high frequency green s function for planar periodic phased arrays with skewed grid and polygonal contour the derivation of an uniform high frequency asymptotic representation of the array green s function agf for finite planar periodic phased arrays with arbitrary polygonal contour and skewed grid is presented this result generalizes those obtained in a series of recent papers in the case of rectangular phased arrays with rectangular grid for the treatment of the high frequency phenomena the actual finite array is rigorously decomposed in terms of canonical constituents i e infinite semi infinite and sectoral arrays the final result is a representation of the agf in terms of spatially truncated floquet waves fws and fw induced diffracted fields arising from the edges and vertices of the polygonal rim of the array consequently the number of field contributions necessary to reconstruct the total field is independent of the number of elements of the array leading to a very efficient algorithm a series of numerical results is provided to demonstrate the effectiveness of the high frequency representation

the fast multipole method fmm for electromagnetic scattering problems the fast multipole method fmm developed by v rokhlin 1990 to efficiently solve acoustic scattering problems is modified and adapted to the second kind integral equation formulation of electromagnetic scattering problems in two dimensions the present implementation treats the exterior dirichlet problem for two dimensional closed conducting objects of arbitrary geometry the fmm reduces the operation count for solving the second kind integral equation from o n sup 3 for gaussian elimination to o n sup 4 3 per conjugate gradient iteration where n is the number of sample points on the boundary of the scatterer a sample technique for accelerating convergence of the iterative method termed complexifying k the wavenumber is also presented this has the effect of bounding the condition number of the discrete system consequently the operation count of the entire fmm all iterations becomes o n sup 4 3 computational results for moderate values of ka where a is the characteristic size of the scatterer are given

a stream virtual element formulation of the stokes problem on polygonal meshes in this paper we propose and analyze a novel stream formulation of the virtual element method vem for the solution of the stokes problem the new formulation hinges upon the introduction of a suitable stream function space characterizing the divergence free subspace of discrete velocities and it is equivalent to the velocity pressure inf sup stable mimetic scheme presented in l beirao da veiga et al j comput phys 228 2009 pp 7215 7232 up to a suitable reformulation into the vem framework both schemes are thus stable and linearly convergent but the new method results to be more desirable as it employs much less degrees of freedom and it is based on a positive definite algebraic problem several numerical experiments assess the convergence properties of the new method and show its computational advantages with respect to the mimetic one

efficient calculation of large finite periodic structures based on surface wave analysis the electromagnetic modeling of practical finite periodic structures is a topic of growing interest due to the truncation of infinite periodic structures surface waves will be excited and localized near discontinuous interfaces leading to the edge effect in this work surface waves are numerically extracted and their magnitudes and decay rates are analyzed for different materials and geometries based on the exponential decay of the surface wave a novel method is developed by connecting the solution to the large finite array problem with that to a relatively small one to achieve low complexity and memory consumption the method numerically reconstructs propagating bloch waves and surface waves according to the bloch floquet theorem of periodic structures and translation invariant properties of semi infinite periodic structures respectively numerical examples are shown for near field distributions and far field radiation patterns the results obtained from small finite periodic structures capture the edge effect and agree well with the results by the rigorous element by element approach

the virtual element method for discrete fracture network simulations abstract in this work an optimization based approach presented in berrone et al 2013 2014 10 12 for discrete fracture network simulations is coupled with the virtual element method vem for the space discretization of the underlying darcy law the great flexibility of the vem in handling rather general polygonal elements allows in a natural way for an effective description of irregular solutions starting from an arbitrary triangulation which is built independently of the mesh on other fractures only partial conformity is in fact obtained with this approach numerical results performed on several dfn configurations confirm the viability and efficiency of the resulting method

barycentric coordinates for polytopes in wachspress 1975 1 theory was developed for constructing rational basis functions for convex polygons and polyhedra these barycentric coordinates were positive within the elements generalization to higher space dimensions is described here the gadj algorithm developed by dasgupta 2003 5 and in dasgupta and wachspress 2008 6 is crucial for simple construction of rational barycentric basis functions

acceleration of fast multipole method for large scale periodic structures with finite sizes using sub entire domain basis functions an acceleration technique to the fast multipole method fmm has been proposed to handle large scale problems of periodic structures in free space with finite sizes based on the accurate sub entire domain basis functions in the proposed algorithm only nine or 27 elements in the whole impedance matrix are required to be computed and stored for a two dimensional or three dimensional periodic structure and the matrix vector multiply can be performed efficiently using the combination of fast fourier transform and fmm the theoretical analysis and numerical results show that both the memory requirement and computational complexity are only of the order of o n with small constants where n is the total number of unknowns

virtual element methods for hyperbolic problems on polygonal meshes in the present paper we develop the virtual element method for hyperbolic problems on polygonal meshes considering the linear wave equations as our model problem after presenting the semi discrete scheme we derive the convergence estimates in h 1 semi norm and l 2 norm moreover we develop a theoretical analysis on the stability for the fully discrete problem by comparing the newmark method and the bathe method finally we show the practical behaviour of the proposed method through a large set of numerical tests

non null lie quadratics in e3 interpolation problems in the space so 3 of rotations of euclidean 3 space e3 are reviewed in secs i s2 as background and motivation to a study of curves in e3 called lie quadratics except for a special class called null lie quadratics have resisted analysis until now the rest of the present paper is devoted to new results showing non null lie quadratics have rich analytical geometrical and asymptotic structures rates of growth are studied using differential equations and inequalities lie quadratics are proved to be extendible over the whole of r and existence of axes is proved under fairly general conditions examples show sharpness of many results

virtual element method for a nonlocal elliptic problem of kirchhoff type on polygonal meshes abstract we consider the discretization of the nonlocal elliptic problem of kirchhoff type using the virtual element method vem over polygonal meshes the nonlocal diffusion coefficient is approximated by using the l 2 projection operator which is directly computable from the degrees of freedom however the presence of the nonlocal term reduces the sparsity of the jacobian matrix which would increase the computational burden to avoid this and to retain the sparsity of the jacobian the nonlinear system is replaced by an equivalent system inspired by the work on the fem by gudi 2012 the numerical results show that the proposed methodology yields optimal convergence rate in the l 2 norm theoretical estimates are derived for h 1 norms and are verified by solving a numerical example

parallel solvers for virtual element discretizations of elliptic equations in mixed form abstract the aim of this paper is twofold on the one hand we numerically test the performance of mixed virtual elements in three dimensions to solve the mixed formulation of three dimensional elliptic equations on polyhedral meshes on the other hand we focus on the parallel solution of the linear system arising from such discretization considering both direct and iterative parallel solvers in the latter case we develop two block preconditioners one based on the approximate schur complement and one on a regularization technique both these topics are numerically validated by several parallel tests performed on a linux cluster more specifically we show that the proposed virtual element discretization recovers the expected theoretical convergence rates and we analyze the performance of the direct and iterative parallel solvers taken into account

virtual element methods for plate bending problems abstract we discuss the application of virtual elements to linear plate bending problems in the kirchhoff love formulation as we shall see in the virtual element environment the treatment of the c 1 continuity condition is much easier than for traditional finite elements the main difference consists in the fact that traditional finite elements for every element k and for every given set of degrees of freedom require the use of a space of polynomials or piecewise polynomials for composite elements for which the given set of degrees of freedom is unisolvent for virtual elements instead we only need unisolvence for a space of smooth functions that contains a subset made of polynomials whose degree determines the accuracy as we shall see the non polynomial part of our local spaces does not need to be known in detail and therefore the construction of the local stiffness matrix is simple and can be done for much more general geometries

inexact trajectory planning and inverse problems in the hamilton pontryagin framework we study a trajectory planning problem whose solution path evolves by means of a lie group action and passes near a designated set of target positions at particular times this is a higher order variational problem in optimal control motivated by potential applications in computational anatomy and quantum control reduction by symmetry in such problems naturally summons methods from lie group theory and riemannian geometry a geometrically illuminating form of the euler lagrange equations is obtained from a higher order hamilton pontryagin variational formulation in this context the previously known node equations are recovered with a new interpretation as legendre ostrogradsky momenta possessing certain conservation properties three example applications are discussed as well as a numerical integration scheme that follows naturally from the hamilton pontryagin principle and preserves the geometric properties of the continuous time solution

on the virtual element method for three dimensional linear elasticity problems on arbitrary polyhedral meshes abstract we explore the recently proposed virtual element method vem for the numerical solution of boundary value problems on arbitrary polyhedral meshes more specifically we focus on the linear elasticity equations in three dimensions and elaborate upon the key concepts underlying the first order vem while the point of departure is a conforming galerkin framework the distinguishing feature of vem is that it does not require an explicit computation of the trial and test spaces thereby circumventing a barrier to standard finite element discretizations on arbitrary grids at the heart of the method is a particular kinematic decomposition of element deformation states which in turn leads to a corresponding decomposition of strain energy by capturing the energy of linear deformations exactly one can guarantee satisfaction of the patch test and optimal convergence of numerical solutions the decomposition itself is enabled by local projection maps that appropriately extract the rigid body motion and constant strain components of the deformation as we show computing these projection maps and subsequently the local stiffness matrices in practice reduces to the computation of purely geometric quantities in addition to discussing aspects of implementation of the method we present several numerical studies in order to verify convergence of the vem and evaluate its performance for various types of meshes

higher order bem based fem on polygonal meshes the bem based finite element method is reviewed and extended with higher order basis functions on general polygonal meshes these functions are defined implicitly as local solutions of the underlying homogeneous problem with constant coefficients they are treated by means of boundary integral formulations and are approximated using the boundary element method in the numerics to obtain higher order convergence a new approximation of the material coefficient is proposed since previous strategies are not sufficient following recent ideas error estimates are proved which guarantee quadratic convergence in the h 1 norm and cubic convergence in the l 2 norm the numerical realization is discussed and several experiments confirm the theoretical results

invariant higher order variational problems we investigate higher order geometric k splines for template matching on lie groups this is motivated by the need to apply diffeomorphic template matching to a series of images e g in longitudinal studies of computational anatomy our approach formulates euler poincar theory in higher order tangent spaces on lie groups in particular we develop the euler poincar formalism for higher order variational problems that are invariant under lie group transformations the theory is then applied to higher order template matching and the corresponding curves on the lie group of transformations are shown to satisfy higher order euler poincar equations the example of so 3 for template matching on the sphere is presented explicitly various cotangent bundle momentum maps emerge naturally that help organize the formulas we also present hamiltonian and hamilton ostrogradsky lie poisson formulations of the higher order euler poincar theory for applications on the hamiltonian side

convergence of the mimetic finite difference method for diffusion problems on polyhedral meshes the stability and convergence properties of the mimetic finite difference method for diffusion type problems on polyhedral meshes are analyzed the optimal convergence rates for the scalar and vector variables in the mixed formulation of the problem are proved

extended finite element method on polygonal and quadtree meshes in this paper we present mesh independent modeling of discontinuous flelds on polygonal and quadtree flnite element meshes this approach falls within the class of extended and generalized flnite element methods where the partition of unity framework is used to introduce additional enrichment functions within the classical displacement based flnite element approximation for crack modeling a discontinuous function and the two dimensional asymptotic crack tip flelds are used as enrichment functions linearly complete partition of unity approximations are adopted on polygonal convex and nonconvex elements and quadtree meshes excellent agreement with reference solution results is obtained for mixed mode stress intensity factors on benchmark crack problems and crack growth simulations without remeshing are conducted on polygonal and quadtree meshes to reveal the potential of the proposed techniques in computational failure mechanics

frequency domain green s function for a planar periodic semi infinite phased array i truncated floquet wave formulation this two part sequence deals with the derivation and physical interpretation of a uniform high frequency solution for the field radiated at finite distance by a planar semi infinite phased array of parallel elementary electric dipoles the field obtained by direct summation over the contributions from the individual radiators is restructured into a double series of wavenumber spectral integrals whose asymptotic reduction yields a series encompassing propagating and evanescent floquet waves fws together with corresponding diffracted rays which arise from scattering of the fw at the edge of the array the formal aspects of the solution are treated in the present paper they involve a sequence of manipulations in the complex spectral wavenumber planes that prepare the integrands for subsequent efficient and physically incisive asymptotics based on the method of steepest descent different species of spectral poles define the various species of propagating and evanescent fw their interception by the steepest descent path sdp determines the variety of shadow boundaries for the edge truncated fw the uniform asymptotic reduction of the sdp integrals performed by the van der waerden 1951 procedure and yielding a variety of edge diffracted fields completes the formal treatment

an improved monotone finite volume scheme for diffusion equation on polygonal meshes we construct a new nonlinear monotone finite volume scheme for diffusion equation on polygonal meshes the new scheme uses the cell edge unknowns instead of cell vertex unknowns as the auxiliary unknowns in order to improve the accuracy of monotone scheme our scheme is locally conservative and has only cell centered unknowns numerical results are presented to show how our scheme works for preserving positivity on various distorted meshes specially numerical results show that the new scheme is robust and more accurate than the existing monotone scheme on some kinds of meshes

a truncated floquet wave diffraction method for the full wave analysis of large phased arrays ii generalization to 3 d cases for pt i see ibid vol 48 no 3 p 594 600 2000 this paper deals with the generalization to three dimensional 3 d arrays of the truncated floquet wave tfw diffraction method for the full wave analysis of large arrays this generalization potentially includes arrays consisting of microstrip excited slots cavity backed apertures and patches the formulation is carried out first by deriving an appropriate fringe integral equation ie and next by defining entire domain basis functions in terms of global array functions shaped as tfw diffracted rays whose analytical expression is derived on the basis of prototype canonical problems the efficiency and the accuracy of this method is demonstrated by comparison with the results of an element by element full wave approach for a rectangular slot array

a displacement based finite element formulation for general polyhedra using harmonic shape functions summary a displacement based continuous galerkin finite element formulation for general polyhedra is presented for applications in nonlinear solid mechanics the polyhedra can have an arbitrary number of vertices or faces the faces of the polyhedra can have an arbitrary number of edges and can be nonplanar the polyhedra can be nonconvex with only the mild restriction of star convexity with respect to the vertex averaged centroid conforming shape functions are constructed using harmonic functions defined on the undeformed configuration thus requiring the use of a total lagrangian finite element formulation in large deformation applications for nonlinear applications with computationally intensive constitutive models it is important to minimize the number of element quadrature points for this reason an integration scheme is adopted in which the number of quadrature points is equal to the number of vertices as a first step toward verifying the element behavior in the general nonlinear setting several linear verification examples are presented using both random voronoi meshes and distorted hexahedral meshes for the hexahedral meshes results for the polyhedral formulation are compared to those of the standard trilinear hexahedral formulation the element behavior in the nearly incompressible regime is also examined copyright 2013 john wiley sons ltd

extendability of kirchhoff elastic rods in complete riemannian manifolds the kirchhoff elastic rod is a classical mathematical model of equilibrium configurations of thin elastic rods and is defined to be a solution of the euler lagrange equations associated to the energy with the effect of bending and twisting we consider the initial value problem for the euler lagrange equations in a riemannian manifold in a previous paper the author proved the existence and uniqueness of global solutions of the initial value problem in the case where the ambient space is a space form in the present paper we extend this result to the case where the ambient space is a general complete riemannian manifold this implies that an arbitrary kirchhoff elastic rod of finite length in a complete riemannian manifold extends to that of infinite length

asymptotic high frequency green s function for a large rectangular planar periodic phased array of dipoles with weakly tapered excitation in two dimensions this paper deals with the derivation and physical interpretation of a uniform high frequency representation of the green s function for a large planar rectangular phased array of dipoles with weakly varying excitation thereby our earlier published results valid for equiamplitude excitation and those for tapered illumination in one dimension are extended to tapering along both dimensions including dipole amplitudes tending to zero at the edges as previously the field obtained by direct summation over the contributions from the individual radiators is restructured into a double spectral integral whose high frequency asymptotic reduction yields a series of propagating and evanescent floquet waves fws together with corresponding fw modulated diffracted fields which arise from fw scattering at the array edges and vertexes to accommodate the weak amplitude tapering new generalized periodicity modulated edge and vertex slope transition functions are introduced accompanied by a systematic procedure for their numerical evaluation special attention is given to the analysis and physical interpretation of the complex vertex diffracted ray fields a sample calculation is included to demonstrate the accuracy of the asymptotic algorithm the resulting array green s function forms the basic building block for the full wave analysis of planar weakly amplitude tapered phased array antennas and for the description of electromagnetic radiation and scattering from weakly amplitude tapered rectangular periodic structures

a c 1 virtual element method for the cahn hilliard equation with polygonal meshes in this paper we develop an evolution of the c 1 virtual elements of minimal degree for the approximation of the cahn hilliard equation the proposed method has the advantage of being conforming in h 2 and making use of a very simple set of degrees of freedom namely 3 degrees of freedom per vertex of the mesh moreover although the present method is new also on triangles it can make use of general polygonal meshes as a theoretical and practical support we prove the convergence of the semidiscrete scheme and investigate the performance of the fully discrete scheme through a set of numerical tests

polygonal finite elements for topology optimization a unifying paradigm in topology optimization literature the parameterization of design is commonly carried out on uniform grids consisting of lagrangian type finite elements e g linear quads these formulations however suffer from numerical anomalies such as checkerboard patterns and one node connections which has prompted extensive research on these topics a problem less often noted is that the constrained geometry of these discretizations can cause bias in the orientation of members leading to mesh dependent sub optimal designs thus to address the geometric features of the spatial discretization we examine the use of unstructured meshes in reducing the influence of mesh geometry on topology optimization solutions more specifically we consider polygonal meshes constructed from voronoi tessellations which in addition to possessing higher degree of geometric isotropy allow for greater flexibility in discretizing complex domains without suffering from numerical instabilities copyright 2009 john wiley sons ltd

conforming polygonal finite elements summary in this paper conforming finite elements on polygon meshes are developed polygonal finite elements provide greater flexibility in mesh generation and are better suited for applications in solid mechanics which involve a significant change in the topology of the material domain in this study recent advances in meshfree approximations computational geometry and computer graphics are used to construct different trial and test approximations on polygonal elements a particular and notable contribution is the use of meshfree natural neighbour nn basis functions on a canonical element combined with an affine map to construct conforming approximations on convex polygons this numerical formulation enables the construction of conforming approximation on n gons n 3 and hence extends the potential applications of finite elements to convex polygons of arbitrary order numerical experiments on second order elliptic boundary value problems are presented to demonstrate the accuracy and convergence of the proposed method copyright 2004 john wiley sons ltd

truncated floquet wave full wave analysis of large phased arrays of open ended waveguides with a nonuniform amplitude excitation recently an efficient hybrid asymptotic method of moments mom approach has been proposed for the analysis of large periodic planar arrays of elements excited with equal amplitude and linear phase the aforementioned method which is based on a floquet wave diffraction representation of the array green s function agf is here extended to treat arrays with tapered amplitude excitation to this end the asymptotic agf is refined by introducing additional slope diffraction contributions an appropriate fringe integral equation solved via a mom scheme provides the effects of array truncation in addition to the infinite array solution the dimension of the corresponding linear algebraic system is independent of the number of elements of the array numerical results are provided to prove the accuracy and the efficiency of this method with respect to an ordinary element by element mom

null cubics and lie quadratics riemannian cubics are curves in a riemannian manifold m satisfying a variational condition they arise in computer graphics and in trajectory planning problems for rigid body motion where m is the group so 3 of rotations of euclidean three space e3 riemannian cubics on a lie group correspond to lie quadratics in the lie algebra there are only a few cases where closed form expressions are available for lie quadratics the present article is a qualitative analysis of null quadratics in so 3 focusing on long term dynamics and internal symmetries conclusions are drawn for asymptotics and symmetries of null cubics in so 3

a hybrid spectral spatial method to evaluate the active green s function of large planar rectangular arrays a combined asymptotic numerical algorithm the article illustrates a formulation to evaluate the array green s function agf of large finite planar phased array for observation points on the array plane possibly close to the array contour the procedure is based on the agf representation in terms of a double spectral integral whose integration paths are properly deformed to have an exponential attenuation of the integrand the diffraction integral is evaluated numerically for point close to the array edges while an asymptotic treatment is proposed far from the edges this latter comprises higher order contributions thanks to the convergence properties the final algorithm is numerically accurate stable and more efficient with respect to the individual element summation for large arrays it also constitutes the basic step for the efficient evaluation of the agf of a multilayer environment

a truncated floquet wave diffraction method for the full wave analysis of large phased arrays i basic principles and 2 d cases this two part sequence deals with the formulation of an efficient method for the full wave analysis of large phased array antennas this is based on the method of moments mom solution of a fringe integral equation ie in which the unknown function is the difference between the exact solution of the finite array and that of the associated infinite array the unknown currents can be interpreted as produced by the field diffracted at the array edge which is excited by the floquet waves fws pertinent to the infinite configuration following this physical interpretation the unknown in the ie is efficiently represented by a very small number of basis functions with domain on the entire array aperture in order to illustrate the basic concepts the first part of this sequence deals with the two dimensional example of a linearly phased slit array it is shown that the dominant phenomenon fur describing the current perturbation with respect to the infinite array is accurately represented in most cases by only three diffracted ray shaped unknown functions this also permits a simple interpretation of the element by element current oscillation which was described by other authors

a virtual element method for the acoustic vibration problem we analyze in this paper a virtual element approximation for the acoustic vibration problem we consider a variational formulation relying only on the fluid displacement and propose a discretization by means of mathrm h mathrm div h div virtual elements with vanishing rotor under standard assumptions on the meshes we show that the resulting scheme provides a correct approximation of the spectrum and prove optimal order error estimates with this end we prove approximation properties of the proposed virtual elements we also report some numerical tests supporting our theoretical results

riemannian cubics in quadratic matrix lie groups abstract quadratic matrix lie groups are subgroups of the general linear group that satisfy a quadratic matrix identity the main purpose of this paper is to consider riemannian cubics in quadratic matrix lie groups with left invariant metrics results for riemannian cubics in quadratic matrix lie groups extend those in so n since the group so n with bi invariant metric is a very special case by examining riemannian cubics in so 2 1 and so 3 1 we find that the so called null lie quadratics in so p q p 0 q 0 and even more generally for any quadratic matrix lie group can be given in closed forms in terms of lie quadratics in so p and so q further we present some quantitative analyses of non null lie quadratics in so p q

mimetic finite difference methods for hamiltonian wave equations in 2d abstract in this paper we consider the numerical solution of the hamiltonian wave equation in two spatial dimensions we construct a two step procedure in which we first discretize the space by the mimetic finite difference mfd method and then we employ a standard symplectic scheme to integrate the semi discrete hamiltonian system derived the main characteristic of the mfd methods when applied to stationary problems is to mimic important properties of the continuous system this approach yields a full numerical procedure suitable to integrate hamiltonian problems a complete theoretical analysis of the method and some numerical simulations are developed in the paper

arbitrary order nodal mimetic discretizations of elliptic problems on polygonal meshes we develop and analyze a new family of mimetic methods on unstructured polygonal meshes for the diffusion problem in primal form these methods are derived from the local consistency condition that is exact for polynomials of any degree m geq1 the degrees of freedom are a solution values at the quadrature nodes of the gauss lobatto formulas on each mesh edge and b solution moments inside polygons the convergence of the method is proven theoretically and an optimal error estimate is derived in a mesh dependent norm that mimics the energy norm numerical experiments confirm the convergence rate that is expected from the theory

a multilevel matrix decomposition algorithm for analyzing scattering from large structures a multilevel algorithm is presented for analyzing scattering from electrically large surfaces the algorithm accelerates the iterative solution of integral equations that arise in computational electromagnetics the algorithm permits a fast matrix vector multiplication by decomposing the traditional method of moment matrix into a large number of blocks with each describing the interaction between distant scatterers the multiplication of each block by a trial solution vector is executed using a multilevel scheme that resembles a fast fourier transform fft and that only relies on well known algebraic techniques the computational complexity and the memory requirements of the proposed algorithm are o n log sup 2 n

finding interpolating curves minimizing l infty acceleration in the euclidean space via optimal control theory we study the problem of finding an interpolating curve passing through prescribed points in the euclidean space the interpolating curve minimizes the pointwise maximum length i e l infty norm of its acceleration we reformulate the problem as an optimal control problem and employ simple but effective tools of optimal control theory we characterize solutions associated with singular and nonsingular controls some of the results we obtain are new even for the scalar interpolating function case we reduce the infinite dimensional interpolation problem to an ensuing finite dimensional one and derive closed form expressions for interpolating curves consequently we devise efficient numerical techniques and illustrate them with examples

jupp and kent s cubics in lie groups we study a generalization of the cubic polynomial to riemannian manifolds and other affine connection spaces modifying the differential equation x 4 0 by replacing higher derivatives with covariant derivatives in matrix groups with two particular choices of a left invariant connection we can convert the equation into a system of first order linear differential equations we give asymptotics in a generic case in gl n and in the n sphere

truncated floquet wave full wave t fw sup 2 analysis of large periodic arrays of rectangular waveguides a new hybrid technique has been recently proposed for the analysis of large periodic arrays this method is based on a high frequency representation of the active green s function of a finite array involving a floquet wave fw expansion with the relevant edge and vertex diffracted ray fields originating at the array border using this representation the unknown current of an appropriate fringe integral equation is expanded in terms of a few basis functions shaped as fw induced diffracted rays this representation drastically reduces the numerical effort and provides a physical insight into the mechanism of the array truncation in this paper this method is applied to the analysis of large arrays of rectangular waveguides opened on an infinite ground plane numerical results are shown to demonstrate the effectiveness and the numerical efficiency of the method

spectral properties and conservation laws in mimetic finite difference methods for pdes the mimetic finite difference mfd methods for pdes mimic crucial properties of mathematical systems duality and self adjointness of differential operators conservation laws and properties of the solution on general polytopal meshes in this article the structure and the spectral properties of the linear systems derived by the spatial discretization of diffusion problem are analysed in addition the numerical approximation of parabolic equations is discussed where the mfd approach is used in the space discretization while implicit method and explicit runge kutta chebyshev schemes are used in time discretization moreover we will show how the numerical solution preserves certain conservation laws of the theoretical solution

equivalent projectors for virtual element methods in the original virtual element space with degree of accuracy k projector operators in the h 1 seminorm onto polynomials of degree k can be easily computed on the other hand projections in the l 2 norm are available only on polynomials of degree k 2 directly from the degrees of freedom here we present a variant of the virtual element method that allows the exact computations of the l 2 projections on all polynomials of degree k the interest of this construction is illustrated with some simple examples including the construction of three dimensional virtual elements the treatment of lower order terms the treatment of the right hand side and the l 2 error estimates

numerical integration over arbitrary polygonal domains based on schwarz christoffel conformal mapping this paper presents a new numerical integration technique oil arbitrary polygonal domains the polygonal domain is mapped conformally to the unit disk using schwarz christoffel mapping and a midpoint quadrature rule defined oil this unit disk is used this method eliminates the need for a two level isoparametric mapping usually required moreover the positivity of the jacobian is guaranteed numerical results presented for a few benchmark problems in the context of polygonal finite elements show that the proposed method yields accurate results

multiresolution analysis of printed antennas and circuits a dual isoscalar approach a new approach is presented for the integral equation analysis of multilayer printed circuits antennas and arrays it is based on the introduction of new multiresolution vector functions with properties similar to those of the scalar wavelets and flexible enough to accommodate for general shapes the resulting method of moments mom impedance matrix shows a good conditioning that allows its safe sparsification and the efficient use of iterative methods for the solution of the linear system the results of the analysis of various real life structures show the advantage of the method

cubic spline algorithms for orientation interpolation this article presents a class of spline algorithms for generating orientation trajectories that approximately minimize angular acceleration each algorithm constructs a twice differentiable curve on the rotation group so 3 that interpolates a given ordered set of rotation matrices at specified knot times rotation matrices are parametrized respectively by the unit quaternion canonical co ordinate and cayley rodrigues representations all the algorithms share the common feature of i being invariant with respect to choice of fixed and moving frames bi invariant and ii being cubic in the parametrized co ordinates we assess the performance of these algorithms by comparing the resulting trajectories with the minimum angular acceleration curve copyright 1999 john wiley sons ltd

virtual elements for linear elasticity problems we discuss the application of virtual elements to linear elasticity problems for both the compressible and the nearly incompressible case virtual elements are very close to mimetic finite differences see for linear elasticity l beirao da veiga m2an math model numer anal 44 2010 pp 231 250 and in particular to higher order mimetic finite differences as such they share the good features of being able to represent in an exact way certain physical properties conservation incompressibility etc and of being applicable in very general geometries the advantage of virtual elements is the ductility that easily allows high order accuracy and high order continuity