was rapid and small spherical agglomerates were produced. Since the agglomerates floated, they were separated from the nonfloating tailings in a settling chamber. By employing this process in numerous agglomeration tests of moderately hydrophobic coals with 26 wt.% ash, it was shown that the ash content would be reduced to 6--7 wt.% while achieving a coal recovery of 75 to 85% on a dry, ash-free basis. This was accomplished by employing a solids concentration of 3 to 5 w/w%, an air saturation pressure of 136 to 205 kPa (5 to 15 psig), and an i-octane concentration of 1.0 v/w% based on the weight of coal.
Towards Optimal Multigrid Efficiency for the Navier-Stokes Equations
NASA Technical Reports Server (NTRS)
Swanson, R. C.
2001-01-01
A fast multigrid solver for the steady incompressible Navier-Stokes 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. Numerical solutions are shown for flow over a flat plate and a Karman-Trefftz airfoil. Using collective Gauss-Seidel line relaxation in both the vertical and horizontal directions, multigrid convergence behavior approaching that of O(N) methods is achieved. The computational efficiency of the numerical scheme is compared with that of a Runge-Kutta based multigrid method.
A multigrid fluid pressure solver handling separating solid boundary conditions.
Chentanez, Nuttapong; Müller-Fischer, Matthias
2012-08-01
We present a multigrid method for solving the linear complementarity problem (LCP) resulting from discretizing the Poisson equation subject to separating solid boundary conditions in an Eulerian liquid simulation’s pressure projection step. The method requires only a few small changes to a multigrid solver for linear systems. Our generalized solver is fast enough to handle 3D liquid simulations with separating boundary conditions in practical domain sizes. Previous methods could only handle relatively small 2D domains in reasonable time, because they used expensive quadratic programming (QP) solvers. We demonstrate our technique in several practical scenarios, including nonaxis-aligned containers and moving solids in which the omission of separating boundary conditions results in disturbing artifacts of liquid sticking to solids. Our measurements show, that the convergence rate of our LCP solver is close to that of a standard multigrid solver. PMID:22411885
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.
Fast Multigrid Techniques in Total Variation-Based Image Reconstruction
NASA Technical Reports Server (NTRS)
Oman, Mary Ellen
1996-01-01
Existing multigrid techniques are used to effect an efficient method for reconstructing an image from noisy, blurred data. Total Variation minimization yields a nonlinear integro-differential equation which, when discretized using cell-centered finite differences, yields a full matrix equation. A fixed point iteration is applied with the intermediate matrix equations solved via a preconditioned conjugate gradient method which utilizes multi-level quadrature (due to Brandt and Lubrecht) to apply the integral operator and a multigrid scheme (due to Ewing and Shen) to invert the differential operator. With effective preconditioning, the method presented seems to require Omicron(n) operations. Numerical results are given for a two-dimensional example.
Some multigrid algorithms for elliptic problems on data parallel machines
Bandy, V.A.; Dendy, J.E. Jr.; Spangenberg, W.H.
1998-01-01
Previously a semicoarsening multigrid algorithm suitable for use on data parallel architectures was investigated. Through the use of new software tools, the performance of this algorithm has been considerably improved. The method has also been extended to three space dimensions. The method performs well for strongly anisotropic problems and for problems with coefficients jumping by orders of magnitude across internal interfaces. The parallel efficiency of this method is analyzed, and its actual performance on the CM-5 is compared with its performance on the CRAY Y-MP and the Sparc-5. A standard coarsening multigrid algorithm is also considered, and they compare its performance on these three platforms as well.
Black box multigrid solver for definite and indefinite problems
Shapira, Yair
1997-02-01
A two-level analysis method for certain separable problems is introduced. It motivates the definition of improved versions of Black Box Multigrid for diffusion problems with discontinuous coefficients and indefinite Helmholtz equations. For anisotropic problems, it helps in choosing suitable implementations for frequency decomposition multigrid methods. For highly indefinite problems, it provides a way to choose in advance a suitable mesh size for the coarsest grid used. Numerical experiments confirm the analysis and show the advantage of the present methods for several examples.
A diagonally inverted LU implicit multigrid scheme
NASA Technical Reports Server (NTRS)
Yokota, Jeffrey W.; Caughey, David A.; Chima, Rodrick V.
1988-01-01
A new Diagonally Inverted LU Implicit scheme is developed within the framework of the multigrid method for the 3-D unsteady Euler equations. The matrix systems that are to be inverted in the LU scheme are treated by local diagonalizing transformations that decouple them into systems of scalar equations. Unlike the Diagonalized ADI method, the time accuracy of the LU scheme is not reduced since the diagonalization procedure does not destroy time conservation. Even more importantly, this diagonalization significantly reduces the computational effort required to solve the LU approximation and therefore transforms it into a more efficient method of numerically solving the 3-D Euler equations.
Möller, T; Korsatko, W
2000-06-01
Due to its low melting range approx. 53 degrees C optically pure ibuprofen can be regarded as problematic in a pharmaceutic-technological sense. With regard to the non-solvent shock agglomeration method this means that the process and product temperatures must strictly be kept in the range of 10 K above the melting point of the substance. Higher temperatures can induce degradation of S(+)ibuprofen. During storage under stress conditions (31 degrees C for a period of 18 months) ibuprofen shows extreme stability independent of its optical activity. Racemic ibuprofen is inert to the influence of light; in individual cases optically pure substance containing an increased level of impurities can show slight degradation tendencies. The thermal and photo stability of ibuprofen is independent of the preparation technology. For comparison, conventional, fluid bed granulated, briquetted and from organic solvents especially recrystallised and optically active substances were investigated besides the shock agglomerated substances. PMID:10907254
Multigrid and cyclic reduction applied to the Helmholtz equation
NASA Technical Reports Server (NTRS)
Brackenridge, Kenneth
1993-01-01
We consider the Helmholtz equation with a discontinuous complex parameter and inhomogeneous Dirichlet boundary conditions in a rectangular domain. A variant of the direct method of cyclic reduction (CR) is employed to facilitate the design of improved multigrid (MG) components, resulting in the method of CR-MG. We demonstrate the improved convergence properties of this method.
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.
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.
Multigrid and multilevel domain decomposition for unstructured grids
Chan, T.; Smith, B.
1994-12-31
Multigrid has proven itself to be a very versatile method for the iterative solution of linear and nonlinear systems of equations arising from the discretization of PDES. In some applications, however, no natural multilevel structure of grids is available, and these must be generated as part of the solution procedure. In this presentation the authors will consider the problem of generating a multigrid algorithm when only a fine, unstructured grid is given. Their techniques generate a sequence of coarser grids by first forming an approximate maximal independent set of the vertices and then applying a Cavendish type algorithm to form the coarser triangulation. Numerical tests indicate that convergence using this approach can be as fast as standard multigrid on a structured mesh, at least in two dimensions.
Reducing Communication in Algebraic Multigrid Using Additive Variants
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 good performance on future exascale architectures.
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.
Compatible Relaxation and Coarsening in Algebraic Multigrid
Brannick, J J; Falgout, R D
2009-09-22
We introduce a coarsening algorithm for algebraic multigrid (AMG) based on the concept of compatible relaxation (CR). The algorithm is significantly different from standard methods, most notably because it does not rely on any notion of strength of connection. We study its behavior on a number of model problems, and evaluate the performance of an AMG algorithm that incorporates the coarsening approach. Lastly, we introduce a variant of CR that provides a sharper metric of coarse-grid quality and demonstrate its potential with two simple examples.
A multigrid preconditioner for the semiconductor equations
Meza, J.C.; Tuminaro, R.S.
1994-12-31
Currently, integrated circuits are primarily designed in a {open_quote}trial and error{close_quote} fashion. That is, prototypes are built and improved via experimentation and testing. In the near future, however, it may be possible to significantly reduce the time and cost of designing new devices by using computer simulations. To accurately perform these complex simulations in three dimensions, however, new algorithms and high performance computers are necessary. In this paper the authors discuss the use of multigrid preconditioning inside a semiconductor device modeling code, DANCIR. The DANCIR code is a full three-dimensional simulator capable of computing steady-state solutions of the drift-diffusion equations for a single semiconductor device and has been used to simulate a wide variety of different devices. At the inner core of DANCIR is a solver for the nonlinear equations that arise from the spatial discretization of the drift-diffusion equations on a rectangular grid. These nonlinear equations are resolved using Gummel`s method which requires three symmetric linear systems to be solved within each Gummel iteration. It is the resolution of these linear systems which comprises the dominant computational cost of this code. The original version of DANCIR uses a Cholesky preconditioned conjugate gradient algorithm to solve these linear systems. Unfortunately, this algorithm has a number of disadvantages: (1) it takes many iterations to converge (if it converges), (2) it can require a significant amount of computing time, and (3) it is not very parallelizable. To improve the situation, the authors consider a multigrid preconditioner. The multigrid method uses iterations on a hierarchy of grids to accelerate the convergence on the finest grid.
Crane, N K; Parsons, I D; Hjelmstad, K D
2002-03-21
Adaptive mesh refinement selectively subdivides the elements of a coarse user supplied mesh to produce a fine mesh with reduced discretization error. Effective use of adaptive mesh refinement coupled with an a posteriori error estimator can produce a mesh that solves a problem to a given discretization error using far fewer elements than uniform refinement. A geometric multigrid solver uses increasingly finer discretizations of the same geometry to produce a very fast and numerically scalable solution to a set of linear equations. Adaptive mesh refinement is a natural method for creating the different meshes required by the multigrid solver. This paper describes the implementation of a scalable adaptive multigrid method on a distributed memory parallel computer. Results are presented that demonstrate the parallel performance of the methodology by solving a linear elastic rocket fuel deformation problem on an SGI Origin 3000. Two challenges must be met when implementing adaptive multigrid algorithms on massively parallel computing platforms. First, although the fine mesh for which the solution is desired may be large and scaled to the number of processors, the multigrid algorithm must also operate on much smaller fixed-size data sets on the coarse levels. Second, the mesh must be repartitioned as it is adapted to maintain good load balancing. In an adaptive multigrid algorithm, separate mesh levels may require separate partitioning, further complicating the load balance problem. This paper shows that, when the proper optimizations are made, parallel adaptive multigrid algorithms perform well on machines with several hundreds of processors.
An evaluation of parallel multigrid as a solver and a preconditioner for singular perturbed problems
Oosterlee, C.W.; Washio, T.
1996-12-31
In this paper we try to achieve h-independent convergence with preconditioned GMRES and BiCGSTAB for 2D singular perturbed equations. Three recently developed multigrid methods are adopted as a preconditioner. They are also used as solution methods in order to compare the performance of the methods as solvers and as preconditioners. Two of the multigrid methods differ only in the transfer operators. One uses standard matrix- dependent prolongation operators from. The second uses {open_quotes}upwind{close_quotes} prolongation operators, developed. Both employ the Galerkin coarse grid approximation and an alternating zebra line Gauss-Seidel smoother. The third method is based on the block LU decomposition of a matrix and on an approximate Schur complement. This multigrid variant is presented in. All three multigrid algorithms are algebraic methods.
Annaratone, B. M.; Arnas, C.; Elskens, Y.
2008-09-07
The agglomeration of the matter in plasma, from the atomic level up to millimetre size particles, is here considered. In general we identify a continuous growth, due to deposition, and two agglomeration steps, the first at the level of tens of nanometres and the second above the micron. The agglomeration of nano-particles is attributed to electrostatic forces in presence of charge polarity fluctuations. Here we present a model based on discrete currents. With increasing grain size the positive charge permanence decreases, tending to zero. This effect is only important in the range of nanometre for dust of highly dispersed size. When the inter-particle distance is of the order of the screening length another agglomeration mechanism dominates. It is based on attractive forces, shadow forces or dipole-dipole interaction, overcoming the electrostatic repulsion. In bright plasma radiation pressure also plays a role.
On the parallel efficiency of the Frederickson-McBryan multigrid
NASA Technical Reports Server (NTRS)
Decker, Naomi H.
1990-01-01
To take full advantage of the parallelism in a standard multigrid algorithm requires as many processors as points. However, since coarse grids contain fewer points, most processors are idle during the coarse grid iterations. Frederickson and McBryan claim that retaining all points on all grid levels (using all processors) can lead to a superconvergent algorithm. The purpose of this work is to show that the parellel superconvergent multigrid (PSMG) algorithm of Frederickson and McBryan, though it achieves perfect processor utilization, is no more efficient than a parallel implementation of standard multigrid methods. PSMG is simply a new and perhaps simpler way of achieving the same results.
A Hexahedral Multigrid Approach for Simulating Cuts in Deformable Objects.
Dick, C; Georgii, J; Westermann, R
2011-11-01
We present a hexahedral finite element method for simulating cuts in deformable bodies using the corotational formulation of strain at high computational efficiency. Key to our approach is a novel embedding of adaptive element refinements and topological changes of the simulation grid into a geometric multigrid solver. Starting with a coarse hexahedral simulation grid, this grid is adaptively refined at the surface of a cutting tool until a finest resolution level, and the cut is modeled by separating elements along the cell faces at this level. To represent the induced discontinuities on successive multigrid levels, the affected coarse grid cells are duplicated and the resulting connectivity components are distributed to either side of the cut. Drawing upon recent work on octree and multigrid schemes for the numerical solution of partial differential equations, we develop efficient algorithms for updating the systems of equations of the adaptive finite element discretization and the multigrid hierarchy. To construct a surface that accurately aligns with the cuts, we adapt the splitting cubes algorithm to the specific linked voxel representation of the simulation domain we use. The paper is completed by a convergence analysis of the finite element solver and a performance comparison to alternative numerical solution methods. These investigations show that our approach offers high computational efficiency and physical accuracy, and that it enables cutting of deformable bodies at very high resolutions. PMID:21173453
Coarse Spaces by Algebraic Multigrid: Multigrid Convergence and Upscaled Error Estimates
Vassilevski, P S
2010-04-30
We give an overview of a number of algebraic multigrid methods targeting finite element discretization problems. The focus is on the properties of the constructed hierarchy of coarse spaces that guarantee (two-grid) convergence. In particular, a necessary condition known as 'weak approximation property', and a sufficient one, referred to as 'strong approximation property' are discussed. Their role in proving convergence of the TG method (as iterative method) and also on the approximation properties of the AMG coarse spaces if used as discretization tool is pointed out. Some preliminary numerical results illustrating the latter aspect are also reported.
Effect of temperature on wet agglomeration of crystals
Maghsoodi, Maryam; Yari, Zahra
2014-01-01
Objective(s): This study dealt with the wet agglomeration process in which a small quantity of binder liquid was added into a suspension of crystals, directly in the stirring vessel where the crystallization took place. The purpose of this investigation was evaluation of the effect of temperature on the agglomeration process in order to gain insight into the mechanism of the formation of the agglomerates. Materials and Methods: Carbamazepine was used as a model drug and water/ethanol and isopropyl acetate were used as crystallization system and binder liquid, respectively. The agglomeration of crystals was carried out at various temperatures and the agglomerates were characterized in terms of size, morphology, density and mechanical strength. Results: Evaluation of the agglomerates along the course of agglomeration shows that the properties of the particles change gradually but substantially. Higher temperature of the system during agglomeration process favors the formation of more regular agglomerates with mechanically stronger and denser structure; this can be explained by the promotion effect of temperature on the agglomeration process. Conclusion: With optimized wet agglomeration temperature, spherical, dense, and strong agglomerates can be obtained. PMID:24967063
Operator induced multigrid algorithms using semirefinement
NASA Technical Reports Server (NTRS)
Decker, Naomi; Vanrosendale, John
1989-01-01
A variant of multigrid, based on zebra relaxation, and a new family of restriction/prolongation operators is described. Using zebra relaxation in combination with an operator-induced prolongation leads to fast convergence, since the coarse grid can correct all error components. The resulting algorithms are not only fast, but are also robust, in the sense that the convergence rate is insensitive to the mesh aspect ratio. This is true even though line relaxation is performed in only one direction. Multigrid becomes a direct method if an operator-induced prolongation is used, together with the induced coarse grid operators. Unfortunately, this approach leads to stencils which double in size on each coarser grid. The use of an implicit three point restriction can be used to factor these large stencils, in order to retain the usual five or nine point stencils, while still achieving fast convergence. This algorithm achieves a V-cycle convergence rate of 0.03 on Poisson's equation, using 1.5 zebra sweeps per level, while the convergence rate improves to 0.003 if optimal nine point stencils are used. Numerical results for two and three dimensional model problems are presented, together with a two level analysis explaining these results.
Operator induced multigrid algorithms using semirefinement
NASA Technical Reports Server (NTRS)
Decker, Naomi Henderson; Van Rosendale, John
1989-01-01
A variant of multigrid, based on zebra relaxation, and a new family of restriction/prolongation operators is described. Using zebra relaxation in combination with an operator-induced prolongation leads to fast convergence, since the coarse grid can correct all error components. The resulting algorithms are not only fast, but are also robust, in the sense that the convergence rate is insensitive to the mesh aspect ratio. This is true even though line relaxation is performed in only one direction. Multigrid becomes a direct method if an operator-induced prolongation is used, together with the induced coarse grid operators. Unfortunately, this approach leads to stencils which double in size on each coarser grid. The use of an implicit three point restriction can be used to factor these large stencils, in order to retain the usual five or nine point stencils, while still achieving fast convergence. This algorithm achieves a V-cycle convergence rate of 0.03 on Poisson's equation, using 1.5 zebra sweeps per level, while the convergence rate improves to 0.003 if optimal nine point stencils are used. Numerical results for two- and three-dimensional model problems are presented, together with a two level analysis explaining these results.
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.
The multigrid algorithm applied to a degenerate equation: A convergence analysis
NASA Astrophysics Data System (ADS)
Almendral Vázquez, Ariel; Fredrik Nielsen, Bjørn
2009-03-01
In this paper we analyze the convergence properties of the Multigrid Method applied to the Black-Scholes differential equation arising in mathematical finance. We prove, for the discretized single-asset Black-Scholes equation, that the multigrid V-cycle possesses optimal convergence properties. Furthermore, through a series of numerical experiments we test the performance of the method for single-asset option problems. Throughout the paper we focus on models of European options.
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).
Uniform convergence of multigrid v-cycle iterations for indefinite and nonsymmetric problems
Bramble, J.H. . Dept. of Mathematics); Kwak, D.Y. . Dept. of Mathematics); Pasciak, J.E. . Dept. of Applied Science)
1994-12-01
In this paper, an analysis of a multigrid method for nonsymmetric and/or indefinite elliptic problems is presented. In this multigrid method various types of smothers may be used. One type of smoother considered is defined in terms of an associated symmetric problem and includes point and line, Jacobi, and Gauss-Seidel iterations. Smothers based entirely on the original operator are also considered. One smoother is based on the normal form, that is, the product of the operator and its transpose. Other smothers studied include point and line, Jacobi, and Gauss-Seidel. It is shown 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 dependent on the number of multigrid levels).
Multigrid algorithms for tensor network states.
Dolfi, Michele; Bauer, Bela; Troyer, Matthias; Ristivojevic, Zoran
2012-07-13
The widely used density matrix renormalization group (DRMG) method often fails to converge in systems with multiple length scales, such as lattice discretizations of continuum models and dilute or weakly doped lattice models. The local optimization employed by DMRG to optimize the wave function is ineffective in updating large-scale features. Here we present a multigrid algorithm that solves these convergence problems by optimizing the wave function at different spatial resolutions. We demonstrate its effectiveness by simulating bosons in continuous space and study nonadiabaticity when ramping up the amplitude of an optical lattice. The algorithm can be generalized to tensor network methods and combined with the contractor renormalization group method to study dilute and weakly doped lattice models. PMID:23030148
Adaptive Multigrid Solution of Stokes' Equation on CELL Processor
NASA Astrophysics Data System (ADS)
Elgersma, M. R.; Yuen, D. A.; Pratt, S. G.
2006-12-01
We are developing an adaptive multigrid solver for treating nonlinear elliptic partial-differential equations, needed for mantle convection problems. Since multigrid is being used for the complete solution, not just as a preconditioner, spatial difference operators are kept nearly diagonally dominant by increasing density of the coarsest grid in regions where coefficients have rapid spatial variation. At each time step, the unstructured coarse grid is refined in regions where coefficients associated with the differential operators or boundary conditions have rapid spatial variation, and coarsened in regions where there is more gradual spatial variation. For three-dimensional problems, the boundary is two-dimensional, and regions where coefficients change rapidly are often near two-dimensional surfaces, so the coarsest grid is only fine near two-dimensional subsets of the three-dimensional space. Coarse grid density drops off exponentially with distance from boundary surfaces and rapid-coefficient-change surfaces. This unstructured coarse grid results in the number of coarse grid voxels growing proportional to surface area, rather than proportional to volume. This results in significant computational savings for the coarse-grid solution. This coarse-grid solution is then refined for the fine-grid solution, and multigrid methods have memory usage and runtime proportional to the number of fine-grid voxels. This adaptive multigrid algorithm is being implemented on the CELL processor, where each chip has eight floating point processors and each processor operates on four floating point numbers each clock cycle. Both the adaptive grid algorithm and the multigrid solver have very efficient parallel implementations, in order to take advantage of the CELL processor architecture.
Agglomeration of ceramic powders
NASA Technical Reports Server (NTRS)
Cawley, James D.; Larosa, Judith; Dirkse, Fredrick
1989-01-01
A research program directed at a critical comparison of numerical models for power agglomeration with experimental observations is currently underway. Central to this program is the quantitative characterization of the distribution of mass within an agglomerate as a function of time. Current experiments are designed to restrict agglomeration to a surface, which is oriented perpendicular to the force of gravity. These experiments are discussed with reference to: their significance to ceramic processing; artifacts which may be avoided in microgravity experiments; and the comparison of information available in real space (from optical microscopy) to that in reciprocal space (from light scattering). The principle machine requirement appears to be a need to obtain information at small scattering angles.
Successfully use agglomeration for size enlargement
Pietsch, W.
1996-04-01
The processing of fine and ultrafine particles by size enlargement finds an ever increasing application. At the same time, undesirable agglomeration such as buildup, caking, bridging, and uncontrolled aggregation of fine particles can occur during processing and handling of these particulate solids. This article will provide a survey of the phenomena of agglomeration and discuss the unit operation of size enlargement by agglomeration. This article is also an invitation, particularly to young engineers, to become interested in agglomeration. Considering that mechanical process technologies are requiring more energy every year than any other group of consumers and efficiencies are typically in the single digits or teens at best, considerable rewards can be expected from the development of scientifically modified, more energy-efficient methods and equipment.
Mechanisms for selective agglomeration of coals
Wheelock, T.D.; Drzymala, J.; Allen, R.W.; Hu, Y.-C.; Tyson, D.; Xiaoping, Qiu; Lessa, A.
1989-10-01
Measurement and control of the surface properties of coal and pyrite are important in the application of selective oil agglomeration for coal beneficiation and both received further study and consideration. One method of surface characterization involves measuring the heat of immersion of coal in water or other liquids. To develop a useful and consistent measurement technique, numerous measurements were conducted with Illinois No. 6 coal to study the effects of coal particle size and moisture content on the heat of immersion in heptane, water, hexadecane and methanol. The effect of particle size was also studied. Also, ground mineral pyrite was pretreated with dilute solutions of sodium sulfide at various Ph and then agglomerated with heptane. To achieve better control over the oil agglomeration process, oil agglomeration experiments were conducted with aqueous suspensions of graphite which were first degassed with a vacuum pump. 7 refs., 16 figs., 2 tabs.
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.
An adaptive multigrid model for hurricane track prediction
NASA Technical Reports Server (NTRS)
Fulton, Scott R.
1993-01-01
This paper describes a simple numerical model for hurricane track prediction which uses a multigrid method to adapt the model resolution as the vortex moves. The model is based on the modified barotropic vorticity equation, discretized in space by conservative finite differences and in time by a Runge-Kutta scheme. A multigrid method is used to solve an elliptic problem for the streamfunction at each time step. Nonuniform resolution is obtained by superimposing uniform grids of different spatial extent; these grids move with the vortex as it moves. Preliminary numerical results indicate that the local mesh refinement allows accurate prediction of the hurricane track with substantially less computer time than required on a single uniform grid.
Multi-grid calculation of transonic potential flows
NASA Technical Reports Server (NTRS)
Caughey, D. A.; Shmilovich, A.
1985-01-01
The finite-volume method discussed by Jameson and Caughey (1977), and Caughey and Jameson (1979, 1980) has made it possible to calculate the transonic potential flow past any configuration for which a suitable boundary-conforming coordinate grid can be constructed. However, computations for practical three-dimensional problems have remained quite expensive in terms of the required computer time. The reason for this is primarily related to the large number of grid cells necessary for adequate resolution in these complex three-dimensional problems, taking into account the large number of iterations required to achieve even modest convergence on these fine grids. The present chapter provides a description of work directed at removing this latter difficulty by making use of the multigrid method. Attention is given to finite-volume formulation, multigrid iteration, geometrical aspects, and computed results.
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 remove 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 viscous flow over a blunt biconic.
Rapid determination of plasmonic nanoparticle agglomeration status in blood.
Jenkins, Samir V; Qu, Haiou; Mudalige, Thilak; Ingle, Taylor M; Wang, Rongrong; Wang, Feng; Howard, Paul C; Chen, Jingyi; Zhang, Yongbin
2015-05-01
Plasmonic nanomaterials as drug delivery or bio-imaging agents are typically introduced to biological systems through intravenous administration. However, the potential for agglomeration of nanoparticles in biological systems could dramatically affect their pharmacokinetic profile and toxic potential. Development of rapid screening methods to evaluate agglomeration is urgently needed to monitor the physical nature of nanoparticles as they are introduced into blood. Here, we establish novel methods using darkfield microscopy with hyperspectral detection (hsDFM), single particle inductively-coupled plasma mass spectrometry (spICP-MS), and confocal Raman microscopy (cRM) to discriminate gold nanoparticles (AuNPs) and their agglomerates in blood. Rich information about nanoparticle agglomeration in situ is provided by hsDFM monitoring of the plasmon resonance of primary nanoparticles and their agglomerates in whole blood; cRM is an effective complement to hsDFM to detect AuNP agglomerates in minimally manipulated samples. The AuNPs and the particle agglomerates were further distinguished in blood for the first time by quantification of particle mass using spICP-MS with excellent sensitivity and specificity. Furthermore, the agglomeration status of synthesized and commercial NPs incubated in blood was successfully assessed using the developed methods. Together, these complementary methods enable rapid determination of the agglomeration status of plasmonic nanomaterials in biological systems, specifically blood. PMID:25771013
Rapid Determination of Plasmonic Nanoparticle Agglomeration Status in Blood
Jenkins, Samir V.; Qu, Haiou; Mudalige, Thilak; Ingle, Taylor; Wang, RongRong; Wang, Feng; Howard, Paul C.; Chen, Jingyi; Zhang, Yongbin
2015-01-01
Plasmonic nanomaterials as drug delivery or bio-imaging agents are typically introduced to biological systems through intravenous administration. However, the potential for agglomeration of nanoparticles in biological systems could dramatically affect their pharmacokinetic profile and toxic potential. Development of rapid screening methods to evaluate agglomeration is urgently needed to monitor the physical nature of nanoparticles as they are introduced into blood. Here, we establish novel methods using darkfield microscopy with hyperspectral detection (hsDFM), single particle inductively-coupled plasma mass spectrometry (spICP-MS), and confocal Raman microscopy (cRM) to discriminate gold nanoparticles (AuNPs) and their agglomerates in blood. Rich information about nanoparticle agglomeration in situ is provided by hsDFM monitoring of the plasmon resonance of primary nanoparticles and their agglomerates in whole blood; cRM is an effective complement to hsDFM to detect AuNP agglomerates in minimally manipulated samples. The AuNPs and the particle agglomerates were further distinguished in blood for the first time by quantification of particle mass using spICP-MS with excellent sensitivity and specificity. Furthermore, the agglomeration status of synthesized and commercial NPs incubated in blood was successfully assessed using the developed methods. Together, these complementary methods enable rapid determination of the agglomeration status of plasmonic nanomaterials in biological systems, specifically blood. PMID:25771013
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.
Reducing Communication in Algebraic Multigrid Using Additive Variants
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
Analysis and synthesis of solutions for the agglomeration process modeling
NASA Astrophysics Data System (ADS)
Babuk, V. A.; Dolotkazin, I. N.; Nizyaev, A. A.
2013-03-01
The present work is devoted development of model of agglomerating process for propellants based on ammonium perchlorate (AP), ammonium dinitramide (ADN), HMX, inactive binder, and nanoaluminum. Generalization of experimental data, development of physical picture of agglomeration for listed propellants, development and analysis of mathematical models are carried out. Synthesis of models of various phenomena taking place at agglomeration implementation allows predicting of size and quantity, chemical composition, structure of forming agglomerates and its fraction in set of condensed combustion products. It became possible in many respects due to development of new model of agglomerating particle evolution on the surface of burning propellant. Obtained results correspond to available experimental data. It is supposed that analogical method based on analysis of mathematical models of particular phenomena and their synthesis will allow implementing of the agglomerating process modeling for other types of metalized solid propellants.
3DRISM Multigrid Algorithm for Fast Solvation Free Energy Calculations.
Sergiievskyi, Volodymyr P; Fedorov, Maxim V
2012-06-12
In this paper we present a fast and accurate method for modeling solvation properties of organic molecules in water with a main focus on predicting solvation (hydration) free energies of small organic compounds. The method is based on a combination of (i) a molecular theory, three-dimensional reference interaction sites model (3DRISM); (ii) a fast multigrid algorithm for solving the high-dimensional 3DRISM integral equations; and (iii) a recently introduced universal correction (UC) for the 3DRISM solvation free energies by properly scaled molecular partial volume (3DRISM-UC, Palmer et al., J. Phys.: Condens. Matter2010, 22, 492101). A fast multigrid algorithm is the core of the method because it helps to reduce the high computational costs associated with solving the 3DRISM equations. To facilitate future applications of the method, we performed benchmarking of the algorithm on a set of several model solutes in order to find optimal grid parameters and to test the performance and accuracy of the algorithm. We have shown that the proposed new multigrid algorithm is on average 24 times faster than the simple Picard method and at least 3.5 times faster than the MDIIS method which is currently actively used by the 3DRISM community (e.g., the MDIIS method has been recently implemented in a new 3DRISM implicit solvent routine in the recent release of the AmberTools 1.4 molecular modeling package (Luchko et al. J. Chem. Theory Comput. 2010, 6, 607-624). Then we have benchmarked the multigrid algorithm with chosen optimal parameters on a set of 99 organic compounds. We show that average computational time required for one 3DRISM calculation is 3.5 min per a small organic molecule (10-20 atoms) on a standard personal computer. We also benchmarked predicted solvation free energy values for all of the compounds in the set against the corresponding experimental data. We show that by using the proposed multigrid algorithm and the 3DRISM-UC model, it is possible to obtain good
Interactive multigrid refinement for deformable image registration.
Zhou, Wu; Xie, Yaoqin
2013-01-01
Deformable image registration is the spatial mapping of corresponding locations between images and can be used for important applications in radiotherapy. Although numerous methods have attempted to register deformable medical images automatically, such as salient-feature-based registration (SFBR), free-form deformation (FFD), and demons, no automatic method for registration is perfect, and no generic automatic algorithm has shown to work properly for clinical applications due to the fact that the deformation field is often complex and cannot be estimated well by current automatic deformable registration methods. This paper focuses on how to revise registration results interactively for deformable image registration. We can manually revise the transformed image locally in a hierarchical multigrid manner to make the transformed image register well with the reference image. The proposed method is based on multilevel B-spline to interactively revise the deformable transformation in the overlapping region between the reference image and the transformed image. The resulting deformation controls the shape of the transformed image and produces a nice registration or improves the registration results of other registration methods. Experimental results in clinical medical images for adaptive radiotherapy demonstrated the effectiveness of the proposed method. PMID:24232828
Garala, Kevin; Patel, Jaydeep; Patel, Anjali; Raval, Mihir; Dharamsi, Abhay
2012-01-01
Purpose: The purpose of the present investigation was to improve the flow and mechanical properties of racecadotril by a crystallo-co-agglomeration (CCA) technique. Direct tableting is a requirement of pharmaceutical industries. Poor mechanical properties of crystalline drug particles require wet granulation which is uneconomical, laborious, and tedious. Materials and Methods: The objective of this work was to study the influence of various polymers/excipients and processing conditions on the formation of directly compressible agglomerates of the water-insoluble drug, racecadotril, an antidiarrheal agent. The agglomerates of racecadotril were prepared using dichloromethane (DCM)–water as the crystallization system. DCM acted as a good solvent for racecadotril as well as a bridging liquid for the agglomeration of the crystallized drug and water as the nonsolvent. The prepared agglomerates were tested for micromeritic and mechanical properties. Results: The process yielded ~90 to 96% wt/ wt spherical agglomerates containing racecadotril with the diameter between 299 and 521 μ. A higher rotational speed of crystallization system reduces the size of the agglomerates and disturbs the sphericity. Spherical agglomerates were generated with a uniform dispersion of the crystallized drug. CCA showed excellent flowability and crushing strength. Conclusion: Excipients and processing conditions can play a key role in preparing spherical agglomerates of racecadotril by CCA, an excellent alternative to the wet granulation process to prepare intermediates for direct compression. PMID:23580935
Comparative Convergence Analysis of Nonlinear AMLI-Cycle Multigrid
Hu, Xiaozhe; Vassilevski, Panayot S.; Xu, Jinchao
2013-04-30
The purpose of our paper is to provide a comprehensive convergence analysis of the nonlinear algebraic multilevel iteration (AMLI)-cycle multigrid (MG) method for symmetric positive definite problems. We show that the nonlinear AMLI-cycle MG method is uniformly convergent, based on classical assumptions for approximation and smoothing properties. Furthermore, under only the assumption that the smoother is convergent, we show that the nonlinear AMLI-cycle method is always better (or not worse) than the respective V-cycle MG method. Finally, numerical experiments are presented to illustrate the theoretical results.
A parallel multigrid-based preconditioner for the 3D heterogeneous high-frequency Helmholtz equation
Riyanti, C.D. . E-mail: C.D.Riyanti@tudelft.nl; Kononov, A.; Erlangga, Y.A.; Vuik, C.; Oosterlee, C.W.; Plessix, R.-E.; Mulder, W.A.
2007-05-20
We investigate the parallel performance of an iterative solver for 3D heterogeneous Helmholtz problems related to applications in seismic wave propagation. For large 3D problems, the computation is no longer feasible on a single processor, and the memory requirements increase rapidly. Therefore, parallelization of the solver is needed. We employ a complex shifted-Laplace preconditioner combined with the Bi-CGSTAB iterative method and use a multigrid method to approximate the inverse of the resulting preconditioning operator. A 3D multigrid method with 2D semi-coarsening is employed. We show numerical results for large problems arising in geophysical applications.
Geometric and algebraic multigrid techniques for fluid dynamics problems on unstructured grids
NASA Astrophysics Data System (ADS)
Volkov, K. N.; Emel'yanov, V. N.; Teterina, I. V.
2016-02-01
Issues concerning the implementation and practical application of geometric and algebraic multigrid techniques for solving systems of difference equations generated by the finite volume discretization of the Euler and Navier-Stokes equations on unstructured grids are studied. The construction of prolongation and interpolation operators, as well as grid levels of various resolutions, is discussed. The results of the application of geometric and algebraic multigrid techniques for the simulation of inviscid and viscous compressible fluid flows over an airfoil are compared. Numerical results show that geometric methods ensure faster convergence and weakly depend on the method parameters, while the efficiency of algebraic methods considerably depends on the input parameters.
Zook, Justin M; Rastogi, Vinayak; Maccuspie, Robert I; Keene, Athena M; Fagan, Jeffrey
2011-10-25
Agglomeration of nanoparticles during measurements in relevant biological and environmental media is a frequent problem in nanomaterial property characterization. The primary problem is typically that any changes to the size distribution can dramatically affect the potential nanotoxicity or other size-determined properties, such as the absorbance signal in a biosensor measurement. Herein we demonstrate analytical ultracentrifugation (AUC) as a powerful method for measuring two critical characteristics of nanoparticle (NP) agglomerates in situ in biological media: the NP agglomerate size distribution, and the localized surface plasmon resonance (LSPR) absorbance spectrum of precise sizes of gold NP agglomerates. To characterize the size distribution, we present a theoretical framework for calculating the hydrodynamic diameter distribution of NP agglomerates from their sedimentation coefficient distribution. We measure sedimentation rates for monomers, dimers, and trimers, as well as for larger agglomerates with up to 600 NPs. The AUC size distributions were found generally to be broader than the size distributions estimated from dynamic light scattering and diffusion-limited colloidal aggregation theory, an alternative bulk measurement method that relies on several assumptions. In addition, the measured sedimentation coefficients can be used in nanotoxicity studies to predict how quickly the agglomerates sediment out of solution under normal gravitational forces, such as in the environment. We also calculate the absorbance spectra for monomer, dimer, trimer, and larger gold NP agglomerates up to 600 NPs, to enable a better understanding of LSPR biosensors. Finally, we validate a new method that uses these spectra to deconvolute the net absorbance spectrum of an unknown bulk sample and approximate the proportions of monomers, dimers, and trimers in a polydisperse sample of small agglomerates, so that every sample does not need to be measured by AUC. These results
Oprsal, Jakub; Blaha, Ludek; Pouzar, Miloslav; Knotek, Petr; Vlcek, Milan; Hrda, Katerina
2015-12-01
Formation of agglomerates and their rapid sedimentation during aquatic ecotoxicity testing of nanoparticles is a major issue with a crucial influence on the risk assessment of nanomaterials. The present work is aimed at developing and testing a new approach based on the periodic replacement of liquid media during an ecotoxicological experiment which enabled the efficient monitoring of exposure conditions. A verified mathematical model predicted the frequencies of media exchanges which checked for formation of agglomerates from silver nanoparticles AgNP with 50 nm average size of the original colloid. In the model experiments, embryos of common carp Cyprinus carpio were exposed repeatedly for 6 h to AgNPs (5-50 μm Ag L(-1)) either under semistatic conditions (exchange of media after 6 h) or in variants with frequent media exchanges (varying from 20 to 300 min depending on the AgNP colloid concentration and the desired maximum agglomerate size of 200 or 400 nm). In contrast to other studies, where dissolved free metals are usually responsible for toxic effects, our 144-h experiments demonstrated the importance of AgNP agglomerates in the adverse effects of nanosilver. Direct adsorption of agglomerates on fish embryos locally increased Ag concentrations which resulted in pronounced toxicity particularly in variants with larger 400 nm agglomerates. The present study demonstrates the suitability of the novel methodology in controlling the conditions during aquatic nanomaterial toxicity testing. It further provided insights into the mechanisms underlying the effects of AgNP, which rank on a global scale among the most widely used nanomaterials. PMID:26233755
Adaptive Algebraic Multigrid for Finite Element Elliptic Equations with Random Coefficients
Kalchev, D
2012-04-02
This thesis presents a two-grid algorithm based on Smoothed Aggregation Spectral Element Agglomeration Algebraic Multigrid (SA-{rho}AMGe) combined with adaptation. The aim is to build an efficient solver for the linear systems arising from discretization of second-order elliptic partial differential equations (PDEs) with stochastic coefficients. Examples include PDEs that model subsurface flow with random permeability field. During a Markov Chain Monte Carlo (MCMC) simulation process, that draws PDE coefficient samples from a certain distribution, the PDE coefficients change, hence the resulting linear systems to be solved change. At every such step the system (discretized PDE) needs to be solved and the computed solution used to evaluate some functional(s) of interest that then determine if the coefficient sample is acceptable or not. The MCMC process is hence computationally intensive and requires the solvers used to be efficient and fast. This fact that at every step of MCMC the resulting linear system changes, makes an already existing solver built for the old problem perhaps not as efficient for the problem corresponding to the new sampled coefficient. This motivates the main goal of our study, namely, to adapt an already existing solver to handle the problem (with changed coefficient) with the objective to achieve this goal to be faster and more efficient than building a completely new solver from scratch. Our approach utilizes the local element matrices (for the problem with changed coefficients) to build local problems associated with constructed by the method agglomerated elements (a set of subdomains that cover the given computational domain). We solve a generalized eigenproblem for each set in a subspace spanned by the previous local coarse space (used for the old solver) and a vector, component of the error, that the old solver cannot handle. A portion of the spectrum of these local eigen-problems (corresponding to eigenvalues close to zero) form the
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.
Implementation and Optimization of miniGMG - a Compact Geometric Multigrid Benchmark
Williams, Samuel; Kalamkar, Dhiraj; Singh, Amik; Deshpande, Anand M.; Straalen, Brian Van; Smelyanskiy, Mikhail; Almgren, Ann; Dubey, Pradeep; Shalf, John; Oliker, Leonid
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, 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.
Fast and Robust Sixth Order Multigrid Computation for 3D Convection Diffusion Equation.
Wang, Yin; Zhang, Jun
2010-10-15
We present a sixth order explicit compact finite difference scheme to solve the three dimensional (3D) convection diffusion equation. We first use multiscale multigrid method to solve the linear systems arising from a 19-point fourth order discretization scheme to compute the fourth order solutions on both the coarse grid and the fine grid. Then an operator based interpolation scheme combined with an extrapolation technique is used to approximate the sixth order accurate solution on the fine grid. Since the multigrid method using a standard point relaxation smoother may fail to achieve the optimal grid independent convergence rate for solving convection diffusion equation with a high Reynolds number, we implement the plane relaxation smoother in the multigrid solver to achieve better grid independency. Supporting numerical results are presented to demonstrate the efficiency and accuracy of the sixth order compact scheme (SOC), compared with the previously published fourth order compact scheme (FOC). PMID:21151737
Multigrid-based 'shifted-Laplacian' preconditioning for the time-harmonic elastic wave equation
NASA Astrophysics Data System (ADS)
Rizzuti, G.; Mulder, W. A.
2016-07-01
We investigate the numerical performance of an iterative solver for a frequency-domain finite-difference discretization of the isotropic elastic wave equation. The solver is based on the 'shifted-Laplacian' preconditioner, originally designed for the acoustic wave equation. This preconditioner represents a discretization of a heavily damped wave equation and can be efficiently inverted by a multigrid iteration. However, the application of multigrid to the elastic case is not straightforward because standard methods, such as point-Jacobi, fail to smooth the S-wave wavenumber components of the error when high P-to-S velocity ratios are present. We consider line smoothers as an alternative and apply local-mode analysis to evaluate the performance of the various components of the multigrid preconditioner. Numerical examples in 2-D demonstrate the efficacy of our method.
BOLD response analysis by iterated local multigrid priors.
da Rocha Amaral, Selene; Rabbani, Said R; Caticha, Nestor
2007-06-01
We present a non parametric Bayesian multiscale method to characterize the Hemodynamic Response HR as function of time. This is done by extending and adapting the Multigrid Priors (MGP) method proposed in (S.D.R. Amaral, S.R. Rabbani, N. Caticha, Multigrid prior for a Bayesian approach to fMRI, NeuroImage 23 (2004) 654-662; N. Caticha, S.D.R. Amaral, S.R. Rabbani, Multigrid Priors for fMRI time series analysis, AIP Conf. Proc. 735 (2004) 27-34). We choose an initial HR model and apply the MGP method to assign a posterior probability of activity for every pixel. This can be used to construct the map of activity. But it can also be used to construct the posterior averaged time series activity for different regions. This permits defining a new model which is only data-dependent. Now in turn it can be used as the model behind a new application of the MGP method to obtain another posterior probability of activity. The method converges in just a few iterations and is quite independent of the original HR model, as long as it contains some information of the activity/rest state of the patient. We apply this method of HR inference both to simulated and real data of blocks and event-related experiments. Receiver operating characteristic (ROC) curves are used to measure the number of errors with respect to a few hyperparameters. We also study the deterioration of the results for real data, under information loss. This is done by decreasing the signal to noise ratio and also by decreasing the number of images available for analysis and compare the robustness to other methods. PMID:17258909
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.
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.
Gao, Hao; Phan, Lan; Lin, Yuting
2012-09-01
A graphics processing unit-based parallel multigrid solver for a radiative transfer equation with vacuum boundary condition or reflection boundary condition is presented for heterogeneous media with complex geometry based on two-dimensional triangular meshes or three-dimensional tetrahedral meshes. The computational complexity of this parallel solver is linearly proportional to the degrees of freedom in both angular and spatial variables, while the full multigrid method is utilized to minimize the number of iterations. The overall gain of speed is roughly 30 to 300 fold with respect to our prior multigrid solver, which depends on the underlying regime and the parallelization. The numerical validations are presented with the MATLAB codes at https://sites.google.com/site/rtefastsolver/. PMID:23085905
Multigrid on unstructured grids using an auxiliary set of structured grids
Douglas, C.C.; Malhotra, S.; Schultz, M.H.
1996-12-31
Unstructured grids do not have a convenient and natural multigrid framework for actually computing and maintaining a high floating point rate on standard computers. In fact, just the coarsening process is expensive for many applications. Since unstructured grids play a vital role in many scientific computing applications, many modifications have been proposed to solve this problem. One suggested solution is to map the original unstructured grid onto a structured grid. This can be used as a fine grid in a standard multigrid algorithm to precondition the original problem on the unstructured grid. We show that unless extreme care is taken, this mapping can lead to a system with a high condition number which eliminates the usefulness of the multigrid method. Theorems with lower and upper bounds are provided. Simple examples show that the upper bounds are sharp.
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 in energy preconditioner for Krylov solvers
Slaybaugh, R.N.; Evans, T.M.; Davidson, G.G.; Wilson, P.P.H.
2013-06-01
We have added a new multigrid in energy (MGE) preconditioner to the Denovo discrete-ordinates radiation transport code. This preconditioner takes advantage of a new multilevel parallel decomposition. A multigroup Krylov subspace iterative solver that is decomposed in energy as well as space-angle forms the backbone of the transport solves in Denovo. The space-angle-energy decomposition facilitates scaling to hundreds of thousands of cores. The multigrid in energy preconditioner scales well in the energy dimension and significantly reduces the number of Krylov iterations required for convergence. This preconditioner is well-suited for use with advanced eigenvalue solvers such as Rayleigh Quotient Iteration and Arnoldi.
Highly indefinite multigrid for eigenvalue problems
Borges, L.; Oliveira, S.
1996-12-31
Eigenvalue problems are extremely important in understanding dynamic processes such as vibrations and control systems. Large scale eigenvalue problems can be very difficult to solve, especially if a large number of eigenvalues and the corresponding eigenvectors need to be computed. For solving this problem a multigrid preconditioned algorithm is presented in {open_quotes}The Davidson Algorithm, preconditioning and misconvergence{close_quotes}. Another approach for solving eigenvalue problems is by developing efficient solutions for highly indefinite problems. In this paper we concentrate on the use of new highly indefinite multigrid algorithms for the eigenvalue problem.
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.
Particle Agglomeration in Bipolar Barb Agglomerator Under AC Electric Field
NASA Astrophysics Data System (ADS)
Huang, Chao; Ma, Xiuqin; Sun, Youshan; Wang, Meiyan; Zhang, Changping; Lou, Yueya
2015-04-01
The development of an efficient technology for removing fine particles in flue gas is essential as the haze is becoming more and more serious. To improve agglomeration effectiveness of fine particles, a dual zone electric agglomeration device consisting of a charging chamber and an agglomeration chamber with bipolar barb electrodes was developed. The bipolar barb electric agglomerator with a polar distance of 200 mm demonstrates good agglomeration effectiveness for particles with a size less than 8.0 μm under applied AC electric field. An optimal condition for achieving better agglomeration effectiveness was found to be as follows: flue gas flow velocity of 3.00 m/s, particle concentration of 2.00 g/m3, output voltage of 35 kV and length of the barb of 16 mm. In addition, 4.0-6.0 μm particles have the best effectiveness with the variation of particle volume occupancy of -3.2. supported by the Key Technology R&D Program of Hebei, China (No. 13211207D)
Agglomeration and Sedimentation of MWCNTS in Chloroform
NASA Astrophysics Data System (ADS)
Eremin, Yu. S.; Kolesnikova, A. A.; Grekhov, A. M.
The kinetics of agglomeration of multiwalled carbon nanotubes dispersed in chloroform has been studied by the methods of optical spectroscopy and dynamic light scattering. With the use of the models of the diffusion of cylindrical particles, the sizes of particles obtained by this method can be recalculated to the DLS data and the concentration at which the dispersion of individual МWCNTs occurs can be determined.
Multigrid properties of upwind-biased data reconstructions
NASA Technical Reports Server (NTRS)
Warren, Gary P.; Roberts, Thomas W.
1993-01-01
The multigrid properties of two data reconstruction methods used for achieving second-order spatial accuracy when solving the two-dimensional Euler equations are examined. The data reconstruction methods are used with an implicit upwind algorithm which uses linearized backward-Euler time-differencing. The solution of the resulting linear system is performed by an iterative procedure. In the present study only regular quadrilateral grids are considered, so a red-black Gauss-Seidel iteration is used. Although the Jacobian is approximated by first-order upwind extrapolation, two alternative data reconstruction techniques for the flux integral that yield higher-order spatial accuracy at steady state are examined. The first method, probably most popular for structured quadrilateral grids, is based on estimating the cell gradients using one-dimensional reconstruction along curvilinear coordinates. The second method is based on Green's theorem. Analysis and numerical results for the two dimensional Euler equations show that data reconstruction based on Green's theorem has superior multigrid properties as compared to the one-dimensional data reconstruction method.
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.
Parallel Algebraic Multigrids for Structural mechanics
Brezina, M; Tong, C; Becker, R
2004-05-11
This paper presents the results of a comparison of three parallel algebraic multigrid (AMG) preconditioners for structural mechanics applications. In particular, they are interested in investigating both the scalability and robustness of the preconditioners. Numerical results are given for a range of structural mechanics problems with various degrees of difficulty.
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.
Microbial effects on colloidal agglomeration
Hersman, L.
1995-11-01
Colloidal particles are known to enhance the transport of radioactive metals through soil and rock systems. This study was performed to determine if a soil microorganism, isolated from the surface samples collected at Yucca Mountain, NV, could affect the colloidal properties of day particles. The agglomeration of a Wyoming bentonite clay in a sterile uninoculated microbial growth medium was compared to the agglomeration in the medium inoculated with a Pseudomonas sp. In a second experiment, microorganisms were cultured in the succinate medium for 50 h and removed by centrifugation. The agglomeration of the clay in this spent was compared to sterile uninoculated medium. In both experiments, the agglomeration of the clay was greater than that of the sterile, uninoculated control. Based on these results, which indicate that this microorganism enhanced the agglomeration of the bentonite clay, it is possible to say that in the presence of microorganisms colloidal movement through a rock matrix could be reduced because of an overall increase in the size of colloidal particle agglomerates. 32 refs.
MTCI acoustic agglomeration particulate control
Chandran, R.R.; Mansour, M.N.; Scaroni, A.W.; Koopmann, G.H.; Loth, J.L.
1994-10-01
The overall objective of this project is to demonstrate pulse combination induced acoustic enhancement of coal ash agglomeration and sulfur capture at conditions typical of direct coal-fired turbines and PFBC hot gas cleanup. MTCI has developed an advanced compact pulse combustor island for direct coal-firing in combustion gas turbines. This combustor island comprises a coal-fired pulse combustor, a combined ash agglomeration and sulfur capture chamber (CAASCC), and a hot cyclone. In the MTCI proprietary approach, the pulse combustion-induced high intensity sound waves improve sulfur capture efficiency and ash agglomeration. The resulting agglomerates allow the use of commercial cyclones and achieve very high particulate collection efficiency. In the MTCI proprietary approach, sorbent particles are injected into a gas stream subjected to an intense acoustic field. The acoustic field serves to improve sulfur capture efficiency by enhancing both gas film and intra-particle mass transfer rates. In addition, the sorbent particles act as dynamic filter foci, providing a high density of stagnant agglomerating centers for trapping the finer entrained (in the oscillating flow field) fly ash fractions. A team has been formed with MTCI as the prime contractor and Penn State University and West Virginia University as subcontractors to MTCI. MTCI is focusing on hardware development and system demonstration, PSU is investigating and modeling acoustic agglomeration and sulfur capture, and WVU is studying aerovalve fluid dynamics. Results are presented from all three studies.
An efficient non-linear multigrid procedure for the incompressible Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Sivaloganathan, S.; Shaw, G. J.
An efficient Full Approximation multigrid scheme for finite volume discretizations of the Navier-Stokes equations is presented. The algorithm is applied to the driven cavity test problem. Numerical results are presented and a comparison made with PACE, a Rolls-Royce industrial code, which uses the SIMPLE pressure correction method as an iterative solver.
A fast multigrid algorithm for energy minimization under planar density constraints.
Ron, D.; Safro, I.; Brandt, A.; Mathematics and Computer Science; Weizmann Inst. of Science
2010-09-07
The two-dimensional layout optimization problem reinforced by the efficient space utilization demand has a wide spectrum of practical applications. Formulating the problem as a nonlinear minimization problem under planar equality and/or inequality density constraints, we present a linear time multigrid algorithm for solving a correction to this problem. The method is demonstrated in various graph drawing (visualization) instances.
A Cell-Centered Multigrid Algorithm for All Grid Sizes
NASA Technical Reports Server (NTRS)
Gjesdal, Thor
1996-01-01
Multigrid methods are optimal; that is, their rate of convergence is independent of the number of grid points, because they use a nested sequence of coarse grids to represent different scales of the solution. This nesting does, however, usually lead to certain restrictions of the permissible size of the discretised problem. In cases where the modeler is free to specify the whole problem, such constraints are of little importance because they can be taken into consideration from the outset. We consider the situation in which there are other competing constraints on the resolution. These restrictions may stem from the physical problem (e.g., if the discretised operator contains experimental data measured on a fixed grid) or from the need to avoid limitations set by the hardware. In this paper we discuss a modification to the cell-centered multigrid algorithm, so that it can be used br problems with any resolution. We discuss in particular a coarsening strategy and choice of intergrid transfer operators that can handle grids with both an even or odd number of cells. The method is described and applied to linear equations obtained by discretization of two- and three-dimensional second-order elliptic PDEs.
Lazarov, R; Pasciak, J; Jones, J
2002-02-01
Construction, analysis and numerical testing of efficient solution techniques for solving elliptic PDEs that allow for parallel implementation have been the focus of the research. A number of discretization and solution methods for solving second order elliptic problems that include mortar and penalty approximations and domain decomposition methods for finite elements and finite volumes have been investigated and analyzed. Techniques for parallel domain decomposition algorithms in the framework of PETC and HYPRE have been studied and tested. Hierarchical parallel grid refinement and adaptive solution methods have been implemented and tested on various model problems. A parallel code implementing the mortar method with algebraically constructed multiplier spaces was developed.
Multigrid-Based Methodology for Implicit Solvation Models in Periodic DFT.
Garcia-Ratés, Miquel; López, Núria
2016-03-01
Continuum solvation models have become a widespread approach for the study of environmental effects in Density Functional Theory (DFT) methods. Adding solvation contributions mainly relies on the solution of the Generalized Poisson Equation (GPE) governing the behavior of the electrostatic potential of a system. Although multigrid methods are especially appropriate for the solution of partial differential equations, up to now, their use is not much extended in DFT-based codes because of their high memory requirements. In this Article, we report the implementation of an accelerated multigrid solver-based approach for the treatment of solvation effects in the Vienna ab initio Simulation Package (VASP). The stated implicit solvation model, named VASP-MGCM (VASP-Multigrid Continuum Model), uses an efficient and transferable algorithm for the product of sparse matrices that highly outperforms serial multigrid solvers. The calculated solvation free energies for a set of molecules, including neutral and ionic species, as well as adsorbed molecules on metallic surfaces, agree with experimental data and with simulation results obtained with other continuum models. PMID:26771105
Modeling Agglomeration of Dust Particles in Plasma
Matthews, Lorin S.; Land, Victor; Ma Qianyu; Perry, Jonathan D.; Hyde, Truell W.
2011-11-29
The charge on an aggregate immersed in a plasma environment distributes itself over the aggregate's surface; this can be approximated theoretically by assuming a multipole distribution. The dipole-dipole (or higher order) charge interactions between fractal aggregates lead to rotations of the grains as they interact. Other properties of the dust grains also influence the agglomeration process, such as the monomer shape (spherical or ellipsoidal) or the presence of magnetic material. Finally, the plasma and grain properties also determine the morphology of the resultant aggregates. Porous and fluffy aggregates are more strongly coupled to the gas, leading to reduced collisional velocities, and greater collisional cross sections. These factors in turn can determine the growth rate of the aggregates and evolution of the dust cloud. This paper gives an overview of the numerical and experimental methods used to study dust agglomeration at CASPER and highlights some recent results.
Encapsulation of hazardous wastes into agglomerates
Guloy, A.
1992-01-28
The objective of this study was to investigate the feasibility of using the cementitious properties and agglomeration characteristics of coal conversion byproducts to encapsulate and immobilize hazardous waste materials. The intention was to establish an economical way of co-utilization and co-disposal of wastes. In addition, it may aid in the eradication of air pollution problems associated with the fine-powdery nature of fly ash. Encapsulation into agglomerates is a novel approach of treating toxic waste. Although encapsulation itself is not a new concept, existing methods employ high-cost resins that render them economically unfeasible. In this investigation, the toxic waste was contained in a concrete-like matrix whereby fly ash and other cementitious waste materials were utilized. The method incorporates the principles of solidification, stabilization and agglomeration. Another aspect of the study is the evaluation of the agglomeration as possible lightweight aggregates. Since fly ash is commercially used as an aggregate, it would be interesting to study the effect of incorporating toxic wastes in the strength development of the granules. In the investigation, the fly ash self-cementation process was applied to electroplating sludges as the toxic waste. The process hoped to provide a basis for delisting of the waste as hazardous and, thereby greatly minimize the cost of its disposal. Owing to the stringent regulatory requirements for hauling and disposal of hazardous waste, the cost of disposal is significant. The current practice for disposal is solidifying the waste with portland cement and dumping the hardened material in the landfill where the cost varies between $700--950/ton. Partially replacing portland cement with fly ash in concrete has proven beneficial, therefore applying the same principles in the treatment of toxic waste looked very promising.
Multigrid MALDI mass spectrometry imaging (mMALDI MSI).
Urbanek, Annett; Hölzer, Stefan; Knop, Katrin; Schubert, Ulrich S; von Eggeling, Ferdinand
2016-05-01
Matrix-assisted laser desorption/ionization mass spectrometry imaging (MALDI MSI) is an important technique for the spatially resolved molecular analysis of tissue sections. The selection of matrices influences the resulting mass spectra to a high degree. For extensive and simultaneous analysis, the application of different matrices to one tissue sample is desirable. To date, only a single matrix could be applied to a tissue section per experiment. However, repetitive removal of the matrix makes this approach time-consuming and damaging to tissue samples. To overcome these drawbacks, we developed a multigrid MALDI MSI technique (mMALDI MSI) that relies on automated inkjet printing to place differing matrices onto predefined dot grids. We used a cooled printhead to prevent cavitation of low viscosity solvents in the printhead nozzle. Improved spatial resolution of the dot grids was achieved by using a triple-pulse procedure that reduced droplet volume. The matrices can either be applied directly to the thaw-mounted tissue sample or by precoating the slide followed by mounting of the tissue sample. During the MALDI imaging process, we were able to precisely target different matrix point grids with the laser to simultaneously produce distinct mass spectra. Unlike the standard method, the prespotting approach optimizes the spectra quality, avoids analyte delocalization, and enables subsequent hematoxylin and eosin (H&E) staining. Graphical Abstract Scheme of the pre-spotted multigrid MALDI MSI workflow. PMID:27039200
Multigrid calculations of 3-D turbulent viscous flows
NASA Technical Reports Server (NTRS)
Yokota, Jeffrey W.
1989-01-01
Convergence properties of a multigrid algorithm, developed to calculate compressible viscous flows, are analyzed by a vector sequence eigenvalue estimate. The full 3-D Reynolds-averaged Navier-Stokes equations are integrated by an implicit multigrid scheme while a k-epsilon turbulence model is solved, uncoupled from the flow equations. Estimates of the eigenvalue structure for both single and multigrid calculations are compared in an attempt to analyze the process as well as the results of the multigrid technique. The flow through an annular turbine is used to illustrate the scheme's ability to calculate complex 3-D flows.
A unified multigrid solver for the Navier-Stokes equations on mixed element meshes
NASA Technical Reports Server (NTRS)
Mavriplis, D. J.; Venkatakrishnan, V.
1995-01-01
A unified multigrid solution technique is presented for solving the Euler and Reynolds-averaged Navier-Stokes equations on unstructured meshes using mixed elements consisting of triangles and quadrilaterals in two dimensions, and of hexahedra, pyramids, prisms, and tetrahedra in three dimensions. While the use of mixed elements is by no means a novel idea, the contribution of the paper lies in the formulation of a complete solution technique which can handle structured grids, block structured grids, and unstructured grids of tetrahedra or mixed elements without any modification. This is achieved by discretizing the full Navier-Stokes equations on tetrahedral elements, and the thin layer version of these equations on other types of elements, while using a single edge-based data-structure to construct the discretization over all element types. An agglomeration multigrid algorithm, which naturally handles meshes of any types of elements, is employed to accelerate convergence. An automatic algorithm which reduces the complexity of a given triangular or tetrahedral mesh by merging candidate triangular or tetrahedral elements into quadrilateral or prismatic elements is also described. The gains in computational efficiency afforded by the use of non-simplicial meshes over fully tetrahedral meshes are demonstrated through several examples.
Textbook Multigrid Efficiency for Fluid Simulations
NASA Astrophysics Data System (ADS)
Thomas, James L.
Recent advances in achieving textbook multigrid efficiency for fluid simulations are presented. Textbook multigrid efficiency is defined as attaining the solution to the governing system of equations in a computational work that is a small multiple of the operation counts associated with discretizing the system. Strategies are reviewed to attain this efficiency by exploiting the factorizability properties inherent to a range of fluid simulations, including the compressible Navier-Stokes equations. Factorizability is used to separate the elliptic and hyperbolic factors contributing to the target system; each of the factors can then be treated individually and optimally. Boundary regions and discontinuities are addressed with separate (local) treatments. New formulations and recent calculations demonstrating the attainment of textbook efficiency for aerodynamic simulations are shown.
Multigrid shallow water equations on an FPGA
NASA Astrophysics Data System (ADS)
Jeffress, Stephen; Duben, Peter; Palmer, Tim
2015-04-01
A novel computing technology for multigrid shallow water equations is investigated. As power consumption begins to constrain traditional supercomputing advances, weather and climate simulators are exploring alternative technologies that achieve efficiency gains through massively parallel and low power architectures. In recent years FPGA implementations of reduced complexity atmospheric models have shown accelerated speeds and reduced power consumption compared to multi-core CPU integrations. We continue this line of research by designing an FPGA dataflow engine for a mulitgrid version of the 2D shallow water equations. The multigrid algorithm couples grids of variable resolution to improve accuracy. We show that a significant reduction of precision in the floating point representation of the fine grid variables allows greater parallelism and thus improved overall peformance while maintaining accurate integrations. Preliminary designs have been constructed by software emulation. Results of the hardware implementation will be presented at the conference.
Fast Tree Multigrid Transport Application for the Simplified P{sub 3} Approximation
Kotiluoto, Petri
2001-07-15
Calculation of neutron flux in three-dimensions is a complex problem. A novel approach for solving complicated neutron transport problems is presented, based on the tree multigrid technique and the Simplified P{sub 3} (SP{sub 3}) approximation. Discretization of the second-order elliptic SP{sub 3} equations is performed for a regular three-dimensional octree grid by using an integrated scheme. The octree grid is generated directly from STL files, which can be exported from practically all computer-aided design-systems. Marshak-like boundary conditions are utilized. Iterative algorithms are constructed for SP{sub 3} approximation with simple coarse-to-fine prolongation and fine-to-coarse restriction operations of the tree multigrid technique. Numerical results are presented for a simple cylindrical homogeneous one-group test case and for a simplistic two-group pressurized water reactor pressure vessel fluence calculation benchmark. In the former homogeneous test case, a very good agreement with 1.6% maximal deviation compared with DORT results was obtained. In the latter test case, however, notable discrepancies were observed. These comparisons show that the tree multigrid technique is capable of solving three-dimensional neutron transport problems with a very low computational cost, but that the SP{sub 3} approximation itself is not satisfactory for all problems. However, the tree multigrid technique is a very promising new method for neutron transport.
Multigrid with red black SOR revisited
Yavneh, I.
1994-12-31
Optimal relaxation parameters are obtained for red-black point Gauss-Seidel relaxation in multigrid solvers of a family of elliptic equations. The resulting relaxation schemes are found to retain high efficiency over an appreciable range of coefficients of the elliptic operator, yielding simple, inexpensive and fully parallelizable smoothers in many situations where more complicated and less cost-effective block-relaxation and/or partial coarsening are commonly used.
Zygarlicke, C.J.; Mann, M.D.; Laudal, D.L.; Miller, S.J.
1994-01-01
The Energy & Environmental Research Center (EERC) has been developing advanced indices that rank coals according to their fouling and slagging propensity in utility boilers. The indices are based on sophisticated analytical techniques for identifying and quantifying coal inorganics and are useful in predicting the effects of proposed operational changes on ash deposition in coal-fired boilers. These indices are intended to provide an economical way to reduce the amount of full-scale testing needed to determine the best means of minimizing ash-related problems. The successful design and operation of the fluidized-bed combustor requires the ability to control and mitigate ash-related problems. The major ash-related problems in FBC are agglomeration of bed material, ash deposition on heat-transfer surfaces, ash deposition on refractory and uncooled surfaces, corrosion, and erosion. The focus of the Development of Methods to Predict Agglomeration and Deposition in FBCs is on the agglomeration and deposition problems in atmospheric bubbling and circulating beds. The 1990 Clean Air Act Amendments require study of air toxic emissions from coal combustion systems. Since most of the toxic metals present in coal will be in particulate form, a high level of fine-particle control appears to be the best approach to achieving a high level of air toxics control. However, over 50% of mercury and a portion of selenium emissions are in vapor form and are not typically collected in particulate control devices. Therefore, the goal of this project is to develop methods that capture the vapor-phase metals while simultaneously achieving ultrahigh collection efficiency of particulate air toxics.
Compression behavior of porous dust agglomerates
NASA Astrophysics Data System (ADS)
Seizinger, A.; Speith, R.; Kley, W.
2012-05-01
Context. The early planetesimal growth proceeds through a sequence of sticking collisions of dust agglomerates. Very uncertain is still the relative velocity regime in which growth rather than destruction can take place. The outcome of a collision depends on the bulk properties of the porous dust agglomerates. Aims: Continuum models of dust agglomerates require a set of material parameters that are often difficult to obtain from laboratory experiments. Here, we aim at determining those parameters from ab initio molecular dynamics simulations. Our goal is to improve on the existing model that describe the interaction of individual monomers. Methods: We use a molecular dynamics approach featuring a detailed micro-physical model of the interaction of spherical grains. The model includes normal forces, rolling, twisting and sliding between the dust grains. We present a new treatment of wall-particle interaction that allows us to perform customized simulations that directly correspond to laboratory experiments. Results: We find that the existing interaction model by Dominik & Tielens leads to a too soft compressive strength behavior for uni- and omni-directional compression. Upon making the rolling and sliding coefficients stiffer we find excellent agreement in both cases. Additionally, we find that the compressive strength curve depends on the velocity with which the sample is compressed. Conclusions: The modified interaction strengths between two individual dust grains will lead to a different behavior of the whole dust agglomerate. This will influences the sticking probabilities and hence the growth of planetesimals. The new parameter set might possibly lead to an enhanced sticking as more energy can be stored in the system before breakup.
Air agglomeration of hydrophobic particles
Drzymala, J.; Wheelock, T.D.
1995-12-31
The agglomeration of hydrophobic particles in an aqueous suspension was accomplished by introducing small amounts of air into the suspension while it was agitated vigorously. The extent of aggregation was proportional both to the air to solids ratio and to the hydrophobicity of the solids. For a given air/solids ratio, the extent of aggregation of different materials increased in the following order: graphite, gilsonite, coal coated with heptane, and Teflon. The structure of agglomerates produced from coarse Teflon particles differed noticeably from the structure of bubble-particle aggregates produced from smaller, less hydrophobic particles.
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.
Development of a multigrid transonic potential flow code for cascades
NASA Technical Reports Server (NTRS)
Steinhoff, John
1992-01-01
Finite-volume methods for discretizing transonic potential flow equations have proven to be very flexible and accurate for both two and three dimensional problems. Since they only use local properties of the mapping, they allow decoupling of the grid generation from the rest of the problem. A very effective method for solving the discretized equations and converging to a solution is the multigrid-ADI technique. It has been successfully applied to airfoil problems where O type, C type and slit mappings have been used. Convergence rates for these cases are more than an order of magnitude faster than with relaxation techniques. In this report, we describe a method to extend the above methods, with the C type mappings, to airfoil cascade problems.
Multigrid solver for the reference interaction site model of molecular liquids theory.
Sergiievskyi, Volodymyr P; Hackbusch, Wolfgang; Fedorov, Maxim V
2011-07-15
In this article, we propose a new multigrid-based algorithm for solving integral equations of the reference interactions site model (RISM). We also investigate the relationship between the parameters of the algorithm and the numerical accuracy of the hydration free energy calculations by RISM. For this purpose, we analyzed the performance of the method for several numerical tests with polar and nonpolar compounds. The results of this analysis provide some guidelines for choosing an optimal set of parameters to minimize computational expenses. We compared the performance of the proposed multigrid-based method with the one-grid Picard iteration and nested Picard iteration methods. We show that the proposed method is over 30 times faster than the one-grid iteration method, and in the high accuracy regime, it is almost seven times faster than the nested Picard iteration method. PMID:21455965
Low-rank coal oil agglomeration
Knudson, Curtis L.; Timpe, Ronald C.
1991-01-01
A low-rank coal oil agglomeration process. High mineral content, a high ash content subbituminous coals are effectively agglomerated with a bridging oil which is partially water soluble and capable of entering the pore structure, and usually coal derived.
Adapting agglomeration techniques to today's needs
Brown, D.C.
1984-07-01
New industries and economic trends have created new problems and opportunities for which applications of agglomeration have been developed. These applications are presented and discussed briefly. The areas include sintering of finely divided ores, briquetting feed stocks, agglomerate forms for air pollution control, hazardous waste immobilization, briquetting solid fuels for energy conservation, manufacturing synfuel charges, biomass densification, and agglomerate forms for metallurgical coke.
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.
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.
Interpolation between Sobolev spaces in Lipschitz domains with an application to multigrid theory
Bramble, J.H. |
1995-10-01
In this paper the author describes an interpolation result for the Sobolev spaces H{sub 0}{sup S}({Omega}) where {Omega} is a bounded domain with a Lipschitz boundary. This result is applied to derive discrete norm estimates related to multilevel preconditioners and multigrid methods in the finite element method. The estimates are valid for operators of order 2m with Dirichlet boundary conditions. 11 refs.
Microstickies agglomeration by electric field.
Du, Xiaotang Tony; Hsieh, Jeffery S
2016-01-01
Microstickies deposits on both paper machine and paper products when it agglomerates under step change in ionic strength, pH, temperature and chemical additives. These stickies increase the down time of the paper mill and decrease the quality of paper. The key property of microstickies is its smaller size, which leads to low removal efficiency and difficulties in measurement. Thus the increase of microstickies size help improve both removal efficiency and reduce measurement difficulty. In this paper, a new agglomeration technology based on electric field was investigated. The electric treatment could also increase the size of stickies particles by around 100 times. The synergetic effect between electric field treatment and detacky chemicals/dispersants, including polyvinyl alcohol, poly(diallylmethylammonium chloride) and lignosulfonate, was also studied. PMID:27332828
Coal beneficiation by gas agglomeration
Wheelock, Thomas D.; Meiyu, Shen
2003-10-14
Coal beneficiation is achieved by suspending coal fines in a colloidal suspension of microscopic gas bubbles in water under atmospheric conditions to form small agglomerates of the fines adhered by the gas bubbles. The agglomerates are separated, recovered and resuspended in water. Thereafter, the pressure on the suspension is increased above atmospheric to deagglomerate, since the gas bubbles are then re-dissolved in the water. During the deagglomeration step, the mineral matter is dispersed, and when the pressure is released, the coal portion of the deagglomerated gas-saturated water mixture reagglomerates, with the small bubbles now coming out of the solution. The reagglomerate can then be separated to provide purified coal fines without the mineral matter.
Wheelock, T.D.
1995-12-31
The preliminary laboratory-scale development of a gas-promoted, oil agglomeration process for cleaning coal advanced in three major research areas. One area of research resulted in the development of a method for measuring the rate of agglomeration of dilute particle suspensions and using the method to relate the rate of agglomeration of coal particles to various key parameters. A second area of research led to the development of a method for monitoring a batch agglomeration process by measuring changes in agitator torque. With this method it was possible to show that the agglomeration of a concentrated coal particle suspension is triggered by the introduction of a small amount of gas. The method was also used in conjunction with optical microscopy to study the mechanism of agglomeration. A third area of research led to the discovery that highly hydrophobic particles in an aqueous suspension can be agglomerated by air alone.
Algebraic multigrid preconditioner for the cardiac bidomain model.
Plank, Gernot; Liebmann, Manfred; Weber dos Santos, Rodrigo; Vigmond, Edward J; Haase, Gundolf
2007-04-01
The bidomain equations are considered to be one of the most complete descriptions of the electrical activity in cardiac tissue, but large scale simulations, as resulting from discretization of an entire heart, remain a computational challenge due to the elliptic portion of the problem, the part associated with solving the extracellular potential. In such cases, the use of iterative solvers and parallel computing environments are mandatory to make parameter studies feasible. The preconditioned conjugate gradient (PCG) method is a standard choice for this problem. Although robust, its efficiency greatly depends on the choice of preconditioner. On structured grids, it has been demonstrated that a geometric multigrid preconditioner performs significantly better than an incomplete LU (ILU) preconditioner. However, unstructured grids are often preferred to better represent organ boundaries and allow for coarser discretization in the bath far from cardiac surfaces. Under these circumstances, algebraic multigrid (AMG) methods are advantageous since they compute coarser levels directly from the system matrix itself, thus avoiding the complexity of explicitly generating coarser, geometric grids. In this paper, the performance of an AMG preconditioner (BoomerAMG) is compared with that of the standard ILU preconditioner and a direct solver. BoomerAMG is used in two different ways, as a preconditioner and as a standalone solver. Two 3-D simulation examples modeling the induction of arrhythmias in rabbit ventricles were used to measure performance in both sequential and parallel simulations. It is shown that the AMG preconditioner is very well suited for the solution of the bidomain equation, being clearly superior to ILU preconditioning in all regards, with speedups by factors in the range 5.9-7.7. PMID:17405366
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.
Algebraic multigrid domain and range decomposition (AMG-DD / AMG-RD)*
Bank, R.; Falgout, R. D.; Jones, T.; Manteuffel, T. A.; McCormick, S. F.; Ruge, J. W.
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
Algebraic multigrid domain and range decomposition (AMG-DD / AMG-RD)*
Bank, R.; Falgout, R. D.; Jones, T.; Manteuffel, T. A.; McCormick, S. F.; Ruge, J. W.
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 in 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.
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.
MGGHAT: Elliptic PDE software with adaptive refinement, multigrid and high order finite elements
NASA Technical Reports Server (NTRS)
Mitchell, William F.
1993-01-01
MGGHAT (MultiGrid Galerkin Hierarchical Adaptive Triangles) is a program for the solution of linear second order elliptic partial differential equations in two dimensional polygonal domains. This program is now available for public use. It is a finite element method with linear, quadratic or cubic elements over triangles. The adaptive refinement via newest vertex bisection and the multigrid iteration are both based on a hierarchical basis formulation. Visualization is available at run time through an X Window display, and a posteriori through output files that can be used as GNUPLOT input. In this paper, we describe the methods used by MGGHAT, define the problem domain for which it is appropriate, illustrate use of the program, show numerical and graphical examples, and explain how to obtain the software.
Multigrid acceleration and turbulence models for computations of 3D turbulent jets in crossflow
NASA Technical Reports Server (NTRS)
Demuren, A. O.
1992-01-01
A multigrid method is presented for the calculation of three-dimensional turbulent jets in crossflow. Turbulence closure is achieved with either the standard k-epsilon model or a Reynolds stress model (RSM). Multigrid acceleration enables convergence rates which are far superior to that for a single grid method to be obtained with both turbulence models. With the k-epsilon model the rate approaches that for laminar flow, but with RSM it is somewhat slower. The increased stiffness of the system of equation in the latter may be responsible. Computed results with both turbulence models are compared to experimental data for a pair of opposed jets in crossflow. Both models yield reasonable agreement for the mean flow velocity, but RSM yields better predictions of the Reynolds stresses.
Multigrid acceleration and turbulence models for computations of 3D turbulent jets in crossflow
NASA Technical Reports Server (NTRS)
Demuren, A. O.
1991-01-01
A multigrid method is presented for the calculation of three-dimensional turbulent jets in crossflow. Turbulence closure is achieved with either the standard k-epsilon model or a Reynolds Stress Model (RSM). Multigrid acceleration enables convergence rates which are far superior to that for a single grid method. With the k-epsilon model the rate approaches that for laminar flow, but with RSM it is somewhat slower. The increased stiffness of the system of equations in the latter may be responsible. Computed results with both turbulence models are compared with experimental data for a pair of opposed jets in crossflow. Both models yield reasonable agreement with mean flow velocity but RSM yields better prediction of the Reynolds stresses.
Desulfurization and deashing of Hazro coal by selective oil agglomeration in various water mediums
Halime Abakay Temel; Fatma Deniz Ayhan
2006-10-15
The aim of this study was to study the effects of various water mediums on desulfurization and deashing of Hazro coal by the agglomeration method. For this purpose, three groups of agglomeration experiments were made. The effects of some parameters that markedly influence the effectiveness of selective oil agglomeration, such as solid concentration, bridging liquid concentration, and pH, on the agglomeration were investigated in the first group of experiments. The effects of different salts (NaCl, MgCl{sub 2}, and FeCl{sub 3}) on the agglomeration were investigated in the second group of experiments. The effects of lake water and sea water on the agglomeration were investigated in the third group of experiments. The influences of the Mediterranean Sea water and Aegean Sea water on the removal of ash and total sulfur were found to be important. 22 refs., 7 figs., 6 tabs.
Development and scale-up of particle agglomeration processes for coal beneficiation
NASA Astrophysics Data System (ADS)
Shen, Meiyu
The development of two modified agglomeration processes for coal beneficiation is presented separately in Parts I and II of this dissertation. Part I is based on research which was conducted to study the mechanism and characteristics of a gas-promoted oil agglomeration process. Part II is based on research which was carried out to develop a newer and more innovative method for agglomerating coal particles with microscopic gas bubbles in aqueous suspensions. In Part I, the development of a gas-promoted oil agglomeration process for cleaning coal was carried out with scale model mixing systems in which aqueous suspensions of ultrafine coal particles were treated with a liquid hydrocarbon and a small amount of air. The resulting agglomerates were recovered by screening. During batch agglomeration tests the progress of agglomeration was monitored by observing changes in agitator torque in the case of concentrated suspension. A key parameter turned out to be the minimum time te required to produce compact spherical agglomerates. Other important parameters included the projected area mean particle diameter of the agglomerates recovered at the end of a test as well as the ash content and yield of agglomerates. Batch agglomeration tests were conducted with geometrically similar mixing tanks which ranged in volume from 0.346 to 11.07 liters. It was shown that gas bubbles trigger the process of agglomeration and participate in a very complex mechanism involving the interaction of particles, oil droplets, and gas bubbles. The process takes place in stages involving dispersion of oil and gas, flocculation, coagulation, and agglomerate building. Numerous agglomeration tests were conducted with two kinds of coal in concentrated suspensions to determine the important characteristics of the process and to study the effects of the following operating parameters: i-octane concentration, air concentration, particle concentration, tank diameter, impeller diameter, and impeller speed
Advanced physical fine coal cleaning spherical agglomeration. Final report
Not Available
1990-09-01
The project included process development, engineering, construction, and operation of a 1/3 tph proof-of-concept (POC) spherical agglomeration test module. The POC tests demonstrated that physical cleaning of ultrafine coal by agglomeration using heptane can achieve: (1) Pyritic sulfur reductions beyond that possible with conventional coal cleaning methods; (2) coal ash contents below those which can be obtained by conventional coal cleaning methods at comparable energy recoveries; (3) energy recoveries of 80 percent or greater measured against the raw coal energy content; (4) complete recovery of the heptane bridging liquid from the agglomerates; and (5) production of agglomerates with 3/8-inch size and less than 30 percent moisture. Test results met or exceeded all of the program objectives. Nominal 3/8-inch size agglomerates with less than 20 percent moisture were produced. The clean coal ash content varied between 1.5 to 5.5 percent by weight (dry basis) depending on feed coal type. Ash reductions of the run-of-mine (ROM) coal were 77 to 83 percent. ROM pyritic sulfur reductions varied from 86 to 90 percent for the three test coals, equating to total sulfur reductions of 47 to 72 percent.
Multigrid for refined triangle meshes
Shapira, Yair
1997-02-01
A two-level preconditioning method for the solution of (locally) refined finite element schemes using triangle meshes is introduced. In the isotropic SPD case, it is shown that the condition number of the preconditioned stiffness matrix is bounded uniformly for all sufficiently regular triangulations. This is also verified numerically for an isotropic diffusion problem with highly discontinuous coefficients.
A monolithic FEM-multigrid solver for non-isothermal incompressible flow on general meshes
NASA Astrophysics Data System (ADS)
Damanik, H.; Hron, J.; Ouazzi, A.; Turek, S.
2009-06-01
We present special numerical simulation methods for non-isothermal incompressible viscous fluids which are based on LBB-stable FEM discretization techniques together with monolithic multigrid solvers. For time discretization, we apply the fully implicit Crank-Nicolson scheme of 2nd order accuracy while we utilize the high order Q2P1 finite element pair for discretization in space which can be applied on general meshes together with local grid refinement strategies including hanging nodes. To treat the nonlinearities in each time step as well as for direct steady approaches, the resulting discrete systems are solved via a Newton method based on divided differences to calculate explicitly the Jacobian matrices. In each nonlinear step, the coupled linear subproblems are solved simultaneously for all quantities by means of a monolithic multigrid method with local multilevel pressure Schur complement smoothers of Vanka type. For validation and evaluation of the presented methodology, we perform the MIT benchmark 2001 [M.A. Christon, P.M. Gresho, S.B. Sutton, Computational predictability of natural convection flows in enclosures, in: First MIT Conference on Computational Fluid and Solid Mechanics, vol. 40, Elsevier, 2001, pp. 1465-1468] of natural convection flow in enclosures to compare our results with respect to accuracy and efficiency. Additionally, we simulate problems with temperature and shear dependent viscosity and analyze the effect of an additional dissipation term inside the energy equation. Moreover, we discuss how these FEM-multigrid techniques can be extended to monolithic approaches for viscoelastic flow problems.
Kucukboyaci, Vefa; Haghighat, Alireza
2001-06-17
New angular multigrid formulations have been developed, including the Simplified Angular Multigrid (SAM), Nested Iteration (NI), and V-Cycle schemes, which are compatible with the parallel environment and the adaptive differencing strategy of the PENTRAN three-dimensional parallel S{sub N} code. Through use of the Fourier analysis method for an infinite, homogeneous medium, the effectiveness of the V-Cycle scheme was investigated for different problem parameters including scattering ratio, spatial differencing weights, quadrature order, and mesh size. The theoretical analysis revealed that the V-Cycle scheme is effective for a large range of scattering ratios and is insensitive to mesh size. The effectiveness of the new schemes was also investigated for practical shielding applications such as the Kobayashi benchmark problem and the boiling water reactor core shroud problem.
Design and implementation of a multigrid code for the Euler equations
NASA Technical Reports Server (NTRS)
Jespersen, D. C.
1983-01-01
The steady-state equations of inviscid fluid flow, the Euler equations, are a nonlinear nonelliptic system of equations admitting solutions with discontinuities (for example, shocks). The efficient numerical solution of these equations poses a strenuous challenge to multigrid methods. A multigrid code has been developed for the numerical solution of the Euler equations. In this paper some of the factors that had to be taken into account in the design and development of the code are reviewed. These factors include the importance of choosing an appropriate difference scheme, the usefulness of local mode analysis as a design tool, and the crucial question of how to treat the nonlinearity. Sample calculations of transonic flow about airfoils will be presented. No claim is made that the particular algorithm presented is optimal.
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.
NASA Astrophysics Data System (ADS)
Kamarajugadda, Sai; Mazumder, Sandip
2012-06-01
The flooded agglomerate model has found prolific usage in modeling the oxygen reduction reaction within the cathode catalyst layer of a polymer electrolyte membrane fuel cell (PEMFC). The assumption made in this model is that the ionomer-coated carbon-platinum agglomerate is spherical in shape and that the spheres are non-overlapping. This assumption is convenient because the governing equations lend themselves to closed-form analytical solution when a spherical shape is assumed. In reality, micrographs of the catalyst layer show that the agglomerates are best represented by sets of overlapping spheres of unequal radii. In this article, the flooded agglomerate is generalized by considering overlapping spheres of unequal radii. As a first cut, only two overlapping spheres are considered. The governing reaction-diffusion equations are solved numerically using the unstructured finite-volume method. The volumetric current density is extracted for various parametric variations, and tabulated. This sub-grid-scale generalized flooded agglomerate model is first validated and finally coupled to a computational fluid dynamics (CFD) code for predicting the performance of the PEMFC. Results show that when the agglomerates are small (<200 nm equivalent radius), the effect of agglomerate shape on the overall PEMFC performance is insignificant. For large agglomerates, on the other hand, the effect of agglomerate shape was found to be critical, especially for high current densities for which the mass transport resistance within the agglomerate is strongly dependent on the shape of the agglomerate, and was found to correlate well with the surface-to-volume ratio of the agglomerate.
Powder agglomeration in a microgravity environment
NASA Technical Reports Server (NTRS)
Cawley, James D.
1994-01-01
This is the final report for NASA Grant NAG3-755 entitled 'Powder Agglomeration in a Microgravity Environment.' The research program included both two types of numerical models and two types of experiments. The numerical modeling included the use of Monte Carlo type simulations of agglomerate growth including hydrodynamic screening and molecular dynamics type simulations of the rearrangement of particles within an agglomerate under a gravitational field. Experiments included direct observation of the agglomeration of submicron alumina and indirect observation, using small angle light scattering, of the agglomeration of colloidal silica and aluminum monohydroxide. In the former class of experiments, the powders were constrained to move on a two-dimensional surface oriented to minimize the effect of gravity. In the latter, some experiments involved mixture of suspensions containing particles of opposite charge which resulted in agglomeration on a very short time scale relative to settling under gravity.
Zonal multigrid solution of compressible flow problems on unstructured and adaptive meshes
NASA Technical Reports Server (NTRS)
Mavriplis, Dimitri J.
1989-01-01
The simultaneous use of adaptive meshing techniques with a multigrid strategy for solving the 2-D Euler equations in the context of unstructured meshes is studied. To obtain optimal efficiency, methods capable of computing locally improved solutions without recourse to global recalculations are pursued. A method for locally refining an existing unstructured mesh, without regenerating a new global mesh is employed, and the domain is automatically partitioned into refined and unrefined regions. Two multigrid strategies are developed. In the first, time-stepping is performed on a global fine mesh covering the entire domain, and convergence acceleration is achieved through the use of zonal coarse grid accelerator meshes, which lie under the adaptively refined regions of the global fine mesh. Both schemes are shown to produce similar convergence rates to each other, and also with respect to a previously developed global multigrid algorithm, which performs time-stepping throughout the entire domain, on each mesh level. However, the present schemes exhibit higher computational efficiency due to the smaller number of operations on each level.
Implicit multigrid algorithms for the three-dimensional flux split Euler equations. Ph.D. Thesis
NASA Technical Reports Server (NTRS)
Anderson, W. K.
1986-01-01
The full approximation scheme multigrid method is applied to several implicit flux-split algorithms for solving the three-dimensional Euler equations in a body fitted coordinate system. Each uses a variation of approximate factorization and is implemented in a finite volume formulation. The algorithms are all vectorizable with little or no scalar computations required. The flux vectors are split into upwind components using both the splittings of Steger-Warming and Van Leer. Results comparing pressure distributions with experimental data using both splitting types are shown. 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. Using the multigrid method on both subsonic and transonic wing calculations, the final lift coefficient is obtained to within 0.1 percent of its final value in a few as 15 cycles for a mesh with over 210,000 points. A spectral radius of 0.89 is achieved for both subsonic and transonic flow over the ONERA M6 wing while a spectral radius of 0.83 is obtained for supersonic flow over an analytically defined forebody. Results compared with experiment for all cases show good agreement.
Ice slurry cooling research: Storage tank ice agglomeration and extraction
Kasza, K.; Hayashi, Kanetoshi
1999-08-01
A new facility has been built to conduct research and development on important issues related to implementing ice slurry cooling technology. Ongoing studies are generating important information on the factors that influence ice particle agglomeration in ice slurry storage tanks. The studies are also addressing the development of methods to minimize and monitor agglomeration and improve the efficiency and controllability of tank extraction of slurry for distribution to cooling loads. These engineering issues impede the utilization of the ice slurry cooling concept that has been under development by various groups.
Multigrid-based reconstruction algorithm for quantitative photoacoustic tomography
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-based reconstruction algorithm for quantitative photoacoustic tomography.
Li, Shengfu; Montcel, Bruno; Yuan, Zhen; Liu, Wanyu; Vray, Didier
2015-07-01
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
Multidimensional nature of fluidized nanoparticle agglomerates.
de Martín, Lilian; Bouwman, Wim G; van Ommen, J Ruud
2014-10-28
We show that fluidized nanoparticle agglomerates are hierarchical fractal structures with three fractal dimensions: one characterizing sintered aggregates formed during nanoparticle synthesis, one that is also found in stored agglomerates and represents unbroken agglomerates, and one describing the large agglomerates broken during fluidization. This has been possible by using spin-echo small-angle neutron scattering-a relatively novel technique that, for the first time, allowed to characterize in situ the structure of fluidized nanoparticle agglomerates from 21 nm to ∼20 μm. The results show that serial agglomeration mechanisms in the gas phase can generate nanoparticle clusters with different fractal dimensions, contradicting the common approach that considers fluidized nanoparticle agglomerates as single fractals, in analogy to the agglomerates formed by micron-sized particles. This work has important implications for the fluidization field but also has a wider impact. Current studies deal with the formation and properties of clusters where the building blocks are particles and the structure can be characterized by only one fractal dimension. However, fluidized nanoparticle agglomerates are low-dimensional clusters formed by higher-dimensional clusters that are formed by low-dimensional clusters. This multifractality demands a new type of multiscale model able to capture the interplay between different scales. PMID:25313446
A Multigrid Algorithm for Immersed Interface Problems
NASA Technical Reports Server (NTRS)
Adams, Loyce
1996-01-01
Many physical problems involve interior interfaces across which the coefficients in the problem, the solution, its derivatives, the flux, or the source term may have jumps. These interior interfaces may or may not align with a underlying Cartesian grid. Zhilin Li, in his dissertation, showed how to discretize such elliptic problems using only a Cartesian grid and the known jump conditions to second order accuracy. In this paper, we describe how to apply the full multigrid algorithm in this context. In particular, the restriction, interpolation, and coarse grid problem will be described. Numerical results for several model problems are given to demonstrate that good rates can be obtained even when jumps in the coefficients are large and do not align with the grid.
Challenges of Algebraic Multigrid across Multicore Architectures
Baker, A H; Gamblin, T; Schulz, M; Yang, U M
2010-04-12
Algebraic multigrid (AMG) is a popular solver for large-scale scientific computing and an essential component of many simulation codes. AMG has shown to be extremely efficient on distributed-memory architectures. However, when executed on modern multicore architectures, we face new challenges that can significantly deteriorate AMG's performance. We examine its performance and scalability on three disparate multicore architectures: a cluster with four AMD Opteron Quad-core processors per node (Hera), a Cray XT5 with two AMD Opteron Hex-core processors per node (Jaguar), and an IBM BlueGene/P system with a single Quad-core processor (Intrepid). We discuss our experiences on these platforms and present results using both an MPI-only and a hybrid MPI/OpenMP model. We also discuss a set of techniques that helped to overcome the associated problems, including thread and process pinning and correct memory associations.
Distance-Two Interpolation for Parallel Algebraic Multigrid
De Sterck, H; Falgout, R; Nolting, J; Yang, U M
2007-05-08
Algebraic multigrid (AMG) is one of the most efficient and scalable parallel algorithms for solving sparse linear systems on unstructured grids. However, for large three-dimensional problems, the coarse grids that are normally used in AMG often lead to growing complexity in terms of memory use and execution time per AMG V-cycle. Sparser coarse grids, such as those obtained by the Parallel Modified Independent Set coarsening algorithm (PMIS) [7], remedy this complexity growth, but lead to non-scalable AMG convergence factors when traditional distance-one interpolation methods are used. In this paper we study the scalability of AMG methods that combine PMIS coarse grids with long distance interpolation methods. AMG performance and scalability is compared for previously introduced interpolation methods as well as new variants of them for a variety of relevant test problems on parallel computers. It is shown that the increased interpolation accuracy largely restores the scalability of AMG convergence factors for PMIS-coarsened grids, and in combination with complexity reducing methods, such as interpolation truncation, one obtains a class of parallel AMG methods that enjoy excellent scalability properties on large parallel computers.
Ewing, R.E.; Saevareid, O.; Shen, J.
1994-12-31
A multigrid algorithm for the cell-centered finite difference on equilateral triangular grids for solving second-order elliptic problems is proposed. This finite difference is a four-point star stencil in a two-dimensional domain and a five-point star stencil in a three dimensional domain. According to the authors analysis, the advantages of this finite difference are that it is an O(h{sup 2})-order accurate numerical scheme for both the solution and derivatives on equilateral triangular grids, the structure of the scheme is perhaps the simplest, and its corresponding multigrid algorithm is easily constructed with an optimal convergence rate. They are interested in relaxation of the equilateral triangular grid condition to certain general triangular grids and the application of this multigrid algorithm as a numerically reasonable preconditioner for the lowest-order Raviart-Thomas mixed triangular finite element method. Numerical test results are presented to demonstrate their analytical results and to investigate the applications of this multigrid algorithm on general triangular grids.
NASA Astrophysics Data System (ADS)
Pariona, Moisés Meza; de Oliveira, Fabiane; Teleginski, Viviane; Machado, Siliane; Pinto, Marcio Augusto Villela
2016-05-01
Al-1.5 wt% Fe alloy was irradiate by Yb-fiber laser beam using the laser surface remelting (LSR) technique, generating weld fillets that covered the whole surface of the sample. The laser-treatment showed to be an efficient technology for corrosion resistance improvements. In this study, the finite element method was used to simulate the solidification processes by LSR technique. The method Multigrid was employed in order to reduce the CPU time, which is important to the viability for industrial applications. Multigrid method is a technique very promising of optimization that reduced drastically the CPU time. The result was highly satisfactory, because the CPU time has fallen dramatically in comparison when it was not used Multigrid method. To validate the result of numerical simulation with the experimental result was done the microstructural characterization of laser-treated layer by the optical microscopy and SEM techniques and however, that both results showing be consistent.
Low-rank coal oil agglomeration
Knudson, C.L.; Timpe, R.C.
1991-07-16
A low-rank coal oil agglomeration process is described. High mineral content, a high ash content subbituminous coals are effectively agglomerated with a bridging oil which is partially water soluble and capable of entering the pore structure, and is usually coal-derived.
Multigrid optimal mass transport for image registration and morphing
NASA Astrophysics Data System (ADS)
Rehman, Tauseef ur; Tannenbaum, Allen
2007-02-01
In this paper we present a computationally efficient Optimal Mass Transport algorithm. This method is based on the Monge-Kantorovich theory and is used for computing elastic registration and warping maps in image registration and morphing applications. This is a parameter free method which utilizes all of the grayscale data in an image pair in a symmetric fashion. No landmarks need to be specified for correspondence. In our work, we demonstrate significant improvement in computation time when our algorithm is applied as compared to the originally proposed method by Haker et al [1]. The original algorithm was based on a gradient descent method for removing the curl from an initial mass preserving map regarded as 2D vector field. This involves inverting the Laplacian in each iteration which is now computed using full multigrid technique resulting in an improvement in computational time by a factor of two. Greater improvement is achieved by decimating the curl in a multi-resolutional framework. The algorithm was applied to 2D short axis cardiac MRI images and brain MRI images for testing and comparison.
Multigrid solution for the compressible Euler equations by an implicit characteristic-flux-averaging
NASA Astrophysics Data System (ADS)
Kanarachos, A.; Vournas, I.
A formulation of an implicit characteristic-flux-averaging method for the compressible Euler equations combined with the multigrid method is presented. The method is based on correction scheme and implicit Gudunov type finite volume scheme and is applied to two dimensional cases. Its principal feature is an averaging procedure based on the eigenvalue analysis of the Euler equations by means of which the fluxes are evaluated at the finite volume faces. The performance of the method is demonstrated for different flow problems around RAE-2922 and NACA-0012 airfoils and an internal flow over a circular arc.
Engineering development of selective agglomeration. Final report
Not Available
1993-04-01
This report presents the findings of the project entitled ``Engineering Development of Selective Agglomeration.`` The purpose is to develop selective agglomeration technology to a commercially acceptable level by 1993. Engineering development included bench-scale process development, component development adaptation or modification of existing unit operations, proof-of-concept (POC) module design, fabrication, testing, data evaluation, and conceptual design of a commercial facility. The information obtained during POC operation resulted in a technical and economic design base sufficient to support construction and operation of a commercial plant. Throughout this project performance targets for the engineering development of selective agglomeration process were to achieve 85% or greater Btu recovery at 85% or greater pyritic sulfur rejection (PSR). Additional objectives included producing a final clean-coal product with an ash content of 6% or less which is suitable for conventional coal handling systems. The selective agglomeration process, as applied to coal cleaning, is based on differences in the surface chemistry of coal and its associated impurities. Coal particles are hydrophobic (i.e., repel water) while the majority of its impurities are hydrophilic (i.e., stabilized in water). During selective agglomeration, a liquid (the agglomerant) that is immiscible with water is introduced into a coal-water slurry and agitated to disperse it in the slurry, thereby allowing it to come into contact with all particles in the slurry. The coal particles, due to their hydrophobic nature, are attracted to the agglomerant phase. The hydrophilic mineral impurities remain in the water phase. Continued agitation of the agglomerant-coated coal particles causes them to coalesce to form agglomerates. Once the agglomerates are formed, they are separated from the mineral matter-bearing aqueous phase by subsequent processing steps.
Simulation of acoustic agglomeration processes of poly-disperse solid particles
Changdong Sheng; Xianglin Shen
2007-01-15
This article presents the simulation of acoustic agglomeration of poly-disperse solid particles with the direct simulation Monte Carlo method. The modelled processes include the agglomeration due to the orthokinetic and hydrodynamic mechanisms, Brownian coagulation and wall deposition. The aggregates formed during the agglomeration process were characterised as mass fractal aggregates with an equivalent radius to estimate the average radius of the primary particles in individual aggregates. Acoustic agglomeration of fly ash with a lognormal size distribution and TiO{sub 2} particles with a bimodal size distribution was simulated and validated against the experimental data in the literature. It was found that the acoustic agglomeration process of solid particles could be represented with a modified version of Song's orthokinetic model and Koenig's hydrodynamic equation that account for the fractal-like morphology of the aggregates. The fractal dimensions of around 1.8 and 2.2 were obtained for the fly ash and TiO{sub 2} particles, respectively, consistent with the values reported for the aggregates in the literature. The poly-disperse nature of the primary particles is essential to the simulation; assuming mono-disperse primary particles leads to a significant underestimation of the agglomeration rate and the particle size growth particularly during the early stages of the acoustic agglomeration process. Particle deposition on the chamber walls also has some effect on acoustic agglomeration.
Textbook Multigrid Efficiency for Computational Fluid Dynamics Simulations
NASA Technical Reports Server (NTRS)
Brandt, Achi; Thomas, James L.; Diskin, Boris
2001-01-01
Considerable progress over the past thirty years has been made in the development of large-scale computational fluid dynamics (CFD) solvers for the Euler and Navier-Stokes equations. Computations are used routinely to design the cruise shapes of transport aircraft through complex-geometry simulations involving the solution of 25-100 million equations; in this arena the number of wind-tunnel tests for a new design has been substantially reduced. However, simulations of the entire flight envelope of the vehicle, including maximum lift, buffet onset, flutter, and control effectiveness have not been as successful in eliminating the reliance on wind-tunnel testing. These simulations involve unsteady flows with more separation and stronger shock waves than at cruise. The main reasons limiting further inroads of CFD into the design process are: (1) the reliability of turbulence models; and (2) the time and expense of the numerical simulation. Because of the prohibitive resolution requirements of direct simulations at high Reynolds numbers, transition and turbulence modeling is expected to remain an issue for the near term. The focus of this paper addresses the latter problem by attempting to attain optimal efficiencies in solving the governing equations. Typically current CFD codes based on the use of multigrid acceleration techniques and multistage Runge-Kutta time-stepping schemes are able to converge lift and drag values for cruise configurations within approximately 1000 residual evaluations. An optimally convergent method is defined as having textbook multigrid efficiency (TME), meaning 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 the discretized system of equations (residual equations). In this paper, a distributed relaxation approach to achieving TME for Reynolds-averaged Navier-Stokes (RNAS) equations are discussed along with the foundations that form the
Mapping robust parallel multigrid algorithms to scalable memory architectures
NASA Technical Reports Server (NTRS)
Overman, Andrea; Vanrosendale, John
1993-01-01
The convergence rate of standard multigrid algorithms degenerates on problems with stretched grids or anisotropic operators. The usual cure for this is the use of line or plane relaxation. However, multigrid algorithms based on line and plane relaxation have limited and awkward parallelism and are quite difficult to map effectively to highly parallel architectures. Newer multigrid algorithms that overcome anisotropy through the use of multiple coarse grids rather than relaxation are better suited to massively parallel architectures because they require only simple point-relaxation smoothers. In this paper, we look at the parallel implementation of a V-cycle multiple semicoarsened grid (MSG) algorithm on distributed-memory architectures such as the Intel iPSC/860 and Paragon computers. The MSG algorithms provide two levels of parallelism: parallelism within the relaxation or interpolation on each grid and across the grids on each multigrid level. Both levels of parallelism must be exploited to map these algorithms effectively to parallel architectures. This paper describes a mapping of an MSG algorithm to distributed-memory architectures that demonstrates how both levels of parallelism can be exploited. The result is a robust and effective multigrid algorithm for distributed-memory machines.
Mapping robust parallel multigrid algorithms to scalable memory architectures
NASA Technical Reports Server (NTRS)
Overman, Andrea; Vanrosendale, John
1993-01-01
The convergence rate of standard multigrid algorithms degenerates on problems with stretched grids or anisotropic operators. The usual cure for this is the use of line or plane relaxation. However, multigrid algorithms based on line and plane relaxation have limited and awkward parallelism and are quite difficult to map effectively to highly parallel architectures. Newer multigrid algorithms that overcome anisotropy through the use of multiple coarse grids rather than line relaxation are better suited to massively parallel architectures because they require only simple point-relaxation smoothers. The parallel implementation of a V-cycle multiple semi-coarsened grid (MSG) algorithm or distributed-memory architectures such as the Intel iPSC/860 and Paragon computers is addressed. The MSG algorithms provide two levels of parallelism: parallelism within the relaxation or interpolation on each grid and across the grids on each multigrid level. Both levels of parallelism must be exploited to map these algorithms effectively to parallel architectures. A mapping of an MSG algorithm to distributed-memory architectures that demonstrate how both levels of parallelism can be exploited is described. The results is a robust and effective multigrid algorithm for distributed-memory machines.
NASA Technical Reports Server (NTRS)
Yokota, Jeffrey W.
1988-01-01
An LU implicit multigrid algorithm is developed to calculate 3-D compressible viscous flows. This scheme solves the full 3-D Reynolds-Averaged Navier-Stokes equation with a two-equation kappa-epsilon model of turbulence. The flow equations are integrated by an efficient, diagonally inverted, LU implicit multigrid scheme while the kappa-epsilon equations are solved, uncoupled from the flow equations, by a block LU implicit algorithm. The flow equations are solved within the framework of the multigrid method using a four-grid level W-cycle, while the kappa-epsilon equations are iterated only on the finest grid. This treatment of the Reynolds-Averaged Navier-Stokes equations proves to be an efficient method for calculating 3-D compressible viscous flows.
Modeling of particle agglomeration in nanofluids
NASA Astrophysics Data System (ADS)
Krishna, K. Hari; Neti, S.; Oztekin, A.; Mohapatra, S.
2015-03-01
Agglomeration strongly influences the stability or shelf life of nanofluid. The present computational and experimental study investigates the rate of agglomeration quantitatively. Agglomeration in nanofluids is attributed to the net effect of various inter-particle interaction forces. For the nanofluid considered here, a net inter-particle force depends on the particle size, volume fraction, pH, and electrolyte concentration. A solution of the discretized and coupled population balance equations can yield particle sizes as a function of time. Nanofluid prepared here consists of alumina nanoparticles with the average particle size of 150 nm dispersed in de-ionized water. As the pH of the colloid was moved towards the isoelectric point of alumina nanofluids, the rate of increase of average particle size increased with time due to lower net positive charge on particles. The rate at which the average particle size is increased is predicted and measured for different electrolyte concentration and volume fraction. The higher rate of agglomeration is attributed to the decrease in the electrostatic double layer repulsion forces. The rate of agglomeration decreases due to increase in the size of nano-particle clusters thus approaching zero rate of agglomeration when all the clusters are nearly uniform in size. Predicted rates of agglomeration agree adequate enough with the measured values; validating the mathematical model and numerical approach is employed.
Effect of particle agglomeration in nanotoxicology.
Bruinink, Arie; Wang, Jing; Wick, Peter
2015-05-01
The emission of engineered nanoparticles (ENPs) into the environment in increasing quantity and variety raises a general concern regarding potential effects on human health. Compared with soluble substances, ENPs exhibit additional dimensions of complexity, that is, they exist not only in various sizes, shapes and chemical compositions but also in different degrees of agglomeration. The effect of the latter is the topic of this review in which we explore and discuss the role of agglomeration on toxicity, including the fate of nanomaterials after their release and the biological effects they may induce. In-depth investigations of the effect of ENP agglomeration on human health are still rare, but it may be stated that outside the body ENP agglomeration greatly reduces human exposure. After uptake, agglomeration of ENPs reduces translocation across primary barriers such as lungs, skin or the gastrointestinal tract, preventing exposure of "secondary" organs. In analogy, also cellular ENP uptake and intracellular distribution are affected by agglomeration. However, agglomeration may represent a risk factor if it occurs after translocation across the primary barriers, and ENPs are able to accumulate within the tissue and thus reduce clearance efficiency. PMID:25618546
Modeling of particle agglomeration in nanofluids
Krishna, K. Hari; Neti, S.; Oztekin, A.; Mohapatra, S.
2015-03-07
Agglomeration strongly influences the stability or shelf life of nanofluid. The present computational and experimental study investigates the rate of agglomeration quantitatively. Agglomeration in nanofluids is attributed to the net effect of various inter-particle interaction forces. For the nanofluid considered here, a net inter-particle force depends on the particle size, volume fraction, pH, and electrolyte concentration. A solution of the discretized and coupled population balance equations can yield particle sizes as a function of time. Nanofluid prepared here consists of alumina nanoparticles with the average particle size of 150 nm dispersed in de-ionized water. As the pH of the colloid was moved towards the isoelectric point of alumina nanofluids, the rate of increase of average particle size increased with time due to lower net positive charge on particles. The rate at which the average particle size is increased is predicted and measured for different electrolyte concentration and volume fraction. The higher rate of agglomeration is attributed to the decrease in the electrostatic double layer repulsion forces. The rate of agglomeration decreases due to increase in the size of nano-particle clusters thus approaching zero rate of agglomeration when all the clusters are nearly uniform in size. Predicted rates of agglomeration agree adequate enough with the measured values; validating the mathematical model and numerical approach is employed.
Modeling of Particle Agglomeration in Nanofluids
NASA Astrophysics Data System (ADS)
Kanagala, Hari Krishna
Nanofluids are colloidal dispersions of nano sized particles (<100nm in diameter) in dispersion mediums. They are of great interest in industrial applications as heat transfer fluids owing to their enhanced thermal conductivities. Stability of nanofluids is a major problem hindering their industrial application. Agglomeration and then sedimentation are some reasons, which drastically decrease the shelf life of these nanofluids. Current research addresses the agglomeration effect and how it can affect the shelf life of a nanofluid. The reasons for agglomeration in nanofluids are attributable to the interparticle interactions which are quantified by the various theories. By altering the governing properties like volume fraction, pH and electrolyte concentration different nanofluids with instant agglomeration, slow agglomeration and no agglomeration can be produced. A numerical model is created based on the discretized population balance equations which analyses the particle size distribution at different times. Agglomeration effects have been analyzed for alumina nanoparticles with average particle size of 150nm dispersed in de-ionized water. As the pH was moved towards the isoelectric point of alumina nanofluids, the particle size distribution became broader and moved to bigger sizes rapidly with time. Particle size distributions became broader and moved to bigger sizes more quickly with time with increase in the electrolyte concentration. The two effects together can be used to create different temporal trends in the particle size distributions. Faster agglomeration is attributed to the decrease in the electrostatic double layer repulsion forces which is due to decrease in the induced charge and the double layer thickness around the particle. Bigger particle clusters show lesser agglomeration due to reaching the equilibrium size. The procedures and processes described in this work can be used to generate more stable nanofluids.
Percolative fragmentation and spontaneous agglomeration
Hurt, R.; Davis, K.
1999-03-01
Captive particle imaging experiments were performed on over 200 coal and char particles in the pulverized size range from four coals of various rank at oxygen concentration from 3--19 mol% and at gas temperatures of about 1250 K. Despite wide variations in single-particle behavior, the data set reveals two clear trends that provide new information on the nature of char combustion. First, the low-rank coal chars are observed to maintain their high reactivity through the late stages of combustion, thus avoiding the near-extinction events and long burnout tails observed for bituminous coal chars. Secondly, percolative fragmentation in the late stages of combustion is a rare event under these conditions. Some particles reach a percolation threshold rate in combustion, but typically undergo spontaneous agglomeration rather than liberation of the incipient fragments. It is concluded that percolative fragmentation behavior in the pulverized size range is determined not only by solid-phase connectivity, but also by a real competition between disruptive and cohesive forces present at the time of formation of the colloidal-sized incipient fragments.
Transonic Drag Prediction Using an Unstructured Multigrid Solver
NASA Technical Reports Server (NTRS)
Mavriplis, D. J.; Levy, David W.
2001-01-01
This paper summarizes the results obtained with the NSU-3D unstructured multigrid solver for the AIAA Drag Prediction Workshop held in Anaheim, CA, June 2001. The test case for the workshop consists of a wing-body configuration at transonic flow conditions. Flow analyses for a complete test matrix of lift coefficient values and Mach numbers at a constant Reynolds number are performed, thus producing a set of drag polars and drag rise curves which are compared with experimental data. Results were obtained independently by both authors using an identical baseline grid and different refined grids. Most cases were run in parallel on commodity cluster-type machines while the largest cases were run on an SGI Origin machine using 128 processors. The objective of this paper is to study the accuracy of the subject unstructured grid solver for predicting drag in the transonic cruise regime, to assess the efficiency of the method in terms of convergence, cpu time, and memory, and to determine the effects of grid resolution on this predictive ability and its computational efficiency. A good predictive ability is demonstrated over a wide range of conditions, although accuracy was found to degrade for cases at higher Mach numbers and lift values where increasing amounts of flow separation occur. The ability to rapidly compute large numbers of cases at varying flow conditions using an unstructured solver on inexpensive clusters of commodity computers is also demonstrated.
A multiblock multigrid three-dimensional Euler equation solver
NASA Technical Reports Server (NTRS)
Cannizzaro, Frank E.; Elmiligui, Alaa; Melson, N. Duane; Vonlavante, E.
1990-01-01
Current aerodynamic designs are often quite complex (geometrically). Flexible computational tools are needed for the analysis of a wide range of configurations with both internal and external flows. In the past, geometrically dissimilar configurations required different analysis codes with different grid topologies in each. The duplicity of codes can be avoided with the use of a general multiblock formulation which can handle any grid topology. Rather than hard wiring the grid topology into the program, it is instead dictated by input to the program. In this work, the compressible Euler equations, written in a body-fitted finite-volume formulation, are solved using a pseudo-time-marching approach. Two upwind methods (van Leer's flux-vector-splitting and Roe's flux-differencing) were investigated. Two types of explicit solvers (a two-step predictor-corrector and a modified multistage Runge-Kutta) were used with multigrid acceleration to enhance convergence. A multiblock strategy is used to allow greater geometric flexibility. A report on simple explicit upwind schemes for solving compressible flows is included.
Non-Galerkin Coarse Grids for Algebraic Multigrid
Falgout, Robert D.; Schroder, Jacob B.
2014-06-26
Algebraic multigrid (AMG) is a popular and effective solver for systems of linear equations that arise from discretized partial differential equations. And while AMG has been effectively implemented on large scale parallel machines, challenges remain, especially when moving to exascale. Particularly, stencil sizes (the number of nonzeros in a row) tend to increase further down in the coarse grid hierarchy, and this growth leads to more communication. Therefore, as problem size increases and the number of levels in the hierarchy grows, the overall efficiency of the parallel AMG method decreases, sometimes dramatically. This growth in stencil size is due to the standard Galerkin coarse grid operator, $P^T A P$, where $P$ is the prolongation (i.e., interpolation) operator. For example, the coarse grid stencil size for a simple three-dimensional (3D) seven-point finite differencing approximation to diffusion can increase into the thousands on present day machines, causing an associated increase in communication costs. We therefore consider algebraically truncating coarse grid stencils to obtain a non-Galerkin coarse grid. First, the sparsity pattern of the non-Galerkin coarse grid is determined by employing a heuristic minimal “safe” pattern together with strength-of-connection ideas. Second, the nonzero entries are determined by collapsing the stencils in the Galerkin operator using traditional AMG techniques. The result is a reduction in coarse grid stencil size, overall operator complexity, and parallel AMG solve phase times.
Analysis of multigrid algorithms for nonsymmetric and indefinite elliptic problems
Bramble, J.H.; Pasciak, J.E.; Xu, J.
1988-10-01
We prove some new estimates for the convergence of multigrid algorithms applied to nonsymmetric and indefinite elliptic boundary value problems. We provide results for the so-called 'symmetric' multigrid schemes. We show that for the variable V-script-cycle and the W-script-cycle schemes, multigrid algorithms with any amount of smoothing on the finest grid converge at a rate that is independent of the number of levels or unknowns, provided that the initial grid is sufficiently fine. We show that the V-script-cycle algorithm also converges (under appropriate assumptions on the coarsest grid) but at a rate which may deteriorate as the number of levels increases. This deterioration for the V-script-cycle may occur even in the case of full elliptic regularity. Finally, the results of numerical experiments are given which illustrate the convergence behavior suggested by the theory.
Algebraic Multigrid by Smoothed Aggregation for Second and Fourth Order Elliptic Problems
NASA Technical Reports Server (NTRS)
Vanek, Petr; Mandel, Jan; Brezina, Marian
1996-01-01
Multigrid methods are very efficient iterative solvers for system of algebraic equations arising from finite element and finite difference discretization of elliptic boundary value problems. The main principle of multigrid methods is to complement the local exchange of information in point-wise iterative methods by a global one utilizing several related systems, called coarse levels, with a smaller number of variables. The coarse levels are often obtained as a hierarchy of discretizations with different characteristic meshsizes, but this requires that the discretization is controlled by the iterative method. To solve linear systems produced by existing finite element software, one needs to create an artificial hierarchy of coarse problems. The principal issue is then to obtain computational complexity and approximation properties similar to those for nested meshes, using only information in the matrix of the system and as little extra information as possible. Such algebraic multigrid method that uses the system matrix only was developed by Ruge. The prolongations were based on the matrix of the system by partial solution from given values at selected coarse points. The coarse grid points were selected so that each point would be interpolated to via so-called strong connections. Our approach is based on smoothed aggregation introduced recently by Vanek. First the set of nodes is decomposed into small mutually disjoint subsets. A tentative piecewise constant interpolation (in the discrete sense) is then defined on those subsets as piecewise constant for second order problems, and piecewise linear for fourth order problems. The prolongation operator is then obtained by smoothing the output of the tentative prolongation and coarse level operators are defined variationally.
A simplified analysis of the multigrid V-cycle as a fast elliptic solver
NASA Technical Reports Server (NTRS)
Decker, Naomi H.; Taasan, Shlomo
1988-01-01
For special model problems, Fourier analysis gives exact convergence rates for the two-grid multigrid cycle and, for more general problems, provides estimates of the two-grid convergence rates via local mode analysis. A method is presented for obtaining mutigrid convergence rate estimates for cycles involving more than two grids (using essentially the same analysis as for the two-grid cycle). For the simple cast of the V-cycle used as a fast Laplace solver on the unit square, the k-grid convergence rate bounds obtained by this method are sharper than the bounds predicted by the variational theory. Both theoretical justification and experimental evidence are presented.
A multigrid scheme for three dimensional body-fitted coordinates in turbomachine applications
Camarero, R.; Reggio, M.
1983-03-01
An efficient numerical scheme for the generation of curvilinear body-fitted coordinate systems in three dimensions is presented. The grid is obtained by the solution of a system of three elliptic partial differential equations. The method is based on the classical SOR scheme with an acceleration of convergence using the multigrid technique. The full approximation scheme has been used and is described with the overall algorithm. A number of numerical experiments are given with comparisons to illustrate the efficiency of the method. Practical applications to typical three-dimensional turbomachinery geometries are then shown.
Agglomeration of microparticles in complex plasmas
Du, Cheng-Ran; Thomas, Hubertus M.; Ivlev, Alexei V.; Konopka, Uwe; Morfill, Gregor E.
2010-11-15
Agglomeration of highly charged microparticles was observed and studied in complex plasma experiments carried out in a capacitively coupled rf discharge. The agglomeration was caused by strong waves triggered in a particle cloud by decreasing neutral gas pressure. Using a high-speed camera during this unstable regime, it was possible to resolve the motion of individual microparticles and to show that the relative velocities of some particles were sufficiently high to overcome the mutual Coulomb repulsion and hence to result in agglomeration. After stabilizing the cloud again through the increase of the pressure, we were able to observe the aggregates directly with a long-distance microscope. We show that the agglomeration rate deduced from our experiments is in good agreement with theoretical estimates. In addition, we briefly discuss the mechanisms that can provide binding of highly charged microparticles in a plasma.
Bed material agglomeration during fluidized bed combustion
Brown, R.C.; Dawson, M.R.; Noble, S.
1993-02-01
The purpose of this project is to determine the physical and chemical reactions which led to the undesired agglomeration of bed material during fluidized bed combustion and to relate these reactions to specific causes. Survey of industrial-scale fluidized bed combustors is being conducted to determine the occurrence of bed agglomeration and the circumstances under which agglomeration took place. This task should be finished by the end of February. Samples of bed material, agglomerate material, and boiler deposits are being requested from boiler operators as part of the survey. Once received, these sample will be analyzed to determine chemical and mineralogic composition. The bulk chemical determination will be performed using x-ray fluorescence and inductively coupled plasma-optical emission (ICP). Mineralogy will be detected by x-ray diffraction (XRD). Chemical and mineral reactions will be determined by scanning electron microscopy, optical microscopy, and electron microprobe.
Advances in food powder agglomeration engineering.
Cuq, B; Gaiani, C; Turchiuli, C; Galet, L; Scher, J; Jeantet, R; Mandato, S; Petit, J; Murrieta-Pazos, I; Barkouti, A; Schuck, P; Rondet, E; Delalonde, M; Dumoulin, E; Delaplace, G; Ruiz, T
2013-01-01
Food powders are used in everyday life in many ways and offer technological solutions to the problem of food production. The natural origin of food powders, diversity in their chemical composition, variability of the raw materials, heterogeneity of the native structures, and physicochemical reactivity under hydrothermal stresses contribute to the complexity in their behavior. Food powder agglomeration has recently been considered according to a multiscale approach, which is followed in the chapter layout: (i) at the particle scale, by a presentation of particle properties and surface reactivity in connection with the agglomeration mechanisms, (ii) at the mechanisms scale, by describing the structuration dynamics of agglomerates, (iii) at the process scale, by a presentation of agglomeration technologies and sensors and by studying the stress transmission mode in the powder bed, and finally (iv) by an integration of the acquired knowledge, thanks to a dimensional analysis carried out at each scale. PMID:23522795
Chekli, L; Roy, M; Tijing, L D; Donner, E; Lombi, E; Shon, H K
2015-08-15
Titanium dioxide nanoparticles (TiO2 NPs) are currently one of the most prolifically used nanomaterials, resulting in an increasing likelihood of release to the environment. This is of concern as the potential toxicity of TiO2 NPs has been investigated in several recent studies. Research into their fate and behaviour once entering the environment is urgently needed to support risk assessment and policy development. In this study, we used a multi-method approach combining light scattering and field-flow fractionation techniques to assess both the aggregation behaviour and aggregate structure of TiO2 NPs in different river waters. Results showed that both the aggregate size and surface-adsorbed dissolved organic matter (DOM) were strongly related to the initial DOM concentration of the tested waters (i.e. R(2) > 0.90) suggesting that aggregation of TiO2 NPs is controlled by the presence and concentration of DOM. The conformation of the formed aggregates was also found to be strongly related to the surface-adsorbed DOM (i.e. R(2) > 0.95) with increasing surface-adsorbed DOM leading to more compact structures. Finally, the concentration of TiO2 NPs remaining in the supernatant after sedimentation of the larger aggregates was found to decrease proportionally with both increasing IS and decreasing DOM concentration, resulting in more than 95% sedimentation in the highest IS sample. PMID:26067894
Coarse-grid selection for parallel algebraic multigrid
Cleary, A. J., LLNL
1998-06-01
The need to solve linear systems arising from problems posed on extremely large, unstructured grids has sparked great interest in parallelizing algebraic multigrid (AMG) To date, however, no parallel AMG algorithms exist We introduce a parallel algorithm for the selection of coarse-grid points, a crucial component of AMG, based on modifications of certain paallel independent set algorithms and the application of heuristics designed to insure the quality of the coarse grids A prototype serial version of the algorithm is implemented, and tests are conducted to determine its effect on multigrid convergence, and AMG complexity
Vectorizable multigrid algorithms for transonic-flow calculations
NASA Technical Reports Server (NTRS)
Melson, N. D.
1986-01-01
The analysis and the incorporation into a multigrid scheme of several vectorizable algorithms are discussed. von Neumann analyses of vertical-line, horizontal-line, and alternating-direction ZEBRA algorithms were performed; and the results were used to predict their multigrid damping rates. The algorithms were then successfully implemented in a transonic conservative full-potential computer program. The convergence acceleration effect of multiple grids is shown, and the convergence rates of the vectorizable algorithms are compared with those of standard successive-line overrelaxation (SLOR) algorithms.
Multigrid solution of internal flows using unstructured solution adaptive meshes
NASA Astrophysics Data System (ADS)
Smith, Wayne A.; Blake, Kenneth R.
1992-11-01
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.
Ruge, J.; Li, Y.; McCormick, S.F.
1994-12-31
The formulation and time discretization of problems in meteorology are often tailored to the type of efficient solvers available for use on the discrete problems obtained. A common procedure is to formulate the problem so that a constant (or latitude-dependent) coefficient Poisson-like equation results at each time step, which is then solved using spectral methods. This both limits the scope of problems that can be handled and requires linearization by forward extrapolation of nonlinear terms, which, in turn, requires filtering to control noise. Multigrid methods do not suffer these limitations, and can be applied directly to systems of nonlinear equations with variable coefficients. Here, a global barotropic semi-Lagrangian model, developed by the authors, is presented which results in a system of three coupled nonlinear equations to be solved at each time step. A multigrid method for the solution of these equations is described, and results are presented.
Proceedings, volume 17, Institute for Briquetting and Agglomeration
Not Available
1982-01-01
Papers presented discussed pelletizing of coal fines, graphite manufacture, compacting of coal, use of computers in agglomeration, HYL-III process, briquetting of iron ore fines, RECLAFORM, INMETCO process, binders for agglomeration, acoustic agglomeration, pelletizing of lime-fly ash mixtures, extrusion of aluminas for catalysts, and agglomeration of wastes. Seven papers have been abstracted separately.
Adaptive parallel multigrid for Euler and incompressible Navier-Stokes equations
Trottenberg, U.; Oosterlee, K.; Ritzdorf, H.
1996-12-31
The combination of (1) very efficient solution methods (Multigrid), (2) adaptivity, and (3) parallelism (distributed memory) clearly is absolutely necessary for future oriented numerics but still regarded as extremely difficult or even unsolved. We show that very nice results can be obtained for real life problems. Our approach is straightforward (based on {open_quotes}MLAT{close_quotes}). But, of course, reasonable refinement and load-balancing strategies have to be used. Our examples are 2D, but 3D is on the way.
The development of an algebraic multigrid algorithm for symmetric positive definite linear systems
Vanek, P.; Mandel, J.; Brezina, M.
1996-12-31
An algebraic multigrid algorithm for symmetric, positive definite linear systems is developed based on the concept of prolongation by smoothed aggregation. Coarse levels are generated automatically. We present a set of requirements motivated heuristically by a convergence theory. The algorithm then attempts to satisfy the requirements. Input to the method are the coefficient matrix and zero energy modes, which are determined from nodal coordinates and knowledge of the differential equation. Efficiency of the resulting algorithm is demonstrated by computational results on real world problems from solid elasticity, plate blending, and shells.
Multigrid solution of the nonlinear Poisson-Boltzmann equation and calculation of titration curves.
Oberoi, H; Allewell, N M
1993-01-01
Although knowledge of the pKa values and charge states of individual residues is critical to understanding the role of electrostatic effects in protein structure and function, calculating these quantities is challenging because of the sensitivity of these parameters to the position and distribution of charges. Values for many different proteins which agree well with experimental results have been obtained with modified Tanford-Kirkwood theory in which the protein is modeled as a sphere (reviewed in Ref. 1); however, convergence is more difficult to achieve with finite difference methods, in which the protein is mapped onto a grid and derivatives of the potential function are calculated as differences between the values of the function at grid points (reviewed in Ref. 6). Multigrid methods, in which the size of the grid is varied from fine to coarse in several cycles, decrease computational time, increase rates of convergence, and improve agreement with experiment. Both the accuracy and computational advantage of the multigrid approach increase with grid size, because the time required to achieve a solution increases slowly with grid size. We have implemented a multigrid procedure for solving the nonlinear Poisson-Boltzmann equation, and, using lysozyme as a test case, compared calculations for several crystal forms, different refinement procedures, and different charge assignment schemes. The root mean square difference between calculated and experimental pKa values for the crystal structure which yields best agreement with experiment (1LZT) is 1.1 pH units, with the differences in calculated and experimental pK values being less than 0.6 pH units for 16 out of 21 residues. The calculated titration curves of several residues are biphasic. Images FIGURE 8 PMID:8369451
Nanosized rods agglomerates as a new approach for formulation of a dry powder inhaler
Salem, HF; Abdelrahim, ME; Eid, K Abo; Sharaf, MA
2011-01-01
Background: Nanosized dry powder inhalers provide higher stability for poorly water-soluble drugs as compared with liquid formulations. However, the respirable particles must have a diameter of 1–5 μm in order to deposit in the lungs. Controlled agglomeration of the nanoparticles increases their geometric particle size so they can deposit easily in the lungs. In the lungs, they fall apart to reform nanoparticles, thus enhancing the dissolution rate of the drugs. Theophylline is a bronchodilator with poor solubility in water. Methods: Nanosized theophylline colloids were formed using an amphiphilic surfactant and destabilized using dilute sodium chloride solutions to form the agglomerates. Results: The theophylline nanoparticles thus obtained had an average particle size of 290 nm and a zeta potential of −39.5 mV, whereas the agglomerates were 2.47 μm in size with a zeta potential of −28.9 mV. The release profile was found to follow first-order kinetics (r2 > 0.96). The aerodynamic characteristics of the agglomerated nanoparticles were determined using a cascade impactor. The behavior of the agglomerate was significantly better than unprocessed raw theophylline powder. In addition, the nanoparticles and agglomerates resulted in a significant improvement in the dissolution of theophylline. Conclusion: The results obtained lend support to the hypothesis that controlled agglomeration strategies provide an efficient approach for the delivery of poorly water-soluble drugs into the lungs. PMID:21383856
Parallel multigrid preconditioner for the cardiac bidomain model.
Weber dos Santos, Rodrigo; Plank, Gernot; Bauer, Steffen; Vigmond, Edward J
2004-11-01
The bidomain equations are widely used for the simulation of electrical activity in cardiac tissue but are computationally expensive, limiting the size of the problem which can be modeled. The purpose of this study is to determine more efficient ways to solve the elliptic portion of the bidomain equations, the most computationally expensive part of the computation. Specifically, we assessed the performance of a parallel multigrid (MG) preconditioner for a conjugate gradient solver. We employed an operator splitting technique, dividing the computation in a parabolic equation, an elliptical equation, and a nonlinear system of ordinary differential equations at each time step. The elliptic equation was solved by the preconditioned conjugate gradient method, and the traditional block incomplete LU parallel preconditioner (ILU) was compared to MG. Execution time was minimized for each preconditioner by adjusting the fill-in factor for ILU, and by choosing the optimal number of levels for MG. The parallel implementation was based on the PETSc library and we report results for up to 16 nodes on a distributed cluster, for two and three dimensional simulations. A direct solver was also available to compare results for single processor runs. MG was found to solve the system in one third of the time required by ILU but required about 40% more memory. Thus, MG offered an attractive tradeoff between memory usage and speed, since its performance lay between those of the classic iterative methods (slow and low memory consumption) and direct methods (fast and high memory consumption). Results suggest the MG preconditioner is well suited for quickly and accurately solving the bidomain equations. PMID:15536898
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.
Agglomeration and defluidization in FBC of biomass fuels -- Mechanisms and measures for prevention
Nordin, A.; Oehman, M.; Skrifvars, B.J.; Hupa, M.
1996-12-31
The use of biomass fuels in fluidized bed combustion (FBC) and gasification (FBG) is becoming more important because of the environmental benefits associated with these fuel and processes. However, severe bed agglomeration and defluidization have been reported due to the special ash forming constituents of some biomass fuels. Previous results have indicated that this could possibly be prevented by intelligent fuel mixing. In the present work the mechanisms of bed agglomeration using two different biomass fuels as well as the mechanism of the prevention of agglomeration by co-combustion with coal (50/50 %{sub w}) were studied. Several repeated combustion tests with the two biomass fuels, alone (Lucerne and olive flesh), all resulted in agglomeration and defluidization of the bed within less than 30 minutes. By controlled defluidization experiments the initial cohesion temperatures for the two fuels were determined to be as low as 670 C and 940 C, respectively. However, by fuel mixing the initial agglomeration temperature increased to 950 C and more than 1050 C, respectively. When co-combusted with coal during ten hour extended runs, no agglomeration was observed for either of the two fuel mixtures. The agglomeration temperatures were compared with results from a laboratory method, based on compression strength measurements of ash pellets, and results from chemical equilibrium calculations. Samples of bed materials, collected throughout the experimental runs, as well as the produced agglomerated beds, were analyzed using SEM EDS and X-ray diffraction. The results showed that loss of fluidization resulted from formation of molten phases coating the bed materials; a salt melt in the case of Lucerne and a silicate melt in the case of the olive fuel. By fuel mixing, the in-bed ash composition is altered, conferring higher melting temperatures, and thereby agglomeration and defluidization can be prevented.
FAS multigrid calculations of three dimensional flow using non-staggered grids
NASA Technical Reports Server (NTRS)
Matovic, D.; Pollard, A.; Becker, H. A.; Grandmaison, E. W.
1993-01-01
Grid staggering is a well known remedy for the problem of velocity/pressure coupling in incompressible flow calculations. Numerous inconveniences occur, however, when staggered grids are implemented, particularly when a general-purpose code, capable of handling irregular three-dimensional domains, is sought. In several non-staggered grid numerical procedures proposed in the literature, the velocity/pressure coupling is achieved by either pressure or velocity (momentum) averaging. This approach is not convenient for simultaneous (block) solvers that are preferred when using multigrid methods. A new method is introduced in this paper that is based upon non-staggered grid formulation with a set of virtual cell face velocities used for pressure/velocity coupling. Instead of pressure or velocity averaging, a momentum balance at the cell face is used as a link between the momentum and mass balance constraints. The numerical stencil is limited to 9 nodes (in 2D) or 27 nodes (in 3D), both during the smoothing and inter-grid transfer, which is a convenient feature when a block point solver is applied. The results for a lid-driven cavity and a cube in a lid-driven cavity are presented and compared to staggered grid calculations using the same multigrid algorithm. The method is shown to be stable and produce a smooth (wiggle-free) pressure field.
Wang, Yajing; Shen, Jin; Wei, Liu; Dou, Zhenhai; Gao, Shanshan
2013-04-20
For the low accuracy of single-scale inversion method in photon correlation spectroscopy technology, a cascadic multigrid (CMG)-truncated singular value decomposition (TSVD) inversion method that combines the TSVD regularization with CMG technology is proposed. This method decomposes the original problem into several subproblems in different scale grid space. According to the particle sizes inverted from the coarsest scale to the finest scale, the solution of an original inversion problem can be obtained. For the inversion of each subproblem, TSVD method is used. The simulation and experimental data were respectively inverted by TSVD and CMG-TSVD methods. The inversion results demonstrate that the CMG-TSVD method has higher accuracy, more strong noise immunity and better smoothness than the TSVD method. PMID:23669690
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
Higher-order ice-sheet modelling accelerated by multigrid on graphics cards
NASA Astrophysics Data System (ADS)
Brædstrup, Christian; Egholm, David
2013-04-01
Higher-order ice flow modelling is a very computer intensive process owing primarily to the nonlinear influence of the horizontal stress coupling. When applied for simulating long-term glacial landscape evolution, the ice-sheet models must consider very long time series, while both high temporal and spatial resolution is needed to resolve small effects. The use of higher-order and full stokes models have therefore seen very limited usage in this field. However, recent advances in graphics card (GPU) technology for high performance computing have proven extremely efficient in accelerating many large-scale scientific computations. The general purpose GPU (GPGPU) technology is cheap, has a low power consumption and fits into a normal desktop computer. It could therefore provide a powerful tool for many glaciologists working on ice flow models. Our current research focuses on utilising the GPU as a tool in ice-sheet and glacier modelling. To this extent we have implemented the Integrated Second-Order Shallow Ice Approximation (iSOSIA) equations on the device using the finite difference method. To accelerate the computations, the GPU solver uses a non-linear Red-Black Gauss-Seidel iterator coupled with a Full Approximation Scheme (FAS) multigrid setup to further aid convergence. The GPU finite difference implementation provides the inherent parallelization that scales from hundreds to several thousands of cores on newer cards. We demonstrate the efficiency of the GPU multigrid solver using benchmark experiments.
Implicit method for the computation of unsteady flows on unstructured grids
NASA Technical Reports Server (NTRS)
Venkatakrishnan, V.; Mavriplis, D. J.
1995-01-01
An implicit method for the computation of unsteady flows on unstructured grids is presented. Following a finite difference approximation for the time derivative, the resulting nonlinear system of equations is solved at each time step by using an agglomeration multigrid procedure. The method allows for arbitrarily large time steps and is efficient in terms of computational effort and storage. Inviscid and viscous unsteady flows are computed to validate the procedure. The issue of the mass matrix which arises with vertex-centered finite volume schemes is addressed. The present formulation allows the mass matrix to be inverted indirectly. A mesh point movement and reconnection procedure is described that allows the grids to evolve with the motion of bodies. As an example of flow over bodies in relative motion, flow over a multi-element airfoil system undergoing deployment is computed.
Linear Multigrid Techniques in Self-consistent Electronic Structure Calculations
Fattebert, J-L
2000-05-23
Ab initio DFT electronic structure calculations involve an iterative process to solve the Kohn-Sham equations for an Hamiltonian depending on the electronic density. We discretize these equations on a grid by finite differences. Trial eigenfunctions are improved at each step of the algorithm using multigrid techniques to efficiently reduce the error at all length scale, until self-consistency is achieved. In this paper we focus on an iterative eigensolver based on the idea of inexact inverse iteration, using multigrid as a preconditioner. We also discuss how this technique can be used for electrons described by general non-orthogonal wave functions, and how that leads to a linear scaling with the system size for the computational cost of the most expensive parts of the algorithm.
NASA Astrophysics Data System (ADS)
Yu, Z. Q.; Tan, R. B. H.; Chow, P. S.
2005-06-01
Effects of agitation speed and feeding rate on agglomeration and habit of paracetamol crystals in anti-solvent crystallization from water-acetone mixture are reported. Water is used as anti-solvent and is added in a semi-batch manner to a baffled 1-l crystallizer equipped with a marine-type impeller. A simple new method to characterize agglomeration degree has been proposed. Results show that agglomeration degree of crystals depends on particle size and elevated agitation reduces agglomeration degree of big particles. Particle mean size exhibits a maximum with increasing agitation intensity in the range of 200-600 rpm, which is explained from the perspective of anti-solvent dispersion and crystal agglomeration/disruption. Agglomeration degree of products deteriorates with increasing feeding rate ranging from 1 to 20 g/min due to enhanced nucleation. Crystal habit changes when feeding rate is altered, mainly in the faces of [0 0 1] and [1 1 0]. Focused beam reflectance measurement (FBRM) was used to monitor indirectly the particle size distribution in situ. The data demonstrated that FBRM may potentially be used as a tool to control crystallization process.
Scaling Algebraic Multigrid Solvers: On the Road to Exascale
Baker, A H; Falgout, R D; Gamblin, T; Kolev, T; Schulz, M; Yang, U M
2010-12-12
Algebraic Multigrid (AMG) solvers are an essential component of many large-scale scientific simulation codes. Their continued numerical scalability and efficient implementation is critical for preparing these codes for exascale. Our experiences on modern multi-core machines show that significant challenges must be addressed for AMG to perform well on such machines. We discuss our experiences and describe the techniques we have used to overcome scalability challenges for AMG on hybrid architectures in preparation for exascale.
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.
Glowinski, Roland . E-mail: roland@math.uh.edu; Toivanen, Jari . E-mail: jatoivan@ncsu.edu
2005-07-20
We study the efficient solution of non-equilibrium radiation diffusion problems. An implicit time discretization leads to the solution of systems of non-linear equations which couple radiation energy and material temperature. We consider the implicit Euler method, the mid-point scheme, the two-step backward differentiation formula, and a two-stage implicit Runge-Kutta method for time discretization. We employ a Newton-Krylov method in the solution of arising non-linear problems. We describe the computation of the Jacobian matrix for Newton's method using automatic differentiation based on the operator overloading in Fortran 90. For GMRES iterations, we propose a simple multigrid preconditioner applied directly to the coupled linearized problems. We demonstrate the efficiency and scalability of the proposed solution procedure by solving one-dimensional and two-dimensional model problems.
Analysis of Urban Agglomeration and Its Meaning for Rural People.
ERIC Educational Resources Information Center
Spiegelman, Robert G.
Agglomeration--the clustering of people, businesses, or structures within an area--is investigated for two purposes: (1) defining the nature of agglomeration and erecting a suitable agglomeration theory, and (2) suggesting further research. These two objectives are seen as being vital to help improve the economic well-being of rural people by…
Engineering development of selective agglomeration. Final report
Not Available
1993-10-01
This report presents the findings of the project entitled {open_quotes}Engineering Development of Selective Agglomeration.{close_quotes} In 1989 the US Department of Energy contracted with Southern Company Services, Inc. (DOE Contract No. DE-AC22-89PC88879) to develop selective agglomeration technology to a commercially acceptable level by 1993. This project is part of DOE`s program to advance the state of physical coal cleaning technologies in order to accelerate the utilization of high-sulfur coals while complying with environmental regulations. Such projects assume added importance in light of the 1990 Clean Air Act Amendments. Appropriate utilization of the abundant reserves of high-sulfur coal in the United States can make a significant contribution to achieving the goal of energy independence.
Chander, S.; Hogg, R.
1995-01-01
The development of practical technologies for the deep cleaning of coal has been seriously hampered by the problems of carrying out efficient coal/mineral separations at the very fine sizes (often finer than 10 mm) needed to achieve adequate liberation of the mineral matter from the coal matrix. It is generally recognized that surface-based separation processes such as froth flotation or selective agglomeration offer considerable potential for such applications but there remain many problems in obtaining the required selectivity with acceptable recovery of combustible matter. In froth flotation, selectivity is substantially reduced at fine sizes due, primarily, to overloading of the froth phase which leads to excessive carryover of water and entrained mineral matter. Oil agglomeration, on the other hand, can provide good selectivity at low levels of oil addition but the agglomerates tend to be too fragile for separation by the screening methods normally used. The addition of larger amounts of oil can yield large, strong agglomerates which are easily separated but the selectivity is reduced and reagent costs can become excessive. We are investigating the use of a hybrid process - micro-agglomerate flotation - which is a combination of oil-agglomeration and froth flotation. The basic concept is to use small quantities of oil to promote the formation of dense micro-agglomerates with minimal entrapment of water and mineral particles, and to use froth flotation to extract these micro-agglomerates from the water/dispersed-mineral phase. Since the floating units are agglomerates (about 30-50 mm in size) rather than individual coal particles (1-10 mm) the problems of froth overload and water/mineral carryover should be significantly alleviated. Micro-agglomerate flotation has considerable potential for the practical deep cleaning of coal on a commercial scale.
Laakso, Ilkka; Hirata, Akimasa
2012-12-01
In transcranial magnetic stimulation (TMS), the distribution of the induced electric field, and the affected brain areas, depends on the position of the stimulation coil and the individual geometry of the head and brain. The distribution of the induced electric field in realistic anatomies can be modelled using computational methods. However, existing computational methods for accurately determining the induced electric field in realistic anatomical models have suffered from long computation times, typically in the range of tens of minutes or longer. This paper presents a matrix-free implementation of the finite-element method with a geometric multigrid method that can potentially reduce the computation time to several seconds or less even when using an ordinary computer. The performance of the method is studied by computing the induced electric field in two anatomically realistic models. An idealized two-loop coil is used as the stimulating coil. Multiple computational grid resolutions ranging from 2 to 0.25 mm are used. The results show that, for macroscopic modelling of the electric field in an anatomically realistic model, computational grid resolutions of 1 mm or 2 mm appear to provide good numerical accuracy compared to higher resolutions. The multigrid iteration typically converges in less than ten iterations independent of the grid resolution. Even without parallelization, each iteration takes about 1.0 s or 0.1 s for the 1 and 2 mm resolutions, respectively. This suggests that calculating the electric field with sufficient accuracy in real time is feasible. PMID:23128377
Development of a Gas-Promoted Oil Agglomeration Process
C. Nelson; F. Zhang; J. Drzymala; M. Shen; R. Abbott; T. D. Wheelock
1997-11-01
The preliminary laboratory-scale development of a gas-promoted, oil agglomeration process for cleaning coal was carried out with scale model mixing systems in which aqueous suspensions of ultrafine coal particles were treated with a liquid hydrocarbon and a small amount of air. The resulting agglomerates were recovered by screening. During a batch agglomeration test the progress of agglomeration was monitored by observing changes in agitator torque in the case of concentrated suspensions or by observing changes in turbidity in the case of dilute suspensions. Dilute suspensions were employed for investigating the kinetics of agglomeration, whereas concentrated suspensions were used for determining parameters that characterize the process of agglomeration. A key parameter turned out to be the minimum time te required to produce compact spherical agglomerates. Other important parameters included the projected area mean particle diameter of the agglomerates recovered at the end of a test as well as the ash content and yield of agglomerates. Batch agglomeration tests were conducted with geometrically similar mixing tanks which ranged in volume from 0.346 to 11.07 liters. Each tank was enclosed to control the amount of air present. A variable speed agitator fitted with a six blade turbine impeller was used for agitation. Tests were conducted with moderately hydrophobic Pittsburgh No. 8 coal and with more hydrophobic Upper Freeport coal using either n-heptane, i-octane, or hexadecane as an agglomerant.
NASA Technical Reports Server (NTRS)
Woods, Claudia M.; Brewe, David E.
1988-01-01
A numerical solution to a theoretical model of vapor cavitation in a dynamically loaded journal bearing is developed utilizing a multigrid iteration technique. The method is compared with a noniterative approach in terms of computational time and accuracy. The computational model is based on the Elrod algorithm, a control volume approach to the Reynolds equation which mimics the Jakobsson-Floberg and Olsson cavitation theory. Besides accounting for a moving cavitation boundary and conservation of mass at the boundary, it also conserves mass within the cavitated region via a smeared mass or striated flow extending to both surfaces in the film gap. The mixed nature of the equations (parabolic in the full film zone and hyperbolic in the cavitated zone) coupled with the dynamic aspects of the problem create interesting difficulties for the present solution approach. Emphasis is placed on the methods found to eliminate solution instabilities. Excellent results are obtained for both accuracy and reduction of computational time.
NASA Technical Reports Server (NTRS)
Woods, C. M.; Brewe, D. E.
1989-01-01
A numerical solution to a theoretical model of vapor cavitation in a dynamically loaded journal bearing is developed utilizing a multigrid iteration technique. The method is compared with a noniterative approach in terms of computational time and accuracy. The computational model is based on the Elrod algorithm, a control volume approach to the Reynolds equation which mimics the Jakobsson-Floberg and Olsson cavitation theory. Besides accounting for a moving cavitation boundary and conservation of mass at the boundary, it also conserves mass within the cavitated region via a smeared mass or striated flow extending to both surfaces in the film gap. The mixed nature of the equations (parabolic in the full film zone and hyperbolic in the cavitated zone) coupled with the dynamic aspects of the problem create interesting difficulties for the present solution approach. Emphasis is placed on the methods found to eliminate solution instabilities. Excellent results are obtained for both accuracy and reduction of computational time.
The analysis of multigrid algorithms for pseudodifferential operators of order minus one
Bramble, J.H.; Leyk, Z.; Pasciak, J.E. ||
1994-10-01
Multigrid algorithms are developed to solve the discrete systems approximating the solutions of operator equations involving pseudodifferential operators of order minus one. Classical multigrid theory deals with the case of differential operators of positive order. The pseudodifferential operator gives rise to a coercive form on H{sup {minus}1/2}({Omega}). Effective multigrid algorithms are developed for this problem. These algorithms are novel in that they use the inner product on H{sup {minus}1}({Omega}) as a base inner product for the multigrid development. The authors show that the resulting rate of iterative convergence can, at worst, depend linearly on the number of levels in these novel multigrid algorithms. In addition, it is shown that the convergence rate is independent of the number of levels (and unknowns) in the case of a pseudodifferential operator defined by a single-layer potential. Finally, the results of numerical experiments illustrating the theory are presented. 19 refs., 1 fig., 2 tabs.
Wei, Feng; Zhang, Jun-ying; Zheng, Chu-guang
2005-01-01
In order to remove efficiently haled-particles emissions from coal combustions, a new way was used to put forward the process of agglomeration and the atomization was produced by the nozzle and then sprayed into the flue before precipitation devices of power station boiler in order to make inhaled-particles agglomerate into bigger particles, which can be easily removed but not change existing running conditions of boiler. According to this idea, a model is set up to study agglomeration rate and effect forces between fly ash inhaled-particles and atomized agglomerator particles. The developed agglomeration rate was expressed by relative particle number decreasing speed per unit volume. The result showed that viscosity force and flow resistance force give main influences on agglomeration effect of inhaled-particles, while springiness force and gravity have little effect on agglomeration effect of theirs. Factors influencing the agglomeration rate and effect forces are studied, including agglomerator concentration, agglomerator flux and agglomerator density, atomized-particles diameters and inhaled-particles diameter and so on. PMID:16295917
A catheterization-training simulator based on a fast multigrid solver.
Li, Shun; Guo, Jixiang; Wang, Qiong; Meng, Qiang; Chui, Yim-Pan; Qin, Jing; Heng, Pheng-Ann
2012-01-01
A VR-based simulator helps trainees develop skills for catheterization, a fundamental but difficult procedure in vascular interventional radiology. A deformable model simulates the complicated behavior of guide wires and catheters, using the principle of minimum total potential energy. A fast, stable multigrid solver ensures realistic simulation and real-time interaction. In addition, the system employs geometrically and topologically accurate vascular models based on improved parallel-transport frames, and it implements efficient collision detection. Experiments evaluated the method's stability, the solver's execution time, how well the simulation preserved the catheter's curved tip, and the catheter deformation's realism. An empirical study based on a typical selective-catheterization procedure assessed the system's feasibility and effectiveness. PMID:24807310
Implicit/Multigrid Algorithms for Incompressible Turbulent Flows on Unstructured Grids
NASA Technical Reports Server (NTRS)
Anderson, W. Kyle; Rausch, Russ D.; Bonhaus, Daryl L.
1997-01-01
An implicit code for computing inviscid and viscous incompressible flows on unstructured grids is described. The foundation of the code is a backward Euler time discretization for which the linear system is approximately solved at each time step with either a point implicit method or a preconditioned Generalized Minimal Residual (GMRES) technique. For the GMRES calculations, several techniques are investigated for forming the matrix-vector product. Convergence acceleration is achieved through a multigrid scheme that uses non-nested coarse grids that are generated using a technique described in the present paper. Convergence characteristics are investigated and results are compared with an exact solution for the inviscid flow over a four-element airfoil. Viscous results, which are compared with experimental data, include the turbulent flow over a NACA 4412 airfoil, a three-element airfoil for which Mach number effects are investigated, and three-dimensional flow over a wing with a partial-span flap.
Adaptive Multigrid Algorithm for the Lattice Wilson-Dirac Operator
Babich, R.; Brower, R. C.; Rebbi, C.; Brannick, J.; Clark, M. A.; Manteuffel, T. A.; McCormick, S. F.; Osborn, J. C.
2010-11-12
We present an adaptive multigrid solver for application to the non-Hermitian Wilson-Dirac system of QCD. The key components leading to the success of our proposed algorithm are the use of an adaptive projection onto coarse grids that preserves the near null space of the system matrix together with a simplified form of the correction based on the so-called {gamma}{sub 5}-Hermitian symmetry of the Dirac operator. We demonstrate that the algorithm nearly eliminates critical slowing down in the chiral limit and that it has weak dependence on the lattice volume.
Adaptive multigrid algorithm for the lattice Wilson-Dirac operator.
Babich, R; Brannick, J; Brower, R C; Clark, M A; Manteuffel, T A; McCormick, S F; Osborn, J C; Rebbi, C
2010-11-12
We present an adaptive multigrid solver for application to the non-Hermitian Wilson-Dirac system of QCD. The key components leading to the success of our proposed algorithm are the use of an adaptive projection onto coarse grids that preserves the near null space of the system matrix together with a simplified form of the correction based on the so-called γ5-Hermitian symmetry of the Dirac operator. We demonstrate that the algorithm nearly eliminates critical slowing down in the chiral limit and that it has weak dependence on the lattice volume. PMID:21231217
Fast multigrid solution of the advection problem with closed characteristics
Yavneh, I.; Venner, C.H.; Brandt, A.
1996-12-31
The numerical solution of the advection-diffusion problem in the inviscid limit with closed characteristics is studied as a prelude to an efficient high Reynolds-number flow solver. It is demonstrated by a heuristic analysis and numerical calculations that using upstream discretization with downstream relaxation-ordering and appropriate residual weighting in a simple multigrid V cycle produces an efficient solution process. We also derive upstream finite-difference approximations to the advection operator, whose truncation terms approximate {open_quotes}physical{close_quotes} (Laplacian) viscosity, thus avoiding spurious solutions to the homogeneous problem when the artificial diffusivity dominates the physical viscosity.
Ayhan, F.D.
2009-11-15
The aim of this study was to investigate desulfurization and de-ashing of a mixture of subbituminous coal and gangue minerals by the agglomeration method. For this purpose, experimental studies were conducted on a mixture containing subbituminous coal, pyrite, quartz and calcite. The effects of some parameters that markedly influence the effectiveness of selective oil agglomeration, such as solid concentration, pH, bridging liquid type and concentration, and depressant type and amount, were investigated. Agglomeration results showed that the usage of various depressants (Na{sub 2}SiO{sub 3}, FeCl3, corn starch, wheat starch) in the agglomeration medium has a positive effect on the reduction of ash and total sulfur content of agglomerates. It was found that an agglomerate product containing 3.03% total sulfur and 25.01% ash with a total sulfur reduction of 56.71% was obtained from a feed that contained 7% total sulfur and 43.58% ash when FeCl{sub 3} was used in the agglomeration medium.
Identification of micro parameters for discrete element simulation of agglomerates
NASA Astrophysics Data System (ADS)
Palis, Stefan; Antonyuk, Sergiy; Dosta, Maksym; Heinrich, Stefan
2013-06-01
The mechanical behaviour of solid particles like agglomerates, granules or crystals strongly depends on their micro structure, e.g. structural defects and porosity. In order to model the mechanical behaviour of these inhomogeneous media the discrete element method has been proven to be an appropriate tool. The model parameters used are typically micro parameters like bond stiffness, particle-particle contact stiffness, strength of the bonds. Due to the lack of general methods for a direct micro parameter determination, normally laborious parameter adaptation has to be done in order to fit experiment and simulation. In this contribution a systematic and automatic way for parameter adaptation using real experiments is proposed. Due to the fact, that discrete element models are typically systems of differential equations of very high order, gradient based methods are not suitable. Hence, the focus will be on derivative free methods.
NASA Astrophysics Data System (ADS)
Prestidge, Clive A.; Ametov, Igor
2000-02-01
Rheological methods have been used to study the influence of the liquor cation (sodium versus potassium) on the time-dependent gibbsite particle interactions that occur during Bayer process crystallisation. The temperature, supersaturation and seeding levels investigated simulate those experienced in industrial crystallisers. Gibbsite agglomeration was shown to occur by reversible aggregation followed by irreversible cementation. These two sub-steps were individually characterised by careful choice of seed surface area and liquor supersaturation during batch crystallisation. At seed loading levels less than 10% w/w aggregates are rapidly cemented into agglomerates, this is more pronounced in sodium- than potassium-based liquors. These suspensions were Newtonian and the extent of agglomeration correlated with their viscosity. At seed loading levels greater than 20% w/w particle aggregation resulted in extensively time-dependent and non-Newtonian rheology. However, the aggregates did not undergo cementation into agglomerates and no irreversible size enlargement was evident. Yield stress development with time was used to probe the kinetics of aggregation and quantify the particle interaction behaviour. The rate and extent of the particle network formation is more pronounced in sodium rather than potassium-based liquors, supersaturation dependent, alkali concentration dependent, but only weakly temperature dependent. These findings are discussed with respect to the chemical and physical mechanisms of agglomeration in Bayer crystallisation and the role of cation.
Agglomeration defects on irradiated carbon nanotubes
Steini Moura, Cassio; Balzaretti, Naira Maria; Amaral, Livio; Gribel Lacerda, Rodrigo; Pimenta, Marcos A.
2012-03-15
Aligned carbon nanotubes (CNT) were irradiated in the longitudinal and perpendicular directions, with low energy carbon and helium ions in order to observe the formation of defects in the atomic structure. Analysis through Raman spectroscopy and scanning electron microscopy indicated bundle rupture and ion track formation on nanotube bundles. Aligned CNT presented a kind of defect comprising ravine formation and tube agglomeration on top of the substrate. The latter structure is possibly caused by static charge accumulation induced by the incoming ions. Fluence plays a role on the short range order. Higher fluence irradiation transforms CNT into amorphous carbon nanowires.
Combination Chemotherapeutic Dry Powder Aerosols via Controlled Nanoparticle Agglomeration
El-Gendy, Nashwa; Berkland, Cory
2014-01-01
Purpose To develop an aerosol system for efficient local lung delivery of chemotherapeutics where nanotechnology holds tremendous potential for developing more valuable cancer therapies. Concurrently, aerosolized chemotherapy is generating interest as a means to treat certain types of lung cancer more effectively with less systemic exposure to the compound. Methods Nanoparticles of the potent anticancer drug, paclitaxel, were controllably assembled to form low density microparticles directly after preparation of the nanoparticle suspension. The amino acid, L-leucine, was used as a colloid destabilizer to drive the assembly of paclitaxel nanoparticles. A combination chemotherapy aerosol was formed by assembling the paclitaxel nanoparticles in the presence of cisplatin in solution. Results Freeze-dried powders of the combination chemotherapy possessed desirable aerodynamic properties for inhalation. In addition, the dissolution rates of dried nanoparticle agglomerate formulations (~60% to 66% after 8 h) were significantly faster than that of micronized paclitaxel powder as received (~18% after 8 h). Interestingly, the presence of the water soluble cisplatin accelerated the dissolution of paclitaxel. Conclusions Nanoparticle agglomerates of paclitaxel alone or in combination with cisplatin may serve as effective chemotherapeutic dry powder aerosols to enable regional treatment of certain lung cancers. PMID:19415471
Multifrequency scanning probe microscopy study of nanodiamond agglomerates
NASA Astrophysics Data System (ADS)
Aravind, Vasudeva; Lippold, Stephen; Li, Qian; Strelcov, Evgheny; Okatan, Baris; Legum, Benjamin; Kalinin, Sergei; Clarion University Team; Oak Ridge National Laboratory Team
Due to their rich surface chemistry and excellent mechanical properties and non-toxic nature, nanodiamond particles have found applications such as biomedicine, tribology and lubrication, targeted drug delivery systems, tissue scaffolds and surgical implants. Although single nanodiamond particles have diameters about 4-5nm, they tend to form agglomerates. While these agglomerates can be useful for some purposes, many applications of nanodiamonds require single particle, disaggregated nanodiamonds. This work is oriented towards studying forces and interactions that contribute to agglomeration in nanodiamonds. In this work, using multifrequency scanning probe microscopy techniques, we show that agglomerate sizes can vary between 50-100nm in raw nanodiamonds. Extremeties of particles and Interfaces between agglomerates show dissipative forces with scanning probe microscope tip, indicating agglomerates could act as points of increased adhesion, thus reducing lubricating efficiency when nanodiamonds are used as lubricant additives. This research was conducted at the Center for Nanophase Materials Sciences, which is a DOE Office of Science User Facility.
General concepts of hydrargillite Al(OH) 3, agglomeration
NASA Astrophysics Data System (ADS)
Veesler, S.; Roure, S.; Boistelle, R.
1994-02-01
Agglomeration is an important stage of the Bayer process aiming at increasing the initial size of Al(OH) 3 particles. In the present work, we investigate the effects of supersaturation, seed charge and stirring rate on the agglomeration of hydrargillite crystallites, the size of which ranges from about 2 to 10 μm. The experiments are carried out in a batch crystallizer at constant temperature and caustic concentration. It is shown that the agglomeration rate increases with increasing seed charge, but rapidly reaches a plateau before decreasing when the seed charge is too high. On the other hand, agglomeration continuously decreases with increasing stirring rate, while it is favoured by increasing supersaturation. In the latter case, growth of the crystallites contributes to coarsening the agglomerates. We propose the general outlines of an agglomeration model taking collision and disagglomeration probabilities into account.
Brown, R.C.; Dawson, M.R.; Smeenk, J.L.
1995-04-01
Experiments performed support the hypothesis that a reducing atmosphere during fluidized bed coal combustion contributes to the formation of agglomerates. Reducing conditions are imposed by controlling the amount of combustion air supplied to the combustor, 50% of theoretical in these experiments. These localized reducing conditions may arise from either poor lateral bed mixing or oxygen-starved conditions due to the coal feed locations. Deviations from steady-state operating conditions in bed pressure drop may be used to detect agglomerate formation. Interpretation of the bed pressure drop was made more straightforward by employing a moving average difference method. During steady-state operation, the difference between the moving point averages should be close to zero, within {plus_minus}0.03 inches of water. Instability within the combustor, experienced once agglomerates begin to form, can be recognized as larger deviations from zero, on the magnitude of {plus_minus}0.15 inches of water.
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.
Agglomeration in a fluidized bed using multiple jet streams
Rehmat, A.; Abbasian, J. ); Kothari, M.; Hariri, H.; Arastoopour, H. )
1992-01-01
Tests were conducted to determine the overall temperature distribution, temperature in the vicinity of the jets, and the rate of agglomeration in a fluidized bed containing multiple jet streams. Agglomeration of ash during coal gasification increases carbon utilization efficiency considerably. The agglomeration requires a fluidized-bed reactor with a specially designed distributor equipped with a jet to yield a hot zone confined within the bed. The rate of agglomeration depends upon the size and the intensity of the zone. This rate, and hence the unit capacity, could be increased by adding multiple jets to the distributor. The purpose of this study was to verify this phenomenon. The temperature distribution inside the agglomerating fluidized-bed reactor with a single jet was studied by Hariri et al. Various parameters were involved in agglomeration phenomena -- bed material, fluidization velocity, bed temperature, jet velocity, jet temperature, bed geometry, and distributor geometry. Controlled agglomerates were produced in the fluidized bed when a sloped gas distributor consisting of a central jet and a porous plate was used. Gas at temperatures above the melting temperature of a bed material was introduced into the jet and gas at temperatures below the softening temperature was introduced into the distributor. The rate of agglomerate formation was significantly influenced by an increase in either jet air or auxiliary (grid) air temperature. The extent of agglomeration also depended strongly upon the volume of the hot zone confined within the isotherms with temperatures higher than the melting point of the bed material.
Agglomeration in a fluidized bed using multiple jet streams
Rehmat, A.; Abbasian, J.; Kothari, M.; Hariri, H.; Arastoopour, H.
1992-12-31
Tests were conducted to determine the overall temperature distribution, temperature in the vicinity of the jets, and the rate of agglomeration in a fluidized bed containing multiple jet streams. Agglomeration of ash during coal gasification increases carbon utilization efficiency considerably. The agglomeration requires a fluidized-bed reactor with a specially designed distributor equipped with a jet to yield a hot zone confined within the bed. The rate of agglomeration depends upon the size and the intensity of the zone. This rate, and hence the unit capacity, could be increased by adding multiple jets to the distributor. The purpose of this study was to verify this phenomenon. The temperature distribution inside the agglomerating fluidized-bed reactor with a single jet was studied by Hariri et al. Various parameters were involved in agglomeration phenomena -- bed material, fluidization velocity, bed temperature, jet velocity, jet temperature, bed geometry, and distributor geometry. Controlled agglomerates were produced in the fluidized bed when a sloped gas distributor consisting of a central jet and a porous plate was used. Gas at temperatures above the melting temperature of a bed material was introduced into the jet and gas at temperatures below the softening temperature was introduced into the distributor. The rate of agglomerate formation was significantly influenced by an increase in either jet air or auxiliary (grid) air temperature. The extent of agglomeration also depended strongly upon the volume of the hot zone confined within the isotherms with temperatures higher than the melting point of the bed material.
Pauli-Bruns, Anette; Knop, Klaus; Lippold, Bernhard C
2010-03-01
The one-step preparation of sustained release matrix pellets, using a melting procedure in a fluidized bed apparatus, was tested in a 2(3) full factorial design of experiments, using microcrystalline wax as lipophilic binder, theophylline as model drug and talc as additional matrix forming agent. The three influence parameters were (A) size of binder particles, (B) fraction of theophylline in solid particles and (C) fraction of microcrystalline wax in formulation. The response variables were agglomerate size and size distribution, dissolution time, agglomerate crush resistance, sphericity, yield and porosity. Nearly spherical pellets comprising a smooth, closed surface could be obtained with the used method, exhibiting the hollow core typical for the immersion and layering mechanism. The reproducibility was very good concerning all responses. The size of agglomerates is proportional to the size of the binder particles, which serve as cores for pellet formation in the molten state in the fluidized bed. Additionally, the agglomerate size is influenced by the volume of the solid particles in relation to the binder particles, with more solid particles leading to larger agglomerates and vice versa. Dissolution times vary in a very wide range, resulting from the interplay between amount of drug in relation to the meltable matrix substance microcrystalline wax and the non-meltable matrix substance talc. The change of binder particle size does not lead to a structural change of the matrix; both dissolution times and porosity are not significantly altered. Agglomerate crush resistance is low due to the hollow core of the pellets. However, it is significantly increased if the volume fraction of microcrystalline wax in the matrix is high, which means that the matrix is mechanically better stabilized. A theoretical model has been established to quantitatively explain agglomerate growth and very good accordance of the full particle size distributions between predicted and
Domain decomposition multigrid for unstructured grids
Shapira, Yair
1997-01-01
A two-level preconditioning method for the solution of elliptic boundary value problems using finite element schemes on possibly unstructured meshes is introduced. It is based on a domain decomposition and a Galerkin scheme for the coarse level vertex unknowns. For both the implementation and the analysis, it is not required that the curves of discontinuity in the coefficients of the PDE match the interfaces between subdomains. Generalizations to nonmatching or overlapping grids are made.
Chander, S.; Hogg, R.
1995-07-01
The development, of practical technologies for the deep cleaning of coal has been seriously hampered by the problems of carrying out efficient coal/mineral separations at the very fine sizes (often finer than 10 mm) needed to achieve adequate liberation of the mineral matter from the coal matrix. In froth flotation, selectivity is substantially reduced at fine sizes due, primarily, to overloading of the froth phase which leads to excessive carryover of water and entrained mineral matter. Oil agglomeration, on the other hand, can provide good selectivity at low levels of oil addition but the agglomerates tend to be too fragile for separation by the screening methods normally used. This project is concerned with a hydrid process, micro-agglomerate flotation, which is a combination of oil agglomeration and froth flotation.
MULTIGRID FOR THE MORTAR FINITE ELEMENT METHOD. (R825207)
The perspectives, information and conclusions conveyed in research project abstracts, progress reports, final reports, journal abstracts and journal publications convey the viewpoints of the principal investigator and may not represent the views and policies of ORD and EPA. Concl...
Wheelock, T.D.
1994-10-01
During the first year of the project two model mixing systems, which differed in size but were similar in design, were constructed and tested. The systems were equipped for measuring agitator speed and torque and for measuring the turbidity of coal particle suspensions undergoing agglomeration. Preliminary measurements of aqueous suspensions of coal particles showed that the Beer-Lambert law applies to such suspensions at least for low concentrations. Therefore, the measured turbidity can be used as an indicator of particle concentration and a means for monitoring the progress of oil agglomeration. However, the method is not applicable for large particle concentrations so a different technique was tested for monitoring the agglomeration of large concentrations. This technique involves measuring agitator torque and observing changes in torque while agitator speed is held constant. The results of preliminary tests of the technique were encouraging. In these tests significant changes in agitator torque were observed when particle agglomeration took place as long as solids concentration of 25 w/v % or more were utilized. A number of agglomeration tests were conducted using either one or the other of the two monitoring techniques. Both methods showed that even very small amounts of air can promote the oil agglomeration of coal particles suspended in water. Even the amount of air dissolved in water at room temperature and pressure can affect the process providing the air is displaced from the solution by a slightly soluble agglomerant such as heptane. The apparent rate of agglomeration was observed to increase as more air was introduced and also as agitator speed was increased.
MULTIGRID HOMOGENIZATION OF HETEROGENEOUS POROUS MEDIA
Dendy, J.E.; Moulton, J.D.
2000-10-01
This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL); this report, however, reports on only two years research, since this project was terminated at the end of two years in response to the reduction in funding for the LDRD Program at LANL. The numerical simulation of flow through heterogeneous porous media has become a vital tool in forecasting reservoir performance, analyzing groundwater supply and predicting the subsurface flow of contaminants. Consequently, the computational efficiency and accuracy of these simulations is paramount. However, the parameters of the underlying mathematical models (e.g., permeability, conductivity) typically exhibit severe variations over a range of significantly different length scales. Thus the numerical treatment of these problems relies on a homogenization or upscaling procedure to define an approximate coarse-scale problem that adequately captures the influence of the fine-scale structure, with a resultant compromise between the competing objectives of computational efficiency and numerical accuracy. For homogenization in models of flow through heterogeneous porous media, We have developed new, efficient, numerical, multilevel methods, that offer a significant improvement in the compromise between accuracy and efficiency. We recently combined this approach with the work of Dvorak to compute bounded estimates of the homogenized permeability for such flows and demonstrated the effectiveness of this new algorithm with numerical examples.
Soot agglomeration in isolated, free droplet combustion
NASA Technical Reports Server (NTRS)
Choi, M. Y.; Dryer, F. L.; Green, G. J.; Sangiovanni, J. J.
1993-01-01
Under the conditions of an isolated, free droplet experiment, hollow, carbonaceous structures, called soot spheres, were observed to form during the atmospheric pressure, low Reynolds number combustion of 1-methylnaphthalene. These structures which are agglomerates composed of smaller spheroidal units result from both thermophoretic effects induced by the envelope flame surrounding each drop and aerodynamic effects caused by changes in the relative gas/drop velocities. A chemically reacting flow model was used to analyze the process of sootshell formation during microgravity droplet combustion. The time-dependent temperature and gas property field surrounding the droplet was determined, and the soot cloud location for microgravity combustion of n-heptane droplets was predicted. Experiments showed that the sooting propensity of n-alkane fuel droplets can be varied through diluent substitution, oxygen-index variations, and ambient pressure reductions.
Pulse combusted acoustic agglomeration apparatus and process
Mansour, Momtaz N.; Chandran, Ravi
1994-01-01
An improved apparatus and process for removal of particulates entrained in a gas stream are provided. The removal process employs a pulse combustor to provide an acoustic pressure wave to acoustically enhance agglomeration of particulates which may be collected and removed using a conventional separation apparatus. The apparatus may be employed as a direct fired system for improved operation of gas-operated equipment such as a gas turbine, or may, alternatively, be employed as an add-on subsystem for combustion exhaust clean-up. Additionally, added particulates may include a sorbent for effecting sorption of other contaminants such as sulfur. Various other particulates for contaminant removal may also be introduced into the system as exemplified by alkali-gettering agents.
Pulse combusted acoustic agglomeration apparatus and process
Mansour, Momtaz N.
1993-01-01
An improved apparatus and process for removal of particulates entrained in a gas stream are provided. The removal process employs a pulse combustor to provide an acoustic pressure wave to acoustically enhance bimodal agglomeration of particulates which may be collected and removed using a conventional separation apparatus. A particulate having a size different from the size of the particulate in the gas stream to be cleaned is introduced into the system to effectuate the bimodal process. The apparatus may be employed as a direct fired system for improved operation of gas-operated equipment such as a gas turbine, or may, alternatively, be employed as an add-on subsystem for combustion exhaust clean-up. Additionally, the added particulate may be a sorbent for effecting sorption of other contaminants such as sulfur. Various other particulates for contaminant removal may also be introduced into the system as exemplified by alkali-gettering agents.
Biological effects of agglomerated multi-walled carbon nanotubes.
Song, Zheng-Mei; Wang, Lin; Chen, Ni; Cao, Aoneng; Liu, Yuanfang; Wang, Haifang
2016-06-01
The physicochemical properties of nanomaterials play crucial roles in determining their biological effects. Agglomeration of nanomaterials in various systems is a common phenomenon, however, how agglomeration affects the biological consequence of nanomaterials has not been well investigated because of its complexity. Herein, we prepared variable sized agglomerates of oxidized multi-walled carbon nanotubes (O-MWCNTs) by using Ca(2+) and studied their cellular uptake and cytotoxicity in HeLa cells. We found the altered property of O-MWCNTs agglomerates could be controlled and adjusted by the amount of Ca(2+). Agglomeration remarkably facilitated the cellular uptake of O-MWCNTs at the initial contact stage, due to the easy contact of agglomerates with cells. But agglomeration did not induce evident cytotoxicity when the concentration of O-MWCNTs was less than 150μg/mL. That was assayed by cell proliferation, membrane integrity, apoptosis and ROS generation. This study suggests us that the biological behaviors of nanomaterials could be altered by their states of agglomeration. PMID:26930035
Adaptive multigrid domain decomposition solutions for viscous interacting flows
NASA Technical Reports Server (NTRS)
Rubin, Stanley G.; Srinivasan, Kumar
1992-01-01
Several viscous incompressible flows with strong pressure interaction and/or axial flow reversal are considered with an adaptive multigrid domain decomposition procedure. Specific examples include the triple deck structure surrounding the trailing edge of a flat plate, the flow recirculation in a trough geometry, and the flow in a rearward facing step channel. For the latter case, there are multiple recirculation zones, of different character, for laminar and turbulent flow conditions. A pressure-based form of flux-vector splitting is applied to the Navier-Stokes equations, which are represented by an implicit lowest-order reduced Navier-Stokes (RNS) system and a purely diffusive, higher-order, deferred-corrector. A trapezoidal or box-like form of discretization insures that all mass conservation properties are satisfied at interfacial and outflow boundaries, even for this primitive-variable, non-staggered grid computation.
Cold bond agglomeration of waste oxides for recycling
D`Alessio, G.; Lu, W.K.
1996-12-31
Recycling of waste oxides has been an on-going challenge for integrated steel plants. The majority of these waste oxides are collected from the cleaning systems of ironmaking and steelmaking processes, and are usually in the form of fine particulates and slurries. In most cases, these waste materials are contaminated by oils and heavy metals and often require treatment at a considerable expense prior to landfill disposal. This contamination also limits the re-use or recycling potential of these oxides as secondary resources of reliable quality. However, recycling of some selected wastes in blast furnaces or steelmaking vessels is possible, but first requires agglomeration of the fine particulate by such methods as cold bond briquetting. Cold bond briquetting technology provides both mechanical compacting and bonding (with appropriate binders) of the particulates. This method of recycling has the potential to be economically viable and environmentally sustainable. The nature of the present study is cold bond briquetting of iron ore pellet fines with a molasses-cement-H{sub 2}O binder for recycling in a blast furnace. The inclusion of molasses is for its contribution to the green strength of briquettes. During the curing stage, significant gains in strength may be credited to molasses in the presence of cement. The interactions of cement (and its substitutes), water and molasses and their effects on the properties of the agglomerates during and after various curing conditions were investigated. Tensile strengths of briquettes made in the laboratory and subjected to experimental conditions which simulated the top part of a blast furnace shaft were also examined.
Chander, S.; Hogg, R.
1995-04-01
The development of practical technologies for the deep cleaning of coal has been seriously hampered by the problems of carrying out efficient coal/mineral separations at the very fine sizes (often finer than 10 mm) needed to achieve adequate liberation of the mineral matter from the coal matrix. In froth flotation, selectivity is substantially reduced at fine sizes due, primarily, to overloading of the froth phase which leads to excessive carryover of water and entrained mineral matter. Oil agglomeration, on the other hand, can provide good selectivity at low levels of oil addition but the agglomerates tend to be too fragile for separation by the screening methods normally used. The addition of larger amounts of oil can yield large, strong agglomerates which are easily separated but the selectivity is reduced and reagent costs can become excessive. We are investigating the use of a hybrid process - Micro-agglomerate flotation which is a combination of oil-agglomeration and froth flotation. The basic concept is to use small quantities of oil to promote the formation of dense micro-agglomerates with minimal entrapment of water and mineral particles, and to use froth flotation to extract these micro-agglomerates from the water/dispersed-mineral phase. Since the floating units are agglomerates (about 30-50 mm in size) rather than individual coal particles (1-10 mm) the problems of froth overload and water/mineral carryover should be significantly alleviated. There are, however, complications. The process involves at least five phases: two or more solids (coal and mineral), two liquids (oil and water) and one gas (air). It is necessary to maintain precise control over the chemistry of the liquid phases in order to promote the interfacial reactions and interactions between phases necessary to ensure selectivity. Kinetics as well as thermodynamic factors may be critical in determining overall system response.
NASA Astrophysics Data System (ADS)
Choi, Young Joon; Djilali, Ned
2016-01-01
Colloidal agglomeration of nanoparticles in shear flow is investigated by solving the fluid-particle and particle-particle interactions in a 2D system. We use an extended finite element method in which the dynamics of the particles is solved in a fully coupled manner with the flow, allowing an accurate description of the fluid-particle interfaces without the need of boundary-fitted meshes or of empirical correlations to account for the hydrodynamic interactions between the particles. Adaptive local mesh refinement using a grid deformation method is incorporated with the fluid-structure interaction algorithm, and the particle-particle interaction at the microscopic level is modeled using the Lennard-Jones potential. Motivated by the process used in fabricating fuel cell catalysts from a colloidal ink, the model is applied to investigate agglomeration of colloidal particles under external shear flow in a sliding bi-periodic Lees-Edwards frame with varying shear rates and particle fraction ratios. Both external shear and particle fraction are found to have a crucial impact on the structure formation of colloidal particles in a suspension. Segregation intensity and graph theory are used to analyze the underlying agglomeration patterns and structures, and three agglomeration regimes are identified.
Jadhav, Namdeo; Pawar, Atmaram; Paradkar, Anant
2010-03-01
The objective of the investigation was to study the effect of bromhexine hydrochloride (BXH) content and agglomerate size on mechanical, compressional and drug release properties of agglomerates prepared by crystallo-co-agglomeration (CCA). Studies on optimized batches of agglomerates (BXT1 and BXT2) prepared by CCA have showed adequate sphericity and strength required for efficient tabletting. Trend of strength reduction with a decrease in the size of agglomerates was noted for both batches, irrespective of drug loading. However, an increase in mean yield pressure (14.189 to 19.481) with an increase in size was observed for BXT2 having BXH-talc (1:15.7). Surprisingly, improvement in tensile strength was demonstrated by compacts prepared from BXT2, due to high BXH load, whereas BXT1, having a low amount of BXH (BXH-talc, 1:24), showed low tensile strength. Consequently, increased tensile strength was reflected in extended drug release from BXT2 compacts (Higuchi model, R(2) = 0.9506 to 0.9981). Thus, it can be concluded that interparticulate bridges formed by BXH and agglomerate size affect their mechanical, compressional and drug release properties. PMID:20228039
Kojima, A; Hanada, M; Tobari, H; Nishikiori, R; Hiratsuka, J; Kashiwagi, M; Umeda, N; Yoshida, M; Ichikawa, M; Watanabe, K; Yamano, Y; Grisham, L R
2016-02-01
Design techniques for the vacuum insulation have been developed in order to realize a reliable voltage holding capability of multi-aperture multi-grid (MAMuG) accelerators for fusion application. In this method, the nested multi-stage configuration of the MAMuG accelerator can be uniquely designed to satisfy the target voltage within given boundary conditions. The evaluation of the voltage holding capabilities of each acceleration stages was based on the previous experimental results about the area effect and the multi-aperture effect. Since the multi-grid effect was found to be the extension of the area effect by the total facing area this time, the total voltage holding capability of the multi-stage can be estimated from that per single stage by assuming the stage with the highest electric field, the total facing area, and the total apertures. By applying these consideration, the analysis on the 3-stage MAMuG accelerator for JT-60SA agreed well with the past gap-scan experiments with an accuracy of less than 10% variation, which demonstrated the high reliability to design MAMuG accelerators and also multi-stage high voltage bushings. PMID:26932032
Liao, Yuan-Lin; Lu, Chia-Feng; Wu, Chieh-Tsai; Lee, Jiann-Der; Lee, Shih-Tseng; Sun, Yung-Nien; Wu, Yu-Te
2013-02-01
In cranioplasty, neurosurgeons use bone grafts to repair skull defects. To ensure the protection of intracranial tissues and recover the original head shape for aesthetic purposes, a custom-made pre-fabricated prosthesis must match the cranial incision as closely as possible. In our previous study (Liao et al. in Med Biol Eng Comput 49:203-211, 2011), we proposed an algorithm consisting of the 2D snake and image registration using the patient's own diagnostic low-resolution and defective high-resolution computed tomography (CT) images to repair the impaired skull. In this study, we developed a 3D multigrid snake and employed multiresolution image registration to improve the computational efficiency. After extracting the defect portion images, we designed an image-trimming process to remove the bumped inner margin that can facilitate the placement of skull implants without manual trimming during surgery. To evaluate the performance of the proposed algorithm, a set of skull phantoms were manufactured to simulate six different conditions of cranial defects, namely, unilateral, bilateral, and cross-midline defects with 20 or 40% skull defects. The overall image processing time in reconstructing the defect portion images can be reduced from 3 h to 20 min, as compared with our previous method. Furthermore, the reconstruction accuracies using the 3D multigrid snake were superior to those using the 2D snake. PMID:23076880
NASA Astrophysics Data System (ADS)
Kojima, A.; Hanada, M.; Tobari, H.; Nishikiori, R.; Hiratsuka, J.; Kashiwagi, M.; Umeda, N.; Yoshida, M.; Ichikawa, M.; Watanabe, K.; Yamano, Y.; Grisham, L. R.
2016-02-01
Design techniques for the vacuum insulation have been developed in order to realize a reliable voltage holding capability of multi-aperture multi-grid (MAMuG) accelerators for fusion application. In this method, the nested multi-stage configuration of the MAMuG accelerator can be uniquely designed to satisfy the target voltage within given boundary conditions. The evaluation of the voltage holding capabilities of each acceleration stages was based on the previous experimental results about the area effect and the multi-aperture effect. Since the multi-grid effect was found to be the extension of the area effect by the total facing area this time, the total voltage holding capability of the multi-stage can be estimated from that per single stage by assuming the stage with the highest electric field, the total facing area, and the total apertures. By applying these consideration, the analysis on the 3-stage MAMuG accelerator for JT-60SA agreed well with the past gap-scan experiments with an accuracy of less than 10% variation, which demonstrated the high reliability to design MAMuG accelerators and also multi-stage high voltage bushings.
Operational source receptor calculations for large agglomerations
NASA Astrophysics Data System (ADS)
Gauss, Michael; Shamsudheen, Semeena V.; Valdebenito, Alvaro; Pommier, Matthieu; Schulz, Michael
2016-04-01
For Air quality policy an important question is how much of the air pollution within an urbanized region can be attributed to local sources and how much of it is imported through long-range transport. This is critical information for a correct assessment of the effectiveness of potential emission measures. The ratio between indigenous and long-range transported air pollution for a given region depends on its geographic location, the size of its area, the strength and spatial distribution of emission sources, the time of the year, but also - very strongly - on the current meteorological conditions, which change from day to day and thus make it important to provide such calculations in near-real-time to support short-term legislation. Similarly, long-term analysis over longer periods (e.g. one year), or of specific air quality episodes in the past, can help to scientifically underpin multi-regional agreements and long-term legislation. Within the European MACC projects (Monitoring Atmospheric Composition and Climate) and the transition to the operational CAMS service (Copernicus Atmosphere Monitoring Service) the computationally efficient EMEP MSC-W air quality model has been applied with detailed emission data, comprehensive calculations of chemistry and microphysics, driven by high quality meteorological forecast data (up to 96-hour forecasts), to provide source-receptor calculations on a regular basis in forecast mode. In its current state, the product allows the user to choose among different regions and regulatory pollutants (e.g. ozone and PM) to assess the effectiveness of fictive emission reductions in air pollutant emissions that are implemented immediately, either within the agglomeration or outside. The effects are visualized as bar charts, showing resulting changes in air pollution levels within the agglomeration as a function of time (hourly resolution, 0 to 4 days into the future). The bar charts not only allow assessing the effects of emission
Not Available
1992-12-31
A major concern with the utilization of coal in directly fired gas turbines is the control of particulate emissions and reduction of sulfur dioxide, and alkali vapor from combustion of coal, upstream of the gas turbine. Much research and development has been sponsored on methods for particulate emissions control and the direct injection of calcium-based sorbents to reduce SO{sub 2} emission levels. The results of this research and development indicate that both acoustic agglomeration of particulates and direct injection of sorbents have the potential to become a significant emissions control strategy. The Sonic Enhanced Ash Agglomeration and Sulfur Capture program focuses upon the application of an MTCI proprietary invention (Invention Disclosure filed) for simultaneously enhancing sulfur capture and particulate agglomeration of the combustor effluent. This application can be adapted as either a ``hot flue gas cleanup`` subsystem for the current concepts for combustor islands or as an alternative primary pulse combustor island in which slagging, sulfur capture, particulate agglomeration and control, and alkali gettering as well as NO{sub x} control processes become an integral part of the pulse combustion process.
Crystal growth and agglomeration of calcium sulfite hemihydrate crystals
Tai, C.Y.; Chen, P.C.
1995-04-01
Flue gas desulfurization (FGD) processes are most commonly utilized to remove sulfur dioxide from stack gases of coal- or oil-fired plants. In the simple slurry technology, SO{sub 2} is absorbed by a slurry of lime/limestone to form calcium sulfite crystals of acicular habit and its strong agglomeration, requiring large clarifiers and filters to dewater the sludge to make an acceptable landfill. Crystal growth and agglomeration of calcium sulfite hemihydrate crystals from solution were studied by reacting Ca(OH){sub 2} with NaHSO{sub 3} in a pH-stat semibatch crystallizer. Single platelet crystals and agglomerates of platelet crystals were produced in the pH range from 5.80 to 6.80. The crystallization mechanism changed from primary nucleation to crystal growth in the progressive precipitation. Using the titration curves, the growth rate was calculated from the titration rate at the final stage of operation. The crystal growth rates of calcium sulfate hemihydrate crystals were found to obey the parabolic rate law in the low supersaturation range. Another point to be noted is that the precipitates of calcium sulfite hemihydrate in agitated suspensions have a tendency to form agglomerates. It was found that the degree of agglomeration is a weak function of relative supersaturation and magma density, while the pH value is a key factor that affects the degree of agglomeration. Addition of EDTA also has an effect on the agglomeration of calcium sulfite hemihydrates.
Engineering development of selective agglomeration. Executive summary: Final report
Not Available
1993-04-01
Project performance targets for the selective agglomeration process were to achieve 85% or greater Btu recovery at 85% or greater pyritic sulfur rejection (PSR) on a run-of-mine (ROM) coal basis, while producing a final clean-coal product with an ash content of 6% or less which is handleable by conventional coal handling systems. Engineering development of selective agglomeration included: (1) Batch and continuous bench-scale precess development testing; (2) Continuous pilot-scale (3-t/h) component development testing to evaluate the adaptation and/or modification of existing unit operations for selective agglomeration; (3) Continuous pilot-scale (2-t/h) POC testing to optimize the selective agglomeration process and demonstrate precess reliability; (4) Vendor testing to evaluate pelletization and thermal drying precesses as applied to selective agglomeration; (5) Conceptual design of a commercial-scale (200-V/h) selective agglomeration facility; (6) Economic analysis of the selective agglomeration precess at a commercial (200-t/h) scale. The information obtained from the various modes of testing and analysis, particularly POC operations, resulted in a technical and economic design base sufficient to support construction and operation of a commercial plant.
Analysis of atmospheric fluidized bed combustion agglomerates. Final report
Perkins, D. III; Brekke, D.W.; Karner, F.R.
1984-04-01
Chemical and textural studies of AFBC agglomerates have revealed detailed information regarding the mechanisms of agglomeration. The formation of agglomerates in a silica sand bed can be described by a four step process: initial ash coatings of quartz grains; thickening of ash coatings and the formation of nodules; cementation of nodules to each other by a sulfated aluminosilicate matrix; and partial or complete melting of eutectic compositions to produce a sticky glass phase between grains and along fractures. Once agglomeration has begun, large scale solidification and restricted flow within the bed will lead to hot spots, wholesale melting and further agglomeration which ultimately forces a shutdown. Standard operating temperatures during normal AFBC runs come quite close to, or may actually exceed, the minimum temperatures for eutectic melting of the silicate phases in the coal and standard bed materials. The partially melted material may be expected to lead to the formation of dense, sticky areas within the bed, and the formation of hot spots which further exacerbate the problem. Ultimately, large scale bed agglomeration will result. Attempts to eliminate agglomeration by removal of sodium via an ion exchange process have yielded encouraging results. A second approach, used to raise melting temperatures within the bed, has been to use bed materials that may react with low-temperature minerals to produce high-temperature refractory phases such as mullite or other alkali and alkali-earth alumino-silicates.
NASA Astrophysics Data System (ADS)
Zohdi, T. I.
2016-03-01
In industry, particle-laden fluids, such as particle-functionalized inks, are constructed by adding fine-scale particles to a liquid solution, in order to achieve desired overall properties in both liquid and (cured) solid states. However, oftentimes undesirable particulate agglomerations arise due to some form of mutual-attraction stemming from near-field forces, stray electrostatic charges, process ionization and mechanical adhesion. For proper operation of industrial processes involving particle-laden fluids, it is important to carefully breakup and disperse these agglomerations. One approach is to target high-frequency acoustical pressure-pulses to breakup such agglomerations. The objective of this paper is to develop a computational model and corresponding solution algorithm to enable rapid simulation of the effect of acoustical pulses on an agglomeration composed of a collection of discrete particles. Because of the complex agglomeration microstructure, containing gaps and interfaces, this type of system is extremely difficult to mesh and simulate using continuum-based methods, such as the finite difference time domain or the finite element method. Accordingly, a computationally-amenable discrete element/discrete ray model is developed which captures the primary physical events in this process, such as the reflection and absorption of acoustical energy, and the induced forces on the particulate microstructure. The approach utilizes a staggered, iterative solution scheme to calculate the power transfer from the acoustical pulse to the particles and the subsequent changes (breakup) of the pulse due to the particles. Three-dimensional examples are provided to illustrate the approach.
Fragmentation and bond strength of airborne diesel soot agglomerates
Rothenbacher, Sonja; Messerer, Armin; Kasper, Gerhard
2008-01-01
Background The potential of diesel soot aerosol particles to break up into smaller units under mechanical stress was investigated by a direct impaction technique which measures the degree of fragmentation of individual agglomerates vs. impact energy. Diesel aerosol was generated by an idling diesel engine used for passenger vehicles. Both the aerosol emitted directly and aerosol that had undergone additional growth by Brownian coagulation ("aging") was investigated. Optionally a thermo-desoption technique at 280°C was used to remove all high-volatility and the majority of low-volatility HC adsorbates from the aerosol before aging. Results It was found that the primary soot agglomerates emitted directly from the engine could not be fragmented at all. Soot agglomerates permitted to grow additionally by Brownian coagulation of the primary emitted particles could be fragmented to a maximum of 75% and 60% respectively, depending on whether adsorbates were removed from their surface prior to aging or not. At most, these aged agglomerates could be broken down to roughly the size of the agglomerates from the primary emission. The energy required for a 50% fragmentation probability of all bonds within an agglomerate was reduced by roughly a factor of 2 when aging "dry" agglomerates. Average bond energies derived from the data were 0.52*10-16 and 1.2*10-16 J, respectively. This is about 2 orders of magnitude higher than estimates for pure van-der-Waals agglomerates, but agrees quite well with other observations. Conclusion Although direct conclusions regarding the behavior of inhaled diesel aerosol in contact with body fluids cannot be drawn from such measurements, the results imply that highly agglomerated soot aerosol particles are unlikely to break up into units smaller than roughly the size distribution emitted as tail pipe soot. PMID:18533015
Review of ash agglomeration in fluidized bed gasifiers
Matulevicius, E.S.; Golan, L.P.
1984-07-01
The purpose of this study is to review the data and mathematical models which describe the phenomena involved in the agglomeration of ash in fluidized bed coal gasifiers (FBG). Besides highlighting the data and theoretical models, this review lists areas where there is a lack of information regarding the actual mechanisms of agglomeration. Also, potential areas for further work are outlined. The work is directed at developing models of agglomeration which could be included in computer codes describing fluidized bed gasifier phenomena, e.g., FLAG and CHEMFLUB which have been developed for the US Department of Energy. 134 references, 24 figures, 13 tables.
Agglomeration of proteins in acoustically levitated droplets.
Delissen, Friedmar; Leiterer, Jork; Bienert, Ralf; Emmerling, Franziska; Thünemann, Andreas F
2008-09-01
An ultrasonic trap (acoustic levitator) was used as an analytical tool to allow container-free handling of proteins in small sample volumes. This trap was combined for the first time with synchrotron small-angle X-ray scattering (SAXS) for structure analysis of biological macromolecules in a solution. The microfocus beamline at BESSY was used as a source of intense X-ray radiation. Apoferritin (APO) was used as a model protein, and its aggregation behavior in a levitator was followed from a diluted solution to the solid state. Different stages of APO agglomeration were observed without solid container walls, which may influence aggregation behavior and produce a parasitic scattering background. Starting with a volume of 5 microL we analyzed the concentration dependence of APO structure factors in the range from 5 to 1,200 mg/mL (solid protein). The solution was stirred automatically due to convection inside the droplet caused by the ultrasonic field. SAXS data recording of APO was performed in time intervals of 60 s during an aggregation experiment of 30 to 60 min. PMID:18607573
Transport and Deposition of Welding Fume Agglomerates in a Realistic Human Nasal Airway.
Tian, Lin; Inthavong, Kiao; Lidén, Göran; Shang, Yidan; Tu, Jiyuan
2016-07-01
Welding fume is a complex mixture containing ultra-fine particles in the nanometer range. Rather than being in the form of a singular sphere, due to the high particle concentration, welding fume particles agglomerate into long straight chains, branches, or other forms of compact shapes. Understanding the transport and deposition of these nano-agglomerates in human respiratory systems is of great interest as welding fumes are a known health hazard. The neurotoxin manganese (Mn) is a common element in welding fumes. Particulate Mn, either as soluble salts or oxides, that has deposited on the olfactory mucosa in human nasal airway is transported along the olfactory nerve to the olfactory bulb within the brain. If this Mn is further transported to the basal ganglia of the brain, it could accumulate at the part of the brain that is the focal point of its neurotoxicity. Accounting for various dynamic shape factors due to particle agglomeration, the current computational study is focused on the exposure route, the deposition pattern, and the deposition efficiency of the inhaled welding fume particles in a realistic human nasal cavity. Particular attention is given to the deposition pattern and deposition efficiency of inhaled welding fume agglomerates in the nasal olfactory region. For particles in the nanoscale, molecular diffusion is the dominant transport mechanism. Therefore, Brownian diffusion, hydrodynamic drag, Saffman lift force, and gravitational force are included in the model study. The deposition efficiencies for single spherical particles, two kinds of agglomerates of primary particles, two-dimensional planar and straight chains, are investigated for a range of primary particle sizes and a range of number of primary particles per agglomerate. A small fraction of the inhaled welding fume agglomerates is deposited on the olfactory mucosa, approximately in the range 0.1-1%, and depends on particle size and morphology. The strong size dependence of the deposition
Brown, R.C.; Dawson, M.R.; Noble, S.D.
1993-04-01
The purpose of this project is to determine the physical and chemical reactions which lead to the undesired agglomeration of bed material during fluidized bed combustion and to relate these reactions to specific causes. A survey of agglomeration and deposit formation in industrial fluidized bed boilers is in progress. Preliminary results indicate that at least five boilers were experiencing some form of bed material agglomeration. In these instances it was observed that large particles were forming within the bed which were larger that the feed. Four operators could confirm that the larger bed particles had formed due to bed particles sticking together or agglomerating. Deposit formation was reported at nine sites with these deposits being found most commonly at coal feed locations and in cyclones. Other deposit locations included side walls and return loops. Examples of these agglomerates and deposits have been received from five of the surveyed facilities. Also during this quarter, a bulk sample of Illinois No. 6 coal was obtained from the Fossil Energy Program at Ames Laboratory here at Iowa State University and prepared for combustion tests. This sample was first ground to a top-size of 3/8`` using a jaw crusher then a size fraction of 3/8`` {times} 8 (US mesh) was then obtained by sieving using a Gilson Test-Master. This size fraction was selected for the preliminary laboratory-scale experiments designed to simulate the dense bed conditions that exist in the bottom of CFB combustors. To ensure uniformity of fuel composition among combustion runs, the sized coal was riffled using, a cone and long row method and stored in bags for each experiment. During this quarter additional modifications were made to achieve better control of fluidization regimes and to aid in monitoring the hydrodynamic and chemical conditions within the reactor.
Fast GPU-based computation of spatial multigrid multiframe LMEM for PET.
Nassiri, Moulay Ali; Carrier, Jean-François; Després, Philippe
2015-09-01
Significant efforts were invested during the last decade to accelerate PET list-mode reconstructions, notably with GPU devices. However, the computation time per event is still relatively long, and the list-mode efficiency on the GPU is well below the histogram-mode efficiency. Since list-mode data are not arranged in any regular pattern, costly accesses to the GPU global memory can hardly be optimized and geometrical symmetries cannot be used. To overcome obstacles that limit the acceleration of reconstruction from list-mode on the GPU, a multigrid and multiframe approach of an expectation-maximization algorithm was developed. The reconstruction process is started during data acquisition, and calculations are executed concurrently on the GPU and the CPU, while the system matrix is computed on-the-fly. A new convergence criterion also was introduced, which is computationally more efficient on the GPU. The implementation was tested on a Tesla C2050 GPU device for a Gemini GXL PET system geometry. The results show that the proposed algorithm (multigrid and multiframe list-mode expectation-maximization, MGMF-LMEM) converges to the same solution as the LMEM algorithm more than three times faster. The execution time of the MGMF-LMEM algorithm was 1.1 s per million of events on the Tesla C2050 hardware used, for a reconstructed space of 188 x 188 x 57 voxels of 2 x 2 x 3.15 mm3. For 17- and 22-mm simulated hot lesions, the MGMF-LMEM algorithm led on the first iteration to contrast recovery coefficients (CRC) of more than 75 % of the maximum CRC while achieving a minimum in the relative mean square error. Therefore, the MGMF-LMEM algorithm can be used as a one-pass method to perform real-time reconstructions for low-count acquisitions, as in list-mode gated studies. The computation time for one iteration and 60 millions of events was approximately 66 s. PMID:25850980
Column oil agglomeration of fly ash with ultrasonics
Gray, M.L.; Champagne, K.J.; Soong, Y.; Finseth, D.H.
1999-07-01
A promising oil agglomeration process has been developed for the beneficiation of fly ash using a six-foot agglomeration column. Carbon concentrates have been separated from fly ash with yields greater than 60 % and purities of 55 to 74 %. The parameters examined in the study include ultrasonic exposure, pulse rate, frequency, agitation speed, and blade configuration. The effects of the experimental variables on the quality of separation are discussed.
Dispersion of TiO₂ nanoparticle agglomerates by Pseudomonas aeruginosa.
Horst, Allison M; Neal, Andrea C; Mielke, Randall E; Sislian, Patrick R; Suh, Won Hyuk; Mädler, Lutz; Stucky, Galen D; Holden, Patricia A
2010-11-01
Engineered nanoparticles are increasingly incorporated into consumer products and are emerging as potential environmental contaminants. Upon environmental release, nanoparticles could inhibit bacterial processes, as evidenced by laboratory studies. Less is known regarding bacterial alteration of nanoparticles, including whether bacteria affect physical agglomeration states controlling nanoparticle settling and bioavailability. Here, the effects of an environmental strain of Pseudomonas aeruginosa on TiO₂ nanoparticle agglomerates formed in aqueous media are described. Environmental scanning electron microscopy and cryogenic scanning electron microscopy visually demonstrated bacterial dispersion of large agglomerates formed in cell culture medium and in marsh water. For experiments in cell culture medium, quantitative image analysis verified that the degrees of conversion of large agglomerates into small nanoparticle-cell combinations were similar for 12-h-growth and short-term cell contact experiments. Dispersion in cell growth medium was further characterized by size fractionation: for agglomerated TiO₂ suspensions in the absence of cells, 81% by mass was retained on a 5-μm-pore-size filter, compared to only 24% retained for biotic treatments. Filtrate cell and agglomerate sizes were characterized by dynamic light scattering, revealing that the average bacterial cell size increased from 1.4 μm to 1.9 μm because of nano-TiO₂ biosorption. High-magnification scanning electron micrographs showed that P. aeruginosa dispersed TiO₂ agglomerates by preferential biosorption of nanoparticles onto cell surfaces. These results suggest a novel role for bacteria in the environmental transport of engineered nanoparticles, i.e., growth-independent, bacterially mediated size and mass alterations of TiO₂ nanoparticle agglomerates. PMID:20851981
Acoustic agglomeration of power plant fly ash. Final report
Reethof, G.; McDaniel, O.H.
1982-01-01
The work has shown that acoustic agglomeration at practical acoustic intensities and frequencies is technically and most likely economically viable. The following studies were performed with the listed results: The physics of acoustic agglomeration is complex particularly at the needed high acoustic intensities in the range of 150 to 160 dB and frequencies in the 2500 Hz range. The analytical model which we developed, although not including nonlinear acoustic efforts, agreed with the trends observed. We concentrated our efforts on clarifying the impact of high acoustic intensities on the generation of turbulence. Results from a special set of tests show that although some acoustically generated turbulence of sorts exists in the 150 to 170 dB range with acoustic streaming present, such turbulence will not be a significant factor in acoustic agglomeration compared to the dominant effect of the acoustic velocities at the fundamental frequency and its harmonics. Studies of the robustness of the agglomerated particles using the Anderson Mark III impactor as the source of the shear stresses on the particles show that the agglomerates should be able to withstand the rigors of flow through commercial cyclones without significant break-up. We designed and developed a 700/sup 0/F tubular agglomerator of 8'' internal diameter. The electrically heated system functioned well and provided very encouraging agglomeration results at acoustic levels in the 150 to 160 dB and 2000 to 3000 Hz ranges. We confirmed earlier results that an optimum frequency exists at about 2500 Hz and that larger dust loadings will give better results. Studies of the absorption of acoustic energy by various common gases as a function of temperature and humidity showed the need to pursue such an investigation for flue gas constituents in order to provide necessary data for the design of agglomerators. 65 references, 56 figures, 4 tables.
NASA Technical Reports Server (NTRS)
Nishida, Brian A.; Langhi, Ronald G.; Bencze, Daniel P.
1991-01-01
A multiblock/multigrid computation of the inviscid flow over a wing-mounted propfan transport with propwash is presented. An explicit multistage scheme drives the integral Euler equations to a steady state solution, while an actuator disk approximates the slipstream effects of the propfan blades. Practical applications of detailed surface gridding, multiple block field grids and multigrid convergence acceleration are demonstrated.
Low-rank coal oil agglomeration product and process
Knudson, C.L.; Timpe, R.C.; Potas, T.A.; DeWall, R.A.; Musich, M.A.
1992-11-10
A selectively-sized, raw, low-rank coal is processed to produce a low ash and relative water-free agglomerate with an enhanced heating value and a hardness sufficient to produce a non-degradable, shippable fuel. The low-rank coal is treated, under high shear conditions, in the first stage to cause ash reduction and subsequent surface modification which is necessary to facilitate agglomerate formation. In the second stage the treated low-rank coal is contacted with bridging and binding oils under low shear conditions to produce agglomerates of selected size. The bridging and binding oils may be coal or petroleum derived. The process incorporates a thermal deoiling step whereby the bridging oil may be completely or partially recovered from the agglomerate; whereas, partial recovery of the bridging oil functions to leave as an agglomerate binder, the heavy constituents of the bridging oil. The recovered oil is suitable for recycling to the agglomeration step or can serve as a value-added product.
Low-rank coal oil agglomeration product and process
Knudson, Curtis L.; Timpe, Ronald C.; Potas, Todd A.; DeWall, Raymond A.; Musich, Mark A.
1992-01-01
A selectively-sized, raw, low-rank coal is processed to produce a low ash and relative water-free agglomerate with an enhanced heating value and a hardness sufficient to produce a non-decrepitating, shippable fuel. The low-rank coal is treated, under high shear conditions, in the first stage to cause ash reduction and subsequent surface modification which is necessary to facilitate agglomerate formation. In the second stage the treated low-rank coal is contacted with bridging and binding oils under low shear conditions to produce agglomerates of selected size. The bridging and binding oils may be coal or petroleum derived. The process incorporates a thermal deoiling step whereby the bridging oil may be completely or partially recovered from the agglomerate; whereas, partial recovery of the bridging oil functions to leave as an agglomerate binder, the heavy constituents of the bridging oil. The recovered oil is suitable for recycling to the agglomeration step or can serve as a value-added product.
Time-accurate Navier-Stokes calculations with multigrid acceleration
NASA Technical Reports Server (NTRS)
Melson, N. Duane; Atkins, Harold L.; Sanetrik, Mark D.
1993-01-01
A numerical scheme to solve the unsteady Navier-Stokes equations is described. The scheme is implemented by modifying the multigrid-multiblock version of the steady Navier-Stokes equations solver, TLNS3D. The scheme is fully implicit in time and uses TLNS3D to iteratively invert the equations at each physical time step. The design objective of the scheme is unconditional stability (at least for first- and second-order discretizations of the physical time derivatives). With unconditional stability, the choice of the time step is based on the physical phenomena to be resolved rather than limited by numerical stability which is especially important for high Reynolds number viscous flows, where the spatial variation of grid cell size can be as much as six orders of magnitude. An analysis of the iterative procedure and the implementation of this procedure in TLNS3D are discussed. Numerical results are presented to show both the capabilities of the scheme and its speed up relative to the use of global minimum time stepping. Reductions in computational times of an order of magnitude are demonstrated.
An implicit multigrid algorithm for computing hypersonic, chemically reacting viscous flows
Edwards, J.R.
1996-01-01
An implicit algorithm for computing viscous flows in chemical nonequilibrium is presented. Emphasis is placed on the numerical efficiency of the time integration scheme, both in terms of periteration workload and overall convergence rate. In this context, several techniques are introduced, including a stable, O(m{sup 2}) approximate factorization of the chemical source Jacobian and implementations of V-cycle and filtered multigrid acceleration methods. A five species-seventeen reaction air model is used to calculate hypersonic viscous flow over a cylinder at conditions corresponding to flight at 5 km/s, 60 km altitude and at 11.36 km/s, 76.42 km altitude. Inviscid calculations using an eleven-species reaction mechanism including ionization are presented for a case involving 11.37 km/s flow at an altitude of 84.6 km. Comparisons among various options for the implicit treatment of the chemical source terms and among different multilevel approaches for convergence acceleration are presented for all simulations.
Development of an explicit multiblock/multigrid flow solver for viscous flows in complex geometries
NASA Technical Reports Server (NTRS)
Steinthorsson, E.; Liou, M. S.; Povinelli, L. A.
1993-01-01
A new computer program is being developed for doing accurate simulations of compressible viscous flows in complex geometries. The code employs the full compressible Navier-Stokes equations. The eddy viscosity model of Baldwin and Lomax is used to model the effects of turbulence on the flow. A cell centered finite volume discretization is used for all terms in the governing equations. The Advection Upwind Splitting Method (AUSM) is used to compute the inviscid fluxes, while central differencing is used for the diffusive fluxes. A four-stage Runge-Kutta time integration scheme is used to march solutions to steady state, while convergence is enhanced by a multigrid scheme, local time-stepping, and implicit residual smoothing. To enable simulations of flows in complex geometries, the code uses composite structured grid systems where all grid lines are continuous at block boundaries (multiblock grids). Example results shown are a flow in a linear cascade, a flow around a circular pin extending between the main walls in a high aspect-ratio channel, and a flow of air in a radial turbine coolant passage.
An Adaptive Multigrid Algorithm for Simulating Solid Tumor Growth Using Mixture Models
Wise, S.M.; Lowengrub, J.S.; Cristini, V.
2010-01-01
In this paper we give the details of the numerical solution of a three-dimensional multispecies diffuse interface model of tumor growth, which was derived in (Wise et al., J. Theor. Biol. 253 (2008)) and used to study the development of glioma in (Frieboes et al., NeuroImage 37 (2007) and tumor invasion in (Bearer et al., Cancer Research, 69 (2009)) and (Frieboes et al., J. Theor. Biol. 264 (2010)). The model has a thermodynamic basis, is related to recently developed mixture models, and is capable of providing a detailed description of tumor progression. It utilizes a diffuse interface approach, whereby sharp tumor boundaries are replaced by narrow transition layers that arise due to differential adhesive forces among the cell-species. The model consists of fourth-order nonlinear advection-reaction-diffusion equations (of Cahn-Hilliard-type) for the cell-species coupled with reaction-diffusion equations for the substrate components. Numerical solution of the model is challenging because the equations are coupled, highly nonlinear, and numerically stiff. In this paper we describe a fully adaptive, nonlinear multigrid/finite difference method for efficiently solving the equations. We demonstrate the convergence of the algorithm and we present simulations of tumor growth in 2D and 3D that demonstrate the capabilities of the algorithm in accurately and efficiently simulating the progression of tumors with complex morphologies. PMID:21076663
Optimization of refractive liquid crystal lenses using an efficient multigrid simulation.
Milton, Harry; Brimicombe, Paul; Morgan, Philip; Gleeson, Helen; Clamp, John
2012-05-01
A multigrid computational model has been developed to assess the performance of refractive liquid crystal lenses, which is up to 40 times faster than previous techniques. Using this model, the optimum geometries producing an ideal parabolic voltage distribution were deduced for refractive liquid crystal lenses with diameters from 1 to 9 mm. The ratio of insulation thickness to lens diameter was determined to be 1:2 for small diameter lenses, tending to 1:3 for larger lenses. The model is used to propose a new method of lens operation with lower operating voltages needed to induce specific optical powers. The operating voltages are calculated for the induction of optical powers between + 1.00 D and + 3.00 D in a 3 mm diameter lens, with the speed of the simulation facilitating the optimization of the refractive index profile. We demonstrate that the relationship between additional applied voltage and optical power is approximately linear for optical powers under + 3.00 D. The versatility of the computational simulation has also been demonstrated by modeling of in-plane electrode liquid crystal devices. PMID:22565739
An Adaptive Multigrid Algorithm for Simulating Solid Tumor Growth Using Mixture Models.
Wise, S M; Lowengrub, J S; Cristini, V
2011-01-01
In this paper we give the details of the numerical solution of a three-dimensional multispecies diffuse interface model of tumor growth, which was derived in (Wise et al., J. Theor. Biol. 253 (2008)) and used to study the development of glioma in (Frieboes et al., NeuroImage 37 (2007) and tumor invasion in (Bearer et al., Cancer Research, 69 (2009)) and (Frieboes et al., J. Theor. Biol. 264 (2010)). The model has a thermodynamic basis, is related to recently developed mixture models, and is capable of providing a detailed description of tumor progression. It utilizes a diffuse interface approach, whereby sharp tumor boundaries are replaced by narrow transition layers that arise due to differential adhesive forces among the cell-species. The model consists of fourth-order nonlinear advection-reaction-diffusion equations (of Cahn-Hilliard-type) for the cell-species coupled with reaction-diffusion equations for the substrate components. Numerical solution of the model is challenging because the equations are coupled, highly nonlinear, and numerically stiff. In this paper we describe a fully adaptive, nonlinear multigrid/finite difference method for efficiently solving the equations. We demonstrate the convergence of the algorithm and we present simulations of tumor growth in 2D and 3D that demonstrate the capabilities of the algorithm in accurately and efficiently simulating the progression of tumors with complex morphologies. PMID:21076663
Multigrid solution of incompressible turbulent flows by using two-equation turbulence models
Zheng, X.; Liu, C.; Sung, C.H.
1996-12-31
Most of practical flows are turbulent. From the interest of engineering applications, simulation of realistic flows is usually done through solution of Reynolds-averaged Navier-Stokes equations and turbulence model equations. It has been widely accepted that turbulence modeling plays a very important role in numerical simulation of practical flow problem, particularly when the accuracy is of great concern. Among the most used turbulence models today, two-equation models appear to be favored for the reason that they are more general than algebraic models and affordable with current available computer resources. However, investigators using two-equation models seem to have been more concerned with the solution of N-S equations. Less attention is paid to the solution method for the turbulence model equations. In most cases, the turbulence model equations are loosely coupled with N-S equations, multigrid acceleration is only applied to the solution of N-S equations due to perhaps the fact the turbulence model equations are source-term dominant and very stiff in sublayer region.
A fast multigrid-based electromagnetic eigensolver for curved metal boundaries on the Yee mesh
Bauer, Carl A.; Werner, Gregory R.; Cary, John R.
2013-10-15
For embedded boundary electromagnetics using the Dey–Mittra (Dey and Mittra, 1997) [1] algorithm, a special grad–div matrix constructed in this work allows use of multigrid methods for efficient inversion of Maxwell’s curl–curl matrix. Efficient curl–curl inversions are demonstrated within a shift-and-invert Krylov-subspace eigensolver (open-sourced at ([ofortt]https://github.com/bauerca/maxwell[cfortt])) on the spherical cavity and the 9-cell TESLA superconducting accelerator cavity. The accuracy of the Dey–Mittra algorithm is also examined: frequencies converge with second-order error, and surface fields are found to converge with nearly second-order error. In agreement with previous work (Nieter et al., 2009) [2], neglecting some boundary-cut cell faces (as is required in the time domain for numerical stability) reduces frequency convergence to first-order and surface-field convergence to zeroth-order (i.e. surface fields do not converge). Additionally and importantly, neglecting faces can reduce accuracy by an order of magnitude at low resolutions.
Integration of a Multigrid ODE solver into an open medical simulation framework.
Wu, Xunlei; Yao, Jianhua; Enquobahrie, Andinet; Lee, Huai-Ping; Audette, Michel A
2012-01-01
In this paper, we present the implementation of a Multigrid ODE solver in SOFA framework. By combining the stability advantage of coarse meshes and the transient detail preserving virtue of fine meshes, Multigrid ODE solver computes more efficiently than classic ODE solvers based on a single level discretization. With the ever wider adoption of the SOFA framework in many surgical simulation projects, introducing this Multigrid ODE solver into SOFA's pool of ODE solvers shall benefit the entire community. This contribution potentially has broad ramifications in the surgical simulation research community, given that in a single-resolution system, a constitutively realistic interactive tissue response, which presupposes large elements, is in direct conflict with the need to represent clinically relevant critical tissues in the simulation, which are typically be comprised of small elements. PMID:23366578
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.
NASA Astrophysics Data System (ADS)
Wang, Lu; Zhang, Guo-Hua; Wang, Jing-Song; Chou, Kuo-Chih
2016-08-01
An agglomeration of the furnace charge always takes place during the oxidation roasting process of molybdenite concentrate (with the main component of MoS2) in multiple hearth furnaces, which greatly affects the production process and furnace service life. In the present work, a preliminary study about the influence of various components on the agglomeration phenomenon of pure MoS2 have been carried out. The results show that reaction temperature, impurity content, and air flow rate have significant effects on the agglomeration extent. Meanwhile, the impurity type added into the pure MoS2 plays a crucial role. It was found that CaO and MgO have a stronger sulfur-fixing effect and that the desulphurization of the roasted product was uncompleted. It was also concluded that the agglomeration is due to the formation of low-melting-point eutectics, including that between MoO3 and impurities and that between MoO3 and Mo4O11. It is suggested that decreasing the impurities contents, especially K, Cu, Pb, and Fe, is an effective method for reducing the extent of agglomeration.
NASA Astrophysics Data System (ADS)
Wang, Lu; Zhang, Guo-Hua; Wang, Jing-Song; Chou, Kuo-Chih
2016-05-01
An agglomeration of the furnace charge always takes place during the oxidation roasting process of molybdenite concentrate (with the main component of MoS2) in multiple hearth furnaces, which greatly affects the production process and furnace service life. In the present work, a preliminary study about the influence of various components on the agglomeration phenomenon of pure MoS2 have been carried out. The results show that reaction temperature, impurity content, and air flow rate have significant effects on the agglomeration extent. Meanwhile, the impurity type added into the pure MoS2 plays a crucial role. It was found that CaO and MgO have a stronger sulfur-fixing effect and that the desulphurization of the roasted product was uncompleted. It was also concluded that the agglomeration is due to the formation of low-melting-point eutectics, including that between MoO3 and impurities and that between MoO3 and Mo4O11. It is suggested that decreasing the impurities contents, especially K, Cu, Pb, and Fe, is an effective method for reducing the extent of agglomeration.
Colloidal stability of coal-simulated suspensions in selective agglomeration
Schurger, M.L.
1989-01-01
A coal suspension was simulated by using graphite to simulate the carbonaceous fraction and kaolinite clay to simulate the ash fraction. Separate studies on each material established their response to additions of oxidized pyrite (ferrous sulfate) and a humic acid simulate (salicylic acid) in terms of zeta potentials profiles with pH and Ionic strength. Concentrations of iron and salicylic acid evaluated were 4.5 {times} 10{sup {minus}3} M and 2.0 {times} 10{sup {minus}4} M, respectively. The zeta potentials profiles of graphite, clay and hexadecane were negative throughout the pH ranges studied. The addition of iron lowered the zeta potentials all of the suspensions under all pH and ionic strength conditions. Salicylic acid decreased the graphite and hexadecane zeta potentials but had no effect on the clay zeta potential profiles. Agglomeration of graphite with bridging liquid shows distinct time dependent rate mechanisms, a initial growth of graphite agglomerates followed by consolidation phase. Graphite agglomeration was rapid with the maximum amount of agglomerate volume growth occurring in under 2-4 minutes. Agglomeration in the first two minutes was characterized by a 1st order rate mechanism. The presence of either Iron and salicylic acid generally improved the first order rates. The addition of clay also improved the first order rates except in the presence of salicylic acid. Heteroagglomeration of graphite with clay was found by hydrodynamic arguments to be unfavored. A multicomponent population balance model which had been developed for evaluating collision efficiencies of coal, ash and pyrite selective agglomeration was evaluated to explain these results. The growth and consolidation characteristics of graphite agglomeration for the experimental conditions examined herein revealed the limitations of such as model for this application.
Iterative methods for elliptic finite element equations on general meshes
NASA Technical Reports Server (NTRS)
Nicolaides, R. A.; Choudhury, Shenaz
1986-01-01
Iterative methods for arbitrary mesh discretizations of elliptic partial differential equations are surveyed. The methods discussed are preconditioned conjugate gradients, algebraic multigrid, deflated conjugate gradients, an element-by-element techniques, and domain decomposition. Computational results are included.
Vectorizable multigrid algorithms for transonic flow calculations. M.S. Thesis
NASA Technical Reports Server (NTRS)
Melson, N. D.
1985-01-01
The analysis and incorporation into a multigrid scheme of several vectorizable algorithms are discussed. Von Neumann analyses of vertical line, horizontal line, and alternating direction ZEBRA algorithms were performed; and the results were used to predict their multigrid damping rates. The algorithms were then successfully implemented in a transonic conservative full-potential computer program. The convergence acceleration effect of multiple grids is shown and the convergence rates of the vectorizable algorithms are compared to the convergence rates of standard successive line overrelaxation (SLOR) algorithms.
A multigrid algorithm for the cell-centered finite difference scheme
NASA Technical Reports Server (NTRS)
Ewing, Richard E.; Shen, Jian
1993-01-01
In this article, we discuss a non-variational V-cycle multigrid algorithm based on the cell-centered finite difference scheme for solving a second-order elliptic problem with discontinuous coefficients. Due to the poor approximation property of piecewise constant spaces and the non-variational nature of our scheme, one step of symmetric linear smoothing in our V-cycle multigrid scheme may fail to be a contraction. Again, because of the simple structure of the piecewise constant spaces, prolongation and restriction are trivial; we save significant computation time with very promising computational results.
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.
A multigrid solver for semi-implicit global shallow-water models
NASA Technical Reports Server (NTRS)
Barros, Saulo R. M.; Dee, Dick P.; Dickstein, Flavio
1990-01-01
A multigrid solver is developed for the discretized two-dimensional elliptic equation on the sphere that arises from a semiimplicit time discretization of the global shallow-water equations. Different formulations of the semiimplicit scheme result in variable-coefficient Helmholtz-type equations for which no fast direct solvers are available. The efficiency of the multigrid solver is optimal, in the sense that the total operation count is proportional to the number of unknowns. Numerical experiments using initial data derived from actual 300-mb height and wind velocity fields indicate that the present model has very good accuracy and stability properties.
NASA Technical Reports Server (NTRS)
Bates, J. R.; Semazzi, F. H. M.; Higgins, R. W.; Barros, Saulo R. M.
1990-01-01
A vector semi-Lagrangian semi-implicit two-time-level finite-difference integration scheme for the shallow water equations on the sphere is presented. A C-grid is used for the spatial differencing. The trajectory-centered discretization of the momentum equation in vector form eliminates pole problems and, at comparable cost, gives greater accuracy than a previous semi-Lagrangian finite-difference scheme which used a rotated spherical coordinate system. In terms of the insensitivity of the results to increasing timestep, the new scheme is as successful as recent spectral semi-Lagrangian schemes. In addition, the use of a multigrid method for solving the elliptic equation for the geopotential allows efficient integration with an operation count which, at high resolution, is of lower order than in the case of the spectral models. The properties of the new scheme should allow finite-difference models to compete with spectral models more effectively than has previously been possible.
Effect of Drying Phase on the Agglomerates Prepared by Spherical Crystallization
Maghsoodi, Maryam; Yari, Zahra
2015-01-01
In this paper, differences in porosity, compressive strength and tablet- forming ability of carbamazepine crystals agglomerated under similar condition, but subjected to different drying temperatures are reported. The agglomerates were prepared by spherical crystallization method and thereafter dried without agitation at different temperature. An increased drying temperature did not affect the shape and structure texture of dried particles and did not cause them to fracture. Drying of particles at higher temperature suppressed the particle contraction as a consequence of fast evaporation and hence produced particles of larger mean diameter, higher porosity and thus lower compressive strength than those dried at lower temperature. Through a relationship with particle porosity, the drying rate also affected the ability of particles to form tablets. PMID:25561911
Multivariate analysis applied to agglomerated macrobenthic data from an unpolluted estuary.
Conde, Anxo; Novais, Júlio M; Domínguez, Jorge
2013-01-01
We agglomerated species into higher taxonomic aggregations and functional groups to analyse environmental gradients in an unpolluted estuary. We then applied non-metric Multidimensional Scaling and Redundancy Analysis (RDA) for ordination of the agglomerated data matrices. The correlation between the ordinations produced by both methods was generally high. However, the performance of the RDA models depended on the data matrix used to fit the model. As a result, salinity and total nitrogen were only found significant when aggregated data matrices were used rather than species data matrix. We used the results to select a RDA model that explained a higher percentage of variance in the species data set than the parsimonious model. We conclude that the use of aggregated matrices may be considered complementary to the use of species data to obtain a broader insight into the distribution of macrobenthic assemblages in relation to environmental gradients. PMID:23684322
Capillary condensation onto titania (TiO2) nanoparticle agglomerates.
Kim, Seonmin; Ehrman, Sheryl H
2007-02-27
A capillary condensation process was developed for the purpose of forming interconnections between nanoparticles at low temperatures. The process was performed in a temperature-controlled flow chamber on nanoparticle agglomerates deposited at submonolayer coverage on a transmission electron microscope grid. The partial pressure of the condensing species, tetraethyl orthosilicate, and the temperature of the chamber were adjusted in order to obtain the various saturation conditions for capillary condensation. The modified samples were characterized by transmission electron microscopy (TEM), X-ray photoelectron spectroscopy, Fourier transform infrared spectroscopy, BET surface area method, and scanning transmission electron microscopy with electron energy-loss spectrometry. Experimental results show that bridge-shaped layers were dominantly formed in the neck region between particles and were composed of amorphous silica. The analysis of TEM micrographs verified that the coverage of the layers is strongly dependent on the saturation ratio. Image analysis of TEM micrographs shows that this dependency is qualitatively in agreement with theoretical predictions based on the classical Kelvin equation for the specific geometries in our system. PMID:17243733
Detwiler, R.L.; Mehl, S.; Rajaram, H.; Cheung, W.W.
2002-01-01
Numerical solution of large-scale ground water flow and transport problems is often constrained by the convergence behavior of the iterative solvers used to solve the resulting systems of equations. We demonstrate the ability of an algebraic multigrid algorithm (AMG) to efficiently solve the large, sparse systems of equations that result from computational models of ground water flow and transport in large and complex domains. Unlike geometric multigrid methods, this algorithm is applicable to problems in complex flow geometries, such as those encountered in pore-scale modeling of two-phase flow and transport. We integrated AMG into MODFLOW 2000 to compare two- and three-dimensional flow simulations using AMG to simulations using PCG2, a preconditioned conjugate gradient solver that uses the modified incomplete Cholesky preconditioner and is included with MODFLOW 2000. CPU times required for convergence with AMG were up to 140 times faster than those for PCG2. The cost of this increased speed was up to a nine-fold increase in required random access memory (RAM) for the three-dimensional problems and up to a four-fold increase in required RAM for the two-dimensional problems. We also compared two-dimensional numerical simulations of steady-state transport using AMG and the generalized minimum residual method with an incomplete LU-decomposition preconditioner. For these transport simulations, AMG yielded increased speeds of up to 17 times with only a 20% increase in required RAM. The ability of AMG to solve flow and transport problems in large, complex flow systems and its ready availability make it an ideal solver for use in both field-scale and pore-scale modeling.
Detwiler, Russell L; Mehl, Steffen; Rajaram, Harihar; Cheung, Wendy W
2002-01-01
Numerical solution of large-scale ground water flow and transport problems is often constrained by the convergence behavior of the iterative solvers used to solve the resulting systems of equations. We demonstrate the ability of an algebraic multigrid algorithm (AMG) to efficiently solve the large, sparse systems of equations that result from computational models of ground water flow and transport in large and complex domains. Unlike geometric multigrid methods, this algorithm is applicable to problems in complex flow geometries, such as those encountered in pore-scale modeling of two-phase flow and transport. We integrated AMG into MODFLOW 2000 to compare two- and three-dimensional flow simulations using AMG to simulations using PCG2, a preconditioned conjugate gradient solver that uses the modified incomplete Cholesky preconditioner and is included with MODFLOW 2000. CPU times required for convergence with AMG were up to 140 times faster than those for PCG2. The cost of this increased speed was up to a nine-fold increase in required random access memory (RAM) for the three-dimensional problems and up to a four-fold increase in required RAM for the two-dimensional problems. We also compared two-dimensional numerical simulations of steady-state transport using AMG and the generalized minimum residual method with an incomplete LU-decomposition preconditioner. For these transport simulations, AMG yielded increased speeds of up to 17 times with only a 20% increase in required RAM. The ability of AMG to solve flow and transport problems in large, complex flow systems and its ready availability make it an ideal solver for use in both field-scale and pore-scale modeling. PMID:12019641
NASA Technical Reports Server (NTRS)
Liu, Chao-Qun; Shan, H.; Jiang, L.
1999-01-01
Numerical investigation of flow separation over a NACA 0012 airfoil at large angles of attack has been carried out. The numerical calculation is performed by solving the full Navier-Stokes equations in generalized curvilinear coordinates. The second-order LU-SGS implicit scheme is applied for time integration. This scheme requires no tridiagonal inversion and is capable of being completely vectorized, provided the corresponding Jacobian matrices are properly selected. A fourth-order centered compact scheme is used for spatial derivatives. In order to reduce numerical oscillation, a sixth-order implicit filter is employed. Non-reflecting boundary conditions are imposed at the far-field and outlet boundaries to avoid possible non-physical wave reflection. Complex flow separation and vortex shedding phenomenon have been observed and discussed.
Theranostic potential of gold nanoparticle-protein agglomerates.
Sanpui, Pallab; Paul, Anumita; Chattopadhyay, Arun
2015-11-28
Owing to the ever-increasing applications, glittered with astonishing success of gold nanoparticles (Au NPs) in biomedical research as diagnostic and therapeutic agents, the study of Au NP-protein interaction seems critical for maximizing their theranostic efficiency, and thus demands comprehensive understanding. The mutual interaction of Au NPs and proteins at physiological conditions may result in the aggregation of protein, which can ultimately lead to the formation of Au NP-protein agglomerates. In the present article, we try to appreciate the plausible steps involved in the Au NP-induced aggregation of proteins and also the importance of the proteins' three-dimensional structures in the process. The Au NP-protein agglomerates can potentially be exploited for efficient loading and subsequent release of various therapeutically important molecules, including anticancer drugs, with the unique opportunity of incorporating hydrophilic as well as hydrophobic drugs in the same nanocarrier system. Moreover, the Au NP-protein agglomerates can act as 'self-diagnostic' systems, allowing investigation of the conformational state of the associated protein(s) as well as the protein-protein or protein-Au NP interaction within the agglomerates. Furthermore, the potential of these Au NP-protein agglomerates as a novel platform for multifunctional theranostic application along with exciting future-possibilities is highlighted here. PMID:26508277
Theranostic potential of gold nanoparticle-protein agglomerates
NASA Astrophysics Data System (ADS)
Sanpui, Pallab; Paul, Anumita; Chattopadhyay, Arun
2015-11-01
Owing to the ever-increasing applications, glittered with astonishing success of gold nanoparticles (Au NPs) in biomedical research as diagnostic and therapeutic agents, the study of Au NP-protein interaction seems critical for maximizing their theranostic efficiency, and thus demands comprehensive understanding. The mutual interaction of Au NPs and proteins at physiological conditions may result in the aggregation of protein, which can ultimately lead to the formation of Au NP-protein agglomerates. In the present article, we try to appreciate the plausible steps involved in the Au NP-induced aggregation of proteins and also the importance of the proteins' three-dimensional structures in the process. The Au NP-protein agglomerates can potentially be exploited for efficient loading and subsequent release of various therapeutically important molecules, including anticancer drugs, with the unique opportunity of incorporating hydrophilic as well as hydrophobic drugs in the same nanocarrier system. Moreover, the Au NP-protein agglomerates can act as `self-diagnostic' systems, allowing investigation of the conformational state of the associated protein(s) as well as the protein-protein or protein-Au NP interaction within the agglomerates. Furthermore, the potential of these Au NP-protein agglomerates as a novel platform for multifunctional theranostic application along with exciting future-possibilities is highlighted here.
Acoustic agglomeration of fine particles based on a high intensity acoustical resonator
NASA Astrophysics Data System (ADS)
Zhao, Yun; Zeng, Xinwu; Tian, Zhangfu
2015-10-01
Acoustic agglomeration (AA) is considered to be a promising method for reducing the air pollution caused by fine aerosol particles. Removal efficiency and energy consuming are primary parameters and generally have a conflict with each other for the industry applications. It was proved that removal efficiency is increased with sound intensity and optimal frequency is presented for certain polydisperse aerosol. As a result, a high efficiency and low energy cost removal system was constructed using acoustical resonance. High intensity standing wave is generated by a tube system with abrupt section driven by four loudspeakers. Numerical model of the tube system was built base on the finite element method, and the resonance condition and SPL increase were confirmd. Extensive tests were carried out to investigate the acoustic field in the agglomeration chamber. Removal efficiency of fine particles was tested by the comparison of filter paper mass and particle size distribution at different operating conditions including sound pressure level (SPL), and frequency. The experimental study has demonstrated that agglomeration increases with sound pressure level. Sound pressure level in the agglomeration chamber is between 145 dB and 165 dB from 500 Hz to 2 kHz. The resonance frequency can be predicted with the quarter tube theory. Sound pressure level gain of more than 10 dB is gained at resonance frequency. With the help of high intensity sound waves, fine particles are reduced greatly, and the AA effect is enhanced at high SPL condition. The optimal frequency is 1.1kHz for aerosol generated by coal ash. In the resonace tube, higher resonance frequencies are not the integral multiplies of the first one. As a result, Strong nonlinearity is avoided by the dissonant characteristic and shock wave is not found in the testing results. The mechanism and testing system can be used effectively in industrial processes in the future.
Basic principles and mechanisms of selective oil agglomeration
Wheelock, T.D.; Drzymala, J.; Allen, R.W.; Hu, Y.-C.; Tyson, D.; Xiaoping, Qiu; Lessa, A.
1990-01-01
Numerous measurements of the heat of immersion of coal were conducting using several different particle size fractions of No. 2 Gas Seam coal from Raleigh County, West Virginia. The heat of immersion was determined in water, methanol, heptane, hexadecane and neohexane (2,2-dimethybutane). A comparison of the results with those determined previously for Illinois No. 6 coal is discussed. A number of potential pyrite depressants for use in oil agglomeration of coal were screened by testing the response of sulfidized mineral pyrite to agglomeration with heptane in the presence of the potential depressant. The following were tested; sodium dithionite, sodium thiosulfate, ferrous sulfate, ferric sulfate, titanous chloride, hydrogen peroxide, Oxone (a form of potassium monopersulfate), pyrogallol, quebracho (colloidal dispersant derived from tree bark), milk whey, and several organic thiols. Ferric chloride was applied to mixtures of Upper Freeport coal and sulfidized mineral pyrite before subjecting the mixtures to agglomeration with heptane. 7 refs., 23 figs., 3 tabs.
Ultrasonic de-agglomeration of barium titanate powder.
Marković, S; Mitrić, M; Starcević, G; Uskoković, D
2008-01-01
BaTiO3 (BT) powder, with average particle size of 1.4 microm, was synthesized by solid-state reaction. A high-intensity ultrasound irradiation (ultrasonication) was used to de-agglomerate micro-sized powder to nano-sized one. The crystal structure, crystallite size, morphology, particle size, particle size distribution, and specific surface area of the BT powder de-agglomerated for different ultrasonication times (0, 10, 60, and 180 min) were determined. It was found that the particles size of the BT powder was influenced by ultrasonic treatment, while its tetragonal structure was maintained. Therefore, ultrasonic irradiation can be proposed as an environmental-friendly, economical, and effective tool for the de-agglomeration of barium titanate powders. PMID:17845864
Effect of calcium ions on agglomeration of bayer aluminium trihydroxide
NASA Astrophysics Data System (ADS)
Brown, N.
1988-10-01
Small amounts of calcium ions in caustic aluminate solution can lead to enhanced agglomeration of aluminium trihydroxide [Al(OH) 3] particles in the crystallization step of the Bayer process. The present study shows that the magnitude of the effect is strongly dependent on the nature and polycrystallinity of the Al(OH) 3 seed crystals. The more irregular and polycrystalline the seed crystals, the smaller is the optimum amount of added calcium for maximum coarsening ( ≈ 50 mg/l, expressed as CaO). While the same degree of agglomeration can be achieved using well-rounded, smooth-surfaced seed crystals of the same overall size, more calcium is required (75-100 mg/l, expressed as CaO) and the agglomerated particles formed are weaker and less resistant to size reduction on handling.
Helgeson, Zach L; Jenkins, Jed S; Abraham, John P; Sparrow, Ephraim M
2011-01-01
Background: The transport of particles in surrogate and actual arterial geometries has been investigated synergistically by experimentation and numerical simulation. The motivating application for this work is orbital atherectomy which spawns a particle cloud in the process of debulking plaque from arterial walls. Methods: Paired simulations and experiments were performed to prove the capability of the simulation model to predict both fluid and particle motions in branched arterial geometries. The verified model was then employed to predict the pattern of fluid flow in an actual multi-branched arterial geometry, including the flowrates passing through each of the individual branches. These predictions are in very good agreement with experimental data. Focus was then shifted to the issues of particle agglomeration within the flowing fluid and particle accumulation on the vessel walls. Once again, a synergistic approach was used. Flow visualization was employed to track the particle motions and to identify possible particle agglomeration within the fluid. Results and Conclusions: Accumulation of particles on walls was identified by measuring size distributions of effluent and residue within the artery. Scanning Electron Microscopy (SEM) evaluation showed evidence of a size-based sorting as the particles passed through vessels. It was found that plaque-facsimile particles resisted particle-particle agglomeration. They also did not accumulate to the wall of the facsimile artery. In addition, simulations showed that if particle-wall accumulation were to occur, it would be limited to very small regions in the artery branches. PMID:21643425
A pocket model for aluminum agglomeration in composite propellants
NASA Technical Reports Server (NTRS)
Cohen, N. S.
1981-01-01
This paper presents a model for the purpose of estimating the fraction of aluminum powder that will form agglomerates at the surface of deflagrating composite propellants. The basic idea is that the fraction agglomerated depends upon the amount of aluminum that melts within effective binder pocket volumes framed by oxidizer particles. The effective pocket depends upon the ability of ammonium perchlorate modals to encapsulate the aluminum and provide a local temperature sufficient to ignite the aluminum. Model results are discussed in the light of data showing effects of propellant formulation variables and pressure.
Agglomeration behavior of solid nickel on polycrystalline barium titanate
Weil, K Scott; Mast, Eric S; Sprenkle, Vince
2007-11-01
This letter describes the phenomenon that takes place between nickel/barium titanate couples when heated under conditions employed in multilayer ceramic capacitor manufacturing practice: a 4hr, 1300°C isothermal anneal in 1% H_{2} – 99% N_{2}. Dense, sputtered nickel films were observed to dewet the titanate and agglomerate into discrete or interconnected islands via a solid-state process. Up to a critical film thickness value of ~1.4 μm, the degree of agglomeration was found to display an exponential dependence on the thickness of the original nickel film.
Frequency comparative study of coal-fired fly ash acoustic agglomeration.
Liu, Jianzhong; Wang, Jie; Zhang, Guangxue; Zhou, Junhu; Cen, Kefa
2011-01-01
Particulate pollution is main kind of atmospheric pollution. The fine particles are seriously harmful to human health and environment. Acoustic agglomeration is considered as a promising pretreatment technology for fine particle agglomeration. The mechanisms of acoustic agglomeration are very complex and the agglomeration efficiency is affected by many factors. The most important and controversial factor is frequency. Comparative studies between high-frequency and low-frequency sound source to agglomerate coal-fired fly ash were carried out to investigate the influence of frequency on agglomeration efficiency. Acoustic agglomeration theoretical analysis, experimental particle size distributions (PSDs) and orthogonal design were examined. The results showed that the 20 kHz high-frequency sound source was not suitable to agglomerate coal-fired fly ash. Only within the size ranging from 0.2 to 0.25 microm the particles agglomerated to adhere together, and the agglomerated particles were smaller than 2.5 microm. The application of low-frequency (1000-1800 Hz) sound source was proved as an advisable pretreatment with the highest agglomeration efficiency of 75.3%, and all the number concentrations within the measuring range decreased. Orthogonal design L16 (4)3 was introduced to determine the optimum frequency and optimize acoustic agglomeration condition. According to the results of orthogonal analysis, frequency was the dominant factor of coal-fired fly ash acoustic agglomeration and the optimum frequency was 1400 Hz. PMID:22432309
Engineering development of selective agglomeration. Site closeout report
Not Available
1993-04-01
The Selective Agglomeration POC facility consisted of a coal crushing and grinding circuit, followed by an agglomeration circuit and product dewatering. (A plot plan of the facility is shown in Figure 1-2.) The coal crushing and grinding system consisted of a hammermill coal crusher, weigh-belt feeder, two ball mills (primary and secondary), and necessary hoppers, pumps, and conveyors. The mills were capable of providing coal over a range of grinds from a d{sub 50} of 125 to 25 microns. Slurry discharged from the ball mills was pumped to the agglomeration circuit. The agglomeration circuit began with a high-shear mixer, where diesel was added to the slurry to begin the formation of microagglomerates. The high-shear mixer was followed by two stages of conventional flotation cells for microagglomerate recovery. The second-stage-flotation-cell product was pumped to either a rotary-drum vacuum filter or a high-G centrifuge for dewatering. The dewatered product was then convoyed to the product pad from which dump trucks were used to transfer it to the utility plant located next to the facility. Plant tailings were pumped to the water clarifier for thickening and then dewatered in plate-and-frame filter presses. These dewatered tailings were also removed to the utility via dump truck. Clarified water (thickener overflow) was recycled to the process via a head tank.
Basic principles and mechanisms of selective oil agglomeration
Wheelock, T.D.; Drzymala, J.; Allen, R.W.; Hu, Y.C.; Tyson, D.; Ziaoping, Qiu, Lessa, A.
1990-04-01
The overall objective is to determine the basic principles and mechanisms which underlie a number of selective oil agglomeration processes that have been proposed for beneficiating fine-size coal. An understanding of the basic principles and mechanisms will greatly facilitate technical development and application of such processes to various types of coal. 5 refs., 16 figs., 2 tabs.