This paper presents a review of the current state-of-the-art of numerical methods for nonlinear Dirac (NLD) equation. Several methods are extendedly proposed for the (1+1)-dimensional NLD equation with the scalar and vector self-interaction and analyzed in the way of the accuracy and the time reversibility as well as the conservation of the discrete charge, energy and linear momentum. Those met...

In this paper we are going to study the gas evolution dynamics of the exact and approximate Riemann solvers, e.g., the Flux Vector Splitting (FVS) and the Flux Difference Splitting (FDS) schemes. Since the FVS scheme and the Kinetic Flux Vector Splitting (KFVS) scheme have the same physical mechanism and similar flux function, based on the analysis of the discretized KFVS scheme the weakness an...

A kinetic flux-vector splitting (KFVS) scheme is applied for solving a reduced six-equation two-phase flow model of Saurel et al. [1]. The model incorporates single velocity, two pressures and relaxation terms. An additional seventh equation, describing the total mixture energy, is added to the model to guarantee the correct treatment of shocks in the single phase limit. Some salient features o...

An active antenna for transmitter application in S frequency band is designed and analyzed using harmonic balance technique which is based on the nonlinear model of active devices. In this active antenna, the amplifier is integrated with the radiator which is a rectangular patch antenna. This patch antenna is analyzed employing full-wave momentum method. By applying nonlinear model of transisto...

Domain decomposition methods are essential in solving applied problems on parallel computer systems. For boundary value problems for evolutionary equations the implicit schemes are in common use to solve problems at a new time level employing iterative methods of domain decomposition. An alternative approach is based on constructing iteration-free methods based on special schemes of splitting i...

Keywords: Allen–Cahn equation Finite element method Operator splitting method Unconditionally stable scheme a b s t r a c t We present an unconditionally stable hybrid finite element method for solving the Allen– Cahn equation, which describes the temporal evolution of a non-conserved phase-field during the antiphase domain coarsening in a binary mixture. Its various modified forms have been ap...

We show that Horrocks' criterion for the splitting of rank two vector bundles in P 3 can be extended, with some assumptions on the Chern classes, on non singular hypersurfaces in P 4. Extension of other splitting criterions are studied.

We show that Horrocks' criterion for the splitting of rank two vector bundles in P 3 can be extended, with some assumptions on the Chern classes, on non singular hypersurfaces in P 4. Extension of other splitting criterions are studied.

Given far field data of a time-harmonic wave radiated by an ensemble of well separated acoustic or electromagnetic sources as well as a priori information on the locations of these sources, we discuss an algorithm to approximate the far field data radiated by each of these sources separately. The method is based on a Galerkin procedure considering subspaces spanned by the singular vectors of “r...