Use Of Conjugate Gradients Research Articles

Short Term Prediction of Photovoltaic Power Based on FCM and CG-DBN Combination

Affected by many factors, the photovoltaic output power is characterized by nonlinearity, volatility and instability. Therefore, short-term forecasting models are required to have multiple inputs, levels, and categories. In order to solve the above problems and improve the accuracy of predictions, this paper proposes a combined model prediction method based on similar-day clustering and the use of Conjugate Gradient (CG) to improve Deep Belief Network (DBN). The initial method uses fuzzy C-Means Clustering Algorithm (FCM) to perform similar-day clustering on the original data according to the degree of membership. The CG-DBN prediction model is then designed according to the category, with the model ultimately being used to perform the short-term prediction of the PV output power. The proposed scheme uses data from Zhejiang Longyou power station for experimental analysis and verification, and the results were compared with the back propagation neural networks model, Support Vector Machine (SVM) model, and traditional deep belief network. The model’s predicted results are compared. Finally, it is concluded that, in the short-term PV power load forecasting, the prediction performance of the FCM and CG-DBN combination forecast model is better than the above three models and has strong feasibility in short-term PV power forecasting.

Parallelisation study of a three-dimensional environmental flow model

There are many simulation codes in the geosciences that are serial and cannot take advantage of the parallel computational resources commonly available today. One model important for our work in coastal ocean current modelling is EFDC, a Fortran 77 code configured for optimal deployment on vector computers. In order to take advantage of our cache-based, blade computing system we restructured EFDC from serial to parallel, thereby allowing us to run existing models more quickly, and to simulate larger and more detailed models that were previously impractical. Since the source code for EFDC is extensive and involves detailed computation, it is important to do such a port in a manner that limits changes to the files, while achieving the desired speedup. We describe a parallelisation strategy involving surgical changes to the source files to minimise error-prone alteration of the underlying computations, while allowing load-balanced domain decomposition for efficient execution on a commodity cluster. The use of conjugate gradient posed particular challenges due to implicit non-local communication posing a hindrance to standard domain partitioning schemes; a number of techniques are discussed to address this in a feasible, computationally efficient manner. The parallel implementation demonstrates good scalability in combination with a novel domain partitioning scheme that specifically handles mixed water/land regions commonly found in coastal simulations. The approach presented here represents a practical methodology to rejuvenate legacy code on a commodity blade cluster with reasonable effort; our solution has direct application to other similar codes in the geosciences.

Generation of Wannier functions for photonic crystals

We present an approach for the efficient generation of Wannier functions for Photonic Crystal computations that is based on a combination of group-theoretical analysis and efficient minimization strategies. In particular, we describe the symmetry properties that allow for exponential localization of Wannier functions and how they are related to the underlying Bloch mode symmetries of the photonic band structure and we show that no exponentially localized Wannier functions can be created from the physical modes of a three-dimensional crystal. Moreover, we comment on the use of conjugate gradient and randomized minimization algorithms that---together with the group theoretical considerations---facilitate the efficient numerical determination of maximally localized Wannier functions for many bands. This is a requirement for the accurate computation of Photonic Crystal functional elements and devices.

Two‐dimensional inversion of magnetotelluric data with consecutive use of conjugate gradient and least‐squares solution with singular value decomposition algorithms

ABSTRACTI investigated the two‐dimensional magnetotelluric data inversion algorithms in studying two significant aspects within a linearized inversion approach. The first one is the method of minimization and second one is the type of stabilizing functional used in parametric functionals. The results of two well‐known inversion algorithms, namely conjugate gradient and the least‐squares solution with singular value decomposition, were compared in terms of accuracy and CPU time. In addition, magnetotelluric data inversion with various stabilizers, such as L2‐norm, smoothing, minimum support, minimum gradient support and first‐order minimum entropy, were examined.A new inversion algorithm named least‐squares solution with singular value decomposition and conjugate gradient is suggested in seeing the outcomes of the comparisons carried out on least‐squares solutions with singular value decomposition and conjugate gradient algorithms subject to a variety of stabilizers. Inversion results of synthetic data showed that the newly suggested algorithm yields better results than those of the individual implementations of conjugate gradient and least‐squares solution with singular value decomposition algorithms. The suggested algorithm and the above‐mentioned algorithms inversion results for the field data collected along a line crossing the North Anatolian Fault zone were also compared each other and results are discussed.

Detection of small inclusions by elastography

The problem of parameter identification for elastostatics equilibrium equations in two-dimensional inhomogeneous domains is considered. Elastic properties of a linear isotropic material depend on two parameters: Young's modulus E and Poisson coefficient ν, and our objective is to determine the values and the spatial distribution of E in a plane domain Ω, where ν is assumed to be constant. It is assumed that the input data are directional displacements in Ω under a small quasistatic compression; this is consistent with an existing imaging modality called elastography. We prove that this problem involves a compact operator. A method is proposed here to identify the spatial distribution of E up to a multiplicative factor. It is based on an implementation of the Gauss–Newton method that is obtained without the calculation of the Jacobian matrix. It is performed by the use of conjugate gradient, through a combination of reverse (adjoint) and forward (direct) differentiation that makes sense in the case of compact operators. Our method is validated both with numerical and experimental results.

Nonlinear Force-Free Magnetic Field Extrapolations: Comparison of the Grad Rubin and Wheatland Sturrock Roumeliotis Algorithm

We compare the performance of two alternative algorithms which aim to construct a force-free magnetic field given suitable boundary conditions. For this comparison, we have implemented both algorithms on the same finite element grid which uses Whitney forms to describe the fields within the grid cells. The additional use of conjugate gradient and multigrid iterations result in quite effective codes. The Grad Rubin and Wheatland Sturrock Roumeliotis algorithms both perform well for the reconstruction of a known analytic force-free field. For more arbitrary boundary conditions the Wheatland Sturrock Roumeliotis approach has some difficulties because it requires overdetermined boundary information which may include inconsistencies. The Grad Rubin code on the other hand loses convergence for strong current densities. For the example we have investigated, however, the maximum possible current density seems to be not far from the limit beyond which a force-free field cannot exist anymore for a given normal magnetic field intensity on the boundary.

Fully compact higher-order computation of steady-state natural convection in a square cavity.

The flow in a thermally driven square cavity with adiabatic top and bottom walls and differentially heated vertical walls for a wide range of Rayleigh numbers (10(3)< or =Ra< or =10(7)) has been computed with a fourth-order accurate higher-order compact scheme, which was used earlier only for the stream-function vorticity (psi-omega) form of the two-dimensional steady-state Navier-Stokes equations. The boundary conditions used are also compact and of identical accuracy. In particular, a compact fourth-order accurate Neumann boundary condition has been developed for temperature at the adiabatic walls. The treatment of the derivative source term is also compact and has been done in such a way as to give fourth-order accuracy and easy assimilation with the solution procedure. As the discretization for the psi-omega formulation, boundary conditions, and source term treatment are all fourth-order accurate, highly accurate solutions are obtained on relatively coarser grids. Unlike other compact solution procedure in literature for this physical configuration, the present method is fully compact and fully higher-order accurate. Also, use of conjugate gradient and hybrid biconjugate gradient stabilized algorithms to solve the symmetric and nonsymmetric algebraic systems at every outer iteration, ensures good convergence behavior of the method even at higher Rayleigh numbers.

On the use of conjugate gradient-type methods for boundary integral equations

This paper deals with a number of iterative methods for solving matrix equations that result from boundary integral equations. The matrices are non-sparse, and in general neither positive definite nor symmetric. Traditional methods like Gauss-Seidel do not give satisfactory results, therefore the use of conjugate gradient- and Krylov-type methods is investigated based on work of Kleinman and Van den Berg, who presented a general framework for these methods. Eleven of these algorithms are given and their performance (without preconditioning) is compared in a test case involving four different integral operators arising in potential theory. For all four matrix equations the Generalized Minimal Residual method (GMRES) outperforms all other iterative methods in both computation time per iteration and total computation time. For the Fredholm equations of the first kind this method also is the fastest with respect to the number of iterations. The Bi-conjugate gradient method (Bi-CG) and the Quasi-minimal residual method (QMR) are the best alternatives. For the Fredholm equations of the second kind more methods can be used efficiently besides GMRES. The Conjugate Gradient Squared method (CGS), the Bi-conjugate gradient method (Bi-CG), its stabilized version (Bi-CGSTAB) and the Quasi Minimal Residual method (QMR) are efficient alternatives.

Iterative Solution Methods for Plate Bending Problems: Multigrid and Preconditionedcgalgorithm

The numerical solution of the linear equations arising from a discretization of the plate bending problem based on the Zienkiewicz triangle is studied. The finite element scheme proceeds from the Mindlin–Reissner formulation with modified shear energy. However, the Kirchhoff condition is imposed on discrete points. A multigrid algorithm is analyzed and numerical examples are provided. Furthermore, a suitable preconditioning is established for the use of conjugate gradients.

The Use of Conjugate Gradients for Systems of Linear Equations Possessing “Property A”

It is shown that for systems possessing Young’s “Property A” [7] the work in applying the conjugate gradients algorithm [3] may be approximately halved and a vector of storage may be saved by using a technique analogous to that of Golub and Varga [2] for Chebyshev semi-iteration. We illustrate by numerical results on two test problems, and comment on the advantages of the algorithm over successive overrelaxation and Chebyshev semi-iteration.