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Multiplier Function (multiplier + function)

Distribution by Scientific Domains
Mathematics and Statistics75%

Selected Abstracts

An embedded Dirichlet formulation for 3D continua

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2010
A. Gerstenberger
Abstract This paper presents a new approach for imposing Dirichlet conditions weakly on non-fitting finite element meshes. Such conditions, also called embedded Dirichlet conditions, are typically, but not exclusively, encountered when prescribing Dirichlet conditions in the context of the eXtended finite element method (XFEM). The method's key idea is the use of an additional stress field as the constraining Lagrange multiplier function. The resulting mixed/hybrid formulation is applicable to 1D, 2D and 3D problems. The method does not require stabilization for the Lagrange multiplier unknowns and allows the complete condensation of these unknowns on the element level. Furthermore, only non-zero diagonal-terms are present in the tangent stiffness, which allows the straightforward application of state-of-the-art iterative solvers, like algebraic multigrid (AMG) techniques. Within this paper, the method is applied to the linear momentum equation of an elastic continuum and to the transient, incompressible Navier,Stokes equations. Steady and unsteady benchmark computations show excellent agreement with reference values. The general formulation presented in this paper can also be applied to other continuous field problems. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Low-gain adaptive stabilization of semilinear second-order hyperbolic systems

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 18 2004
Toshihiro Kobayashi
Abstract In this paper low-gain adaptive stabilization of undamped semilinear second-order hyperbolic systems is considered in the case where the input and output operators are collocated. The linearized systems have an infinite number of poles and zeros on the imaginary axis. The adaptive stabilizer is constructed by a low-gain adaptive velocity feedback. The closed-loop system is governed by a non-linear evolution equation. First, the well-posedness of the closed-loop system is shown. Next, an energy-like function and a multiplier function are introduced and the exponential stability of the closed-loop system is analysed. Some examples are given to illustrate the theory. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Operator,valued Fourier multiplier theorems on Besov spaces

MATHEMATISCHE NACHRICHTEN, Issue 1 2003
Maria Girardi
Presented is a general Fourier multiplier theorem for operator,valued multiplier functions on vector,valued Besov spaces where the required smoothness of the multiplier functions depends on the geometry of the underlying Banach space (specifically, its Fourier type). The main result covers many classical multiplier conditions, such as Mihlin and Hörmander conditions. [source]