A space-domain preconditioned spectral method for non-linear boundary value problems

A novel spectral procedure for the numerical solution of non-linear boundary value problems is presented. The discrete spectral equations are solved by an iterative algorithm using space-domain preconditioning. The preconditioning operator is obtained by spatial weighting (or windowing) of the exact differential operator. Convergence behaviour of the iterative solution is investigated using an eigenvalue analysis. Theoretical estimates for the convergence rate and accuracy are compared with that achieved in a numerical application—a non-linear boundary value problem from semiconductor device modelling. The method combines the infinite-order exponential accuracy of spectral discretizations with the sparse structure of finite difference equations. This offers numerical advantages in comparison to previously developed Fourier–Galerkin algorithms, particularly important for physically ill-conditioned and strongly non-linear problems. The tradeoff of achievable accuracy versus computer time is easily controlled, thus making essential speed-ups possible for moderate accuracy requirements.     

Parallel FETI‐DP algorithm for efficient simulation of large‐scale EM problems

An efficient parallelization of the dual‐primal finite‐element tearing and interconnecting (FETI‐DP) algorithm is presented for large‐scale electromagnetic simulations. As a nonoverlapping domain decomposition method, the FETI‐DP algorithm formulates a global interface problem, whose iterative solution is accelerated with a solution of a global corner problem. To achieve a good load balance for parallel computation, the original computational domain is decomposed into subdomains with similar sizes and shapes. The subdomains are then distributed to processors based on their close proximity to minimize inter‐processor communication. The parallel generalized minimal residual method, enhanced with the iterative classical Gram‐Schmidt orthogonalization scheme to reduce global communication, is adopted to solve the global interface problem with a fast convergence rate. The global corner‐related coarse problem is solved iteratively with a parallel communication‐avoiding biconjugate gradient stabilized method to minimize global communication, and its convergence is accelerated by a diagonal preconditioner constructed from the coarse system matrix. To alleviate neighboring communication overhead, the non‐blocking communication approach is employed in both generalized minimal residual and communication‐avoiding biconjugate gradient stabilized iterative solutions. Three numerical examples are presented to demonstrate the accuracy, scalability, and capability of the proposed parallel FETI‐DP algorithm for electromagnetic modeling of general objects and antenna arrays. Copyright © 2016 John Wiley & Sons, Ltd.     

Numerical solution of inhomogeneous and non-linear ordinary differential equations using the TLM multicompartment model

The paper presents a simple algorithm for solving a system of inhomogeneous high order differential equations with variable coefficients. The method also provides a numerical solution to non-linear ordinary differential equations. The technique is based on reducing the high order equations into a system of first order rate equations. Through a simple translation process, the variables in the reduced set of equations are solved simultaneously by an iterative scheme using the TLM multicompartment model. The numerical technique is demonstrated by solving well-known second order differential equations. The numerical solutions are compared with the analytical solutions to the differential equations.     

Passivity–preserving interpolation‐based parameterized model order reduction of PEEC models based on scattered grids

The increasing operating frequencies and decreasing IC feature size call for 3‐D electromagnetic (EM) methods, such as the Partial Element Equivalent Circuit (PEEC) method, as necessary tools for the analysis and design of high‐speed systems. Very large systems of equations are often generated by 3‐D EM methods and model order reduction (MOR) techniques are commonly used to reduce such a high model complexity. A typical design process includes optimization and design space exploration, and hence requires multiple simulations for different design parameter values. Traditional MOR techniques perform model reduction only with respect to frequency and such design activities call for parameterized MOR (PMOR) methods that can reduce large systems of equations with respect to frequency and other design parameters of the circuit, such as geometrical layout or substrate characteristics. We present a novel PMOR technique applicable to the PEEC method that provides parametric reduced order models, stable and passive by construction, over a user defined design space. We treat the construction of parametric reduced order models on scattered design space grids. Pertinent numerical examples validate the proposed approach. Copyright © 2010 John Wiley & Sons, Ltd.     

Full-wave solutions to the propagation characteristics of buried microstrip lines by VFEM and ABCs

The propagation factors of buried microstrip lines are considered. The associated eigenvalue problems are solved by the edge-based vectorial finite element method (VFEM). To improve the higher-order VFEM solutions, the problem infinite domain is truncated by second-order absorbing boundary conditions (ABCs). This reduces the number of unknowns and, consequently, the numerical effort. Owing to the many advantages of both the edge-based VFEM and the second-order ABCs, this full-wave method is implemented by a general computer program for solving unbounded domain problems involving complex geometries and inhomogeneous media. The examples presented show the validity of this technique. © 1998 John Wiley & Sons, Ltd.     

On the solvability and computation of D.C. transistor networks

A study of non-linear d.c. networks containing transistors, diodes, linear resistors, independent voltage and current sources and linear controlled voltage and current sources, described by Tf(x) + Gx = b is presented. A few theorems concerning both the solvability and numerical computation of d.c. transistor networks are proved. The conditions sufficient for the existence of at least one solution and of a unique solution are defined. A method for numerical computation of the networks without the need to determine inverse matrices is presented and the convergence of the iterative technique is analysed. Suggestions are formulated regarding applicability of the method for computation of an approximate solution (close to the exact solution) which may subsequently be quickly corrected using the Newton-Raphson method.     

A Monte Carlo Method Seamlessly Linking Quantum and Classical Transport Calculations

A Monte Carlo method for carrier transport is presented, which simultaneously takes into account quantum interference and dissipation effects. The method solves the space-dependent Wigner equation including semi-classical scattering through the Boltzmann collision operator. To this equation a particle model is assigned, which interprets the non-local potential operator as a generation term for numerical particles of positive and negative statistical weight. A numerical technique to control the avalanche of numerical particles is discussed. Since the Wigner equation simplifies to the Boltzmann equation in classical device regions, the solutions of the quantum kinetic equation and the classical one are linked in a natural way. This approach allows the simulation of a quantum region embedded in an extended classical region. Results of this approach are demonstrated for a resonant tunneling diode.     

Consistent material operators for tetrahedral grids based on geometrical principles

This paper is focused on analysis of the properties of material operators for geometrical methods on tetrahedral grids. The stiffness matrix in electrodynamics, as well as the one in electrostatics, are mathematically proven to be the same for every material operator satisfying a condition which is sufficient for the consistency of the numerical scheme. This gives a new and better insight into the strong similarities existing between the finite element method (FEM) and the finite integration technique (FIT). A symmetrization of the microcell method, which also ensures the positive definiteness of the material operators, based on geometrical properties of tetrahedra, is proposed. Numerical results in time and frequency domain for resonant cavities are presented and compared to the FEM. Copyright © 2004 John Wiley & Sons, Ltd.     

SSOR preconditioned GPBiCG method for the linear interference cancellation of asynchronous CDMA systems

The decorrelator or the linear minimum mean-squared-error (LMMSE) detector has its computational complexity of O(K ³) where K is the number of users. On the other hand, the computational complexity of iterative detector algorithms such as conjugate gradient (CG) and generalized product bi-conjugate gradient (GPBiCG) methods only require the computational complexity O(K ²) per iteration. In this paper, the symmetric successive overrelaxation (SSOR) preconditioning scheme is applied to the GPBiCG method. The performance of the detectors is investigated and it is found that the SSOR preconditioned GPBiCG method can provide significantly faster convergence.     

应用对偶方法的TV图像去噪

介绍了基于梯度算子和基于拉普拉斯算子的TV模型图像去噪,指出了传统模型求解过程中存在不可微项的问题,对传统模型进行改进,提出了基于梯度算子和拉普拉斯算子相结合的TV模型,并用对偶方法求其数值解.引入对偶变量,解决了传统的最优化方法求解过程中存在不可微项的问题,使得所求得的数值解更加接近于原始图像.最后通过实验验证,证明该方法能有效去除噪声,同时能够保持图像边缘,减弱传统模型产生的阶梯效应,并能大幅提高去噪效率.     

A new a priori ordering method for sparse systems of equations based on an ordered output set

In the context of solution to the sparse systems of equations arising in computer-aided analysis and design of electrical networks using the Gaussian elimination (GE) process it is well-known that an a priori reordering for equations and unknowns is almost mandatory. In this paper we present a new approach for a priori ordering for the equations and unknowns using the theory of output sets. Our approach yields an ordered output set as the pivot sequence for an associated GE process. Our algorithm is simple and is more general than the existing ones and leads to an s-minimal GE process. An example is presented for illustrating the algorithm and the computational complexity of the new method has been analysed. Additional work needed in the area is indicated.     

基于模态级数法和轨迹灵敏度的励磁调节器参数优化

基于模态级数法及轨迹灵敏度分析的励磁调节器参数优化方法通过模态级数法得到较精确的系统状态轨迹的封闭解，利用数值微商算法得到系统的轨迹灵敏度，即目标函数的梯度信息，再应用共轭梯度技术优化励磁调节器参数。模态级数法考虑了系统非线性模式的影响，所得状态轨迹解逼近时域仿真结果，所以该方法能有效地阻尼系统受到大扰动后的振荡。通过算例可验证该方法的有效性。     

AN FFT-BASED FORMULATION FOR THE COMPUTATION OF ELECTROMAGNETIC SCATTERING FROM 3-D,PERFECTLY CONDUCTING BODIES

An FFT-based formulation for the computation of electromagnetic scattering from 3-D, perfectly conducting objects is presented. The formulation solves the EFIE iteratively via a conjugate gradient scheme and has the major advantage of a low storage requirement for scatterers in the resonance region. This factor, coupled with the low run-times resulting from use of the FFT to compute the associated matrices, makes the formulation a particularly efficient one. Numerical results encompassing current distributions and far-field radar cross-sections are presented for PEC cubes of resonant size. It is shown that the computed results yield good agreement compared with other numerical techniques and experimental data.     

Development of a new algorithm for power flow analysis

This paper presents a new iterative solution technique for power flow analysis to reduce the computation complexity, hence time of the conventional solution techniques. In the proposed method, the impedance matrix has been used instead of admittance matrix. This method does not involve any other jacobian matrix or any other inversion of matrix, hence there is no problem of singularity. Memory requirement of the proposed method is also less. The new method has been tested on IEEE standard 5-bus, 14-bus, 30-bus, 57-bus, 118-bus and 300-bus test systems with high precession. The test results have been compared with the same of popular conventional solution methods. The method has also been tested under different practical security constraints. The test results presented reveal the superiority of the proposed method.     

Computation of the magnetic field generated by an undergroundpipe-type cable

A hybrid computational method for predicting the magnetic field in the vicinity of an underground three-phase pipe-type cable is presented in this paper. This hybrid method combines the numerical techniques of the finite element method and the unimoment method. An iterative solution procedure is developed and employed to treat the nonlinear B-H characteristic of the steel pipe. To validate the computational method, measurements were made and the numerical results are compared with the measured data and with the results obtained previously by using a different numerical method. The result of the comparison is satisfactory     

A fast numerical algorithm for transient stability studies of power systems

A fast numerical solution of a technique for improving the speed of the transient stability solution of power systems is presented in this paper. The system is described by a set of first-order differential equations which consist of both linear and nonlinear parts. The linear set of equations is considered separately and is solved by modal analysis using closed-form solutions. The nonlinear part of the equations is solved by a numerical method. As explicit solutions are available for the linear part of the equations, the solution time is considerably reduced. The proposed technique is employed for computing the transient stability of a sample power system represented in detail. A comparison is made with a conventional solution procedure.     

基于预处理共轭梯度法的电力系统机电暂态仿真

把基于不完全LU分解的预处理共轭梯度法(ILUCG)用于电力系统暂态稳定仿真计算,提出了一种与矩阵方程直接求解法相结合的混合算法.该方法采用不完全LU分解对暂态稳定计算中的雅可比矩阵进行预处理,以改善其条件数;对预处理之后的方程组,采用改进的共轭梯度法进行迭代求解,在系统收敛困难的情况下,改用直接求解法求解矩阵方程;在迭代过程中,充分利用当前已有的预处理后的等价雅可比矩阵进行迭代计算,而当雅可比矩阵及相关变量变化较大时,重新计算雅可比矩阵并进行相应的预处理操作,以提高算法的效率和计算速度;多个算例表明,对于电力系统暂态仿真的计算,本文算法的计算速度明显优于直接分解求解法和单纯的ILUCG,并易于在并行计算平台上实现,具有一定的实际应用前景.     

Parallel computation of 3-D electromagnetic scattering using finite elements

The finite element method (FEM) with local absorbing boundary conditions has been recently applied to compute electromagnetic scattering from large 3-D geometries. In this paper, we present details pertaining to code implementation and optimization. Various types of sparse matrix storage schemes are discussed and their performance is examined in terms of vectorization and net storage requirements. The system of linear equations is solved using a preconditioned biconjugate gradient (BCG) algorithm and a fairly detailed study of existing point and block preconditioners (diagonal and incomplete LU) is carried out. A modified ILU preconditioning scheme is also introducted which works better than the traditional version for our matrix systems. The parallelization of the iterative sparse solver and the matrix generation/assembly as implemented on the KSR1 multiprocessor is described and the interprocessor communication patterns are analysed in detail. Near-linear speed-up is obtained for both the iterative solver and the matrix generation/assembly phases. Results are presented for a problem having 224,476 unknowns and validated by comparison with measured data.     

A frequency‐domain approach to the analysis of stability and bifurcations in nonlinear systems described by differential‐algebraic equations

A general numerical technique is proposed for the assessment of the stability of periodic solutions and the determination of bifurcations for limit cycles in autonomous nonlinear systems represented by ordinary differential equations in the differential‐algebraic form. The method is based on the harmonic balance (HB) technique, and exploits the same Jacobian matrix of the nonlinear system used in the Newton iterative numerical solution of the HB equations for the determination of the periodic steady state. To demonstrate the approach, it is applied to the determination of the bifurcation curves in the parameters' space of Chua's circuit with cubic nonlinearity, and to the study of the dynamics of the limit cycle of a Colpitts oscillator. Copyright © 2007 John Wiley & Sons, Ltd.     

Optimal short term hydro scheduling including security constraints

A method is presented for short-term production scheduling in a hydro system. The solution technique is based on iterative network linear programming and heuristic techniques. The method handles security constraints due to single branch and specified multiple contingencies. The postcontingency rescheduling capabilities are modeled explicitly in a DC optimal load flow. Using the rescheduling capabilities increases the transmission network utilization