Search results for "Mathematical analysis"

Approximation of piecewise smooth functions and images by edge-adapted (ENO-EA) nonlinear multiresolution techniques

2008

Abstract This paper introduces and analyzes new approximation procedures for bivariate functions. These procedures are based on an edge-adapted nonlinear reconstruction technique which is an intrinsically two-dimensional extension of the essentially non-oscillatory and subcell resolution techniques introduced in the one-dimensional setting by Harten and Osher. Edge-adapted reconstructions are tailored to piecewise smooth functions with geometrically smooth edge discontinuities, and are therefore attractive for applications such as image compression and shock computations. The local approximation order is investigated both in L p and in the Hausdorff distance between graphs. In particular, i…

On the ultradistributions of Beurling type

2009

Sea un conjunto abierto no vac´ýo del espacio euclideo . En este articulo se demuestra que si S es una ultradistribucion en , perteneciente a una clase de tipo Beurling que sea estable frente a operadores diferenciales, entonces S se puede representar en la formaP2Nk0 Df, donde f es una funcion compleja definida en que es Lebesgue medible y esencialmente acotada en cada subconjunto compacto de . Tambi´en se obtienen otros resultados de estructura de ciertas ultradistribuciones.

Identification of small inhomogeneities: Asymptotic factorization

2007

We consider the boundary value problem of calculating the electrostatic potential for a homogeneous conductor containing finitely many small insulating inclusions. We give a new proof of the asymptotic expansion of the electrostatic potential in terms of the background potential, the location of the inhomogeneities and their geometry, as the size of the inhomogeneities tends to zero. Such asymptotic expansions have already been used to design direct (i.e. noniterative) reconstruction algorithms for the determination of the location of the small inclusions from electrostatic measurements on the boundary, e.g. MUSIC-type methods. Our derivation of the asymptotic formulas is based on integral …

A sufficient condition for the instability of theq-d algorithm

1959

Multiple solutions for a discrete boundary value problem involving the p-Laplacian.

2008

Multiple solutions for a discrete boundary value problem involving the p-Laplacian are established. Our approach is based on critical point theory.

Local Total Variation Bounded Methods for Hyperbolic Conservation Laws

2003

Solving a model for 1-D, three-phase flow vertical equilibrium processes in a homogeneous porous medium by means of a Weighted Essentially Non Oscill…

2013

Mathematical models of multi-phase flow are useful in some engineering applications like enhanced oil recovery, filtration of pollutants into subsurface, etc. In this work, we derive a mathematical model for the motion of one-dimensional three-phase flow in a porous medium under the condition of vertical equilibrium, which can be viewed as an extension of some two-phase flow models described in the literature. Our model involves a system of two partial differential equations in the form of viscous conservation laws, whose solutions may contain very sharp transitions. We show that a high-order/high resolution Weighted Essentially Non Oscillatory scheme is an appropriate tool to discretize th…

On a topology optimization problem governed by two-dimensional Helmholtz equation

2015

The paper deals with a class of shape/topology optimization problems governed by the Helmholtz equation in 2D. To guarantee the existence of minimizers, the relaxation is necessary. Two numerical methods for solving such problems are proposed and theoretically justified: a direct discretization of the relaxed formulation and a level set parametrization of shapes by means of radial basis functions. Numerical experiments are given.

Projective Reeds-Shepp car onS2with quadratic cost

2008

Fix two points x, ¯ ∈ S 2 and two directions (without orientation) η,¯ η of the velocities in these points. In this paper we are interested to the problem of minimizing the cost

Explicit Characterization of Inclusions in Electrical Impedance Tomography

2001

In electrical impedance tomography one seeks to recover the spatial conductivity distribution inside a body from knowledge of the Neumann--Dirichlet map. In many practically relevant situations the conductivity is smooth apart from some inhomogeneities where the conductivity jumps to a higher or lower value. An explicit characterization of these inclusions is developed in this paper. To this end a class of dipole-like indicator functions is introduced, for which one has to check whether their boundary values are contained in the range of an operator determined by the measured Neumann--Dirichlet map. It is shown that this holds true if and only if the dipole singularity lies inside the inhom…