Fully coupled Newton's method is combined with conjugategradient-like iterative algorithms to form inexact Newton-Krylov algorithms for solving the steady, incompressible, Navier-Stokes and energy equations in pr...
详细信息
Fully coupled Newton's method is combined with conjugategradient-like iterative algorithms to form inexact Newton-Krylov algorithms for solving the steady, incompressible, Navier-Stokes and energy equations in primitive variables. Finite volume differencing is employed using the power law convection-diffusion scheme on a uniform but staggered mesh. The well-known model problem of natural convection in an enclosed cavity is solved. Three conjugategradient-like algorithms are selected from a class of algorithms based upon the Lanczos biorthogonalization procedure;namely, the conjugategradients squared algorithm, the transpose-free quasi-minimal-residual algorithm, and a more smoothly convergent version of the biconjugategradients algorithm. A fourth algorithm is based upon the Arnoldi process, namely the popular generalized minimal residual algorithm (GMRES). The performance of a standard inexact Newton's method implementation is compared with a matrix-free implementation. Results indicate that the performance of the matrix-free implementation is strongly dependent upon grid size (number of unknowns) and the selection of the conjugategradient-like method. GMRES appeared to be superior to the Lanczos based algorithms within the context of a matrix-free implementation.
Today the adjustment of structural models is an essential step in the modeling of complex structures. In this paper, we are interested in the improvement of finite element models. Our approach is a parametric updating...
详细信息
Today the adjustment of structural models is an essential step in the modeling of complex structures. In this paper, we are interested in the improvement of finite element models. Our approach is a parametric updating using modal test results, which supply eigenvalues and associated eigenvectors. It is based on the computation of the error measure on the constitutive relation and allows us to correct both the stiffness and the mass matrices. In particular, this paper shows how this tuning strategy can improve a given finite element model when the measures are noisy. Several simulation examples illustrate the behavior of this method.
The conjugate gradient algorithm for solving Hermitian positive definite linear systems is usually combined with preconditioning in order to speed up convergence. In recent years, there has been a revival of polynomia...
详细信息
The conjugate gradient algorithm for solving Hermitian positive definite linear systems is usually combined with preconditioning in order to speed up convergence. In recent years, there has been a revival of polynomial preconditioning, motivated by the attractive features of the method on modem architectures. Standard techniques for choosing the preconditioning polynomial are based only on bounds for the extreme eigenvalues. Here a different approach is proposed that aims at adapting the preconditioner to the eigenvalue distribution of the coefficient matrix. The technique is based on the observation that good estimates for the eigenvalue distribution can be derived after only a few steps of the Lanczos process. This information is then used to construct a weight function for a suitable Chebyshev approximation problem. The solution of this problem yields the polynomial preconditioner. In particular, polynomial preconditioners associated with Bernstein-Szego weights are studied. Results of numerical experiments are reported.
Explicit and implicit time integration algorithms for the two-dimensional Euler equations on unstructured grids are presented. Both cell-centered and cell-vertex finite volume upwind schemes utilizing Roe's approx...
详细信息
Explicit and implicit time integration algorithms for the two-dimensional Euler equations on unstructured grids are presented. Both cell-centered and cell-vertex finite volume upwind schemes utilizing Roe's approximate Riemann solver are developed. For the cell-vertex scheme, a four-stage Runge-Kutta time integration, a four-stage Runge-Kutta time integration with implicit residual averaging, a point Jacobi method, a symmetric point Gauss-Seidel method, and two methods utilizing preconditioned sparse matrix solvers are presented. For the cell-centered scheme, a Runge-Kutta scheme, an implicit tridiagonal relaxation scheme modeled after line Gauss-Seidel, a fully implicit lower-upper (LU) decomposition, and a hybrid scheme utilizing both Runge-Kutta and LU methods are presented. A reverse Cuthill-McKee renumbering scheme is employed for the direct solver to decrease CPU time by reducing the fill of the Jacobian matrix. A comparison of the various time integration schemes is made for both first-order and higher order accurate solutions using several mesh sizes. higher order accuracy is achieved by using multidimensional monotone linear reconstruction procedures. The results obtained for a transonic flow over a circular arc suggest that the preconditioned sparse matrix solvers perform better than the other methods as the number of elements in the mesh increases.
A minimax problem is introduced for the terminal control of a generic dynamical system without disturbances. The maximum magnitude of the weighted output of the system is minimized over a finite interval by the contro...
详细信息
A minimax problem is introduced for the terminal control of a generic dynamical system without disturbances. The maximum magnitude of the weighted output of the system is minimized over a finite interval by the control input of a prescribed class. Such important characteristics of the controlled system appear explicitly in the proposed problem as the maximum magnitude and settling property of the output. Two numerical examples are shown to illustrate the problem. A slewing experiment is also presented to demonstrate the application of the minimax optimal control.
Although excellent progress has been made in deriving algorithms that are efficient for certain combinations of system topologies and concurrent multiprocessing hardware, several issues must be resolved to incorporate...
详细信息
Although excellent progress has been made in deriving algorithms that are efficient for certain combinations of system topologies and concurrent multiprocessing hardware, several issues must be resolved to incorporate transient simulation in the control design process for large space structures. Specifically, strategies must be developed that are applicable to systems with numerous degreees of freedom. algorithms are required that induce parallelism on a fine scale, suitable for the emerging class of highly parallel processors. This paper addresses these problems by employing the range space formulation of multibody dynamics and solving for multipliers using the preconditioned conjugategradient method. By employing regular ordering of the system connectivity graph, an extremely efficient preconditioner can be derived from the range space metric. The method can achieve performance rates that depend linearly on the number of substructures. Furthermore, the approach is promising as a potential parallel processing algorithm in that it exhibits fine parallel granularity, is nonassembling, and is easily load balanced among processors without relying an system topology to induce parallelism.
Solution of large sparse linear systems of equations in the form A x = b constitutes a significant amount of the computations in the simulation of physical phenomena [1]. For example, the finite element discretization...
详细信息
Solution of large sparse linear systems of equations in the form A x = b constitutes a significant amount of the computations in the simulation of physical phenomena [1]. For example, the finite element discretization of a regular domain, with proper ordering of the variables x , renders a banded N × N coefficient matrix A . The conjugategradient (CG) [2,3] algorithm is an iterative method for solving sparse matrix equations and is widely used because of its convergence properties. In this paper an implementation of the conjugate gradient algorithm, that exploits both vectorization and parallelization on a 2-dimensional hypercube with vector processors at each node (iPSC-VX/d2), is described. The implementation described here achieves efficient parallelization by using a version of the CG algorithm suitable for coarse grain parallelism [4,5] to reduce the communication steps required and by overlapping the computations on the vector processor with internode communication. With parallelization and vectorization, a speedup of 58 over a μVax II is obtained for large problems, on a two dimensional vector hypercube (iPSC-VX/d2).
There has been a growing interest in the development of new and efficient algorithms for multibody dynamics in recent years. Serial rigid multibody systems form the basic subcomponents of general multibody systems, an...
详细信息
There has been a growing interest in the development of new and efficient algorithms for multibody dynamics in recent years. Serial rigid multibody systems form the basic subcomponents of general multibody systems, and a variety of algorithms to solve the serial chain forward dynamics problem have been proposed. In this paper, the economy of representation and analysis tools provided by the spatial operator algebra are used to clarify the inherent structure of these algorithms, to identify those that are similar, and to study the relationships among the ones that are distinct. For the purposes of this study, the algorithms are categorized into three classes: algorithms that require the explicit computation of the mass matrix, algorithms that are completely recursive in nature, and algorithms of intermediate complexity. In addition, alternative factorizations for the mass matrix and closed form expressions for its inverse are derived. These results provide a unifying perspective, within which these diverse dynamics algorithms arise naturally as a consequence of a progressive exploitation of the structure of the mass matrix.
The matrix representation of a linear operator is used in the conjugate gradient algorithm to solve electromagnetic boundary value problems. The use of this approach obviates the difficult task of finding the adjoint ...
详细信息
The matrix representation of a linear operator is used in the conjugate gradient algorithm to solve electromagnetic boundary value problems. The use of this approach obviates the difficult task of finding the adjoint of the operator
This paper describes the parallel solution of a class of large sparse systems of linear equations produced by an oil reservoir simulator. Specifically, we focus on the implementation of a conjugate gradient algorithm ...
详细信息
This paper describes the parallel solution of a class of large sparse systems of linear equations produced by an oil reservoir simulator. Specifically, we focus on the implementation of a conjugate gradient algorithm for a transputer-based machine. After discussing communications harnesses, we present strategies for decomposing the algorithm on a transputer array, and report the results of measurements of speed-ups for some practical reservoir problems. We then address the problem of preconditioning by first implementing distributed forms of three standard iterative algorithms, namely Jacobi, Gauss-Seidel and Successive Over-relaxation, and determining their convergence and speed-up properties. On the basis of these measurements, we suggest that a Jacobi preconditioned conjugategradient (JPCG) algorithm appears likely to be the most cost-effective for the class of problems under consideration. Finally we implement the JPCG algorithm and present measurements in support of our claim.
暂无评论