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Finite-difference Approximations (finite-difference + approximation)

Distribution by Scientific Domains

Engineering	50%

Selected Abstracts

Finite-difference approximation for the u(k) -derivative with O(hM,k+1) accuracy: An analytical expression

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 5 2006
Vadim Dubovsky
Abstract An approximation of function u(x) as a Taylor series expansion about a point x0 at M points xi, , i = 1,2,,,M is used where xi are arbitrary-spaced. This approximation is a linear system for the derivatives u(k) with an arbitrary accuracy. An analytical expression for the inverse matrix A,1 where A = [Aik] = (xi , x0)k is found. A finite-difference approximation of derivatives u(k) of a given function u(x) at point x0 is derived in terms of the values u(xi). © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006 [source]

A New Numerical Approach for a Detailed Multicomponent Gas Separation Membrane Model and AspenPlus Simulation

CHEMICAL ENGINEERING & TECHNOLOGY (CET), Issue 7 2005
M. H. Murad Chowdhury
Abstract A new numerical solution approach for a widely accepted model developed earlier by Pan [1] for multicomponent gas separation by high-flux asymmetric membranes is presented. The advantage of the new technique is that it can easily be incorporated into commercial process simulators such as AspenPlusTM [2] as a user-model for an overall membrane process study and for the design and simulation of hybrid processes (i.e., membrane plus chemical absorption or membrane plus physical absorption). The proposed technique does not require initial estimates of the pressure, flow and concentration profiles inside the fiber as does in Pan's original approach, thus allowing faster execution of the model equations. The numerical solution was formulated as an initial value problem (IVP). Either Adams-Moulton's or Gear's backward differentiation formulas (BDF) method was used for solving the non-linear differential equations, and a modified Powell hybrid algorithm with a finite-difference approximation of the Jacobian was used to solve the non-linear algebraic equations. The model predictions were validated with experimental data reported in the literature for different types of membrane gas separation systems with or without purge streams. The robustness of the new numerical technique was also tested by simulating the stiff type of problems such as air dehydration. This demonstrates the potential of the new solution technique to handle different membrane systems conveniently. As an illustration, a multi-stage membrane plant with recycle and purge streams has been designed and simulated for CO2 capture from a 500,MW power plant flue gas as a first step to build hybrid processes and also to make an economic comparison among different existing separation technologies available for CO2 separation from flue gas. [source]

Third-order methods for first-order hyperbolic partial differential equations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 1 2004
T. A. Cheema
Abstract In this paper numerical methods for solving first-order hyperbolic partial differential equations are developed. These methods are developed by approximating the first-order spatial derivative by third-order finite-difference approximations and a matrix exponential function by a third-order rational approximation having distinct real poles. Then parallel algorithms are developed and tested on a sequential computer for an advection equation with constant coefficient and a non-linear problem. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Shape optimization of piezoelectric devices using an enriched meshfree method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2009
C. W. Liu
Abstract We present an enriched reproducing kernel particle method for shape sensitivity analysis and shape optimization of two-dimensional electromechanical domains. This meshfree method incorporates enrichment functions for better representation of discontinuous electromechanical fields across internal boundaries. We use cubic splines for delineating the geometry of internal/external domain boundaries; and the nodal coordinates and slopes of these splines at their control points become the design parameters. This approach enables smooth manipulations of bi-material interfaces and external boundaries during the optimization process. It also enables the calculation of displacement and electric-potential field sensitivities with respect to the design parameters through direct differentiation, for which we adopt the classical material derivative approach. We verify this implementation of sensitivity calculations against an exact solution to a variant of Lamé's problem, and also, finite-difference approximations. We follow a sequential quadratic programming approach to minimize the cost function; and demonstrate the utility of the overall technique through a model problem that involves the shape optimization of a piezoelectric fan. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Proximal point method for optimal control processes governed by ordinary differential equations,

ASIAN JOURNAL OF CONTROL, Issue 1 2010
Vadim Azhmyakov
Abstract This paper is concerned with the proximal-based approach to linear and finite-difference approximations of constrained convex optimal control problems. We consider control systems governed by ordinary differential equations in the presence of additional terminal/state inequalities and propose a numerical method derived from the proximal point algorithm. The aim of the paper is to study the convergence properties of the obtained conceptual algorithm and to show that it can be used to compute approximate optimal controls. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source]