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Two new mixed finite element schemes for discretizing current continuity equations are presented. Together with the good features of the already‐known mixed scheme (current preservation and good approximation of sharp shapes), they provide M‐matrices, even when a zero order term is present in the equations.

A mixed variational formulation of the free boundary problem involved in the analysis of reverse‐biased semiconductor devices is put forward. This can be profitably used in the investigation of the field distribution near the junction and at the surface of devices. A peculiar feature of the new formulation is that the electric field is assumed as a variable in the solution, together with the potential, thus enabling the electric field to be determined directly and accurately. The numerical algorithm associated with the method turns out to be quite simple and can be easily and readily implemented even on a desktop computer.

The mixed variational formulation in two‐dimensional magnetostatics and the corresponding discretization are presented in a systematic way. The comparison between the mixed finite element approach and the classical one is shown with reference to some case studies; numerical results are reported.

Electrical potentials in a junction field transistor can be calculated using a simplified model based on a complete depletion assumption. This gives rise to a free boundary problem. We show here how we can approximate this problem with a quasi‐variational inequality technique and the shape optimization method. A detailed analysis of these methods is presented. Using some numerical experiments we compare our results with the solution of the discrete drift‐diffusion system, accomplished with a Gummel‐like algorithm. The numerical results suggest that the methods proposed here work successfully and that the shape optimization technique provides a reasonably free boundary without excessive iterations.

We briefly summarize the theoretical formulations of our MITC plate bending elements and then present numerical convergence results. The elements are based on Reissner‐Mindlin plate theory and a mixed‐interpolation of the transverse displacement, section rotations and transverse shear strain components. We consider our 4, 9 and 16‐node quadrilateral elements and our 7 and 12‐node triangular elements. The theoretical and numerical results indicate the high reliability and effectiveness of our elements.

The purpose of this paper is to describe a novel implementation of a multispatial method, multitime-scheme subdomain differential algebraic equation (DAE) framework allowing a mix of different space discretization methods and different time schemes by a robust generalized single step single solve (GS4) family of linear multistep (LMS) algorithms on a single body analysis for the first-order nonlinear transient systems.

This proposed method allows the coupling of different numerical methods, such as the finite element method and particle methods, and different implicit and/or explicit algorithms in each subdomain into a single analysis with the GS4 framework. The DAE, which constrains both space and time in multi-subdomain analysis, combined with the GS4 framework ensures the second-order time accuracy in all primary variables and Lagrange multiplier. With the appropriate GS4 parameters, the algorithmic temperature rate variable shift can be matched for all time steps using the DAE. The proposed method is used to solve various combinations of spatial methods and time schemes between subdomains in a single analysis of nonlinear first-order system problems.

The proposed method is capable of coupling different spatial methods for multiple subdomains and different implicit/explicit time integration schemes in the GS4 framework while sustaining second-order time accuracy.

Traditional approaches do not permit such robust and flexible coupling features. The proposed framework encompasses most of the LMS methods that are second-order time accurate and unconditionally stable.

A fully parallel algorithm for the solution of a finite element system using a MIMD (multiple‐instruction multiple‐data architecture) parallel computer is presented. The formulation includes a simple domain decomposer that automatically divides a finite element mesh into a list of subdomains to guarantee the load balancing. Furthermore, each subdomain is assigned to a processor of a parallel computer and treated as a sub‐finite element system with information exchanged through the interface between two adjacent subdomains. With this new algorithm, these sub‐finite element systems are solved fully parallelly as independent finite element systems, not only the computations of the interior nodes but also the computations of the interface nodes can be executed parallelly. Also, the inherently sequential Gauss‐Seidel and SOR schemes are altered into fully parallel iterative schemes. An implementation of this new scheme on an iPSC/2 D5 Hypercube Concurrent Computer reached an efficiency of more than 100% when compared with the sequential SOR scheme.

We present an abstract mathematical and numerical analysis for Drift‐Diffusion equation of heterojunction semiconductor devices with Fermi‐Dirac statistic. For the approximation, a mixed finite element method is considered. This can be profitably used in the investigation of the current through the device structure. A peculiar feature of this mixed formulation is that the electric displacement D and the current densities jn and jp for electrons and holes, are taken as unknowns, together with the potential φ and quas‐Fermi levels φn and φp. This enably D, jn and jp to be determined directly and accurately. For decoupled system, existence, uniqueness, regularity and stability results of the approximate solution are given. A priori and a posteriori error estimates are also presented. A nonlinear implicit scheme with local time steps is used. This algorithm appears to be efficient and gives satisfactory results. Numerical results for an heterojunction bipolar transistor, In two dimension, are presented.

In this paper, we present the results of submicron pseudomorphic AlGaAs/InGaAs/ GaAs HEMT simulations. Our main interest is the study of electronic temperature behavior in the device and improvement of the current‐voltage characteristic curves. Three types of models are being used. The first is the well known drift‐diffusion model. The second is of the hydrodynamic type and the third is a combination of the two preceding models. The numerical treatment is based on the discretization by the Galerkin finite element method for both Poisson and continuity equations with the streamline‐diffusion method being used for the energy equation. A comparison of the different approaches have been realized and a synthesis on the validity of each of these models is being drawn.

This study aims to focus on the development of a high-order discontinuous Galerkin method for the solution of unsteady, incompressible, multiphase flows with level set interface formulation.

Nodal discontinuous Galerkin discretization is used for incompressible Navier–Stokes, level set advection and reinitialization equations on adaptive unstructured elements. Implicit systems arising from the semi-explicit time discretization of the flow equations are solved with a p-multigrid preconditioned conjugate gradient method, which minimizes the memory requirements and increases overall run-time performance. Computations are localized mostly near the interface location to reduce computational cost without sacrificing the accuracy.

The proposed method allows to capture interface topology accurately in simulating wide range of flow regimes with high density/viscosity ratios and offers good mass conservation even in relatively coarse grids, while keeping the simplicity of the level set interface modeling. Efficiency, local high-order accuracy and mass conservation of the method are confirmed through distinct numerical test cases of sloshing, dam break and Rayleigh–Taylor instability.

A fully discontinuous Galerkin, high-order, adaptive method on unstructured grids is introduced where flow and interface equations are solved in discontinuous space.