3 edition of Spectral methods for exterior elliptic problems found in the catalog.
Spectral methods for exterior elliptic problems
by National Aeronautics and Space Administration, Langley Research Center in Hampton, Va
Written in English
|Statement||C. Canuto, S.I. Hariharan, L. Lustman|
|Series||NASA contractor report -- 172380, ICASE report -- no. 84-21|
|Contributions||Hariharan, S. I, Lustman, L, Langley Research Center, Institute for Computer Applications in Science and Engineering|
|The Physical Object|
A Petrov-Galerkin Spectral Element Method for Fractional Elliptic Problems Ehsan Kharazmi and Mohsen Zayernouri Department of Computational Mathematics, Science, and Engineering & Department of Mechanical Engineering Problem Definition Fractional Helmholtz equation, subjected to Dirichlet boundary conditions. This book presents the key ideas along with many figures, examples, and short, elegant MATLAB programs for readers to adapt to their own needs. It covers ODE and PDE boundary value problems, eigenvalues and pseudospectra, linear and nonlinear waves, and numerical quadrature.
Spectral Method for Acoustic Scattering in Elliptic Domains three-dimensional acoustic scattering [5,9,11,12]. The method has proven to be very ef-ﬁcient for obstacles that can be considered as a perturbation of a disk in 2-D or a sphere in 3-D. While in principle the algorithms in [5,9]can be applied to elongated scatters (e.g. A SEQUENTIAL SPECTRAL METHOD FOR NONLINEAR ELLIPTIC INTEGRO-DIFFERENTIAL EQUATIONS M. J. GANDER, A. MANSOORA AND K. K. TAM ABSTRACT. A sequential spectral method (SSM) is a spectral method in which the unknown coeﬃcients of the ap-proximate spectral expansion are computed sequentially, one at a time, instead of simultaneously, like in a Cited by: 1.
Spectral method are global method, generally a faster method and is more accurate for su ciently regular geometries than other two methods . In dealing with PDEs let say time dependent, the solution with spectral method is obtained by writing it in the summation . Finally, the book presents 2D exterior (radiation and scattering) problems and sample solutions using coupled hp finite/infinite elements. In "Computing with hp-Adaptive Finite Elements", the information provided, including many unpublished details, aids in solving elliptic and Maxwell problems. (source: Nielsen Book Data).
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This paper deals with spectral approximations for exterior elliptic problems in two dimensions. As in the conventional finite difference or finite element methods, it is found that the accuracy of the numerical solutions is limited by the order of the numerical farfield conditions.
We introduce a spectral boundary treatment at infinity, which is compatible with the “infinite order Cited by: Get this from a library. Spectral methods for exterior elliptic problems.
[C Canuto; S I Hariharan; L Lustman; Langley Research Center.; Institute for Computer Applications in Science and Engineering.]. A spectral method is described for solving coupled elliptic problems on an interior and an exterior domain.
The method is formulated and tested on the two-dimensional interior Poisson and exterior Laplace problems, whose solutions and their normal derivatives are required to Cited by: 1. A spectral method is Spectral methods for exterior elliptic problems book for solving coupled elliptic problems on an interior and an exterior domain.
The method is formulated and tested on the two-dimensional interior Poisson and exterior. There is a rich literature on spectral methods for solving partial di⁄erential equations.
From the more recent literature, we cite , , , and . Their bibliographies contain references to earlier papers on spectral methods. The present paper is a continuation of the work in  in which a spectral method is.
Perturbation of essential spectra of exterior elliptic problems. arXivv2 Article (PDF Available) in Applicable Analysis 90(1) November with 14 Reads How we measure 'reads'. Spectral Problems Associated with Corner Singularities of Solutions to Elliptic Equations (Mathematical Surveys & Monographs) [V.
Kozlov] on *FREE* shipping on qualifying offers. This book focuses on the analysis of eigenvalues and eigenfunctions that describe singularities of solutions to elliptic boundary value problems in domains with corners and by: Stable and efficient spectral methods using Laguerre functions are proposed and analyzed for model elliptic equations on regular unbounded domains.
It is shown that spectral-Galerkin approximations based on Laguerre functions are stable and convergent with spectral accuracy in the usual (not weighted) Sobolev spaces. Efficient, accurate, and well-conditioned algorithms using Laguerre functions Cited by: We provide a framework for the analysis of a large class of discontinuous methods for second-order elliptic problems.
It allows for the understanding and comparison of most of the discontinuous Galerkin methods that have been proposed over the past three decades for the numerical treatment of Cited by: This paper describes spectral representations and approximations of solutions of second order, self-adjoint, linear elliptic boundary value problems on exterior regions U in R N, for N ≥ geneous Dirichlet, Robin and Neumann boundary conditions are by: 9.
Get this from a library. Numerical methods for exterior problems. [Long'an Ying] -- This book provides a comprehensive introduction to the numerical methods for the exterior problems in partial differential equations frequently encountered in science and engineering computing.
The. A SPECTRAL METHOD FOR THE EIGENVALUE PROBLEM FOR ELLIPTIC EQUATIONS KENDALL ATKINSON∗ AND OLAF HANSEN† Abstract. Let Ω be an open, simply connected, and bounded region in Rd, d ≥ 2, and assume its boundary ∂Ω is smooth.
We develop a new C0-continuous Petrov-Galerkin spectral element method for one-dimensional fractional elliptic problems of the form 0 D x au(x) lu(x)= f(x), a2(1;2], subject to homogeneous boundary conditions.
We employ the standard (modal) spectral element bases and the Jacobi poly-fractonomials as the test func-tions . This book provides a comprehensive introduction to the numerical methods for the exterior problems in partial differential equations frequently encountered in science and engineering computing.
The coverage includes both traditional and novel methods. This paper describes a spectral representation of solutions of self-adjoint elliptic problems with immersed interfaces.
The interface is assumed to be a simple non-self-intersecting closed curve that obeys some weak regularity conditions. The problem is decomposed into two problems, one with zero interface data and the other with zero exterior boundary : G.
Auchmuty, P. Klouček. and can be especially attractive to deal with problems with non-local features. However, there are only a few efforts on using spectral methods for problems with non-local boundary conditions, e.g., Chebyshev spectral collocation method  and pseudospectral LegendreFile Size: KB.
AbstractA locally conservative, hybrid spectral difference method (HSD) is presented and analyzed for the Poisson equation. The HSD is composed of two types of finite difference approximations; the cell finite difference and the interface finite difference.
Embedded static condensation on cell interior unknowns considerably reduces the global couplings, resulting in the system of equations in Cited by: 3. elliptic. To do so, use the results given in Brenner and Scott [6, §§], combined with the methods of the present paper.
We have chosen to restrict our work to the more standard symmetric problem (1). There is a rich literature on spectral methods for solving partial di⁄erential equations. During the years many books and articles have been published on this topic, considering spectral properties of elliptic differential operators from different points of view.
This is one more book on these properties. This book is devoted to the study of some classical problems of the spectral theory of elliptic differential by: Publications of Jie Shen Books; Spectral Methods: Algorithms, Analysis and Applications (Springer Series in Computational Mathematics, V.
41) (by Jie Shen, Tao Tang and Li-Lian Wang, Springer, Aug. ), Erratum and the associated Matlab codes. Spectral and High-Order Methods with Applications (by Jie Shen and Tao Tang, Science Press of China, ); Erratum and Matlab & Fortran codes for the. bibliographies contain references to earlier papers on spectral methods.
The present paper is a continuation of the work in  in which a spectral method is given for a general elliptic equation with a Dirichlet boundary condition. Our approach is somewhat .Elliptic Curves by David Loeffler.
This note provides the explanation about the following topics: Definitions and Weierstrass equations, The Group Law on an Elliptic Curve, Heights and the Mordell-Weil Theorem, The curve, Completion of the proof of Mordell-Weil, Examples of rank calculations, Introduction to the P-adic numbers, Motivation, Formal groups, Points of finite order, Minimal.elliptic systems with uniform eﬃciency, andapply our new approach todevelop accurate and eﬃcient new spectral methods for elliptic problems in periodic domains.
The new methods promise uniform accuracy for nonsmooth solutions and complex domains which are inaccessible to classical Fourier by: