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Local Approximation (local + approximation)
Selected AbstractsComparison of two wave element methods for the Helmholtz problemINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 1 2009T. Huttunen Abstract In comparison with low-order finite element methods (FEMs), the use of oscillatory basis functions has been shown to reduce the computational complexity associated with the numerical approximation of Helmholtz problems at high wave numbers. We compare two different wave element methods for the 2D Helmholtz problems. The methods chosen for this study are the partition of unity FEM (PUFEM) and the ultra-weak variational formulation (UWVF). In both methods, the local approximation of wave field is computed using a set of plane waves for constructing the basis functions. However, the methods are based on different variational formulations; the PUFEM basis also includes a polynomial component, whereas the UWVF basis consists purely of plane waves. As model problems we investigate propagating and evanescent wave modes in a duct with rigid walls and singular eigenmodes in an L-shaped domain. Results show a good performance of both methods for the modes in the duct, but only a satisfactory accuracy was obtained in the case of the singular field. On the other hand, both the methods can suffer from the ill-conditioning of the resulting matrix system. Copyright © 2008 John Wiley & Sons, Ltd. [source] An improved meshless collocation method for elastostatic and elastodynamic problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 8 2008P. H. Wen Abstract Meshless methods for solving differential equations have become a promising alternative to the finite element and boundary element methods. In this paper, an improved meshless collocation method is presented for use with either moving least square (MLS) or compactly supported radial basis functions (RBFs). A new technique referred to as an indirect derivative method is developed and compared with the direct derivative technique used for evaluation of second-order derivatives and higher-order derivatives of the MLS and RBF shape functions at the field point. As the derivatives are obtained from a local approximation (MLS or compact support RBFs), the new method is computationally economical and efficient. Neither the connectivity of mesh in the domain/boundary nor integrations with fundamental/particular solutions is required in this approach. The accuracy of the two techniques to determine the second-order derivative of shape function is assessed. The applications of meshless method to two-dimensional elastostatic and elastodynamic problems have been presented and comparisons have been made with benchmark analytical solutions. Copyright © 2007 John Wiley & Sons, Ltd. [source] Meshfree point collocation method for elasticity and crack problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2004Sang-Ho Lee Abstract A generalized diffuse derivative approximation is combined with a point collocation scheme for solid mechanics problems. The derivatives are obtained from a local approximation so their evaluation is computationally very efficient. This meshfree point collocation method has other advantages: it does not require special treatment for essential boundary condition nor the time-consuming integration of a weak form. Neither the connectivity of the mesh nor differentiability of the weight function is necessary. The accuracy of the solutions is exceptional and generally exceeds that of element-free Galerkin method with linear basis. The performance and robustness are demonstrated by several numerical examples, including crack problems. Copyright © 2004 John Wiley & Sons, Ltd. [source] Fluid,solid interaction problems with thermal convection using the immersed element-free Galerkin methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2010Claudio M. Pita Abstract In this work, the immersed element-free Galerkin method (IEFGM) is proposed for the solution of fluid,structure interaction (FSI) problems. In this technique, the FSI is represented as a volumetric force in the momentum equations. In IEFGM, a Lagrangian solid domain moves on top of an Eulerian fluid domain that spans over the entire computational region. The fluid domain is modeled using the finite element method and the solid domain is modeled using the element-free Galerkin method. The continuity between the solid and fluid domains is satisfied by means of a local approximation, in the vicinity of the solid domain, of the velocity field and the FSI force. Such an approximation is achieved using the moving least-squares technique. The method was applied to simulate the motion of a deformable disk moving in a viscous fluid due to the action of the gravitational force and the thermal convection of the fluid. An analysis of the main factors affecting the shape and trajectory of the solid body is presented. The method shows a distinct advantage for simulating FSI problems with highly deformable solids. Copyright © 2009 John Wiley & Sons, Ltd. [source] Time-dependent density functional theory calculations of X-ray absorptionINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 4-5 2003J. J. Rehr Abstract There has been dramatic progress in recent years both in calculations and in the interpretation of X-ray absorption spectra (XAS). Often an independent-electron approximation with final state potentials is adequate. However, for soft X-rays (i.e., energies less than about 1 keV) local field effects can be important. Such local fields arise from the dynamic screening of both the external X-ray field and the coupling to the core hole created in the absorption process. These effects require a theory that goes beyond the independent-electron approximation. We developed an efficient approach for treating such effects in molecules and solids based on a generalization of time-dependent density functional theory (TDDFT), with a local approximation for the screening response. The approach has been implemented in our self-consistent, real-space Green's function code FEFF8 in terms of screened dipole transition matrix elements. Typical results are discussed for the XAS of the N4,5 edges of solid Xe and for the L2,3 edges of 3d transition metals. Our approach accounts for the deviations of the L3/L2 intensity branching ratio from the 2:1 value of the independent electron approximation. For the N4,5 edges of Xe, the approach also accounts for the observed fine structure. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003 [source] Novel strategies to approximate probability trees in penniless propagationINTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 2 2003Andrés Cano In this article we introduce some modifications over the Penniless propagation algorithm. When a message through the join tree is approximated, the corresponding error is quantified in terms of an improved information measure, which leads to a new way of pruning several values in a probability tree (representing a message) by a single one, computed from the value stored in the tree being pruned but taking into account the message stored in the opposite direction. Also, we have considered the possibility of replacing small probability values by zero. Locally, this is not an optimal approximation strategy, but in Penniless propagation many different local approximations are carried out in order to estimate the posterior probabilities and, as we show in some experiments, replacing by zeros can improve the quality of the final approximations. © 2003 Wiley Periodicals, Inc. [source] | ||||||||||