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Boundary Points (boundary + point)
Selected AbstractsCarathéodory,Julia type conditions and symmetries of boundary asymptotics for analytic functions on the unit diskMATHEMATISCHE NACHRICHTEN, Issue 11 2009Vladimir Bolotnikov Abstract It is shown that the following conditions are equivalent for the generalized Schur class functions at a boundary point t0 , ,,: 1) Carathéodory,Julia type condition of order n; 2) agreeing of asymptotics of the original function from inside and of its continuation by reflection from outside of the unit disk ,, up to order 2n + 1; 3) t0 -isometry of the coefficients ofthe boundary asymptotics; 4) a certain structured matrix , constructed from these coefficients being Hermitian. It is also shown that for an arbitrary analytic function, properties 2), 3), 4) are still equivalent to each other and imply 1) (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Reliability Analysis of Technical Systems/Structures by means of Polyhedral Approximation of the Safe/Unsafe DomainGAMM - MITTEILUNGEN, Issue 2 2007K. Marti Abstract Reliability analysis of technical structures and systems is based on an appropriate (limit) state function separating the safe and unsafe/states in the space of random parameters. Starting with the survival conditions, hence, the state equation and the condition for the admissibility of states, an optimizational representation of the state function can be given in terms of the minimum function of a certainminimization problem. Selecting a certain number of boundary points of the safe/unsafe domain, hence, on the limit state surface, the safe/unsafe domain is approximated by a convex polyhedron defined by the intersection of the half spaces in the parameter space generated by the tangent hyperplanes to the safe/unsafe domain at the selected boundary points on the limit state surface. The resulting approximative probability functions are then defined by means of probabilistic linear constraints in the parameter space, where, after an appropriate transformation, the probability distribution of the parameter vector can be assumed to be normal with zero mean vector and unit covariance matrix. Working with separate linear constraints, approximation formulas for the probability of survival of the structure are obtained immediately. More exact approximations are obtained by considering joint probability constraints, which, in a second approximation step, can be evaluated by using probability inequalities and/or discretization of the underlying probability distribution. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] An accurate integral-based scheme for advection,diffusion equationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2001Tung-Lin Tsai Abstract This paper proposes an accurate integral-based scheme for solving the advection,diffusion equation. In the proposed scheme the advection,diffusion equation is integrated over a computational element using the quadratic polynomial interpolation function. Then elements are connected by the continuity of first derivative at boundary points of adjacent elements. The proposed scheme is unconditionally stable and results in a tridiagonal system of equations which can be solved efficiently by the Thomas algorithm. Using the method of fractional steps, the proposed scheme can be extended straightforwardly from one-dimensional to multi-dimensional problems without much difficulty and complication. To investigate the computational performances of the proposed scheme five numerical examples are considered: (i) dispersion of Gaussian concentration distribution in one-dimensional uniform flow; (ii) one-dimensional viscous Burgers equation; (iii) pure advection of Gaussian concentration distribution in two-dimensional uniform flow; (iv) pure advection of Gaussian concentration distribution in two-dimensional rigid-body rotating flow; and (v) three-dimensional diffusion in a shear flow. In comparison not only with the QUICKEST scheme, the fully time-centred implicit QUICK scheme and the fully time-centred implicit TCSD scheme for one-dimensional problem but also with the ADI-QUICK scheme, the ADI-TCSD scheme and the MOSQUITO scheme for two-dimensional problems, the proposed scheme shows convincing computational performances. Copyright © 2001 John Wiley & Sons, Ltd. [source] A new fast hybrid adaptive grid generation technique for arbitrary two-dimensional domainsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2010Mohamed S. Ebeida Abstract This paper describes a new fast hybrid adaptive grid generation technique for arbitrary two-dimensional domains. This technique is based on a Cartesian background grid with square elements and quadtree decomposition. A new algorithm is introduced for the distribution of boundary points based on the curvature of the domain boundaries. The quadtree decomposition is governed either by the distribution of the boundary points or by a size function when a solution-based adaptive grid is desired. The resulting grid is quaddominant and ready for the application of finite element, multi-grid, or line-relaxation methods. All the internal angles in the final grid have a lower bound of 45° and an upper bound of 135°. Although our main interest is in grid generation for unsteady flow simulations, the technique presented in this paper can be employed in many other fields. Several application examples are provided to illustrate the main features of this new approach. Copyright © 2010 John Wiley & Sons, Ltd. [source] A promising boundary element formulation for three-dimensional viscous flowINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2005Xiao-Wei Gao Abstract In this paper, a new set of boundary-domain integral equations is derived from the continuity and momentum equations for three-dimensional viscous flows. The primary variables involved in these integral equations are velocity, traction, and pressure. The final system of equations entering the iteration procedure only involves velocities and tractions as unknowns. In the use of the continuity equation, a complex-variable technique is used to compute the divergence of velocity for internal points, while the traction-recovery method is adopted for boundary points. Although the derived equations are valid for steady, unsteady, compressible, and incompressible problems, the numerical implementation is only focused on steady incompressible flows. Two commonly cited numerical examples and one practical pipe flow problem are presented to validate the derived equations. Copyright © 2004 John Wiley & Sons, Ltd. [source] A three-dimensional mesh refinement algorithm with low boundary reflections for the finite-difference time-domain simulation of metallic structuresINTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 3 2010W. H. P. Pernice Abstract We present a method for including areas of high grid density into a general grid for the finite-difference time-domain method in three dimensions. Reflections occurring at the boundaries separating domains of different grid size are reduced significantly by introducing appropriate interpolation methods for missing boundary points. Several levels of refinement can be included into one calculation using a hierarchical refinement architecture. The algorithm is implemented with an auxiliary differential equation technique that allows for the simulation of metallic structures. We illustrate the performance of the algorithm through the simulation of metal nano-particles included in a coarser grid and by investigating gold optical antennas. Copyright © 2009 John Wiley & Sons, Ltd. [source] On a quadrature algorithm for the piecewise linear wavelet collocation applied to boundary integral equationsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 11 2003Andreas Rathsfeld Abstract In this paper, we consider a piecewise linear collocation method for the solution of a pseudo-differential equation of order r=0, ,1 over a closed and smooth boundary manifold. The trial space is the space of all continuous and piecewise linear functions defined over a uniform triangular grid and the collocation points are the grid points. For the wavelet basis in the trial space we choose the three-point hierarchical basis together with a slight modification near the boundary points of the global patches of parametrization. We choose linear combinations of Dirac delta functionals as wavelet basis in the space of test functionals. For the corresponding wavelet algorithm, we show that the parametrization can be approximated by low-order piecewise polynomial interpolation and that the integrals in the stiffness matrix can be computed by quadrature, where the quadrature rules are composite rules of simple low-order quadratures. The whole algorithm for the assembling of the matrix requires no more than O(N [logN]3) arithmetic operations, and the error of the collocation approximation, including the compression, the approximative parametrization, and the quadratures, is less than O(N,(2,r)/2). Note that, in contrast to well-known algorithms by Petersdorff, Schwab, and Schneider, only a finite degree of smoothness is required. In contrast to an algorithm of Ehrich and Rathsfeld, no multiplicative splitting of the kernel function is required. Beside the usual mapping properties of the integral operator in low order Sobolev spaces, estimates of Calderón,Zygmund type are the only assumptions on the kernel function. Copyright © 2003 John Wiley & Sons, Ltd. [source] Generating Pareto-optimal boundary points in multiparty negotiations using constraint proposal methodNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 3 2001Pirja Heiskanen Abstract In this paper a constraint proposal method is developed for computing Pareto-optimal solutions in multiparty negotiations over continuous issues. Constraint proposal methods have been previously studied in a case where the decision set is unconstrained. Here we extend the method to situations with a constrained decision set. In the method the computation of the Pareto-optimal solutions is decentralized so that the DMs do not have to know each others' value functions. During the procedure they have to indicate their optimal solutions on different sets of linear constraints. When the optimal solutions coincide, the common optimum is a candidate for a Pareto-optimal point. The constraint proposal method can be used to generate either one Pareto-optimal solution dominating the status quo solution or several Pareto-optimal solutions. In latter case a distributive negotiation among the efficient points can be carried out afterwards. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 210,225, 2001 [source] Compact difference schemes for heat equation with Neumann boundary conditionsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2009Zhi-Zhong Sun Abstract In this article, two recent proposed compact schemes for the heat conduction problem with Neumann boundary conditions are analyzed. The first difference scheme was proposed by Zhao, Dai, and Niu (Numer Methods Partial Differential Eq 23, (2007), 949,959). The unconditional stability and convergence are proved by the energy methods. The convergence order is O(,2 + h2.5) in a discrete maximum norm. Numerical examples demonstrate that the convergence order of the scheme can not exceeds O(,2 + h3). An improved compact scheme is presented, by which the approximate values at the boundary points can be obtained directly. The second scheme was given by Liao, Zhu, and Khaliq (Methods Partial Differential Eq 22, (2006), 600,616). The unconditional stability and convergence are also shown. By the way, it is reported how to avoid computing the values at the fictitious points. Some numerical examples are presented to show the theoretical results. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 [source] Numerical solution to a linearized KdV equation on unbounded domainNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2008Chunxiong Zheng Abstract Exact absorbing boundary conditions for a linearized KdV equation are derived in this paper. Applying these boundary conditions at artificial boundary points yields an initial-boundary value problem defined only on a finite interval. A dual-Petrov-Galerkin scheme is proposed for numerical approximation. Fast evaluation method is developed to deal with convolutions involved in the exact absorbing boundary conditions. In the end, some numerical tests are presented to demonstrate the effectiveness and efficiency of the proposed method.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008 [source] Moving boundary vortices for a thin-film limit in micromagneticsCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 5 2005Roger Moser We study the limiting behavior of solutions of the Landau-Lifshitz-Gilbert equation belonging to thin films of ferromagnetic materials. In the appropriate time scale and under reasonable conditions, there is a subsequence converging to a map that has vortices at two boundary points. The vortices move Hölder-continuously in time, and the map satisfies a formal Euler-Lagrange equation away from the vortices. © 2004 Wiley Periodicals, Inc. [source] | |||||||||||||