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Showing 1 to 20 of 118 for “"Conjugate-gradient"”.
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Polynomial Preconditioning for Conjugate Gradient Methods
… When A is hermitian positive definite (hpd), the conjugate gradient method of Hestenes and Stiefel is popular. When A is hermitian indefinite (hid), the conjugate residual method may be used. If A is ill-conditioned, these methods may converge slowly, in which case a preconditioner is needed. In …
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Preconditioned conjugate gradient methods for the Navier-Stokes equations
A generalized Conjugate Gradient like method is used to solve the linear systems of equations formed at each time-integration step of the unsteady, two-dimensional, compressible Navier-Stokes equations of fluid flow. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux …
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A hardware acceleration technique for gradient descent and conjugate gradient
Gradient descent, conjugate gradient, and other iterative algorithms are a powerful class of algorithms; however, they can take a long time for conver- gence. Baseline accelerator designs feature insu cient coverage of operations and do not work well on the problems we target. In this thesis we …
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A Modified Preconditioned Conjugate Gradient Method for Approximating the Scattering Amplitude
… is easily obtained.</p> <p>We derive a conjugate gradient-like iteration for a nonsymmetric saddle point matrix that is constructed to have a real positive spectrum. We investigate the use of Schur Complement preconditioners with block-diagonal factorization to speed up the convergence …
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Conjugate gradient density matrix search: A linear scaling alternative to diagonalization
… step for very large systems. In this work, a conjugate gradient density matrix search (CG-DMS) method has been successfully extended and computationally implemented for use with first principles calculations. A Cholesky decomposition of the overlap matrix and its inverse, which can be formed …
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Preconditioned sequential and parallel conjugate gradient algorithms for homotopy curve tracking
… sparse Jacobian matrices use a preconditioned conjugate gradient algorithm for the computation of the kernel of the homotopy Jacobian matrix, a required linear algebra step for homotopy curve tracking. Variants of the conjugate gradient algorithm along with different preconditioners are …
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Construction of Centroidal Voronoi Tessellations Using A Conjugate Gradient Method Based On Trust Regions
… present a new algorithm for computing CVTs--the conjugate gradient method based on trust regions (CGTR). This algorithm significantly speeds up the computation of CVTs. Numerical experiments are also conducted to substantiate theoretical analysis.</p>
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A "HUM" conjugate gradient algorithm for constrained nonlinear optimal control : terminal and regular problems
… of convergence when solved by, for instance, a conjugate gradient procedure (denoted here TRCG). Total computational time scales roughly as twice the order of magnitude of the computational cost of a single initial-value problem.
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On the Implementation and Performance of Iterative Methods for Computational Electromagnetics (Scattering, Moment-Method, Conjugate-Gradient)
The numerical solution of electromagnetic scattering problems involves approximating an exact equation by a finite-dimensional matrix equation. The use of an iterative algorithm to solve the matrix equation sometimes results in a considerable savings in computer memory requirements. For a fixed …
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A study of iterative methods on forward and inverse scattering problems
… and acoustic wave scattering. Both the conjugate gradient and bi-conjugate gradient methods combined with the fast Fourier transform (CGFFT and BiCGFFT) are employed as efficient solvers in forward and inverse scattering problems for penetrable bodies.
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Multi-scale problems: an improved non-intrusive algorithm that enhances FEA platforms with the generalized finite element method; An improved preconditioned conjugate gradient solver for hierarchical generalized finite element systems of equations
… An iterative solver called the preconditioned conjugate gradient method is investigated within this context, and a preconditioner is proposed for the method. This thesis shows that its proposed iterative solver is faster than previous iterative solvers. The proposed iterative solver is also …
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GPU-accelerated Linear Solvers for High-order Finite Element Methods in Poisson Problems
… convergence and efficiency of the preconditioned conjugate gradient (PCG) algorithm for high-order finite element methods on Graphics Processing Units (GPUs). The conjugate gradient algorithm iteratively refines an initial approximate solution until a specified stopping criterion is met, with its …
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A Parallel Aggregation Algorithm for Inter-Grid Transfer Operators in Algebraic Multigrid
… even better they can be used to precondition the conjugate gradient method, yielding better results in general. Capabilities of multigrid algorithms rely on the effectiveness of the inter-grid transfer operators. In this thesis we focus on the aggregation approach, discussing how different …
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The direct determination of nonlinear displacements of arbitrarily supported shallow shells using mathematical programming techniques
… include the method of steepest descent, the conjugate gradient method, the variable metric method and the generalized Newton-Raphson procedure. A combination of the conjugate gradient method and the generalized Newton-Raphson procedure is found most suitable. Results of the present …
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Comparison of energy minimization with direct stiffness for linear structural analysis
… analyzed. From the survey of variable metric and conjugate gradient algorithms included in this study, the Davidon-Fletcher-Powell variable metric algorithm and the FletcherReeves conjugate gradient algorithm were chosen to minimize the total potential energy. A description of both algorithms is …
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An updating rule for the penalty constant used in the penalty function method for mathematical programming problems
… constraints. Each example is solved with the conjugate gradient algorithm and the modified quasilinearization algorithm for several starting values of the penalty constant. From the numerical experiments, the following conclusions, concerning the number of iterations for convergence, arise: …
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