检索结果-内蒙古大学图书馆

Jacobian-Free Poincare-Krylov Method to Determine the Stability of Periodic Orbits of Electric Power Systems

IEEE TRANSACTIONS ON POWER SYSTEMS 2022年第1期37卷 429-442页

作者： Garcia, Norberto Luisa Romero, Maria Acha, Enrique Univ Michoacana Fac Elect Engn Morelia 58000 Michoacan Mexico Tampere Univ Fac Informat Technol & Commun Sci Tampere 33100 Finland

A first application of a time domain Poincare-Krylov approach for the study of the all-important stability of periodic solutions of nonlinear power networks is reported in this work. Whilst a Newton method solves the nonlinear algebraic equations resulting from the Poincare map method, an iterative Krylov-subspace method based on a gmres algorithm is applied for solving the Newton correction equations. More importantly, a QR factorization of the Hessenberg matrix involved in the gmres least square problem is implemented using Givens rotations in order to avoid the linear growth of the computational complexity in large-scale power networks. Further, the stability of periodic solutions is determined by computing the Floquet multipliers using Ritz values and the Hessenberg matrix. Numerical tests carried out on a modified three-phase version of the IEEE 118-node system with a hydro-turbine synchronous generator and a grid-tied power converter demonstrate that speedup factors up to 8 are attainable with the Krylov-Subspace approach with respect to the standard Poincare map method. An outstanding outcome of the comparative study is that the incorporation of QR factorization to the Hessenberg least square problem outperformed the classic periodic steady-state solvers, providing further computational savings up to 50%.

关键词： Power system stability Stability analysis Jacobian matrices Power system dynamics Numerical stability Steady-state Power system harmonics Stability periodic steady-state Poincare map method Newton method Krylov subspace gmres algorithm

来源：评论

学校读者我要写书评

暂无评论

Solution of skin-effect problems by means of the hybrid SDBCI method

引用

COMPEL-THE INTERNATIONAL JOURNAL FOR COMPUTATION AND MATHEMATICS IN ELECTRICAL AND ELECTRONIC ENGINEERING 2014年第6期33卷 1935-1949页

作者： Aiello, Giovanni Alfonzetti, Salvatore Salerno, Nunzio Univ Catania Dipartimento Ingn Elettr Elettron & Informat Catania Italy

Purpose - The purpose of this paper is to present a modified version of the hybrid Finite Element Method-Dirichlet Boundary Condition Iteration method for the solution of open-boundary skin effect problems. Design/methodology/approach - The modification consists of overlapping the truncation and the integration boundaries of the standard method, so that the integral equation becomes singular as in the well-known Finite Element Method-Boundary Element Method (FEM-BEM) method. The new method is called FEM-SDBCI. Assuming an unknown Dirichlet condition on the truncation boundary, the global algebraic system is constituted by the sparse FEM equations and by the dense integral equations, in which singularities arise. Analytical formulas are provided to compute these singular integrals. The global system is solved by means of a Generalized Minimal Residual iterative procedure. Findings - The proposed method leads to slightly less accurate numerical results than FEM-BEM, but the latter requires much more computing time. Practical implications - Then FEM-SDBCI appears more appropriate than FEM-BEM for applications which require a shorter computing time, for example in the stochastic optimization of electromagnetic devices. Originality/value - Note that FEM-SDBCI assumes a Dirichlet condition on the truncation boundary, whereas FEM-BEM assumes a Neumann one.

关键词： Finite element methods Integral equations gmres algorithm Hybrid technique Skin-effect

来源：评论

学校读者我要写书评

暂无评论

An iterative algorithm for finite element analysis

引用

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2004年 164卷 469-491页

作者： Laouafa, F Royis, P Ecole Natl Travaux Publ Etat CNRS URA 1652 Dept Genie Civil & Batiment F-69518 Vaulx En Velin France Inst Natl Environ Ind & RISques F-60550 Verneuil En Halatte France

In this paper, we state in a new form the algebraic problem arising from the one-field displacement finite element method (FEM). The displacement approach, in this discrete form, can be considered as the dual approach (force or equilibrium) with subsidiary constraints. This approach dissociates the nonlinear operator to the linear ones and their sizes are linear functions of integration rule which is of interest in the case of reduced integration. This new form of the problem leads to an inexpensive improvement of FEM computations, which acts at local, elementary and global levels. We demonstrate the numerical performances of this approach which is independent of the mesh structure. Using the gmres algorithm we build, for nonsymmetric problems, a new algorithm based upon the discretized field of strain. The new algorithms proposed are more closer to the mechanical problem than the classical ones because all fields appear during the resolution process. The sizes of the different operators arising in these new forms are linear functions of integration rule, which is of great interest in the case of reduced integration. (C) 2003 Elsevier B.V. All rights reserved.

关键词： finite element method mixed element gmres algorithm strain algorithm

来源：评论

学校读者我要写书评

暂无评论

Parametric continuation of the solitary traveling pulse solution in the reaction-diffusion system using the Newton-Krylov method

引用

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2009年第4期49卷 623-637页

作者： Makeev, A. G. Semendyaeva, N. L. Moscow MV Lomonosov State Univ Fac Computat Math & Cybernet Moscow 119992 Russia

The matrix-free Newton-Krylov method that uses the gmres algorithm (an iterative algorithm for solving systems of linear algebraic equations) is used for the parametric continuation of the solitary traveling pulse solution in a three-component reaction-diffusion system. Using the results of integration on a short time interval, we replace the original system of nonlinear algebraic equations by another system that has more convenient (from the viewpoint of the spectral properties of the gmres algorithm) Jacobi matrix. The proposed parametric continuation proved to be efficient for large-scale problems, and it made it possible to thoroughly examine the dependence of localized solutions on a parameter of the model.

关键词： reaction-diffusion equations localized structures parametric continuation of self-similar solutions Newton-Krylov method gmres algorithm bifurcation analysis

来源：评论

学校读者我要写书评

暂无评论

Implementation of the spectral element discretization of the nonstationary velocity-vorticity-pressure Stokes formulation

引用

BOUNDARY VALUE PROBLEMS 2024年第1期2024卷 1-19页

作者： Chorfi, Nejmeddine Ouertani, Henda King Saud Univ Coll Sci Dept Math POB 2455 Riyadh Saudi Arabia King Saud Univ Coll Comp & Informat Sci Informat Technol Dept Riyadh 11451 Saudi Arabia

This paper deals with the resolution of the time-dependent velocity-vorticity-pressure formulation of Stokes problem in a two- and three-dimensional domain. The discretization is based on the spectral element method with respect to the space variable and Euler's implicit scheme with respect to the time variable. We implement the asymmetric linear system to solve the full spectral element discrete problem. Detailed numerical experiments lead to confirm the usefulness of the discretization.

关键词： Nonstationary Stokes problem Spectral element method Implicit Euler scheme gmres algorithm

来源：评论

学校读者我要写书评

暂无评论

Imposing symmetry in augmented linear systems

引用

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS 2014年第6期21卷 781-795页

作者： Szularz, M. Univ Ulster Sch Comp & Informat Engn Coleraine BT52 1SA Londonderry North Ireland

This paper discusses the methods of imposing symmetry in the augmented system formulation (ASF) for least-squares (LS) problems. A particular emphasis is on upper Hessenberg problems, where the challenge lies in leaving all zero-by-definition elements of the LS matrix unperturbed. Analytical solutions for optimal perturbation matrices are given, including upper Hessenberg matrices. Finally, the upper Hessenberg LS problems represented by unsymmetric ASF that indicate a normwise backward stability of the problem (which is not the case in general) are identified. It is observed that such problems normally arise from Arnoldi factorization (for example, in the generalized minimal residual (gmres) algorithm). The problem is illustrated with a number of practical (arising in the gmres algorithm) and some purpose-built' examples. Copyright (c) 2014 John Wiley & Sons, Ltd.

关键词： gmres algorithm least-squares problem Hessenberg matrix Arnoldi method augmented system formulation generalized Kiebasiski-Schwetlick lemma sensitivity of QR factorization quadratic programming with box constraints

来源：评论

学校读者我要写书评

暂无评论

Implementation of Some Iterative Matrix Solvers in Simulation of the Wave Propagation Problem using the Time-harmonic Finite Difference algorithm 17

Implementation of Some Iterative Matrix Solvers in Simulatio...

引用

17th International Conference Computational Problems of Electrical Engineering (CPEE)

作者： Butrylo, Boguslaw Choroszucho, Agnieszka Bialystok Tech Univ Fac Elect Engn Bialystok Poland

ISBN: (纸本)9781509028009

In this paper, the formulation of two-dimensional finite difference frequency domain (FDFD) for heterogeneous and lossy materials is presented. But the main attention is focus on the efficient formulation of the matrix solver. Contemporary, the numerical models are consisted of a large-scale sparse complex matrix, therefore the specific formulation of the solver enable to improve the properties of the proposed algorithm. Two iterative subroutines for the complex equation are presented and validated, i.e. the BiConjugate Gradient Stabilized method (BiCGStab) and the Generalized Minimum Residual method with restarts (gmres(m)). The stability and performance of these algorithms are tested using model based on typical building construction including concrete column.

关键词： finite difference frequency scheme heterogeneous materials iterative large-scale solver gmres algorithm BiCGStab algorithm

来源：评论

学校读者我要写书评

暂无评论

A data completion algorithm using an integral representation of the Steklov-Poincare operator

引用

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2023年 422卷

作者： Abid, Chaima Abda, Amel Ben Fatma, Riadh Ben Boukari, Yosra Univ Tunis El Manar ENIT LAMSIN BP 37 Tunis 1002 Tunisia

In this paper, the Cauchy problem for the Helmholtz equation is investigated. The objective is to recover the missing data on some part of the boundary of a bounded domain from overspecified data on the remaining part of the boundary. We propose a preconditioned Krylov algorithm to solve this ill-posed problem, based on the represen-tation of the solution with surface integral equations and the Steklov-Poincare operator. We give a theoretical and numerical validation of the proposed method conducted in the 3D setting. We show the fast convergence of the proposed algorithm tested on various synthetic examples. The numerical results show a high precision of the reconstruction obtained for different levels of noisy data.(c) 2022 Elsevier B.V. All rights reserved.

关键词： Data completion algorithm Cauchy problem gmres algorithm Boundary integral equations Steklov-Poincar? operator

来源：评论

学校读者我要写书评

暂无评论

A comparison between hybrid methods: FEM-BEM versus FEM-DBCI

引用

COMPEL-THE INTERNATIONAL JOURNAL FOR COMPUTATION AND MATHEMATICS IN ELECTRICAL AND ELECTRONIC ENGINEERING 2013年第6期32卷 1901-1911页

作者： Aiello, Giovanni Alfonzetti, Salvatore Borzi, Giuseppe Rizzo, Santi Agatino Salerno, Nunzio Univ Catania Dipartimento Ingn Elettr Elettron & Informat Catania Italy Univ Messina Dipartimento Ingn Civile Messina Italy

Purpose - This paper compares the hybrid FEM-BEM and FEM-DBCI methods for the solution of open-boundary static and quasi-static electromagnetic field problems. Design/methodology/approach - After a brief review of the two methods (both coupling a differential equation for the interior problem with an integral equation for the exterior one), they are compared in terms of accuracy, memory and computing time requirements by means of a set of simple examples. Findings - The comparison suggests that FEM-BEM is more accurate than FEM-DBCI but requires more computing time. Practical implications - Then FEM-DBCI appears more appropriate for applications which require a shorter computing time, for example in the stochastic optimization of electromagnetic devices. Conversely, FEM-BEM is more appropriate in cases in which a high level of precision is required in a single computation. Originality/value - Note that the FEM-BEM considered in this paper is a non standard one in which the nodes of the normal derivative on the truncation boundary are placed in positions different from those of the potential.

关键词： Finite element method Boundary element method Integral equations Hybrid technique gmres algorithm Electrostatics Finite element analysis Electrostatics Finite element method Boundary element methods Integral equations

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：