PSEUDOSPECTRAL LEAST SQUARES METHOD FOR STOKES-DARCY EQUATIONS

We investigate the first order system least squares Legendre and Chebyshev pseudospectral method for coupled Stokes-Darcy equations. A least squares functional is defined by summing up the weighted L-2-norm of residuals of the first order system for coupled Stokes-Darcy equations and that of Beavers-Joseph-Saffman interface conditions. Continuous and discrete homogeneous functionals are shown to be equivalent to a combination of weighted H(div) and H-1-norms for Stokes and Darcy equations. The spectral convergence for the Legendre and Chebyshev methods is derived. Some numerical experiments are demonstrated to validate our analysisopen0

Numerical solution for elliptic interface problems using spectral element collocation method

The aim of this paper is to solve an elliptic interface problem with a discontinuous coefficient and a singular source term by the spectral collocation method. First, we develop an algorithm for the elliptic interface problem defined in a rectangular domain with a line interface. By using the Gordon-Hall transformation, we generalize it to a domain with a curve boundary and a curve interface. The spectral element collocation method is then employed to complex geometries; that is, we decompose the domain into some nonoverlaping subdomains and the spectral collocation solution is sought in each subdomain. We give some numerical experiments to show efficiency of our algorithm and its spectral convergence.open0

An input relaxation model for evaluating congestion in fuzzy DEA

This paper develops a BCC input relaxation model for identifying input congestion as a severe form of inefficiency of decision-making units in fuzzy data envelopment analysis. The possibility approach is presented to obtain the models equivalent to fuzzy models. We use a one-model approach to determine input congestion based on the BCC input relaxation model. A numerical example is given to illustrate the proposed model and identify the congestion with precise and imprecise data. The proposed model is also used to determine the congestion in 16 hospitals using four fuzzy inputs and two fuzzy outputs with a symmetrical triangular membership function

Regularization of chaos by noise in electrically driven nanowire systems

The electrically driven nanowire systems are of great importance to nanoscience and engineering. Due to strong nonlinearity, chaos can arise, but in many applications it is desirable to suppress chaos. The intrinsically high-dimensional nature of the system prevents application of the conventional method of controlling chaos. Remarkably, we find that the phenomenon of coherence resonance, which has been well documented but for low-dimensional chaotic systems, can occur in the nanowire system that mathematically is described by two coupled nonlinear partial differential equations, subject to periodic driving and noise. Especially, we find that, when the nanowire is in either the weakly chaotic or the extensively chaotic regime, an optimal level of noise can significantly enhance the regularity of the oscillations. This result is robust because it holds regardless of whether noise is white or colored, and of whether the stochastic drivings in the two independent directions transverse to the nanowire are correlated or independent of each other. Noise can thus regularize chaotic oscillations through the mechanism of coherence resonance in the nanowire system. More generally, we posit that noise can provide a practical way to harness chaos in nanoscale systems.open

First order system least squares method for the interface problem of the Stokes equations

The first order system least squares method for the Stokes equation with discontinuous viscosity and singular force along the interface is proposed and analyzed. First, interface conditions are derived. By introducing a physical meaningful variable such as the velocity gradient, the Stokes equation transformed into a first order system of equations. Then the continuous and discrete norm least squares functionals using Legendre and Chebyshev weights for the first order system are defined. We showed that continuous and discrete homogeneous least squares functionals are equivalent to appropriate product norms. The spectral convergence of the proposed method is given. A numerical example is provided to support the method and its analysis.close0

LEAST SQUARES SPECTRAL METHOD FOR VELOCITY-FLUX FORM OF THE COUPLED STOKES-DARCY EQUATIONS

This paper develops least squares Legendre and Chebyshev spectral methods for the first order system of Stokes-Darcy equations. The least squares functional is based on the velocity-flux-pressure formulation with the enforcement of the Beavers-Joseph-Saffman interface conditions. Continuous and discrete homogeneous functionals are shown to be equivalent to the combination of weighted H1H1 and H(div)H(div)-norm for the Stokes and Darcy equations. The spectral convergence for the Legendre and Chebyshev methods are derived and numerical experiments are also presented to illustrate the analysis.clos

Analysis of least squares pseudo-spectral method for the interface problem of the Navier-Stokes equations

The aim of this paper is to propose and analyze the first order system least squares method for the incompressible Navier-Stokes equation with discontinuous viscosity and singular force along the interface as the earlier work of the first author on Stokes interface problem (Hessari, 2014). Interface conditions are derived, and the Navier-Stokes equation transformed into a first order system of equations by introducing velocity gradient as a new variable. The least squares functional is defined based on L2 norm applied to the first order system. Both discrete and continuous least squares functionals are put into the canonical form and the existence and uniqueness of branch of nonsingular solutions are shown. The spectral convergence of the proposed method is given. Numerical studies of the convergence are also provided.close0