BDDC

Abstract: The FETI method and its two-level extension (FETI-2) are two numerically scalable domain decomposition methods with Lagrange multipliers for the iterative solution of second-order solid mechanics and fourth-order beam, plate and shell structural problems, respectively.The FETI-2 method distinguishes itself from the basic or one-level FETI method by a second set of Lagrange multipliers that are introduced at the subdomain cross-points to enforce at each iteration the exact continuity of a subset of the displacement field at these specific locations. In this paper, we present a dual–primal formulation of the FETI-2 concept that eliminates the need for that second set of Lagrange multipliers, and unifies all previously developed one-level and two-level FETI algorithms into a single dual–primal FETI-DP method. We show that this new FETI-DP method is numerically scalable for both second-order and fourth-order problems. We also show that it is more robust and more computationally efficient than existing FETI solvers, particularly when the number of subdomains and/or processors is very large. Copyright © 2001 John Wiley & Sons, Ltd.

Abstract: A preconditioner for substructuring based on constrained energy minimization concepts is presented. The preconditioner is applicable to both structured and unstructured meshes and offers a straightforward approach for the iterative solution of second- and fourth-order structural mechanics problems. The approach involves constraints associated with disjoint sets of nodes on substructure boundaries. These constraints provide the means for preconditioning at both the substructure and global levels. Numerical examples are presented that demonstrate the good performance of the method in terms of iterations, compute time, and condition numbers of the preconditioned equations.

Abstract: In conventional equalizers, the facts of bulky size and high cost are widespread. Particularly, the zero-switching loss and zero-voltage gap (ZVG) between cells are difficult to implement due to the high-frequency hard switching and the voltage drop across power devices. To overcome these difficulties, a direct cell-to-cell battery equalizer based on quasi-resonant LC converter (QRLCC) and boost dc-dc converter (BDDC) is proposed. The QRLCC is employed to gain zero-current switching, leading to a reduction of power losses. The BDDC is employed to enhance the equalization voltage gap for large balancing current and ZVG between cells. Moreover, through controlling the duty cycle of the BDDC, the topology can online adaptively regulate the equalization current according to the voltage difference, which not only effectively prevents overequalization but also abridges the overall balancing time. Instead of a dedicated equalizer for each cell, only one balancing converter is employed and shared by all cells, reducing the size and implementation cost. Simulation and experimental results show the proposed scheme exhibits outstanding balancing performance, and the energy conversion efficiency is higher than 98%. The validity of the proposed equalizer is further verified by a quantitative and systematic comparison with the existing active balancing methods.