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Particular Solution (particular + solution)

Distribution by Scientific Domains

Engineering	40%
Mathematics and Statistics	33%
Physics and Astronomy	20%

Selected Abstracts

An improved meshless collocation method for elastostatic and elastodynamic problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 8 2008
P. 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]

Radial basis functions for solving near singular Poisson problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2003
C. S. Chen
Abstract In this paper, we investigate the use of radial basis functions for solving Poisson problems with a near-singular inhomogeneous source term. The solution of the Poisson problem is first split into two parts: near-singular solution and smooth solution. A method for evaluating the near-singular particular solution is examined. The smooth solution is further split into a particular solution and a homogeneous solution. The MPS-DRM approach is adopted to evaluate the smooth solution. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Exponential basis functions in solution of static and time harmonic elastic problems in a meshless style

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2010
B. Boroomand
Abstract In this paper, exponential basis functions (EBFs) are used in a boundary collocation style to solve engineering problems whose governing partial differential equations (PDEs) are of constant coefficient type. Complex-valued exponents are considered for the EBFs. Two-dimensional elasto-static and time harmonic elasto-dynamic problems are chosen in this paper. The solution procedure begins with first finding a set of appropriate EBFs and then considering the solution as a summation of such EBFs with unknown coefficients. The unknown coefficients are determined by the satisfaction of the boundary conditions through a collocation method with the aid of a consistent and complex discrete transformation technique. The basis and various forms of the transformation have been addressed and discussed. We shall propose several strategies for selection of EBFs with the aid of the basis explained for the transformation. While using the transformation, the number of EBFs should not necessarily be equal to (or less than) the number of boundary information data. A library of EBFs has also been presented for further use. The effect of body forces is included in the solution via construction of particular solution by the use of the discrete transformation and another series of EBFs. A number of sample problems are solved to demonstrate the capabilities of the method. It has been shown that the time harmonic problems with high wave number can be solved without much effort. The method, categorized in meshless methods, can be applied to many other problems in engineering mechanics and general physics since EBFs can easily be found for almost all problems with constant coefficient PDEs. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Nonlinear Riemann,Hilbert problems with circular target curves

MATHEMATISCHE NACHRICHTEN, Issue 9 2008
Christer Glader
Abstract The paper gives a systematic and self-contained treatment of the nonlinear Riemann,Hilbert problem with circular target curves |w , c | = r, sometimes also called the generalized modulus problem. We assume that c and r are Hölder continuous functions on the unit circle and describe the complete set of solutions w in the disk algebra H, , C and in the Hardy space H, of bounded holomorphic functions. The approach is based on the interplay with the Nehari problem of best approximation by bounded holomorphic functions. It is shown that the considered problems fall into three classes (regular, singular, and void) and we give criteria which allow to classify a given problem. For regular problems the target manifold is covered by the traces of solutions with winding number zero in a schlicht manner. Counterexamples demonstrate that this need not be so if the boundary condition is merely continuous. Paying special attention to constructive aspects of the matter we show how the Nevanlinna parametrization of the full solution set can be obtained from one particular solution of arbitrary winding number. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

The particular solutions for thin plates resting on Pasternak foundations under arbitrary loadings

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2010
Chia-Cheng Tsai
Abstract Analytical particular solutions of splines and monomials are obtained for problems of thin plate resting on Pasternak foundation under arbitrary loadings, which are governed by a fourth-order partial differential equation (PDEs). These analytical particular solutions are valuable when the arbitrary loadings are approximated by augmented polyharmonic splines (APS) constructed by splines and monomials. In our derivations, the real coefficient operator in the governing equation is decomposed into two complex coefficient operators whose particular solutions are known in literature. Then, we use the difference trick to recover the analytical particular solutions of the original operator. In addition, we show that the derived particular solution of spline with its first few directional derivatives are bounded as r , 0. This solution procedure may have the potential in obtaining analytical particular solutions of higher order PDEs constructed by products of Helmholtz-type operators. Furthermore, we demonstrate the usages of these analytical particular solutions by few numerical cases in which the homogeneous solutions are complementarily solved by the method of fundamental solutions (MFS). © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010 [source]

Correctness of a particular solution of inverse problem in rocking curve imaging

PHYSICA STATUS SOLIDI (A) APPLICATIONS AND MATERIALS SCIENCE, Issue 8 2009
Isabella Huber
Abstract Local lattice misorientations on crystalline substrates can be visualized by rocking curve imaging. Local deviations from Bragg peak positions are extracted from a series of digital topographs recorded by a CCD detector under different azimuths. Bragg peaks from surface regions such as crystallites with a larger local misorientation overlap on the detector, which requires a back-projection method in order to reconstruct the misorientation components on the sample surface from the measured angular position on the detector planes. From mathematical point of view, the reconstruction problem is an inverse problem. In this paper, we formulate the forward and back-projection problems and we prove the correctness of a particular solution. The usability of the method is demonstrated on a phantom data set. [source]

Exact solutions to the time-dependent supersymmetric Jaynes-Cummings model and the Chiao-Wu model

ANNALEN DER PHYSIK, Issue 3 2003
J.-Q. Shen
Abstract The present paper obtains the exact solutions to the time-dependent supersymmetric two-level multiphoton Jaynes-Cummings model and the Chiao-Wu model that describes the propagation of a photon inside an optical fiber. On the basis of the fact that the two-level multiphoton Jaynes-Cummings model possesses a supersymmetric structure, an invariant is constructed in terms of the supersymmetric generators by working in the sub-Hilbert-space corresponding to a particular eigenvalue of the conserved supersymmetric generators (i.e., the time-independent invariant). By constructing the effective Hamiltonian that describes the interaction of the photon with the medium of the optical fiber, it is further verified that the particular solution to the Schrödinger equation is the eigenfunction of the second-quantized momentum operator of photons field. This, therefore, means that the explicit expression (rather than the hidden form that involves the chronological product) for the time-evolution operator of wave function is obtained by means of the invariant theories. [source]

Emerging uses of SIP in service provider networks

BELL LABS TECHNICAL JOURNAL, Issue 1 2003
Guy J. Zenner
The session initiation protocol (SIP) has emerged as a viable protocol for providing numerous services within today's networks. SIP was closely modeled after http to make it an easily extensible protocol that could provide connectivity in new converged Internet protocol (IP) networks. The inherent extensibility of SIP has allowed SIP to be used in many ways not envisioned by its creators. What started as a simple protocol for setting up a media stream between two endpoints has since found numerous seemingly unrelated uses. With many solutions using SIP being proposed and implemented, it is often hard to determine how best to use SIP for a particular solution. The purpose of this paper is to give the reader a framework for categorizing various SIP capabilities through the concept of usage models and to help the reader understand the various ways SIP can be used in both evolutionary and revolutionary ways in real-world networks. This paper assumes the reader has a basic understanding of SIP and its inner workings. © 2003 Lucent Technologies Inc. [source]

The radial integration method applied to dynamic problems of anisotropic plates

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 9 2007
E. L. Albuquerque
Abstract In this paper, the radial integration method is applied to transform domain integrals into boundary integrals in a boundary element formulation for anisotropic plate bending problems. The inertial term is approximated with the use of radial basis functions, as in the dual reciprocity boundary element method. The transformation of domain integrals into boundary integrals is based on pure mathematical treatments. Numerical results are presented to verify the validity of this method for static and dynamic problems and a comparison with the dual reciprocity boundary element method is carried out. Although the proposed method is more time-consuming, it presents some advantages over the dual reciprocity boundary element method as accuracy and the absence of particular solutions in the formulation. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Krylov precise time-step integration method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2006
T. C. Fung
Abstract An efficient precise time-step integration (PTI) algorithm to solve large-scale transient problems is presented in this paper. The Krylov subspace method and the Padé approximations are applied to modify the original PTI algorithm in order to improve the computational efficiency. Both the stability and accuracy characteristics of the resultant algorithms are investigated. The efficiency can be further improved by expanding the dimension to avoid the computation of the particular solutions. The present algorithm can also be extended to tackle nonlinear problems without difficulty. Two numerical examples are given to illustrate the highly accurate and efficient algorithm. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Effective condition number of Trefftz methods for biharmonic equations with crack singularities

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 2 2009
Zi-Cai Li
Abstract The paper presents the new stability analysis for the collocation Trefftz method (CTM) for biharmonic equations, based on the new effective condition number Cond_eff. The Trefftz method is a special spectral method with the particular solutions as admissible functions, and it has been widely used in engineering. Three crack models in Li et al. (Eng. Anal. Boundary Elements 2004; 28:79,96; Trefftz and Collocation Methods. WIT Publishers: Southampton, Boston, 2008) are considered, and the bounds of Cond_eff and the traditional condition number Cond are derived, to give the polynomial and the exponential growth rates, respectively. The stability analysis explains well the numerical experiments. Hence, the new Cond_eff is more advantageous than Cond. Besides since the bounds of Cond_eff and Cond involve the estimation of the minimal singular value ,min of the discrete matrix F, and since the estimation of ,min is challenging and difficult, the proof for lower bounds of ,min in this paper is important and intriguing. Copyright © 2008 John Wiley & Sons, Ltd. [source]