Convergence theories and a deluxe dual and primal finite element tearing and interconnecting algorithm are developed for a hybrid staggered DG finite element approximation of H(curl) elliptic problems in two dimensions. In addition to the advantages of staggered DG methods, the basis functions of the new hybrid staggered DG method are all locally supported in the triangular elements, and a Lagrange multiplier approach is applied to enforce the global connections of these basis functions. The interface problem on the Lagrange multipliers is further reduced to the resulting problem on the subdomain interfaces, and a dual and primal finite element tearing and interconnecting algorithm with an enriched weight factor is then applied to the resulting problem. Our algorithm is shown to give a condition number bound of <i>C</i>(1+log(<i>H</i><i>h</i>))², independent of the two parameters, where <i>H</i><i>h</i> is the number of

We consider an open quantum dot modeled by a straight hard-wall channel with a potential well. If this potential depends on the longitudinal variable only, the system exhibits embedded eigenvalues. They turn into resonances if the symmetry is violated, either by a magnetic field or by deformation of the well. We construct a perturbation theory of these resonances in the case of a weak perturbation and discuss other properties of the model.

abstract

In this paper, gold ball wire bonding at low temperature using a high frequency transducer was evaluated. The substrates used were FR-4 laminates with two different gold-plated surface finishes: electrolytic and immersion gold-plated. Bonding temperatures of 120/spl deg/C, 80/spl deg/C and 40/spl deg/C were investigated with 1 mil fine pitch gold wire. Prior to wire bonding, the laminates and dice were plasma treated. The surfaces were analyzed prior to and after plasma treatment before wire bonding using XPS and AFM. Bonded areas were also analyzed using SEM. Design of experiment (DOE) techniques have been employed to optimize the bonding parameters at each temperature. The response of the DOE was evaluated by using bond shear and bond pull. The results show that bonding at low temperature is viable with the use of a high frequency transducer wire bonder.

In this paper, a class of FETI-DP preconditioners is developed for a fast solution of the linear system arising from staggered discontinuous Galerkin discretization of the two-dimensional Stokes equations. The discretization has been recently developed and has the distinctive advantages that it is optimally convergent and has a good local conservation property. In order to efficiently solve the linear system, two kinds of FETI-DP preconditioners, namely, lumped and Dirichlet preconditioners, are considered and analyzed. Scalable bounds C (H/h) and C (1+ log (H/h)) 2 are proved for the lumped and Dirichlet preconditioners, respectively, with the constant C depending on the infsup constant of the discrete spaces but independent of any mesh parameters. Here H/h stands for the number of elements across each subdomain. Numerical results are presented to confirm the theoretical estimates.