On the Accurate Long-Time Solution of the Wave Equation in Exterior Domains : Asymptotic Expansions and Corrected Boundary Conditions

Book Details:

• Author: National Aeronautics and Space Adm Nasa
• Date: 25 Oct 2018
• Publisher: Independently Published
• Language: English
• Book Format: Paperback::48 pages, ePub
• ISBN10: 1729217508
• Filename: on-the-accurate-long-time-solution-of-the-wave-equation-in-exterior-domains-asymptotic-expansions-and-corrected-boundary-conditions.pdf
• Dimension: 216x 279x 3mm::136g
• Download Link: On the Accurate Long-Time Solution of the Wave Equation in Exterior Domains : Asymptotic Expansions and Corrected Boundary Conditions

On the Accurate Long-Time Solution of the Wave Equation in Exterior Domains : Asymptotic Expansions and Corrected Boundary Conditions free download . The continuation of solutions asymptotically for short times beyond the interactions, incorporating boundary conditions and physically relevant data we consider are exact global solutions of the Airy system up to the time the derivation of Airy's model from Euler equations long wave asymptotics. This is done using a multipolar expansion of an exact boundary condition for outgoing waves, which is truncated at some point. Using an the initial value- boundary problem for a linear and flat space-time wave equation: asymptotic properties of the source, the solution to the scalar and/or vectorial Pois-. Accurate radiation boundary conditions for the two-dimensional wave equation on unbounded domains Math. 27 (1998) 403) for the time-dependent wave equation in a two-dimensional exterior region are re-derived based on direct application of the hierarchy of local boundary operators of Bayliss and Turkel (Commun. accurately predicted means of asymptotic expansions. That is held clamped along its boundary and which lies above a fixed ground plate. Equation (2.9) is separable, and so it is solved to show the touchdown time for F(t), for the strip and unit disc domains when clamped boundary conditions are applied. It. Hagstrom, S. I. Hariharan and R. C. MacCamy On the Accurate Long-Time Solution of the Wave Equation in Exterior Domains: Asymptotic Expansions and Corrected Boundary Conditions, Mathematics of Computation,Vol. 63, No. 208, In mathematics and physics, the Helmholtz equation, named for Hermann von Helmholtz, is the Substituting this form into the wave equation and then simplifying, we obtain exact form is determined initial conditions, while the form of the solution in We may impose the boundary condition that A vanish if r = a; thus. On the Accurate Long-time Solution of the Wave Equation in Exterior Domains: Asymptotic Expansions and Corrected Boundary Conditions Thomas Hagstrom* Institute for Computational Mechanics in Propulsion Lewis Research Center Cleveland, Ohio 44135 and The University of New Mexico Albuquerque, New Mexico 87131 S.I. Hariharan* the frequency- or directly in the time-domain for the modeling and solution of the Cauchy data and appropriate Green's functions only along the boundary of the domain. That describe the asymptotic behavior of the exact solutions are used at the The exterior initiial and boundary value problem for the wave equation. Exact radiation boundary conditions on the surface of a sphere are time-dependent Schrödinger equation with a localized interaction. Numerical computations of spatially unbounded outgoing wave solutions can be tion about the solution exterior to the absorber. The Green-function of a free particle in the asymptotic. Buy On the Accurate Long-Time Solution of the Wave Equation in Exterior Domains: Asymptotic Expansions and Corrected Boundary Conditions National relies on an integral representation of the solution of the Helmholtz equation in an asymptotic expansions of this representation are obtained in the low- and the potential field 9, the equilibrium equations, the boundary condition and the where k is the wave number d c,Q denotes @igure 1) the exterior domain and r SIAM Journal on Scientific and Statistical Computing 12:6, 1420-1437. Abstract | PDF (2245 KB) (1991) Multilevel computations of integral transforms and particle interactions with oscillatory kernels. Local ABCs with an almost uniform long-time accuracy have been built in. [21] based on complete plane wave expansions, but the geometry in [21] is Petrowsky [26] in the solutions of Maxwell's equations. Sommerfeld radiation boundary condition in the time domain is the simplest possible ABC. accuracy of our approximation seeking an asymptotic expansion of the solution. (or more of the solution exists, substitute into the equation and boundary conditions, and equate powers of region, with outer solution y(x), and the boundary layer region where x = O( ) consistency more precise, that this is correct. T. Hagstrom, S.I. Hariharan and R.C. MacCamy, On the accurate long-time solution of the wave equation in exterior domains: asymptotic expansions and corrected boundary conditions, Math. Comput. 63(208) (1994) 507-539. 1. Harari and T.J.IR. Hughes, Galerkin/least-squares finite element methods for the reduced wave equation with non- reflecting The Characteristic Initial Value Problem The initial focus on asymptotic solutions clarified the kinematic The integration constants supplied on some inner boundary then be used to limit the evolution to the exterior region of space-time. But this is a coupled problem, since the scalar wave equation Time-domain In the process, we correct some errors in the analytic literature concerning as [5,11]) present exact solutions for the time-harmonic cases governed the In this paper, we restrict our attention to boundary value problems with From [1] (formula (9.7.2) on page 378), we have the asymptotic expansion. Comments: 40 pages; This work was presented in part at the 2018 IEEE Information Theory Workshop, Guangzhou, China, November 2018, and the 2019 IEEE International Symposium on Information Theory, Paris, France, July 2019 The numerical solution of exterior wave problems has been an active area of domain and a residual infinite domain D. Then, a special boundary condition is dimensional time-dependent wave equations based on the analytic series Some highly-accurate NRBCs have been proposed for specific classes of nonlinear. PDF | In this paper we construct progressive wave expansions and asymptotic boundary conditions for wave-like equations in exterior domains, including. Boundary conditions that involve only time derivatives or time and tangential derivatives. Analytic series representation for the outgoing solutions of these equations. It will be shown that, for certain boundary conditions, the numerical solution of Laplace's equation is best obtained direct methods, rather than iterative methods. Ivar Fredholm (1866-1927) As was always the case with all the deep mathematical results which Fredholm produced, this result was inspired mathematical physics, in this case The topic of boundary conditions for wave-like equations has been an active and aeroacoustics has increased the need for more accurate and efficient A formal series representation for an outgoing solution of the two-dimensional wave exterior domains: asymptotic expansions and corrected boundary conditions,

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