The Local Taylor Polynomial (LTP) method treats fields and sources as local analytic polynomials for rapid numerical solution of PDE's. Knowledge of the source polynomial would allow sources to be treated analytic...
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ISBN:
(纸本)9781467312257;9781467312226
The Local Taylor Polynomial (LTP) method treats fields and sources as local analytic polynomials for rapid numerical solution of PDE's. Knowledge of the source polynomial would allow sources to be treated analytically in LTP formulas, since the derivatives follow directly for polynomial forms. Aside from idealized cases, such information is seldom available;however, use of macro-particles with finite polynomial shape functions for charge and current deposition can make analytic treatment possible for general cases. The macro-particle polynomial coefficients can be used directly in LTP solution formulas. This scheme allows one to choose a representation of particles that enables high fidelity with fewer particles compared to traditional particle methods, since the polynomials can include information such as transverse profile information from a beam, for example. This paper presents a simple polynomial form for representing macro-particles in numerical simulations. The particle shape must be continuous and differentiable to a specified order, bounded in size and magnitude, zero in magnitude and derivatives at the edges, symmetric, positive definite, with analytic coefficients. Two key properties for use in LTP will be demonstrated: zero derivatives at the particle boundary and analytically computable coefficients.
The inverse problems are formulated for generalized Helmholtz equation describing propagation of acoustics waves in inhomogeneous anisotropic medium. These problems are connected with constructing nonscattering shells...
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The inverse problems are formulated for generalized Helmholtz equation describing propagation of acoustics waves in inhomogeneous anisotropic medium. These problems are connected with constructing nonscattering shells filled with anisotropic fluid. For solving the inverse problems we apply the nonlinear optimization techniques. Based on this approach we formulate the general control problem for the Helmholtz equation under consideration. The control problem consists of minimization of a suitable cost functional depending on the state(acoustic pressure) and unknown functions(controls). The optimality system for the general control problem is derived, the sufficient conditions for data which provide a local stability and uniqueness of control problems under study for concrete tracking-type cost functionals are discussed. The efficient numerical algorithm of solving control problem under study based on Newton's method of solving nonlinear equations and finite element for Helmholtz boundary value problems is proposed.
In this paper we present an implementation of a partly Derivative-Free Optimization (DFO) algorithm for production optimization of a simulated multi-phase flow network. The network consists of well and pipeline simula...
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In this paper we present an implementation of a partly Derivative-Free Optimization (DFO) algorithm for production optimization of a simulated multi-phase flow network. The network consists of well and pipeline simulators, considered to be black-box models without available gradients. The algorithm utilizes local approximations as surrogate models for the complex simulators. A Mixed Integer Nonlinear Programming (MINLP) problem is built from the surrogate models and the known structure of the flow network. The core of the algorithm is IBM's MINLP solver Bonmin, which is run iteratively to solve optimization problems cast in terms of surrogate models. At each iteration the surrogate models are updated to fit local data points from the simulators. The algorithm is tested on an artificial subsea network modeled in FlowManager ™ , a multi-phase flow simulator from FMC Technologies. The results for this special case show that the algorithm converges to a point where the surrogate models fit the simulator, and they both share the optimum.
A novel algorithm for the retrieval of the spatial mutual coherence function of the optical field of a light beam in the quasimonochromatic approximation is presented. The algorithm only requires that the intensity di...
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A novel algorithm for the retrieval of the spatial mutual coherence function of the optical field of a light beam in the quasimonochromatic approximation is presented. The algorithm only requires that the intensity distribution is known in a finite number of transverse planes along the beam. The retrieval algorithm is based on the observation that a partially coherent field can be represented as an ensemble of coherent fields. Each field in the ensemble is propagated with coherent methods between neighboring planes, and the ensemble is then subjected to amplitude restrictions, much in the same way as in conventional phase recovery algorithms for coherent fields. The proposed algorithm is evaluated both for one- and two-dimensional fields using numerical simulations. (C) 2007 Optical Society of America.
We present a new algorithm for computing the Lyapunov exponents spectrum based on a matrix differential equation. The approach belongs to the so-called continuous type, where the rate of expansion of perturbations is ...
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We present a new algorithm for computing the Lyapunov exponents spectrum based on a matrix differential equation. The approach belongs to the so-called continuous type, where the rate of expansion of perturbations is obtained for all times, and the exponents are reached as the limit at infinity. It does not involve exponentially divergent quantities so there is no need of rescaling or realigning of the solution. We show the algorithm's advantages and drawbacks using mainly the example of a particle moving between two contracting walls. (C) 2011 Elsevier B.V. All rights reserved.
The article contains an exposition of the basic idea of construction of numerical algorithms based upon the several local approximations by linear polynomials for every sought-for function of dynamic problems of solid...
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The article contains an exposition of the basic idea of construction of numerical algorithms based upon the several local approximations by linear polynomials for every sought-for function of dynamic problems of solids. We discuss also some problems of determination of physical and geometrical characteristics of layered inhomogeneous medium.
The occurrence of continental delamination has been proposed for a number of areas characterized by highly variable geodynamic settings. In this study we present results of numerical simulations considering different ...
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The occurrence of continental delamination has been proposed for a number of areas characterized by highly variable geodynamic settings. In this study we present results of numerical simulations considering different initial setups, representative for geodynamic scenarios where delamination could potentially develop. To mimic a post-collisional orogenic scenario we have designed an initial state characterized by the presence of an area of orogenic lithosphere, with both crustal and lithospheric roots. In a second setup, we have considered a lithospheric root representative of a remnant slab with a flat overlying crust. We focus on predicted evolution of surface and near-surface observables, namely the crustal structure, surface heat flow and isostatic and dynamic topography evolution. Our results show that a high density orogenic lower crust, likely related to the presence of eclogite, significantly accelerates the sinking of the lithospheric mantle. The pattern of local isostatic elevation is characterized by laterally migrating surface uplift/subsidence. This pattern is shown to be little sensitive to lower crust density variations. In contrast, predicted dynamic topography is more sensitive to these changes, and shows surface subsidence adjacent to the delaminating lithospheric mantle for the model with a high density lower crust, and surface uplift above the slab for a model with a less dense lower crust. The reason for uplift in this second model is that the effect of the positive buoyancy of the thickened crust overwhelms the effect of negative buoyancy of the slowly sinking lithospheric mantle. We infer from our modeling that there is not a specific characteristic pattern of topography changes associated with delamination, but it depends on the interplay between highly variable factors, as slab sinking velocity, asthenospheric upwelling and changes in crustal thickness. (C) 2010 Elsevier B.V. All rights reserved.
numerical methods are used to find exact solution for the nonlinear differential equations. In the last decades Iterative methods have been used for solving fractional differential equations. In this paper, the Homoto...
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numerical methods are used to find exact solution for the nonlinear differential equations. In the last decades Iterative methods have been used for solving fractional differential equations. In this paper, the Homotopy perturbation method has been successively applied for finding approximate analytical solutions of the fractional nonlinear Klein-Cordon equation can be used as numerical algorithm. The behavior of solutions and the effects of different values of fractional order a are shown graphically. Some examples are given to show ability of the method for solving the fractional nonlinear equation. Crown Copyright (C) 2010 Published by Elsevier B.V. All rights reserved.
Generalizing the notion of an eigenvector, invariant subspaces are frequently used in the context of linear eigenvalue problems, leading to conceptually elegant and numerically stable formulations in applications that...
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Generalizing the notion of an eigenvector, invariant subspaces are frequently used in the context of linear eigenvalue problems, leading to conceptually elegant and numerically stable formulations in applications that require the computation of several eigenvalues and/or eigenvectors. Similar benefits can be expected for polynomial eigenvalue problems, for which the concept of an invariant subspace needs to be replaced by the concept of an invariant pair. Little has been known so far about numerical aspects of such invariant pairs. The aim of this paper is to fill this gap. The behavior of invariant pairs under perturbations of the matrix polynomial is studied and a first-order perturbation expansion is given. From a computational point of view, we investigate how to best extract invariant pairs from a linearization of the matrix polynomial. Moreover, we describe efficient refinement procedures directly based on the polynomial formulation. numerical experiments with matrix polynomials from a number of applications demonstrate the effectiveness of our extraction and refinement procedures. (C) 2010 Elsevier Inc. All rights reserved.
In this paper, we study a dimensionally scaled helium atom model for excited states of helium. The mathematical analysis of the corresponding effective energy potential is presented. Two simple numerical algorithms ar...
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In this paper, we study a dimensionally scaled helium atom model for excited states of helium. The mathematical analysis of the corresponding effective energy potential is presented. Two simple numerical algorithms are developed for the computation of the excited states of helium. Comparison between our numerical results and those in the existing literature is given to indicate the accuracy and efficiency of the proposed algorithms. (C) 2010 Elsevier B.V. All rights reserved.
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