基于复合型单开关PFC预调节器的设计

为了解决计算机系统电源保持时间问题,确保输出电压在一段时间稳定在一定范围内。确保计算机在出现输入故障是有足够的时间备份数据或者切换到不间断电源(UPS)下工作。为此提出了一种复合型单开关PFC预调器、并根据需求进行了设计,该设计可以减小储能电容的容量,使输出电流谐波满足IEC1000-302的要求。     

Parallel Newton-Krylov-Schwarz algorithms for the three-dimensional Poisson-Boltzmann equation in numerical simulation of colloidal particle interactions

We investigate fully parallel Newton-Krylov-Schwarz (NKS) algorithms for solving the large sparse nonlinear systems of equations arising from the finite element discretization of the three-dimensional Poisson-Boltzmann equation (PBE), which is often used to describe the colloidal phenomena of an electric double layer around charged objects in colloidal and interfacial science. The NKS algorithm employs an inexact Newton method with backtracking (INB) as the nonlinear solver in conjunction with a Krylov subspace method as the linear solver for the corresponding Jacobian system. An overlapping Schwarz method as a preconditioner to accelerate the convergence of the linear solver. Two test cases including two isolated charged particles and two colloidal particles in a cylindrical pore are used as benchmark problems to validate the correctness of our parallel NKS-based PBE solver. In addition, a truly three-dimensional case, which models the interaction between two charged spherical particles within a rough charged micro-capillary, is simulated to demonstrate the applicability of our PBE solver to handle a problem with complex geometry. Finally, based on the result obtained from a PC cluster of parallel machines, we show numerically that NKS is quite suitable for the numerical simulation of interaction between colloidal particles, since NKS is robust in the sense that INB is able to converge within a small number of iterations regardless of the geometry, the mesh size, the number of processors. With help of an additive preconditioned Krylov subspace method NKS achieves parallel efficiency of 71% or better on up to a hundred processors for a 3D problem with 5 million unknowns.     

H-矩阵方程组的预条件迭代法

针对系数矩阵A为H-矩阵的线性方程组Ax=b,引入了预条件矩阵I＋S_α~β,通过对系数矩阵施行初等行变换,提出了求解线性方程组Ax=b的一种新的预条件Gauss-Seidel方法.论文中首先证明了若A为H-矩阵,则（I＋S_α~β）A仍然是H-矩阵;其次,以定理的形式给出了新的预条件Gauss-Seidel方法收敛的充分条件,即给出了为保证新的预条件Gauss-Seidel方法收敛时参数所需满足的条件;然后从理论上证明了新的预条件Gauss-Seidel迭代方法较经典的Gauss-Seidel迭代方法收敛速度快,论文中提出的新的预条件Gauss-Seidel迭代方法推广了文[1-2]中提出的预条件方法;最后又通过数值算例说明了新的预条件Gauss-Seidel迭代方法的有效性.     

A rapid method of approximating the asymptote to an iterative sequence

We discuss a procedure for the adaptive construction of sparse approximate inverse preconditionings for general sparse linear systems. The approximate inverses are based on minimizing a consistent norm of the difference between the identity and the preconditioned matrix. The analysis provides positive definiteness and condition number estimates for the preconditioned system under certain circumstances. We show that for the 1-norm, restricting the size of the difference matrix below 1 may require dense approximate inverses. However, this requirement does not hold for the 2-norm, and similarly reducing the Frobenius norm below 1 does not generally require that much fill-in. Moreover, for the Frobenius norm, the calculation of the approximate inverses yields naturally column-oriented parallelism. General sparsity can be exploited in a straightforward fashion. Numerical criteria are considered for determining which columns of the sparse approximate inverse require additional fill-in. Spare algorithms are discussed for the location of potential fill-in within each column. Results using a minimum-residual-type iterative method are presented to illustrate the potential of the method.     

Efficient solution of 3D electromagnetic scattering from large homogeneous targets

Based on the combined tangential formulation of surface integral equation, a fast algo- rithm is presented for calculating electromagnetic scattering from electrically large 3D homogeneous objects. In the algorithm, the lower triangular approximate Schur preconditioner is combined with the multilevel fast multipole algorithm （MLFMA）. The coefficient matrix of the near-field coupling element is selected to set up the approximate matrix. For large problems, the incomplete LU factori- zation with dual threshold （ILUT） has better performance than sparse approximate inverse （SAI） of accelerating the convergence of the generalized minimal residual method （ GMRES ） iteration. Nu- merical experiments validate the efficiency and robustness of the presented fast algorithm for homo- geneous dielectric objects.     

A dual mesh multigrid preconditioner for the efficient solution of hydraulically driven fracture problems

We present a novel multigrid (MG) procedure for the efficient solution of the large non‐symmetric system of algebraic equations used to model the evolution of a hydraulically driven fracture in a multi‐layered elastic medium. The governing equations involve a highly non‐linear coupled system of integro‐partial differential equations along with the fracture front free boundary problem. The conditioning of the algebraic equations typically degrades as O(N³). A number of characteristics of this problem present significant new challenges for designing an effective MG strategy. Large changes in the coefficients of the PDE are dealt with by taking the appropriate harmonic averages of the discrete coefficients. Coarse level Green's functions for multiple elastic layers are constructed using a single dual mesh and superposition. Coarse grids that are sub‐sets of the finest grid are used to treat mixed variable problems associated with ‘pinch points.’ Localized approximations to the Jacobian at each MG level are used to devise efficient Gauss–Seidel smoothers and preferential line iterations are used to eliminate grid anisotropy caused by large aspect ratio elements. The performance of the MG preconditioner is demonstrated in a number of numerical experiments. Copyright © 2005 John Wiley & Sons, Ltd.     

Efficient Poisson Solver for Semiconductor Device Modeling Using the Multi-Grid Preconditioned BiCGSTAB Method

This paper presents the performance results of an efficient algorithm for solving the three dimensional Poisson equation. The multi-grid method exploits the efficient oscillatory error reduction of basic iterative methods by smoothing on a set of progressively coarsened grids. When used as a preconditioner for BiCGSTAB method, a computationally demanding solver can be shown to be effective for large scale simulations. Varying the number of grids used and the level of overrelaxation as well as exploring the benefits of semicoarsening in the multi-grid preconditioner reveals the underlying strengths of this combined scheme. The convergence properties of the developed solver are tested on a 3D split-gate silicon on insulator (SOI) device.     

Preconditioning methods for very ill‐conditioned three‐dimensional linear elasticity problems

Finite element models of linear elasticity arise in many application areas of structural analysis. Solving the resulting system of equations accounts for a large portion of the total cost for large, three‐dimensional models, for which direct methods can be prohibitively expensive. Preconditioned Conjugate Gradient (PCG) methods are used to solve difficult problems with small (≪1) average element aspect ratios. Incomplete Cholesky (ILL^T) factorizations based on a drop tolerance parameter are used to form the preconditioning matrices. Various new techniques known as reduction techniques are examined. Combinations of these reduction techniques result in highly effective preconditioners for problems with very poor aspect ratios. Standard and hierarchical triquadratic basis functions are used on hexahedral elements, and test problems comprising a variety of geo‐metries with up to 50 000 degrees of freedom are considered. Manteuffel’s method of perturbing the stiffness matrix to ensure positive pivots occur during factorization is used, and its effects on the convergence of the preconditioned system are discussed. Copyright © 1999 John Wiley & Sons, Ltd.     

Exercise Preconditioning Blunts Early Atrogenes Expression and Atrophy in Gastrocnemius Muscle of Hindlimb Unloaded Mice

A large set of FoxOs-dependent genes play a primary role in controlling muscle mass during hindlimb unloading. Mitochondrial dysfunction can modulate such a process. We hypothesized that endurance exercise before disuse can protect against disuse-induced muscle atrophy by enhancing peroxisome proliferator-activated receptor-γ coactivator-1α (PGC1α) expression and preventing mitochondrial dysfunction and energy-sensing AMP-activated protein kinase (AMPK) activation. We studied cross sectional area (CSA) of muscle fibers of gastrocnemius muscle by histochemistry following 1, 3, 7, and 14 days of hindlimb unloading (HU). We used Western blotting and qRT-PCR to study mitochondrial dynamics and FoxOs-dependent atrogenes’ expression at 1 and 3 days after HU. Preconditioned animals were submitted to moderate treadmill exercise for 7 days before disuse. Exercise preconditioning protected the gastrocnemius from disuse atrophy until 7 days of HU. It blunted alterations in mitochondrial dynamics up to 3 days after HU and the expression of most atrogenes at 1 day after disuse. In preconditioned mice, the activation of atrogenes resumed 3 days after HU when mitochondrial dynamics, assessed by profusion and pro-fission markers (mitofusin 1, MFN1, mitofusin 2, MFN2, optic atrophy 1, OPA1, dynamin related protein 1, DRP1 and fission 1, FIS1), PGC1α levels, and AMPK activation were at a basal level. Therefore, the normalization of mitochondrial dynamics and function was not sufficient to prevent atrogenes activation just a few days after HU. The time course of sirtuin 1 (SIRT1) expression and content paralleled the time course of atrogenes’ expression. In conclusion, seven days of endurance exercise counteracted alterations of mitochondrial dynamics and the activation of atrogenes early into disuse. Despite the normalization of mitochondrial dynamics, the effect on atrogenes’ suppression died away within 3 days of HU. Interestingly, muscle protection lasted until 7 days of HU. A longer or more intense exercise preconditioning may prolong atrogenes suppression and muscle protection.     

HIGH-PERFORMANCE PCG SOLVERS FOR FEM STRUCTURAL ANALYSIS

The preconditioned conjugate gradient algorithm is a well-known and powerful method used to solve large sparse symmetric positive definite linear systems. Such systems are generated by the finite element discretization in structural analysis but users of finite elements in this context generally still rely on direct methods. It is our purpose in the present work to highlight the improvement brought forward by some new preconditioning techniques and show that the preconditioned conjugate gradient method performs better than efficient direct methods.