Search results for "Computational Mathematic"
showing 10 items of 987 documents
Fictitious Domain Methods for the Numerical Solution of Two-Dimensional Scattering Problems
1998
Fictitious domain methods for the numerical solution of two-dimensional scattering problems are considered. The original exterior boundary value problem is approximated by truncating the unbounded domain and by imposing a nonreflecting boundary condition on the artificial boundary. First-order, second-order, and exact nonreflecting boundary conditions are tested on rectangular and circular boundaries. The finite element discretizations of the corresponding approximate boundary value problems are performed using locally fitted meshes, and the discrete equations are solved with fictitious domain methods. A special finite element method using nonmatching meshes is considered. This method uses …
Implementation Aspects of 3D Lattice-BGK: Boundaries, Accuracy, and a New Fast Relaxation Method
1999
In many realistic fluid-dynamical simulations the specification of the boundary conditions, the error sources, and the number of time steps to reach a steady state are important practical considerations. In this paper we study these issues in the case of the lattice-BGK model. The objective is to present a comprehensive overview of some pitfalls and shortcomings of the lattice-BGK method and to introduce some new ideas useful in practical simulations. We begin with an evaluation of the widely used bounce-back boundary condition in staircase geometries by simulating flow in an inclined tube. It is shown that the bounce-back scheme is first-order accurate in space when the location of the non…
Standard polynomials and matrices with superinvolutions
2016
Abstract Let M n ( F ) be the algebra of n × n matrices over a field F of characteristic zero. The superinvolutions ⁎ on M n ( F ) were classified by Racine in [12] . They are of two types, the transpose and the orthosymplectic superinvolution. This paper is devoted to the study of ⁎-polynomial identities satisfied by M n ( F ) . The goal is twofold. On one hand, we determine the minimal degree of a standard polynomial vanishing on suitable subsets of symmetric or skew-symmetric matrices for both types of superinvolutions. On the other, in case of M 2 ( F ) , we find generators of the ideal of ⁎-identities and we compute the corresponding sequences of cocharacters and codimensions.
Convex and expansive liftings close to two-isometries and power bounded operators
2021
Abstract In the context of Hilbert space operators, there is a strong relationship between convex and expansive operators and 2-isometries. In this paper, we investigate the bounded linear operators T on a Hilbert space H which have a 2-isometric lifting S on a Hilbert space K containing H as a closed subspace invariant for S ⁎ S . This last property holds in particular when S | K ⊖ H is an isometry. We relate such 2-isometric liftings S by some convex, concave or expansive liftings of the same type as S. We also examine some power bounded operators with such liftings, as well as an intermediate expansive lifting associated with T on the space H ⊕ l + 2 ( H ) . The latter notion is used to …
Approximation of plurisubharmonic functions
2015
We extend a result by Fornaaess and Wiegerinck [Ark. Mat. 1989;27:257-272] on plurisubharmonic Mergelyan type approximation to domains with boundaries locally given by graphs of continuous functions.
An asymptotic holomorphic boundary problem on arbitrary open sets in Riemann surfaces
2020
Abstract We show that if U is an arbitrary open subset of a Riemann surface and φ an arbitrary continuous function on the boundary ∂ U , then there exists a holomorphic function φ ˜ on U such that, for every p ∈ ∂ U , φ ˜ ( x ) → φ ( p ) , as x → p outside a set of density 0 at p relative to U . These “solutions to a boundary problem” are not unique. In fact they can be required to have interpolating properties and also to assume all complex values near every boundary point. Our result is new even for the unit disc.
An elliptic equation on n-dimensional manifolds
2020
We consider an elliptic equation driven by a p-Laplacian-like operator, on an n-dimensional Riemannian manifold. The growth condition on the right-hand side of the equation depends on the geometry of the manifold. We produce a nontrivial solution by using a Palais–Smale compactness condition and a mountain pass geometry.
Operators intertwining with isometries and Brownian parts of 2-isometries
2016
Abstract For two operators A and T ( A ≥ 0 ) on a Hilbert space H satisfying T ⁎ A T = A and the A-regularity condition A T = A 1 / 2 T A 1 / 2 we study the subspace N ( A − A 2 ) in connection with N ( A T − T A ) , for T belonging to different classes. Our results generalize those due to C. Kubrusly concerning the case when T is a contraction and A = S T is the asymptotic limit of T. Also, the particular case of a 2-isometry in the sense of S. Richter as well as J. Agler and M. Stankus is considered. For such operators, under the same regularity condition we completely describe the reducing Brownian unitary and isometric parts, as well as the invariant Brownian isometric part. Some exampl…
Characterization of greedy bases in Banach spaces
2017
Abstract We shall present a new characterization of greedy bases and 1-greedy bases in terms of certain functionals defined using distances to one dimensional subspaces generated by the basis. We also introduce a new property that unifies the notions of unconditionality and democracy and allows us to recover a better dependence on the constants.
Nonlinear concave-convex problems with indefinite weight
2021
We consider a parametric nonlinear Robin problem driven by the p-Laplacian and with a reaction having the competing effects of two terms. One is a parametric (Formula presented.) -sublinear term (concave nonlinearity) and the other is a (Formula presented.) -superlinear term (convex nonlinearity). We assume that the weight of the concave term is indefinite (that is, sign-changing). Using the Nehari method, we show that for all small values of the parameter (Formula presented.), the problem has at least two positive solutions and also we provide information about their regularity.