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Displaying 41 – 60 of 1318

Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations

Martin A. Grepl, Yvon Maday, Ngoc C. Nguyen, Anthony T. Patera (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, we extend the reduced-basis approximations developed earlier for linear elliptic and parabolic partial differential equations with affine parameter dependence to problems involving (a) nonaffine dependence on the parameter, and (b) nonlinear dependence on the field variable. The method replaces the nonaffine and nonlinear terms with a coefficient function approximation which then permits an efficient offline-online computational decomposition. We first review the coefficient function...

Efficient representations of Green’s functions for some elliptic equations with piecewise-constant coefficients

Yuri Melnikov (2010)

Open Mathematics

Convenient for immediate computer implementation equivalents of Green’s functions are obtained for boundary-contact value problems posed for two-dimensional Laplace and Klein-Gordon equations on some regions filled in with piecewise homogeneous isotropic conductive materials. Dirichlet, Neumann and Robin conditions are allowed on the outer boundary of a simply-connected region, while conditions of ideal contact are assumed on interface lines. The objective in this study is to widen the range of...

Efficient solution of symmetric eigenvalue problems using multigrid preconditioners in the locally optimal block conjugate gradient method.

Knyazev, Andrew V., Neymeyr, Klaus (2003)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Eigencurves for a Steklov problem.

Anane, Aomar, Chakrone, Omar, Karim, Belhadj, Zerouali, Abdellah (2009)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Eigencurves of the $p$ -Laplacian with weights and their asymptotic behavior.

Dakkak, Ahmed, Hadda, Mohammed (2007)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Eigenfunction Expansions and the Pinksy Phenomenon on Compact Manifolds.

Michael Taylor (2001)

The journal of Fourier analysis and applications [[Elektronische Ressource]]

Eigenfunctions and fundamental solutions of the fractional two-parameter Laplacian.

Yakubovich, Semyon (2010)

International Journal of Mathematics and Mathematical Sciences

Eigenfunctions and Nodal Sets

Shiu-Yuen Cheng (1976)

Commentarii mathematici Helvetici

Eigenfunctions of Laplacian by boundedness conditions in bounded hyperfunctions and distributions.

Dhungana, Bishnu P. (2002)

Southwest Journal of Pure and Applied Mathematics [electronic only]

Eigenfunctions of the laplacian, quantum chaos, and computation

Dennis A. Hejhal (1995)

Journées équations aux dérivées partielles

Eigenmodes of the damped wave equation and small hyperbolic subsets

Gabriel Rivière (2014)

Annales de l’institut Fourier

We study stationary solutions of the damped wave equation on a compact and smooth Riemannian manifold without boundary. In the high frequency limit, we prove that a sequence of $β$ -damped stationary solutions cannot be completely concentrated in small neighborhoods of a small fixed hyperbolic subset made of $β$ -damped trajectories of the geodesic flow.The article also includes an appendix (by S. Nonnenmacher and the author) where we establish the existence of an inverse logarithmic strip without eigenvalues...

Eigenschaften der Lösung einer partiellen Differentialgleichung vierter Ordnung

Věra Radochová (1972)

Archivum Mathematicum

Eigenstructure of the equilateral triangle. II: The Neumann problem.

McCartin, Brian J. (2002)

Mathematical Problems in Engineering

Eigenstructure of the equilateral triangle. III: The Robin problem.

McCartin, Brian J. (2004)

International Journal of Mathematics and Mathematical Sciences

Eigenvalue asymptotics for Neumann Laplacian in domains with ultra-thin cusps

Victor Ivrii (1998/1999)

Séminaire Équations aux dérivées partielles

Asymptotics with sharp remainder estimates are recovered for number $N (τ)$ of eigenvalues of the generalized Maxwell problem and for related Laplacians which are similar to Neumann Laplacian. We consider domains with ultra-thin cusps (with $exp (- | x |^{m + 1}$ ) width ; $m > 0$ ) and recover eigenvalue asymptotics with sharp remainder estimates.

Eigenvalue asymptotics for randomly perturbed non-self adjoint operators

Mildred Hager (2007)

Journées Équations aux dérivées partielles

Eigenvalue asymptotics for Schrödinger and Dirac operators with the constant magnetic field and with electric potential decreasing at infinity

Victor Ivrii (1991)

Journées équations aux dérivées partielles

Eigenvalue asymptotics for the Dirac operator in strong constant magnetic fields.

Raikov, G.D. (1999)

Mathematical Physics Electronic Journal [electronic only]

Eigenvalue asymptotics for the Pauli operator in strong nonconstant magnetic fields

Georgi D. Raikov (1999)

Annales de l'institut Fourier

We consider the Pauli operator $H (μ) : = {(\sum_{j = 1}^{m} σ_{j} (- i \frac{\partial}{\partial x_{j}} - μ A_{j}))}^{2} + V$ selfadjoint in $L^{2} (ℝ^{m}; ℂ^{2})$ , $m = 2, 3$ . Here $σ_{j}$ , $j = 1, ..., m$ , are the Pauli matrices, $A : = (A_{1}, ..., A_{m})$ is the magnetic potential, $μ > 0$ is the coupling constant, and $V$ is the electric potential which decays at infinity. We suppose that the magnetic field generated by $A$ satisfies some regularity conditions; in particular, its norm is lower-bounded by a positive constant, and, in the case $m = 3$ , its direction is constant. We investigate the asymptotic behaviour as $μ \to \infty$ of the number of the eigenvalues of $H (μ)$ smaller than...

Eigenvalue asymptotics for the Schrödinger operator with perturbed periodic potential.

G.D. Raikov (1992)

Inventiones mathematicae

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