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Trial Functions (trial + function)
Selected AbstractsComplex variable moving least-squares method: a meshless approximation techniqueINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2007K. M. Liew Abstract Based on the moving least-squares (MLS) approximation, we propose a new approximation method,the complex variable moving least-squares (CVMLS) approximation. With the CVMLS approximation, the trial function of a two-dimensional problem is formed with a one-dimensional basis function. The number of unknown coefficients in the trial function of the CVMLS approximation is less than in the trial function of the MLS approximation, and we can thus select fewer nodes in the meshless method that is formed from the CVMLS approximation than are required in the meshless method of the MLS approximation with no loss of precision. The meshless method that is derived from the CVMLS approximation also has a greater computational efficiency. From the CVMLS approximation, we propose a new meshless method for two-dimensional elasticity problems,the complex variable meshless method (CVMM),and the formulae of the CVMM for two-dimensional elasticity problems are obtained. Compared with the conventional meshless method, the CVMM has a greater precision and computational efficiency. For the purposes of demonstration, some selected numerical examples are solved using the CVMM. Copyright © 2006 John Wiley & Sons, Ltd. [source] An accurate few-parameter ground state wave function for the lithium atomINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 13 2009Nicolais L. Guevara Abstract A simple, seven-parameter trial function is proposed for a description of the ground state of the Lithium atom. It includes both spin functions. Inter-electronic distances appear in exponential form as well as in a pre-exponential factor, and the necessary energy matrix elements are evaluated by numerical integration in the space of the relative coordinates. Encouragingly accurate values of the energy and the cusp parameters as well as for some expectation values are obtained. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [source] Comment on the connected-moments polynomial approachINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 7 2008M. G. Marmorino Abstract Bartashevich has recently proposed two new methods for approximating eigenvalues of a Hamiltonian. The first method uses Hamiltonian moments generated from a trial function and his second method is a generalization of local energy methods. We show that the first method is equivalent to a variational one, a matrix eigenvalue problem using a Lanzcos subspace. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008 [source] Trefftz solutions for piezoelectricity by Lekhnitskii's formalism and boundary-collocation methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2006N. Sheng Abstract In this paper, a solution procedure for plane piezoelectricity is developed by Trefftz boundary-collocation method. Starting with the general plane piezoelectricity solution derived by Lekhnitskii's formalism, the basic sets of Trefftz functions which satisfy the homogeneous governing equations are derived. Moreover, special sets of Trefftz functions are derived for impermeable elliptical voids, impermeable sharp cracks and permeable sharp cracks with arbitrary orientations with respect to the material poling direction. The functions in the special sets satisfy not only the homogeneous governing equations but also the boundary conditions at the peripheries of the pertinent defects. By adopting Trefftz functions as the trial functions, multi-domain Trefftz boundary-collocation method is formulated. Numerical examples are presented to illustrate the efficacy of the formulation. Copyright © 2005 John Wiley & Sons, Ltd. [source] Shape functions for polygonal domains with interior nodesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2004Elisabeth Anna Malsch Abstract The presented formulation follows in a series of publications which outline a method for constructing test functions which satisfy essential edge conditions exactly. The method promises a complete solution, satisfying all of the requirements of a Ritz coordinate function. The influence of interior points on the domain solution is included in this construction. Similar to conformal bubble functions, the test functions are zero along the boundary and single valued only at the points they describe. Unlike the bubble function construction, the interior points can be located at any desired point in the domain. The resulting set of trial functions can satisfy the required global conditions including the exact reproduction of constant and linear fields. Copyright © 2004 John Wiley & Sons, Ltd. [source] Explicit calculation of smoothed sensitivity coefficients for linear problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2003R. A. Bia, ecki Abstract A technique of explicit calculation of sensitivity coefficients based on the approximation of the retrieved function by a linear combination of trial functions of compact support is presented. The method is applicable to steady state and transient linear inverse problems where unknown distributions of boundary fluxes, temperatures, initial conditions or source terms are retrieved. The sensitivity coefficients are obtained by solving a sequence of boundary value problems with boundary conditions and source term being homogeneous except for one term. This inhomogeneous term is taken as subsequent trial functions. Depending on the type of the retrieved function, it may appear on boundary conditions (Dirichlet or Neumann), initial conditions or the source term. Commercial software and analytic techniques can be used to solve this sequence of boundary value problems producing the required sensitivity coefficients. The choice of the approximating functions guarantees a filtration of the high frequency errors. Several numerical examples are included where the sensitivity coefficients are used to retrieve the unknown values of boundary fluxes in transient state and volumetric sources. Analytic, boundary-element and finite-element techniques are employed in the study. Copyright © 2003 John Wiley & Sons, Ltd. [source] Using symbolic computing in building probabilistic models for atomsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 1 2006Silviu Guiasu Abstract This article shows how symbolic computing and the mathematical formalism induced by maximizing entropy and minimizing the mean deviation from statistical equilibrium may be effectively applied to obtaining probabilistic models for the structure of atoms, using trial wave functions compatible with an average shell picture of the atom. The objective is not only to recover the experimental value of the ground state mean energy of the atom, but rather to better approximate the unknown parameters of these trial functions and to calculate both correlations between electrons and the amount of interdependence among different subsets of electrons of the atoms. The examples and numerical results refer to the hydrogen, helium, lithium, and beryllium atoms. The main computer programs, using the symbolic computing software MATHEMATICA, are also given. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006 [source] Dynamic Optimization in Chemical Processes Using Region Reduction Strategy and Control Vector Parameterization with an Ant Colony Optimization AlgorithmCHEMICAL ENGINEERING & TECHNOLOGY (CET), Issue 4 2008A. Asgari Abstract Two different approaches of the dynamic optimization for chemical process control engineering applications are presented. The first approach is based on discretizing both the control region and the time interval. This method, known as the Region Reduction Strategy (RRS), employs the previous solution in its next iteration to obtain more accurate results. Moreover, the procedure will continue unless the control region becomes smaller than a prescribed value. The second approach is called Control Vector Parameterization (CVP) and appears to have a large number of advantages. In this approach, control action is generated in feedback form, i.e., a set of trial functions of the state variables are expanded by multiplying by some unknown coefficients. By utilizing an optimization method, these coefficients are calculated. The Ant Colony Optimization (ACO) algorithm is employed as an optimization method in both approaches. [source] | ||||||||||