scaling and eigenstates for a class of one dimensional quasiperiodic lattices numerical and analytical calculations of the electronic properties of a one dimensional quasiperiodic lattice are presented the lattice consists of two types of bonds a and b whose distribution follows the recursion formula sl 1 sml 1snl where m n 1 2 3 and sl is a building block sequence for l or 2 an exact evaluation of the wavefunctions yields the scaling for several pairs of values of m and n numerical calculations of the wavefunction and the resistance reveal a rich self similar structure as well as localisation for one of the quasiperiodic sequences studied

boundary penalty finite element methods for blending surfaces ii biharmonic equations abstract in this paper the biharmonic equations are discussed and the boundary penalty finite methods bp fems using piecewise cubic hermite elements are chosen to seek their approximate solutions satisfying the normal derivative and periodical boundary conditions theoretical analysis is made to discover that when the penalty power 2 3 or 4 and 0

superior properties of the presb preconditioner for operators on two by two block form with square blocks matrices or operators in two by two block form with square blocks arise in numerous important applications such as in optimal control problems for pdes the problems are normally of very large scale so iterative solution methods must be used thereby the choice of an efficient and robust preconditioner is of crucial importance since some time a very efficient preconditioner the preconditioned square block presb method has been used by the authors and coauthors in various applications in particular for optimal control problems for pdes it has been shown to have excellent properties such as a very fast and robust rate of convergence that outperforms other methods in this paper the fundamental and most important properties of the method are stressed and presented with new and extended proofs under certain conditions the condition number of the preconditioned matrix is bounded by 2 or even smaller furthermore under certain assumptions the rate of convergence is superlinear

sufficient conditions for the asymptotic stability of interval matrices jiang 1987 gave a sufficient condition for the asymptotic stability of interval matrices we shall show here that his results can be derived in a trivial way using the lyapunov equation an extension of his results and a similar result for discrete systems is stated

stability robustness of interval matrices via lyapunov quadratic forms a sufficient condition for the robust stability of a class of interval matrices is derived using the lyapunov approach the matrices considered have elements which are nonlinear functions of a vector of independent and bounded parameters the robust stability condition requires that a quadratic form be positive definite in a finite number of conspicuous points of an enlarged parameter space

a sufficient condition for stability of a polytope of matrices abstract in this paper we study the stability of interval dynamical systems a sufficient condition for the stability of a polytope of matrices which is shown to be necessary and sufficient for a certain class of matrices is obtained the results developed can also be applied to the stability of a positive cone of matrices and sufficient conditions for the stability of interval dynamical systems are obtained a relationship between real parts of eigenvalues and matrix measures is also presented

on the approximation solvability of a class of strongly nonlinear elliptic problems on unbounded domains a class of strongly nonlinear boundary value problems posed on unbounded regions is considered a nonlocal coupling of the linearized far field exterior to an auxiliary boundary allows for approximations to be defined on domains of finite extent constructive existence results for bounded domains are then extended by employing an exhausting sequence of approximating domains in particular well posedness is seen to be equivalent to unique approximation solvability with the rate of convergence dependent upon the radius of the auxiliary boundary application to a model of proteins immersed in an electrolyte solution is made

estimation of the dispersion error in the numerical wave number of standard and stabilized finite element approximations of the helmholtz equation an estimator for the error in the wave number is presented in the context of finite element approximations of the helmholtz equation the proposed estimate is an extension of the ideas introduced in steffens and d iez comput methods appl mech engng 2009 198 1389 1400 in the previous work the error assessment technique was developed for standard galerkin approximations here the methodology is extended to deal also with stabilized approximations of the helmholtz equation thus the accuracy of the stabilized solutions is analyzed including also their sensitivity to the stabilization parameters depending on the mesh topology the procedure builds up an inexpensive approximation of the exact solution using post processing techniques standard in error estimation analysis from which the estimate of the error in the wave number is computed using a simple closed expression the recovery technique used in steffens and diez comput methods appl mech engng 2009 198 1389 1400 is based in a polynomial least squares fitting here a new recovery strategy is introduced using exponential in a complex setup trigonometric local approximations respecting the nature of the solution of the wave problem copyright 2011 john wiley sons ltd

finite element approximation of flow induced vibrations of human vocal folds model effects of inflow boundary conditions and the length of subglottal and supraglottal channel on phonation onset abstract the paper presents the numerical analysis of interaction of the vibrating simplified human vocal folds model with the incompressible viscous airflow in a channel modeling simplified subglottal and supraglottal spaces the flow in the considered 2d computational fluid domain is governed by the navier stokes equations written in the arbitrary lagrangian eulerian form the stabilized finite element method is applied for numerical approximation and the choice of boundary conditions and their implementation is discussed for the considered model problem the prescribed inlet velocity and prescribed pressure difference formulations were numerically analyzed the prescribed inlet velocity formulation was successful in predicting of the flutter velocity value whereas the prescribed pressure difference gave nonphysical results finally a modified inlet boundary condition motivated by the penalization approach is suggested it is shown that this approach gives possibilities to optimize the inlet boundary condition related to a physical reality by changing smoothly the penalty parameter in the interval between the two extremes and to treat the complete closures of the channel

boundary penalty techniques we examine techniques for enforcing dirichlet boundary data in finite element solution of boundary value problems the common programming strategy of adding a large number to certain diagonal entries and scaling the right side is compared with penalty methods by selectively underintegrating the continuous penalty formulation and selecting the penalty parameter e 1 optimally as a function of mesh size h we deduce the large number strategy and hence show that the optimal rate is preserved numerical experiments to study the rates for continuous penalty underintegrated penalty and large number strategies corroborate the argument

error analysis and preconditioning for an enhanced dtn fe algorithm for exterior scattering problems in this paper we present an error analysis for a high order accurate combined dirichlet to neumann dtn map finite element fe algorithm for solving two dimensional exterior scattering problems we advocate the use of an exact dtn or steklov poincare map at an artificial boundary exterior to the scatterer to truncate the unbounded computational region the advantage of using an exact dtn map is that it provides a transparent condition which does not reflect scattered waves unphysically our algorithm allows for the specification of quite general artificial boundaries which are perturbations of a circle to compute the dtn map on such a geometry we utilize a boundary perturbation method based upon recent theoretical work concerning the analyticity of the dtn map we also present some preliminary work concerning the preconditioning of the resulting system of linear equations including numerical experiments

on the convergence rate of the boundary penalty method the convergence rate of the boundary penalty finite element method is discussed for the poisson equation with inhomogeneous dirichlet boundary conditions on a polygonal domain it is proved that under certain circumstances an optimal convergence rate may be achieved which agrees with the rate obtained recently in the numerical experiments by utku and carey

boundary conditions for the numerical solution of elliptic equations in exterior regions elliptic equations in exterior regions frequently require a boundary condition at infinity to ensure the weill posedness of the problem examples of practical applications include the helmholtz equation and laplace s equation computational procedures based on a direct discretization of the elliptic problem require the replacement of the condition at infinity by a boundary condition on a finite artificial surface direct imposition of the condition at infinity along the finite boundary results in large errors a sequence of boundary conditions is developed which provides increasingly accurate approximations to the problem in the infinite domain estimates of the error due to the finite boundary are obtained for several cases computations are presented which demonstrate the increased accuracy that can be obtained by the use of the higher order boundary conditions the examples are based on a finite element formulation but finite difference methods can also be used

finite element approximations of the lame system with penalized ideal contact boundary conditions we consider finite element approximations of the lame system of elasticity with ideal contact boundary conditions imposed with the penalty method for a polygonal or polyhedral boundary we prove convergence estimates in terms of both the penalty and discretization parameters in the case of a smooth curved boundary we show through a numerical two dimensional example that convergence may not hold due to a babuska s type paradox we also propose and test numerically several remedies

finite element methods applied to nearly one way wave propagation abstract a numerical method is developed for approximately solving stationary wave propagation problems for which most of the energy propagates in an angle band of less than 90 about a fixed direction this property often occurs in realistic physical models the numerical method is based on factoring out the principal propagation direction in the solution and then applying the finite element method the method is applied to wave propagation in a duct or waveguide and to the exterior scattering problem it is shown both theoretically and by means of numerical examples that this method requires considerably less grid points and computational cost than standard discretization methods

on a coupled bulk surface allen cahn system with an affine linear transmission condition and its approximation by a robin boundary condition abstract we study a coupled bulk surface allen cahn system with an affine linear transmission condition that is the trace values of the bulk variable and the values of the surface variable are connected via an affine relation and this serves to generalize the usual dynamic boundary conditions we tackle the problem of well posedness via a penalization method using robin boundary conditions in particular for the relaxation problem the strong well posedness and long time behaviour of solutions can be shown for more general and possibly nonlinear relations new difficulties arise since the surface variable is no longer the trace of the bulk variable and uniform estimates in the relaxation parameter are scarce nevertheless weak convergence to the original problem with affine linear relations can be shown using the approach of colli and fukao 2015 we show strong existence to the original problem with affine linear relations and derive an error estimate between solutions to the relaxed and original problems

on sufficient conditions for the stability of interval matrices abstract we investigate the hurwitz and schur stability of interval matrices using lyapunov s second method and interval analysis techniques previous results require a check of the definiteness of 2 n n 1 2 concerns of a certain interval matrix the present results require a check of the definiteness of only 2 n 1 corners

total flux estimates for a finite element approximation of the dirichlet problem using the boundary penalty method this paper considers a fully practical piecewise linear finite element approximation of the dirichlet problem for a second order self adjoint elliptic equation au f in a smooth region n n 2 or 3 by the boundary penalty method using an unfitted mesh that is h an approximation of with dist h ch 2 is not in general a union of elements and assumingu h 4 we show that one can recover the total flux across a segment of the boundary of with an error ofo h 2 we use these results to study a fully practical piecewise linear finite element approximation of an elliptic equation by the boundary penalty method when the prescribed data on part of the boundary is the total flux

subdivision based nonlinear multiscale cloth simulation cloth simulation is an important topic for many applications in computer graphics animation and augmented virtual reality the mechanical behavior of cloth objects can be modeled by the kirchhoff

three dimensional finite element calculations in acoustic scattering using arbitrarily shaped convex artificial boundaries we report on a generalization of the bayliss gunzburger turkel non reflecting boundary conditions to arbitrarily shaped convex artificial boundaries for elongated scatterers such as submarines we show that this generalization can improve significantly the computational efficiency of finite element methods applied to the solution of three dimensional acoustic scattering problems copyright 2001 john wiley sons ltd

finite element approximation of the pure neumann problem using the iterative penalty method when we use penalty method to solve the pure neumann problem the associated stiffness matrix we get is ill conditioned which leads to the unstable computation in this paper we design an iterative penalty method for the problem and prove some error estimates in our algorithm we can use a not very small penalty parameter to avoid the unstable computation numerical examples are given to show the algorithm is very effective and powerful

a highly effective preconditioner for solving the finite element boundary integral matrix equation of 3 d scattering a highly effective preconditioner is presented for solving the system of equations obtained from the application of the hybrid finite element boundary integral fe bi method to three dimensional 3 d electromagnetic scattering problems different from widely used algebraic preconditioners the proposed one is based on a physical approximation and is constructed from the finite element method fem using an absorbing boundary condition abc on the truncation boundary it is shown that the large eigenvalues of the finite element fe abc system are similar to those of the fe bi system hence the preconditioned system has a spectrum distribution clustered around 1 in the complex plane consequently when a krylov subspace based method is employed to solve the preconditioned system the convergence can be greatly accelerated numerical results show that the proposed preconditioner can improve the convergence of an iterative solution by approximately two orders of magnitude for large problems

brief paper simultaneous schur stability of interval matrices interval matrix structures are ubiquitous in nature and engineering ordinarily in an uncertain system there is associated with a set of coupled interval matrices a basic issue of exploring its asymptotic stability here we introduce the notion of simultaneous schur stability by linking the concepts of the majorant and the joint spectral radius and prove the asymptotic stability of a set of interval matrices governed by simultaneous schur stability the present result may lead to the stability analysis of discrete dynamical interval systems

superlinear convergence using block preconditioners for the real system formulation of complex helmholtz equations abstract complex valued helmholtz equations arise in various applications and a lot of research has been devoted to finding efficient preconditioners for the iterative solution of their discretizations in this paper we consider the helmholtz equation rewritten in real valued block form and use a preconditioner in a special two by two block form we show that the corresponding preconditioned krylov iteration converges at a mesh independent superlinear rate

some properties of the arnoldi based methods for linear ill posed problems in this paper we study some properties of the classical arnoldi based methods for solving infinite dimensional linear equations involving compact operators these problems are intrinsically ill posed since a compact operator does not admit a bounded inverse we study the convergence properties and the ability of these algorithms to estimate the dominant singular values of the operator

construction of local boundary conditions for an eigenvalue problem using micro local analysis application to optical waveguide problems we present a general procedure based on the pseudo differential calculus for deriving artificial boundary conditions for an eigenvalue problem that characterizes the propagation of guided modes in optical waveguides this new approach allows the construction of local conditions that a are independent of the frequency regime b preserve the sparsity pattern of the finite element discretization and c are applicable to arbitrarily shaped convex artificial boundaries the last feature has the potential for reducing the size of the computational domain numerical results are presented to highlight the potential of conditions of order 1 2 and 1 for improving significantly the computational efficiency of finite element methods for the solution of optical waveguide problems

computing acoustic waves in an inhomogeneous medium of the plane by a coupling of spectral and finite elements in this paper we analyze a galerkin procedure based on a combination of finite and spectral elements for approximating a time harmonic acoustic wave scattered by a bounded inhomogeneity the finite element method used to approximate the near field in the region of inhomogeneity is coupled with a nonlocal boundary condition which consists in a linear integral equation this integral equation is discretized by a spectral galerkin approximation method we provide error estimates for the galerkin method propose fully discrete schemes based on elementary quadrature formulas and show that the perturbation due to this numerical integration gives rise to a quasi optimal rate of convergence we also suggest a method for implementing the algorithm using the preconditioned gmres method and provide some numerical results

convergence of krylov subspace solvers with schwarz preconditioner for the exterior maxwell problem the consideration of an integral representation as an exact boundary condition for the finite element resolution of wave propagation problems in exterior domain induces algorithmic difficulties in this paper we are interested in the resolution of an exterior maxwell problem in 3d as a first step we focus on the justification of an algorithm described in literature using an interpretation as a schwarz method the study of the convergence indicates that it depends significantly on the thickness of the domain of computation this analysis suggests the use of the finite element term of schwarz method as a preconditioner for use of krylov iterative solvers an analytical study of the case of a spherical perfect conductor indicates the efficiency of such approach the consideration of the preconditioner suggested by the schwarz method leads to a superlinear convergence of the gmres predicted by the analytical study and verified numerically

simplified sufficient conditions for the asymptotic stability of interval matrices it will be shown that the sufficient conditions for the asymptotic stability of interval matrices proved in mansour 1988 can be further simplified by considering only a part of the extreme matrices

towards optimal finite element error estimates for the penalized dirichlet problem in a domain with curved boundary we consider the finite element approximation of an elliptic problem with homogeneous dirichlet boundary conditions on a curved boundary and imposed using the penalty method we establish optimal h 1 error estimates with suitable assumptions on the penalty parameter e as a function of the elements size h our focus is on establishing these results with least restrictive assumptions possible on this dependency

numerical simulation for the problem of infinite elastic foundation in this paper we consider the numerical simulation for the problem of infinite elastic foundation a half circle artificial boundary is introduced and discrete artificial boundary condition on it is designed by using the direct method of lines then the original problem is reduced to a boundary value problem on a bounded computational domain furthermore finite element approximation of this boundary value problem defined in the bounded domain is considered the numerical results show that the artificial boundary condition given in this paper is very effective and more accurate than the neumann boundary condition which is often used in engineering literatures

analytical and numerical investigation of the performance of the bgt2 condition for low frequency acoustic scattering problems a mathematical and numerical analysis is performed to assess the performance of the second order bayliss gunzburger turkel bgt2 condition when applied to solving low frequency acoustic scattering problems in the case of elongated scatterers this investigation suggests that bgt2 retains an acceptable level of accuracy for relatively low wavenumber a damping effect is incorporated to the bgt2 condition in order to extend the range of satisfactory performance this damping procedure consists in adding only a constant imaginary part to the wavenumber the numerical results indicate that the modified version of bgt2 extends the range of satisfactory performance by improving the level of accuracy by up to two orders of magnitude guidelines on the appropriate choice of the damping coefficient are provided

determination of the complex acoustic scattering matrix of a right angled duct a method for determining the complete higher order scattering matrix of an acoustic discontinuity is developed the method is demonstrated for a right angled waveguide bend and the magnitude and phase of the reflection and transmission coefficients are extracted precisely the procedure is straightforward and based on the solutions to the helmholtz equation by the finite element method fem the consistency of the scattering coefficients found by this method is verified by their properties of symmetry and their accuracy is established by the conservation of energy the reliability of the new technique is further proved by means of an arbitrary sound source and by comparing the direct fem response to the reflection matrix calculation some features of the scattering matrix as a function of frequency are surprising such as the steps and reversion of the phase evolution or the complete loss of transmission of the incoming wave the methodology detailed in this paper can be extended to other multiport junctions such as t junctions or size discontinuities in ducts

a priori error analysis for hdg methods using extensions from subdomains to achieve boundary conformity we present the first a priori error analysis of a technique that allows us to numerically solve steady state diffusion problems defined on curved domains by using finite element methods defined in polyhedral subdomains dh for a wide variety of hybridizable discontinuous galerkin and mixed methods we prove that the order of convergence in the l2 norm of the approximate flux and scalar unknowns is optimal as long as the distance between the boundary of the original domain and that of the computational domain h is of order h we also prove that the l 2 norm of a projection of the error of the scalar variable superconverges with a full additional order when the distance between and h is of order h 5 4 but with only half an additional order when such a distance is of order h finally we present numerical experiments confirming the theoretical results and showing that even when the distance between and h is of order h the above mentioned projection of the error of the scalar variable can still superconverge with a full additional order

high frequency numerical analytic approximations for the separable acoustic wave equation abstract an algorithm which employs a combination of asymptotic and numerical methods to solve a sturm liouville problem arising from a separable acoustic wave equation is presented error criteria for switching between methods are derived implementation requires a decomposition of the index of refraction profile into separable subprofiles computing times and accuracies are compared with conventional methods

sufficient conditions for the stability of interval matrices the stability of interval dynamical systems is studied sufficient conditions for the polytope of interval matrices are examined and some of the proofs are greatly simplified more generally sufficient conditions are obtained and the approach taken in the new proofs has the potential for further generalizations of the result obtained in this paper

a nonconforming generalized finite element method for transmission problems we obtain quasi optimal rates of convergence for transmission interface problems on domains with smooth curved boundaries using a nonconforming generalized finite element method gfem more precisely we study the strongly elliptic problem pu sum partial j a ij partial i u f in a smooth bounded domain omega with dirichlet boundary conditions the coefficients a ij are piecewise smooth possibly with jump discontinuities along a smooth closed surface gamma called the interface which does not intersect the boundary of the domain we consider a sequence of approximation spaces s mu satisfying two conditions 1 nearly zero boundary and interface matching and 2 approximability which are similar to those in babuska nistor and tarfulea j comput appl math 218 2008 pp 175 183 then if u mu in s mu mu ge 1 is a sequence of galerkin approximations of the solution u to the interface problem the approximation error u u mu hat h 1 omega is

fixed mesh finite element approximations to a free boundary problem for an elliptic equation with an oblique derivative boundary condition a method for approximating the solution of an elliptic equation with an oblique derivative on a curved boundary using an unfitted finite element mesh is presented and analysed it is shown that the method retains the order of accuracy of the fitted mesh finite element method a similar result is obtained for a variational inequality the usefulness of this approach is then demonstrated by using it to approximate the solution of a free boundary problem on a fixed mesh

enhanced functional evaluation for the finite element penalty method abstract we analyze the impact of using the penalty method on the estimation of a prescribed solution functional or quantity of interest qoi specifically we consider the use of penalty methods to enforce dirichlet boundary constraints focusing our attention on boundary fluxes as qois we propose an enhanced estimator of the boundary flux that includes a term involving the derivative of the flux with respect to the penalty parameter we show that the new estimator reduces the error arising from the use of the penalty method from o to o a well posed adjoint problem associated with the boundary flux is also proposed following an analysis of the penalty method errors in the enhanced flux estimator are then controlled using adjoint based techniques several numerical experiments are presented to demonstrate that the enhanced estimator in combination with adjoint error estimation allows one to efficiently control both the discretization and penalty errors in target qois

simultaneous solution of large scale linear systems and eigenvalue problems with a parallel gmres method a method for simultaneous solution of large and sparse linearized equation sets and the corresponding eigenvalue problems is presented such problems arise from the discretization and the solution of nonlinear problems with the finite element method and newton iteration the method is based on a parallel version of the preconditioned gmres m by deflation the parallel code exploits the architecture of the computational clusters using the mpi message passing interface the convergence rate the parallel speedup and the memory requirements of the proposed method are reported and evaluated

a lagrange multiplier method for the finite element solution of elliptic interface problems using non matching meshes in this paper we propose a lagrange multiplier method for the finite element solution of multi domain elliptic partial differential equations using non matching meshes the interface lagrange multiplier is chosen with the purpose of avoiding the cumbersome integration of products of functions on unrelated meshes e g we will consider global polynomials as multiplier the ideas are illustrated using poisson s equation as a model and the proposed method is shown to be stable and optimally convergent numerical experiments demonstrating the theoretical results are also presented

stabilized lagrange multiplier methods for bilateral elastic contact with friction in most finite element fe codes contact is checked only at the nodes corresponding to the use of pointwise constraints however this approach might not be stable in case the bodies coming into contact have non matching grids at the contact interface to alleviate this problem we propose a stabilized lagrange multiplier method based on a global polynomial multiplier for the finite element solution of non linear elastic contact problems with non matching grids in particular our approach allows us to avoid integrating products of different finite element basis functions on the surface meshes at the contact zone

data driven pod galerkin reduced order model for turbulent flows abstract in this work we present a reduced order model which is specifically designed to deal with turbulent flows in a finite volume setting the method used to build the reduced order model is based on the idea of merging combining projection based techniques with data driven reduction strategies in particular the work presents a mixed strategy that exploits a data driven reduction method to approximate the eddy viscosity solution manifold and a classical pod galerkin projection approach for the velocity and the pressure fields respectively the newly proposed reduced order model has been validated on benchmark test cases in both steady and unsteady settings with reynolds up to r e o 10 5

isogeometric analysis for sixth order boundary value problems of gradient elastic kirchhoff plates abstract sixth order boundary value problems of a one parameter gradient elastic kirchhoff plate model are formulated in a weak form within an h 3 sobolev space setting with the corresponding equilibrium equations and general boundary conditions the corresponding conforming galerkin method is proposed with error estimates for discretizations satisfying c 2 continuity requirements continuity coercivity and consistency of the corresponding bilinear form are utilized for proving the theoretical results numerical computations with conforming isogeometric discretizations of c p 1 continuous nurbs basis functions of order p 3 confirm the theoretical results and illustrate the features of the problem for both statics and free vibrations in particular the effects of the additional boundary conditions and parameter dependent boundary layers corresponding to the gradient elasticity theory are addressed by the numerical examples

superlinear convergence of conjugate gradients we give a theoretical explanation for superlinear convergence behavior observed while solving large symmetric systems of equations using the conjugate gradient method or other krylov subspace methods we present a new bound on the relative error after n iterations this bound is valid in an asymptotic sense when the size n of the system grows together with the number of iterations the bound depends on the asymptotic eigenvalue distribution and on the ratio n n under appropriate conditions we show that the bound is asymptotically sharp our findings are related to some recent results concerning asymptotics of discrete orthogonal polynomials an important tool in our investigations is a constrained energy problem in logarithmic potential theory the new asymptotic bounds for the rate of convergence are illustrated by discussing toeplitz systems as well as a model problem stemming from the discretization of the poisson equation

a necessary and sufficient condition for robust asymptotic stability of time variant discrete systems a necessary and sufficient condition for the stability of time variant interval matrices is presented this condition allows stability to be tested by checking only products of vertex extreme matrices the implementation of the test in the form of an algorithm and two illustrative examples are provided

the finite element method with non uniform mesh sizes applied to the exterior helmholtz problem the finite element method with non uniform mesh sizes is employed to approximately solve helmholtz type equations in unbounded domains the given problem on an unbounded domain is replaced by an approximate problem on a bounded domain with the radiation condition replaced by an approximate radiation boundary condition on the artificial boundary this approximate problem is then solved using the finite element method with the mesh graded systematically in such a way that the element mesh sizes are increased as the distance from the origin increases this results in a great reduction in the number of equations to be solved it is proved that optimal error estimates hold inl 2 h 1 andl provided that certain relationships hold between the frequency mesh size and outer radius

high order unfitted finite element methods on level set domains using isoparametric mappings abstract we introduce a new class of unfitted finite element methods with high order accurate numerical integration over curved surfaces and volumes which are only implicitly defined by level set functions an unfitted finite element method which is suitable for the case of piecewise planar interfaces is combined with a parametric mapping of the underlying mesh resulting in an isoparametric unfitted finite element method the parametric mapping is constructed in a way such that the quality of the piecewise planar interface reconstruction is significantly improved allowing for high order accurate computations of unfitted domain and surface integrals we present the method discuss implementational aspects and present numerical examples which demonstrate the quality and potential of this method

convergence bounds of gmres with schwarz preconditioner for the scattering problem we consider the jacobi preconditioner of the gmres method introduced by liu and jin for the scattering problem ieee trans ante prop 2002 50 132 140 we explain why it is a particular form of the schwarz preconditioner with a complete overlap and specific transmission conditions so far a superlinear convergence has been predicted by the general theory without any additional indication on the convergence rates here we establish error bounds that provide accurate convergence rates in two and three dimensions courant weyl s min max principle applied to some kernel operators together with some polynomial approximation estimates are the milestones for the proofs

coupling of the ultra weak variational formulation and an integral representation using a fast multipole method in electromagnetism many different methods have been developed for the solution of the time harmonic maxwell equations in exterior domains at high frequency volume based methods have the drawback of needing an artificial boundary far from the obstacle integral formulations enable one to avoid this difficulty by solving a problem on the surface of the obstacle however integral operators imply dense systems with bad condition numbers the ultra weak variational formulation uwvf is a volume based method using plane wave basis functions that allows the use of a coarser mesh in comparison with more classical low order finite element methods however the uwvf still involves the problem of the artificial boundary in this paper we suggest the use of an integral representation of the unknown field to obtain an exact artificial boundary condition in this way the distance between the obstacle and the artificial boundary can be reduced the use of the fast multipole method ensures a low cost for the calculation of various integral operators used in the representation in this paper we describe the combined algorithm demonstrate its accuracy on a model problem and discuss the complexity of the algorithm

a note on the superlinear convergence of gmres in the paper it is shown how the rate of convergence of the gmres method for solving a linear operator equation lambda i k u f in a hilbert space is related to the degree of compactness of k measured by the products of its singular values

an interval kalman filtering with minimal conservatism abstract the interval kalman filtering ikf can handle parametric interval uncertainties of the system matrices and it computes the lower and upper boundaries of the estimated states in this paper we propose an alternative form of interval kalman filtering to reduce the conservatism inherent to the existing interval kalman filtering first we address why the existing interval kalman filtering scheme induces conservatism in the boundary estimation then to remove the conservatism we derive noise covariance matrices taking into account of interval uncertainties as well as process and measurement noises following the typical derivation process of the standard kalman filtering a new recursive form of interval kalman filtering is derived through numerical simulations the superiority of the new algorithm over existing ikf is illustrated

a fast finite difference method for propagation predictions over irregular inhomogeneous terrain propagation of electromagnetic waves over irregular inhomogeneous terrain is solved by a finite difference scheme the method is fast and requires considerably less memory than the integral equation methods the method requires a storage space of order o n and an execution time of order o n sup 2 fields generated by a te sub 2 line source are represented in an integral form in terms of the field over a flat constant impedance plane the incident field and the field scattered by the terrain irregularities and inhomogeneities accurate expressions are provided for the incident field and the green s function whose evaluation is otherwise accomplished by the rather time consuming sommerfeld s integrals measured equation of invariance is used to terminate the computational domain the sparse matrix generated by the method is inverted by the ricatti transform numerical results are presented for the ground wave as well as for the sky wave comparison is made for known geometries to establish the validity and limitations of the method

the local convergence of broyden like methods on lipschitzian problems in hilbert spaces the classical local convergence analysis for broyden s method requires a finite number of real variables holder continuity of the jacobian and a rather accurate initial approximation b 0 here these three conditions are relaxed to allow for lipschitz continuous hilbert space operators that can be reasonably well approximated by a linear operator b that is close to b 0 up to an arbitrary compact perturbation to achieve local and r linear convergence broyden s method is modified by a very mild line search condition in case of a continuously differentiable system in euclidean space we obtain r superlinear convergence without restricting b 0 or requiring the jacobian to be holder continuous

numerical accuracy of a pade type non reflecting boundary condition for the finite element solution of acoustic scattering problems at high frequency the present text deals with the numerical solution of two dimensional high frequency acoustic scattering problems using a new high order and asymptotic pade type artificial boundary condition the pade type condition is easy to implement in a galerkin least squares iterative finite element solver for arbitrarily convex shaped boundaries the method accuracy is investigated for different model problems and for the scattering problem by a submarine shaped scatterer as a result relatively small computational domains optimized according to the shape of the scatterer can be considered while yielding accurate computations for high frequencies copyright 2005 john wiley sons ltd

finite element approximation of the dirichlet problem using the boundary penalty method summary this paper considers a finite element approximation of the dirichlet problem for a second order self adjoint elliptic equation a u f in a region f2cn n 2 or 3 by the boundary penalty method if the finite element space defined over d h a union of elements has approximation power h in the l 2 norm then i for f2 d h convex polyhedral we show that choosing the penalty parameter e h x with 2 k yields optimal h 1 and l 2 error bounds if u hk i q

bayliss turkel like radiation conditions on surfaces of arbitrary shape this paper addresses the extension of the bayliss turkel second order radiation condition to an arbitrarily shaped surface the derivation is based mainly on the pseudo differential calculus as well as on the introduction of a criterion providing a precise handling of the approximation process involved in the derivation of the radiation condition the radiation condition then ranges among the most accurate of those of order two as a by product of the derivation almost all known radiation conditions of order less than or equal to two are recovered and their respective accuracies are compared

discrete qmr and bcg in the numerical solution of linear systems of odes in this paper we consider the use of qmr and bcg in the numerical solution of linear systems of odes reformulated as second kind integral equations the implementation of the methods is performed in practice by applying them on suitably discretized equations an important issue in this contest is to compare the behaviour of the discrete and continuous iteration here we consider the case of linear systems of odes the discretization is performed using a continuous runge kutta method a numerical experiment concludes the paper

weighted regularization of maxwell equations in polyhedral domains we present a new method of regularizing time harmonic maxwell equations by a bf grad div term adapted to the geometry of the domain this method applies to polygonal domains in two dimensions as well as to polyhedral domains in three dimensions in the presence of reentrant corners or edges the usual regularization is known to produce wrong solutions due the non density of smooth fields in the variational space we get rid of this undesirable effect by the introduction of special weights inside the divergence integral standard finite elements can then be used for the approximation of the solution this method proves to be numerically efficient

convergence property of interval matrices and interval polynomials in association with robust control system design and analysis the hurwitz property of interval matrices and interval polynomials has recently been actively investigated however its discrete counterpart the convergence property has seemingly not been much discussed in this paper this property is studied in comparison with the hurwitz counterpart some conditions under which interval matrices or interval polynomials are convergent are derived

extended states in aperiodic systems the existence of electronic states in aperiodic chains both the generalized fibonacci gf chain with the inflation rule a to ambn b to a and the generalized thue morse gtm a to ambn b to bnam chain is proved analytically there might be a critical value lambda c for the gf chain if the ratio va vb is greater than lambda c where va and vb are the potentials in the gf hopping hamiltonian our numerical calculation seems to show that the extended state will vanish

a novel hybridization of higher order finite element and boundary integral methods for electromagnetic scattering and radiation problems a novel hybridization of the finite element fe and boundary integral methods is presented for an efficient and accurate numerical analysis of electromagnetic scattering and radiation problems the proposed method derives an adaptive numerical absorbing boundary condition abc for the finite element solution based on boundary integral equations unlike the standard finite element boundary integral approach the proposed method is free of interior resonance and produces a purely sparse system matrix which can be solved very efficiently unlike the traditional finite element absorbing boundary condition approach the proposed method uses an arbitrarily shaped truncation boundary placed very close to the scatterer radiator to minimize the computational domain and more importantly the method produces a solution that converges to the true solution of the problem to demonstrate its great potential the proposed method is implemented using higher order curvilinear vector elements a mixed functional is designed to yield both electric and magnetic fields on an integration surface without numerical differentiation to be used in the calculation of the adaptive abc the required evaluation of boundary integrals is carried out using the multilevel fast multipole algorithm which greatly reduces both the memory requirement and cpu time the finite element equations are solved efficiently using the multifrontal algorithm a mathematical analysis is conducted to study the convergence of the method finally a number of numerical examples are given to illustrate its accuracy and efficiency

sufficient condition for the asymptotic stability of interval matrices the stability of interval matrices has been studied by bialas 1983 but bialas s main theorem on the stability of interval matrices has been shown to be false by barmish 1984 a new sufficient condition for the asymptotic stability of interval matrices is given in the present paper

power law bounds on transfer matrices and quantum dynamics in one dimension ii abstract we establish quantum dynamical lower bounds for a number of discrete one dimensional schrodinger operators these dynamical bounds are derived from power law upper bounds on the norms of transfer matrices we develop further the approach from part i and study many examples particular focus is put on models with finitely or at most countably many exceptional energies for which one can prove power law bounds on transfer matrices the models discussed in this paper include substitution models sturmian models a hierarchical model the prime model and a class of moderately sparse potentials

boundary penalty finite element methods for blending surfaces iii superconvergence and stability and examples abstract this paper is part iii of the study on blending surfaces by partial differential equations pdes the blending surfaces in three dimensions 3d are taken into account by three parametric functions x r t y r t and z r t the boundary penalty techniques are well suited to the complicated tangent i e normal derivative boundary conditions in engineering blending by following the previous papers parts i and ii in li j comput math 16 1998 457 480 j comput appl math 110 1999 155 176 the corresponding theoretical analysis is made to discover that when the penalty power 2 3 or 3 5 and 0 1 5 in the boundary penalty finite element methods bp fems optimal convergence rates superconvergence and optimal numerical stability can be achieved respectively several interesting samples of 3d blending surfaces are provided to display the remarkable advantages of the proposed approaches in this paper unique solutions of blending surfaces optimal blending surfaces in minimum energy ease in handling the complicated boundary constraint conditions and less cpu time and computer storage needed this paper and li j comput math 16 1998 457 480 j comput appl math provide a foundation of blending surfaces by pde solutions a new trend of computer geometric design

three dimensional approximate local dtn boundary conditions for prolate spheroid boundaries we propose a new class of approximate local dtn boundary conditions to be applied on prolate spheroidal shaped exterior boundaries when solving problems of acoustic scattering by elongated obstacles these conditions are a exact for the first modes b easy to implement and to parallelize c compatible with the local structure of the computational finite element scheme and d applicable to exterior ellipsoidal shaped boundaries that are more suitable in terms of cost effectiveness for surrounding elongated scatterers we investigate analytically and numerically the effect of the frequency regime and the slenderness of the boundary on the accuracy of these conditions we also compare their performance to the second order absorbing boundary condition bgt2 designed by bayliss gunzburger and turkel when expressed in prolate spheroid coordinates the analysis reveals that in the low frequency regime the new second order dtn condition dtn2 retains a good level of accuracy regardless of the slenderness of the boundary in addition the dtn2 boundary condition outperforms the bgt2 condition such superiority is clearly noticeable for large eccentricity values

edged based smoothed point interpolation method for acoustic radiation with perfectly matched layer abstract it is known that for exterior acoustics the domain based finite element method always encounters the accuracy loss for high wavenumbers and the difficulty in dealing with the sommerfeld radiation condition in this work by using the polynomial and radial bases with specific node selection schemes the point interpolation method with the generalized gradient smoothing technique is employed to improve the accuracy for acoustic computations the appropriately softened acoustical stiffness of the discrete model is constructed based on the edge based smoothing domains via the gradient smoothing technique in addition the perfectly matched layer technique enables the smoothed point interpolation method to investigate exterior acoustics the complex coordinate transformation is utilized to determine the proper parameters for the perfectly matched layer through theoretical and numerical analyses several typical acoustic problems are analyzed revealing that better accuracy is obtained by the present method compared with the finite element method especially for high wavenumbers