We present a domain decomposition technical for computing the quantum transport phenomena in complex nano-structures. In regular sub-domains, the subband decomposition method is applied, while the finite difference method is used on small irregular sub-domains where the subband decomposition is not applicable. This new approach preserves the efficiency of the original subband decomposition meth...

This paper presents a model which provides a smooth transition between a kinetic and a diffusion domain. The idea is to use a buffer zone, in which both diffusion and kinetic equations will be solved. The solution of the original kinetic equation will be recovered as the sum of the solutions of these two equations. We use an artificial connecting function which makes the equation on each domain...

A schwarz type domain decomposition method for the Helmholtz equation is considered. The interface conditions involve second order tangential derivatives which are optimized (OO2, Optimized Order 2) for a fast convergence. The substructured form of the algorithm is symmetrized so that the symmetric-QMR algorithm can be used as an accelerator of the convergence. Numerical results are shown. We c...

This paper presents a fast iterative solver for Lippmann-Schwinger equation for highfrequency waves scattered by a smooth medium with a compactly supported inhomogeneity. The solver is based on the sparsifying preconditioner [63] and a domain decomposition approach similar to the method of polarized traces [64]. The iterative solver has two levels, the outer level in which a sparsifying precond...

This paper extends an earlier work [Appl. Math. Comput. 140 (2003) 77] to differential-algebraic equations with constraint singularities. Numerical solution of these problems is considered by pseudospectral method with domain decomposition and by giving a condition under which the general linear form problem can easily be transformed to the index reduced form by a simple formulation. Furthermor...

\Tree-codes" and \Multigrid" methods are both hierarchical, recursive algorithms for solving vector eld equations, faster than traditional methods. If the methods are non-adaptive, then both Tree-codes and Multigrid methods require identical parallel communication strategies since they share the same internal structure. This paper contains a description of Tree-codes followed by an overview of ...

Domain decomposition (DD) methods for solving time-dependent problems can be classified by (i) the method of domain decomposition used, (ii) the choice of decomposition operators (exchange of boundary conditions), and (iii) the splitting scheme employed. To construct homogeneous numerical algorithms, overlapping subdomain methods are preferable. Domain decomposition is associated with the corre...

Nevertheless, at present there is still a need to reduce the computational costs of a BEM. Moreover, the straightIn this paper an iterative domain decomposition method for the solution of Laplace’s equation is described and its effectiveness in forward application of a BEM requires a computational time-domain computations of nonlinear water waves with a panel effort that depends approximately q...

Two types of approximation schemes are established for incompressible miscible displacements in porous media. First, standard mixed finite element method is used to approximate the velocity and pressure. And then parallel non-overlapping domain decomposition methods combined with the characteristics method are presented for the concentration. These methods use the characteristic method to handl...