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Showing 1 to 20 of 45 for “"Conjugate Gradient method"”.
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A Modified Preconditioned Conjugate Gradient Method for Approximating the Scattering Amplitude
<p>In this thesis, we look at an iterative method for approximating the scattering amplitude that involves solving two linear systems: a forward system A<strong>x</strong>=<strong>b</strong> and an adjoint system A<sup>T</sup><strong>y</strong>=<strong>g</strong>. Once these two systems are solved, …
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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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The direct determination of nonlinear displacements of arbitrarily supported shallow shells using mathematical programming techniques
… for minimizing the shell potential several methods which have appeared in the literature are evaluated. These 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 …
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Adaptive finite element simulation of incompressible viscous flow
A finite element method is employed for solving two- and three-dimensional incompressible flows. The formulation is based on a segregated solution method. In this segregated formulation, the velocities and pressures are uncoupled and the equations for each are solved one after the other. This …
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Polynomial Preconditioning for Conjugate Gradient Methods
… If A is large and sparse, an iterative method is required. 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 …
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Dynamic relaxation analysis of pretensioned networks supported by compression arches
… with the application of direct integration methods, particularly Dynamic Relaxation, to the nonlinear formfinding and analysis of pretensioned networks supported by compression arches. The development and application of such methods is reviewed in Chapter 2. The automated control of Dynamic …
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A Parallel Aggregation Algorithm for Inter-Grid Transfer Operators in Algebraic Multigrid
… approaches to solve such problems. Multigrid methods can be used to solve large-scale problems, or 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 …
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Investigating a Second-Order Optimization Strategy for Neural Networks
… dissertation investigates the application of the conjugate gradient method CG for the optimization of artificial neural networks (NNs) and compares this method with common first-order optimization methods, especially the stochastic gradient descent (SGD). The presented research results show that …
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Issues related to finite element techniques for two dimensional transmission structures
… will be presented and used In conjunction with a conjugate gradient method to solve linear systems of equations. Application to electromagnetic problems will be demonstrated in the static, quasi-static, and full-field regimes. Laplace's equation is solved for various transmission line geometries …
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Numerical Analysis of Jump-Diffusion Models for Option Pricing
… dense linear system is solved by an iterative method, either a splitting technique or a circulant preconditioned conjugate gradient method. Exploiting the Fast Fourier Transform (FFT) yields the solution in only $O(n\log n)$ operations and just some vectors need to be stored. Second order …
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Algebraic, geometric and numerical methods for Tensor Network Varieties
… we propose a variation of the nonlinear conjugate gradient method used to approximate the ground states of a given Hamiltonian on the variety of matrix product states.
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Parallel Gauss-Newton method for CP decomposition
… squares problem to apply iterative Newton-like methods. Direct solution of linear systems involving an approximated Hessian is an expensive approach, however, recent advancements have shown that use of an implicit representation of the linear system makes these methods competitive with …
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The simulation of surface ship micro-bubble wakes
A method in which the transport and evolution of the bubble population in a surface ship wake is numerically simulated is presented. The simulation is accomplished by constructing an advective-diffusive transport model for the scalar bubble field and solving this model for late times after ship …
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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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Algorithmic and implementation aspects of on-line calibration of Dynamic Traffic Assignment
… state-space formulation. Pattern Search (PS), Conjugate Gradient Method (CG) and Gradient Descent (GD) are presented and validated under the direct optimization formulation. The feasibility of the approach is demonstrated by showing superior accuracy performance over alternative DTA model with …
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Optimization Based Domain Decomposition Methods for Linear and Nonlinear Problems
Optimization based domain decomposition methods for the solution of partial differential equations are considered. The crux of the method is a constrained minimization problem for which the objective functional measures the jump in the dependent variables across the common boundaries between …
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Variational data assimilation for two interface problems
… and analyze the variational data assimilation method with finite element discretization for two interface problems, including the Parabolic Interface equation and the Stokes-Darcy equation with the Beavers-Joseph interface condition. By using Tikhonov regularization and formulating the VDA into …
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Using interior point algorithms for the solution of linear programs with special structural features
… was mainly due to the efficiency of the simplex method. After the appearance of Karmarkar's paper, the focus of most research was shifted to the field of interior point methods. The present work is concerned with investigating and efficiently implementing the latest techniques in this field …
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Methods of fast Fourier transform in diffraction problems of elastic and acoustic waves with applications to crack mechanics
… with a development of modern fast computational methods applied to problems in wave dynamics, acoustics, and boundary-value problems of mechanics with mixed boundary conditions. This includes: 1) Development of fast methods for integral equations with convolution kernels arising in these fields …
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