diffraction by an arbitrary angled dielectric wedge ii correction to physical optics solution for pt i see ibid vol 39 no 9 p 1272 81 1991 the error of the physical optics solution for the e polarized plane wave incidence in connection with diffraction by an arbitrary angled dielectric wedge is corrected by calculating the nonuniform current distributed along the dielectric interfaces two kinds of series expansions to the nonuniform current are employed one is an asymptotic expansion as the multipole line source located at the edge of the dielectric wedge since the correction field seems to be a cylindrical wave emanating from the edge in the far field region the other is arbitrary electric and magnetic surface currents expanded by infinite series of the bessel functions i e the neumann expansion of which fractional order is chosen to satisfy the edge condition near the edge of the dielectric wedge in the static limit both of the two different expansion coefficients for a wedge angle of 45 degrees relative dielectric constants 2 10 and 100 and the e polarized incident angle of 150 degrees are evaluated by solving the dual series equation numerically after finite truncation

convergence analysis and error estimates for a parallel algorithm for solving the navier stokes equations this paper is concerned with the analysis of the convergence and the derivation of error estimates for a parallel algorithm which is used to solve the incompressible navier stokes equations as usual the main idea is to split the main differential operator this allows to consider independently the two main difficulties namely nonlinearity and incompressibility the results justify the observed accuracy of related numerical results

bifurcations of corank greater than two abstract we study the solution branches of stable and unstable bifurcations in certain three dimensional semilinear elliptic eigenvalue problems with dirichlet boundary conditions numerically by the continuation methods recent fast linear solvers for large sparse continuation problems are briefly reviewed sample numerical results on corank 3 bifurcation points with computer graphic output are reported

on the solutions of a class of dual integral equations occurring in diffraction problems it is shown that there exists a category of two dimensional diffraction problems which can be put into a standard form of dual integral equations these diffraction problems include diffraction of electromagnetic waves by a finite strip a finite slit the diffraction of scalar or vector elastic waves by a rigid strip or crack etc a general method for solving such dual integral equations is given by the artifice of constructing a set of functions of compact support biorthogonal to another given set of functions the sufficient conditions for a given dual integral equations to be solvable in this manner are also determined hence the method forms a complement to the weiner hopf method to illustrate the method solutions are obtained for a bench mark problem the diffraction of light by a finite perfectly conducting strip or equivalently the diffraction of sh waves by a crack comparison with results obtained by others for low intermediate and high frequencies show the utility and accuracy of the method for the entire range of frequencies both the near field and the far field are obtained the latter is shown to correspond to the fraunhoffer diffraction pattern for high frequency it is also shown that for the equivalent crack problem the stress intensity factor sif fluctuates rapidly with changes in the angle of incidence for high frequencies thus making the sif especially sensitive to angle of incidence at high frequencies

reconstruction of an impedance cylinder at oblique incidence from the far field data consider scattering of obliquely incident plane electromagnetic waves by an impedance cylinder embedded in a homogeneous background medium under some assumptions the direct scattering problem is governed by a coupled system of the two dimensional helmholtz equations for x 3 components of the electric field and the magnetic field in this paper we study a corresponding inverse scattering problem which is to reconstruct an unknown scattering object from measurement data of the x 3 component of only the electric field a reconstruction scheme called the linear sampling method is established with rigorous mathematical analysis due to the coupled oblique derivative boundary condition some new characteristics appear in our analysis numerical examples are also presented to illustrate the feasibility of the reconstruction algorithm

te scattering by arbitrarily connected conducting strips the scattering by an arbitrary collection of perfectly conducting connected strips is analyzed for te incidence the studied configurations include both closed and open polygonal cross section cylinders as well as more complicated structures in which more than two strips are connected at a point the proposed method is very efficient as few expansion functions are needed in a galerkin scheme this is achieved by means of expansion functions factorizing the correct edge singularity of the electromagnetic field and ensuring the continuity of the current at connecting points

scattering by polygonal cross section dielectric cylinders at oblique incidence we analyze the scattering by polygonal cross section lossless dielectric cylinders illuminated by an obliquely incident plane wave the problem is formulated in terms of a system of surface integral equations opportunely devised so as to be valid for objects with edges and incident angles including the total reflection limit angle by means of galerkin s method in the spectral domain with analytically fourier transformable expansion functions factorizing the correct edge behaviors and continuity conditions of the unknowns convergence of exponential type is achieved and the coefficients of the scattering matrix are reduced to single integrals that can be efficiently evaluated numerical results for both near field and far field parameters are presented showing the quick convergence of the method even when applied to composite cylindrical objects

asymptotic analysis of the optimal filtering problem for two dimensional diffusions measured in a low noise channel we consider the problem of filtering one dimensional diffusions with nonlinear drift coefficients transmitted through a nonlinear fow noise channel we construct an asymptotic solution to zakai s equation for the unnormalized conditional probability density of the signal given the noisy measurements this expansion is used to find the asymptotic expansion of the minimum error variance filter and its mean square estimation error msee we construct approximate filters whose msee agrees with that of the optimal one to a given degree of accuracy the dimension of the approximate filter increases with the required degree of accuracy similarly we expand the maximum a posteriori probability estimator and the minimum energy estimator and compare their performance we also discuss some extended kalman filters and present some examples

the convergence of two numerical schemes for the navier stokes equations this paper deals with some convergence stability results concerning two numerical methods for solving the incompressible nonstationary navier stokes equations the algorithms are of a particular kind in what regards time discretization more precisely of the peaceman rachford and the strang type resp and have been obtained by modifying slightly the numerical treatment of the nonlinear terms in other schemes due to glowinski et al 1980 we first describe the full discretization of the homogeneous dirichlet problem using a general external approximation of the spatial functional spaces involved a particular and simple choice of such an approximation is the standardp 2 lagrange finite element for the velocity field when the fluid is bidimensional then we establish and prove convergence and stability and make some comments on the numerical treatment of other generally nonhomogeneous boundary conditions the theoretical results show that the schemes are at least conditionally stable and convergent which justifies the success of glowinski s methods

a convergence result for a parallel algorithm for solving the navier stokes equations abstract this work is concerned with the convergence stability analysis of a parallel algorithm which is used to solve the incompressible navier stokes problem this relies on a splitting of the main differential operator thanks to which the most important difficulties nonlinearity and incompressibility can be considered independently thus one is led to the formulation of subproblems of two kinds which can be solved simultaneously by two different processors we prove conditional stability and convergence this can serve to justify the accuracy of previous numerical results

mellin transform solution for the static line source excitation of a dielectric wedge an integral transform analysis of the static scattering of the two dimensional potential radiated by a line source in the vicinity of a penetrable wedge is presented the mellin transform is used to derive the exact static solution to laplace s equation for the dielectric wedge in the form of a modal series the important dielectric edge condition behavior is explicitly contained in this analytic solution

the direct electromagnetic scattering problem from an imperfectly conducting cylinder at oblique incidence abstract we consider the scattering of a time harmonic electromagnetic wave by an imperfectly conducting infinite cylinder at oblique incidence we assume that the cylinder is embedded in an inhomogeneous medium but both the cylinder and the medium are uniform along the axis of the cylinder since the x components and y components of electric field and magnetic field can be expressed in terms of their z components if the cylinder is parallel to the z axis we can derive from maxwell s equations and the leontovich impedance boundary condition that our scattering problem is modeled as a boundary value problem for their z components with oblique boundary condition using rellich s lemma the uniqueness of solutions to the boundary value problem is justified to show the existence of its solution the lax phillips method is used the key point for that is to prove the solvability of the associated oblique derivative problem in a bounded domain consisting of two boundaries which are the boundary of the cross section of the cylinder with coupled oblique boundary condition and that of a domain containing this cross section with dirichlet boundary condition

exponentially converging nystrom methods applied to the integral integrodifferential equations of oblique scattering hybrid wave propagation in presence of composite dielectric cylinders of arbitrary cross section systems of singular integral integrodifferential equations are studied that pertain to 2 d oblique scattering and to hybrid wave propagation in presence of a dielectric cylinder with arbitrarily shaped smooth boundary these systems having the tangential to the surface of the cylinder components of the electric and magnetic fields as the unknowns are solved via fast highly accurate algorithms that rely on the nystrom method nm because of our specialized treatment the present solution technique has the following characteristics 1 it fully accounts for the singular nature of the kernels 2 it appears to converge exponentially and 3 it yields simple closed form expressions for all matrix elements in addition an extension of the analysis is presented to account for composite dielectric cylinders that contain arbitrarily shaped dielectric or conducting cylindrical inclusions numerical examples and case studies illustrate the simplicity flexibility and efficiency of the algorithms exhaustive comparisons with available results for several special cases serve to test the correctness of the implementation and bring to light the extremely high accuracy of our algorithms

piecewise monotone filtering with small observation noise nonlinear filtering of markov diffusion processes is considered in the case in which a piecewise monotone function of the state is observed with additive small observation noise under a certain detectability hypothesis statistical tests are given to discriminate among the intervals of monotonicity during time intervals in which the state does not cross critical points of the observation function during such time intervals accurate approximate finite dimensional filters can be used

a spectral iteration technique for analyzing scattering from arbitrary bodies part i cylindrical scatterers with e wave incidence in the past methods for solving electromagnetic scattering problems in the frequency domain have been developed largely for the low frequency moment method and high frequency asymptotic techniques regimes the intermediate frequency range has been analyzed by combinations of these two approaches or by separation of variables when possible this paper is devoted to the development of an independent approach viz the stacked spectral iteration technique which is capable of handling arbitrary scatterers with dimensions ranging from small to moderately large the method takes advantage of the simplicity with which the planar source planar field relationships are expressed in the spectral domain the boundary conditions or constitutive relationships on the other hand are expressed most simply in the spatial domain alternating between the two domains is carried out with the aid of the fast fourier transform fft algorithm the spectral iteration technique sit was applied in the past to thin planar structures which allow the analysis to be carried out on a plane the generalization of the two dimensional formulation to arbitrary three dimensional bodies can be accomplished by sampling the current distribution on the scatterer over a number of parallel planes and using the simple spectral domain interaction relationships between the planes this new approach involves no matrix inversion and is capable of analyzing scatterers whose sizes far exceed those treatable by the moment method in addition to being arbitrarily shaped the scatterer may be conducting dielectric or lossy dielectric thus the sit provides an efficient approach to filling the much needed gap between low and high frequency conventional techniques e g the moment method mom and the geometrical theory of diffraction gtd and to extending the range of applicability to dielectric scatterers with or without loss though the concepts presented herein are applicable to arbitrary three dimensional scatterers the problem of arbitrary cylinders with e polarized excitation is addressed in this paper while the h case is treated in an accompanying work the three dimensional case is to be reported in a future communication which treats the problem of scattering by a lossy inhomogeneons dielectric cylinder of finite length

nonlinear filtering of one dimensional diffusions in the case of a high signal to noise ratio in this paper we are concerned with the asymptotic nonlinear filtering of one dimensional diffusions as the observation noise tends to zero the intensity of the signal noise may be normal small or large we derive evaluations of the conditional moments and obtain one and two dimensional approximate filters we give upper bounds for the approximation errors and compare these filters with some classical suboptimal filters

the two dimensional direct and inverse scattering problems with generalized oblique derivative boundary condition consider the two dimensional exterior problem for the helmholtz equation with a generalized oblique derivative boundary condition which arises in some new scattering problems such as the scattering of tidal waves by islands under suitable assumptions different from the well studied scattering problems with dirichlet neumann and impedance boundary conditions the boundary condition in our new model involves a linear combination of the normal and tangential derivatives of the wave field with complex coefficient compared with the classical scattering models the tangential derivative on the obstacle boundary leads to some essential differences such as the symmetric property of the green function and the reciprocity principle of the scattering data both the direct and inverse scattering problems are studied in this paper first based on the lax phillips method we show the unique solvability of the direct scattering problem and the analyticity of the solution on the wave number second we investigate

an approximate filter for a partially observed piecewise linear system with small observation noise abstract we propose a finite dimensional approximate filter for a piecewise linear system with small observation noise the nonlinearity of our system depends only on state components that can be estimated quickly and accurately under a certain detectability hypothesis then we estimate the distance between our approximate filter and the state process to be filtered

calculation of electromagnetic scattering from a dielectric cylinder using the conjugate gradient method and fft the scattering problem of an axially uniform dielectric cylinder is formulated in terms of the electric field integral equation where the cylinder is of general cross sectional shape inhomogeneity and anisotropy and the incident field is arbitrary using the pulse function expansion and the point matching technique the integral equation is reduced to a system of simultaneous equations then a published procedure for solving the system using the conjugate gradient method and the fast fourier transform fft is generalized to the case of oblique incidence scattering

efficiency of the extended kalman filter for nonlinear systems with small noise the problem of nonlinear filtering is studied asymptotically as the noise tends to zero detectability conditions ensuring that the filtering error tends to zero are derived and under these conditions it is proved that the extended kalman filter provides a good suboptimal filter the smoothing problem is also studied the proofs use some estimates for the linearization of stochastic systems some changes of probability and stochastic differentiation techniques

a parallel algorithm for solving the incompressible navier stokes problems abstract we introduce and analyze a parallel algorithm for solving the navier stokes equations based on the splitting of the two main difficulties involved the presence of nonlinear terms and the zero divergence condition the numerical results obtained by using the proposed algorithm are quite consistent with those furnished by other known algorithms numerical results are discussed as well as the advantages of this new algorithm