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Approximating Unbounded Domains
2016This chapter provides the construction and approximation of two approaches for the treatment of unbounded domains: first by absorbing boundary conditions (ABC), then by perfectly matched layers (PML) for the three wave equations.
Gary Cohen, Sébastien Pernet
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Elliptic Problems on Unbounded Domains
SIAM Journal on Mathematical Analysis, 1986Boundary value problems for elliptic equations of the form \(\sum_{| \alpha |,| \beta | \leq k}(-1)^{| \alpha |}D^{\alpha}(a_{\alpha \beta}D_ u^{\beta})=f\) on unbounded domains \(\Omega \subset {\mathbb{R}}^ n\) are studied. Using weighted Sobolev spaces, variants of the Poincaré and Friedrichs inequalities, and compact embeddings in weighted Sobolev ...
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Adaptive Wavelet Methods on Unbounded Domains
Journal of Scientific Computing, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kestler, Sebastian, Urban, Karsten
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Global Optimization over Unbounded Domains
SIAM Journal on Control and Optimization, 1990Almost all methods for solving the global optimization problem need the assumption that a parallelepiped containing the solution points is known. The boundedness is necessary both for the numerical computation as well as for guaranteeing the convergence properties.
H. Ratschek, R. L. Voller
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2002
Although the physical world is finite, from a mathematical point of view, very large domains must often be modeled as infinite ones. This is particularly true for waves which can be propagated on distances which correspond to several hundreds or even several thousands of wavelengths.
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Although the physical world is finite, from a mathematical point of view, very large domains must often be modeled as infinite ones. This is particularly true for waves which can be propagated on distances which correspond to several hundreds or even several thousands of wavelengths.
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Classical coupled thermoelasticity in unbounded domains
Journal of Elasticity, 1989Some qualitative properties of regular solutions of systems of classical coupled thermoelasticity in unbounded domains are established, the special features of the results consisting in: (1) a weak hypothesis with regard to the temperatur field at large distances, and (2) lack of a constraint of a similar kind with regard to the displacement field ...
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Symmetric Stable Processes on Unbounded Domains
Potential Analysis, 2006The author gives necessary and sufficient conditions for the expectation of a function of the exit time by a symmetric \(\alpha\)-stable process from a horn-shaped domain to be finite. The results of this paper are generalizations of earlier results contained in a paper by \textit{T. Kulczycki} and the author [Trans. Am. Math. Soc. 358, No.
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The Martin Kernel for Unbounded Domains
Potential Analysis, 2009Let \((x_{1},\widetilde{x})\) denote a typical point of \(\mathbb{R}\times \mathbb{R}^{d-1}\), where \(d\geq 3\), and let \(a:[0,\infty )\rightarrow (0,\infty )\) be Lipschitz. This paper is concerned with unbounded domains \(D\) of the form \(\{(x_{1},\widetilde{x}):x_{1}>0,\;\left| \widetilde{x}\right|
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Gaugeability for Unbounded Domains
1990Let D be a Greenian domain in R d(d ≥ 1), namely, its Green function G D(x, y) < ∞ for x, y ∈ D, x ≠ y, and let q ∈ K d (see [1] for definition); if q is only given in D, then we assume q(x) = 0 for x ∈ R d — D.
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Spline interpolation on unbounded domains
AIP Conference Proceedings, 2016Spline interpolation is a splendid tool for multiscale approximation on unbounded domains. In particular, it is well suited for use by the multilevel summation method (MSM) for calculating a sum of pairwise interactions for a large set of particles in linear time.
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