accurate simulation of reflector antennas by the complex source dual series approach the radiation from circular cylindrical reflector antennas is treated in an accurate manner for both polarizations the problem is first formulated in terms of the dual series equations and then is regularized by the riemann hilbert problem technique the resulting matrix equation is solved numerically with a guaranteed accuracy and remarkably little cpu time is needed the feed directivity is included in the analysis by the complex source point method various characteristic patterns are obtained for the front and offset fed reflector antenna geometries with this analysis and some comparisons are made with the high frequency techniques the directivity and radiated power properties are also studied

local error analysis of discontinuous galerkin methods for advection dominated elliptic linear quadratic optimal control problems this paper analyzes the local properties of the symmetric interior penalty upwind discontinuous galerkin sipg method for the numerical solution of optimal control problems governed by linear reaction advection diffusion equations with distributed controls the theoretical and numerical results presented in this paper show that for advection dominated problems the convergence properties of the sipg discretization can be superior to the convergence properties of stabilized finite element discretizations such as the streamline upwind petrov galerkin supg method for example we show that for a small diffusion parameter the sipg method is optimal in the interior of the domain this is in sharp contrast to supg discretizations for which it is known that the existence of boundary layers can pollute the numerical solution of optimal control problems everywhere even into domains where the solution is smooth and as a consequence in general reduces the convergence rates to only first order in order to prove

analysis of stabilized higher order finite element approximation of nonstationary and nonlinear convection diffusion reaction equations abstract in this work the numerical approximation of unsteady and nonlinear convection diffusion reaction models with small diffusion by higher order finite element methods is studied streamline upwind petrov galerkin supg stabilization together with anisotropic shock capturing as an additional stabilization in crosswind direction are used error analyses and the parameter design given in the literature are generalized to the case of nonlinear reaction rates by numerical studies it is illustrated that the combination of these approximation techniques reduce spurious oscillations in crosswind direction and improve the accuracy of simulations

a discontinuous galerkin method for optimal control problems governed by a system of convection diffusion pdes with nonlinear reaction terms in this paper we study the numerical solution of optimal control problems governed by a system of convection diffusion pdes with nonlinear reaction terms arising from chemical processes the symmetric interior penalty galerkin sipg method with upwinding for the convection term is used as a discretization method we use a residual based error estimator for the state and the adjoint variables an adaptive mesh refinement indicated by a posteriori error estimates is applied the arising saddle point system is solved using a suitable preconditioner numerical results are presented to illustrate the performance of the proposed error estimator

adaptive finite element approximation for distributed elliptic optimal control problems in this paper sharp a posteriori error estimators are derived for a class of distributed elliptic optimal control problems these error estimators are shown to be useful in adaptive finite element approximation for the optimal control problems and are implemented in the adaptive approach our numerical results indicate that the sharp error estimators work satisfactorily in guiding the mesh adjustments and can save substantial computational work

une base explicite de symboles modulaires sur les corps de fonctions modular symbols for the congruence subgroup gamma 0 mathfrak n of gl 2 mathbf f q t have been defined by teitelbaum they have a presentation given by a finite number of generators and relations in a formalism similar to manin s for classical modular symbols we completely solve the relations and get an explicit basis of generators when mathfrak n is a prime ideal of odd degree as an application we give a non vanishing statement for l functions of certain automorphic cusp forms for mathbf f q t the main statement also provides a key step for a result towards the uniform boundedness conjecture for drinfeld modules of rank 2

a convergent adaptive algorithm for poisson s equation we construct a converging adaptive algorithm for linear elements applied to poisson s equation in two space dimensions starting from a macro triangulation we describe how to construct an initial triangulation from a priori information then we use a posteriors error estimators to get a sequence of refined triangulation and approximate solutions it is proved that the error measured in the energy norm decreases at a constant rate in each step until a prescribed error bound is reached extension to higher order elements in two space dimension and numerical results are included

dual series solution to em wave scattering by a circular slit pec cylinder enclosing multiple dielectric cylindrical rods a cylindrical structure composed of a circular pec cylinder having a longitudinal slot and enclosing an arbitrary number of eccentric dielectric cylinders embedded in a dielectric sheath is considered in this paper excitation is provided by a plane wave normally incident upon the structure both te and tm polarizations are considered for the incident wave the scattered wave as well as the electromagnetic em field within the scatterer are determined by using a dual series approach combined with the translational addition theorem for cylindrical wave functions the abel integral transform method is applied in order to regularize the dual series equations to a matrix fredholm equation of the second kind the resulting infinite set of linear algebraic equations i s l a e is truncated and solved numerically the solution inherently contains the behavior of the field near the aperture rim as required by meixner s edge condition the numerical application manifests how the internal structure of the scatterer and the polarization of the incident wave affect backscattering by the cylindrical cavity

a priori and a posteriori error analysis of edge stabilization galerkin method for the optimal control problem governed by convection dominated diffusion equation in this paper we study an edge stabilization galerkin approximation scheme for the constrained optimal control problem governed by convection dominated diffusion equation the method uses least square stabilization of the gradient jumps across element edges a priori and a posteriori error estimates are derived for both the state co state and the control the theoretical results are illustrated by two numerical experiments

penetration through slots in conducting cylinders part 2 tm case three methods for determining the penetration through small apertures in closed conducting surfaces are outlined and their salient features discussed these methods are designated 1 the scatterer method 2 the short circuit current method and 3 the equivalent current method they are implemented by integral equation techniques but are amenable to differential equation or hybrid methods procedures for applying each method are outlined as are schemes for repairing singular equations rendered invalid by the presence of false resonances reasons for inaccuracies in the three methods are also delineated data determined for a given structure by all three methods are presented and numerical examples that illustrate important features of the methods and their relative accuracies are described it is pointed out that some methods yield incorrect penetration data an outline is given of the integral equation formulations and numerical schemes needed to accurately determine the field that penetrates through a slot in a conducting cylinder excited by an axially independent te source

the poisson kernel for drinfeld modular curves in an earlier work t 1 the author described a technique for constructing rigid analytic modular forms on the p adic upper half plane by means of an integral transform a poisson kernel in this paper we apply these methods to the study of rigid analytic modular forms on the upper half plane over a complete local field k of characteristic p arising out of the theory of drinfeld modules d these modular forms first studied by goss see gol go2 are in many ways analogous to the classical modular forms for sl2 z for a brief but effective introduction to the theory of these characteristic p modular forms see the introduction to gekeler s paper gekl also useful is gekeler s book gek2 we establish three main results first of all we show that if k is the function field of a complete geometrically irreducible curve c over the finite field lfq with q elements k is a completion of k f is an arithmetic subgroup of gl2 k and u is a measure on pi coming from a harmonic cocycle of weight n for i see definition 1 below then

a posteriori error estimates for a discontinuous galerkin approximation of second order elliptic problems several a posteriori error estimators are introduced and analyzed for a discontinuous galerkin formulation of a model second order elliptic problem in addition to residual type estimators we introduce some estimators that are couched in the ideas and techniques of domain decomposition results of numerical experiments are presented

em wave scattering by an axial slot on a circular pec cylinder with an eccentrically layered inner coating a dual series solution for te polarization a dual series approach is used to formulate scattering of a te polarized plane wave by a circular pec cylinder having a longitudinal slot and enclosing two eccentric cylindrical dielectric layers the dual series equations are analytically regularized to a matrix fredholm equation of the second kind by use of the abel integral transform method the resulting infinite set of linear algebraic equations i s l a e is truncated and solved numerically the aforementioned analytical numerical solution intrinsically takes into consideration the correct edge behavior of the field furthermore the addition theorem of cylindrical wave functions is used to match the field components on any cylindrical interface the numerical application manifests how the structure of the inner loading of this cylindrical cavity is imprinted on backscattering moreover it is shown how the location of the innermost dielectric cylinder may contribute to the suppression or enhancement of resonances

a one dimensional reaction diffusion system with a fast reaction abstract we consider a system of second order ordinary differential equations describing steady state for a three component chemical system with diffusion in the case when one of the reactions is fast we discuss the existence of solutions and the existence uniqueness and characterization of a limit as the rate of the fast reaction approaches infinity

a note on preconditioning for indefinite linear systems preconditioners are often conceived as approximate inverses for nonsingular indefinite matrices of saddle point or kkt form we show how preconditioners incorporating an exact schur complement lead to preconditioned matrices with exactly two or exactly three distinct eigenvalues thus approximations of the schur complement lead to preconditioners which can be very effective even though they are in no sense approximate inverses

fast iterative solution of reaction diffusion control problems arising from chemical processes pde constrained optimization problems and the development of preconditioned iterative methods for the efficient solution of the arising matrix systems is a field of numerical analysis that has recently been attracting much attention in this paper we analyze and develop preconditioners for matrix systems that arise from the optimal control of reaction diffusion equations which themselves result from chemical processes important aspects of our solvers are saddle point theory mass matrix representation and effective schur complement approximation as well as the incorporation of control constraints and application of the outer newton iteration to take into account the nonlinearity of the underlying pdes