A numerical study is performed to investigate the effect of height-to-width aspect ratio, Grashof number, and Schmidt number on the Double-diffusive convection of a fluid contained in a rectangular cavity with partially thermally active side walls. The active part of the left side wall is at a higher temperature and concentration than that of the right side wall. The length of the thermally act...

The red/black ordering scheme is often used to increase the parallelism of iterative methods for solving elliptic partial differential equations (PDEs). However, the convergence rates are also affected, often adversely. This paper provides a unified approach, called the two-color Fourier analysis, to study the convergence rates of iterative algorithms for elliptic problems with the red/black or...

Successive over-relaxation (SOR) is a computationally intensive, yet extremely important iterative solver for solving linear systems. Due to recent trends of exponential growth in amount of data generated and increasing problem sizes, serial platforms have proved to be insufficient in providing the required computational power. In this paper, we present parallel implementations of red-black SOR...

In this paper, we propose efficient numerical techniques for Butterworth filtering and implicit fairing of large irregular triangle meshes, where the corresponding filters are rational polynomials and the resulting large linear systems need to be solved iteratively. We show that significant speed-up can be achieved for Butterworth filtering by factorizing the linear system in the complex domain...

The convergence rates of the explicit group methods derived from the standard and skewed (rotated) finite difference operators depend on the spectral properties of the coefficient matrices resulted from these group discretization formulas. By applying appropriate preconditioner, we may transform the resulting linear system into another equivalent system that has the same solution, but has a bet...

We investigate new algorithms for the solution of nonseparable elliptic equations in irregular domains. Such equations arise frequently in fluid dynamics and other branches of continuum mechanics. We show that the combined use of a fast iteration (involving the use of fast Poisson solvers (FPS) in rectangular domains) and the capacitance matrix method can lead to algorithms which are several ti...

We introduce the standard fourth order compact finite difference formulae. We show how these formulae apply in the special case of the heat equation. It is well known that the American option pricing problem may be formulated in terms of the Black Scholes partial differential equation (PDE) together with a free boundary condition. Standard methods allow this problem to be transformed into a mov...

In this paper, we apply the  homotopy analysis method (HAM) for solving fuzzy  linear systems and present  the necessary and sufficient conditions for the convergence of series solution obtained via the HAM. Also, we present a new criterion for choosing a proper value of convergence-control parameter $hbar$ when the HAM is applied to linear system of equations. Comparisons are made between the ...

A Poisson-type equation arising in a commonly used numerical weather forecasting model is solved using an alternating direction implicit (ADI) method with Wachpress optimum parameters on a trapezoidal domain which coincides with the operational forecast domain. Various optimum parameter sequences were obtained for the corresponding squares which enclose the region under consideration, computati...