calculation of the impedance matrix inner integral to prescribed precision we present a new method for evaluating the inner integral of the impedance matrix element in the traditional rao wilton glisson formulation of the method of moments for perfect conductors in this method we replace the original integrand modified by a constant phase factor by its taylor series and keep enough terms to guarantee a number of significant digits in the integration outcome we develop criteria that relate the number of taylor terms to the number of required significant digits we integrate the leading taylor terms analytically and the rest through iteration formulas we show that the iteration formulas converge for all observation points within a sphere with a radius of half a wavelength and center the triangle s centroid we compare results of our method with existing ones and find them in excellent agreement we also outline a procedure for using cubatures outside the region of convergence

calculation of cfie impedance matrix elements with rwg and n spl times rwg functions the method of moments mom solution of combined field integral equation cfie for electromagnetic scattering problems requires calculation of singular double surface integrals when galerkin s method with triangular vector basis functions rao wilton glisson functions and the cfie are applied to solve electromagnetic scattering by a dielectric object both rwg and n spl times rwg functions n is normal unit vector should be considered as testing functions robust and accurate methods based on the singularity extraction technique are presented to evaluate the impedance matrix elements of the cfie with these basis and test functions in computing the impedance matrix elements including the gradient of the green s function we can avoid the logarithmic singularity on the outer testing integral by modifying the integrand in the developed method all singularities are extracted and calculated in closed form and numerical integration is applied only for regular functions in addition we present compact iterative formulas for computing the extracted terms in closed form by these formulas we can extract any number of terms from the singular kernels of cfie formulations with rwg and n spl times rwg functions

a practical implementation and comparative assessment of the radial angular transform singularity cancellation method a practical numerical integration approach is proposed for the radial angular transform singularity cancellation sc method such that all singular and near singular integrals encountered in the method of moments mom solution of integral equations are evaluated to arbitrary pre specified error levels in the proposed approach the transformed mom integrals are evaluated using the progressive gauss patterson quadrature rules that provide on the fly error estimates these error estimates are used to automate the choice of quadrature rules in the sc method whose performance strongly varies from one impedance matrix entry to another this progressive numerical integration approach is carefully compared to a naive implementation of the sc method that uses static quadrature rules as well as to the more common singularity extraction se method specifically the sc and se methods are applied to the classical solution of the frequency domain electric field integral equation using rwg basis functions and several scattering problems are solved in the low and high frequency regimes of analysis numerical results show that although the proposed approach improves the efficiency of the sc method significantly the se method especially if high order asymptotic forms of green functions can be extracted remains the most efficient alternative when applicable

voter model on sierpinski fractals abstract we investigate the ordering of voter model on fractal lattices sierpinski carpets and sierpinski gasket we obtain a power law ordering in all cases but the dynamics is found to differ significantly for finite and infinite ramification order of investigated fractals

on numerical cubatures of singular surface integrals in boundary element methods we present and analyze methods for the accurate and efficient evaluation of weakly cauchy and hypersingular integrals over piecewise analytic curved surfaces in 3 the class of admissible integrands includes all kernels arising in the numerical solution of elliptic boundary value problems in three dimensional domains by the boundary integral equation method the possibly not absolutely integrable kernels of boundary integral operators in local coordinates are pseudohomogeneous with analytic characteristics depending on the local geometry of the surface at the source point this rules out weighted quadrature approaches with a fixed singular weight for weakly singular integrals it is shown that duffy s triangular coordinates leadalways to a removal of the kernel singularity also asymptotic estimates of the integration error are provided as the size of the boundary element patch tends to zero these are based on the rabinowitz richter estimates in connection with an asymptotic estimate of domains of analyticity in 2 it is further shown that the modified extrapolation approach due to lyness is in the weakly singular case always applicable corresponding error and asymptotic work estimates are presented for the weakly singular as well as for cauchy and hypersingular integrals which e g arise in the study of crack problems we analyze a family of product integration rules in local polar coordinates these rules are hierarchically constructed from finite part integration formulas in radial and gaussian formulas in angular direction again we show how the rabinowitz richter estimates can be applied providing asymptotic error estimates in terms of orders of the boundary element size

fast and accurate computation of hypersingular integrals in galerkin surface integral equation formulations via the direct evaluation method hypersingular 4 d integrals arising in the galerkin discretization of surface integral equation formulations are computed by means of the direct evaluation method the proposed scheme extends the basic idea of the singularity cancellation methods usually employed for the regularization of the singular integral kernel by utilizing a series of coordinate transformations combined with a reordering of the integrations the overall algebraic manipulation results in smooth 2 d integrals that can be easily evaluated via standard quadrature rules finally the reduction of the dimensionality of the original integrals together with the smooth behavior of the associated integrands lead up to unmatched accuracy and efficiency

toward a universal adaptive finite element strategy part 3 design of meshes abstract in this third paper in our series the issue of designing h p meshes which are optimal in some sense is addressed criteria for h p meshes are derived which are based on the idea of minimizing the estimated error over a mesh with a fixed number of degrees of freedom an optimization algorithm is developed based on these criteria and is applied to several model one dimensional and two dimensional elliptic boundary value problems numerical results indicate that the approach can lead to exponential rates of convergence

analysis of the equilibrated residual method for a posteriori error estimation on meshes with hanging nodes the equilibrated residual method is now accepted as the best residual type a posteriori error estimator nevertheless there remains a gap in the theory and practice of the method the present work tackles the problem of existence construction and stability of equilibrated fluxes for hp finite element approximation on hybrid meshes consisting of quadrilateral and triangular elements with hanging nodes a practical algorithm for post processing the finite element approximation is presented and shown to produce equilibrated fluxes for a general one irregular partition the resulting fluxes are shown to be stable in the sense that the associated error estimator provides a lower bound on the local error which does not degenerate with the mesh size numerical examples are included to illustrate the theoretical results

accurate and efficient numerical integration of weakly singular integrals in galerkin efie solutions a galerkin descretization of the electric field integral equation for perfectly conducting surfaces using rao wilton glisson 1982 basis functions requires the numerical evaluation of integrals with singular kernels over triangular regions these singularities have been traditionally handled by utilizing a singularity extraction procedure to produce a regular integral and an analytic function to replace the original singular integral a new approach is presented here in which the four dimensional 4 d weakly singular integrals unique to the galerkin rao wilton glisson electric field integral equation solution for perfectly conducting surfaces are transformed into integrals with regular integrands the transformations allow some of the integrations to be performed analytically in some cases reducing the original 4 d integral into a 1 d numerical integration the accuracy and convergence properties of the new method are demonstrated by evaluating the scalar potential function over a unit triangle

on the calculation of potential integrals for linear source distributions on triangular domains present analytical formulas for the singular field contributions of linear source distributions on triangular domains the formulas can be used for near field calculations of electric and magnetic source currents especially for the calculation of method of moments mom matrix elements due to the solution of surface integral equations for mom self coupling terms involving the scalar green function of free space the authors present expressions comprising analytical solutions of both the source integrals and the testing integrals

a posteriori error estimation of h p finite element approximations of frictional contact problems abstract dynamic and static frictional contact problems are described using the normal compliance law on the contact boundary dynamic problems are recast into quasistatic problems by time discretization an a posteriori error estimator is developed for a nonlinear elliptic equation of corresponding static or quasistatic problems the a posteriori error estimator is applied to a frictionless case and extended to frictional contact problems also an adaptive strategy is introduced and h p finite element meshes are obtained through a procedure based on a priori and a posteriori error estimations numerical examples are given to support the theoretical results

ising model on the sierpinski gasket thermodynamic limit versus infinitesimal field abstract owing to extremely slow decay of correlations the limit h 0 presents a poor approximation for the ising model on the sierpinski gasket we present evidence of the competitive interplay between finite size scaling and thermodynamic scaling for this model where both finite size and finite field induce an apparent phase transition these observations may be relevant for the behavior of porous magnetic materials in real laboratory conditions

on the generalization of directfn for singular integrals over quadrilateral patches a set of fully numerical algorithms for evaluating the 4 d singular integrals arising from galerkin surface integral equation methods over conforming quadrilateral meshes is presented this paper is an extension of directfn which was recently developed for the case of triangular patches utilizing in the same fashion a series of coordinate transformations together with appropriate integration reorderings and is applicable to coincident edge adjacent or vertex adjacent elements the resulting formulas consist of sufficiently smooth kernels and exhibit several favorable characteristics when compared with the vast majority of the methods currently available more specifically they can be applied without modifications to the following challenging cases 1 weakly and strongly singular kernels 2 basis and testing functions of arbitrary order 3 planar and curvilinear patches 4 problem specific green functions e g expressed in spectral integral form and 5 spectral convergence to machine precision finally we show that the overall performance of the fully numerical schemes can be further improved by a judicious choice of the integration order for each dimension

a straightforward structure to construct shape functions for variable p order meshes this paper describes a method for specifying variable p order meshes based on the topological hierarchy of mesh entities defining the finite elements a decomposition of p version mesh entity shape functions into a product of a function defined over the mesh entity and a blending function defined over the elements that the mesh entity bounds is presented the decomposed shape functions allow the effective construction of the shape functions and derivatives needed to construct element matrices for variable p enrichment

on an adaptive monotonic convection diffusion flux discretization scheme abstract the present paper concerns numerical investigation of a two dimensional steady convection diffusion scalar equation specific attention is given to resolving spurious oscillations in a confined region of high gradient in smooth regions a high order accurate solution is desired while in regions containing a sharp gradient the strategy of applying a monotonic capturing scheme is preferred in this paper we model fluxes by means of a finite element model which has spaces spanned by legendre polynomials the propensity to yield an irreducible diagonal dominant stiffness matrix is an attribute of this finite element flux discretization scheme fundamental analyses are extensively conducted in this paper in two areas first by conducting a modified equation analysis we are led to confirm the consistency of the scheme both the stability and monotonicity of the solutions are also addressed a guide for judging whether the stiffness matrix can yield a monotonic solution is rooted in the theory of the m matrix this monotonicity study provides us with greater numerical insight into the importance of the chosen peclet number beyond its critical value oscillatory solutions are present in the flow this monotonic region is however fairly restricted it is this shortcoming which limits the finite element practioner s choices for fairly small grid size the scope of application using the proposed upwind scheme is thus rather small because monotonic solutions are prohibitively expensive to compute circumvention of such deficiency is accomplished by making modifications to the structured grid several test cases have been employed to examine the grid adaption technique for the treatment of advection terms in flow regions having sharp gradients considerable savings in computer storage and execution time are achieved by the employed unstructured grid setting

singularity treatment and high order rwg basis functions for integral equations of electromagnetic scattering we present numerical implementation of high order rwg basis functions for electromagnetic scattering for curved conductor surfaces with a procedure for treating the singularities of dyadic green s functions in the mixed potential formulation of electromagnetic scattering copyright 2001 john wiley sons ltd

combining the higher order method of moments with geometric modeling by nurbs surfaces this paper introduces the nonuniform rational b spline nurbs surfaces to improve the geometric modeling of the higher order method of moments mom the electric field integral equation efie is discretized by the hierarchical higher order basis functions and converted to a matrix equation then the elements of the impedance matrix are efficiently evaluated by a new set of formulas the bistatic radar cross sections rcs obtained by this new technique are compared with those obtained by the commonly used higher order mom the example of a cylinder and a missile shows excellent accuracy of the nurbs surfaces and that of the resultant rcs moreover this new technique can fully exploit the flexibility of the higher order basis functions when the surface is highly curved whereas the commonly used higher order mom can not

toward a universal h p adaptive finite element strategy part 1 constrained approximation and data structure abstract this is the first of a series of papers devoted to the development of an adaptive finite element method to solve various boundary value problems arising in solid and fluid mechanics the paper deals with the general concepts of h p finite element methods constrained approximation and data structure and related issues several numerical examples illustrate the main ideas of the method

wamr an adaptive wavelet method for the simulation of compressible reacting flow part i accuracy and efficiency of algorithm abstract the wavelet adaptive multiresolution representation wamr method provides a robust method for controlling spatial grid adaptation fine grid spacing in regions where a solution varies greatly i e near steep gradients or near singularities and a much coarser grid where the solution varies slowly subsequently a wide range of spatial scales often demanded in challenging continuum physics problems can be efficiently captured furthermore the wavelet transform provides a direct measure of local error at each collocation point effectively producing automatically verified solutions the method is applied to the solution of unsteady compressible reactive flow equations and includes detailed diffusive transport and chemical kinetics models accuracy and performance of the method are examined on several test problems the sparse grids produced by the wamr method exhibit an impressive compression of the solution reducing the number of collocation points used by factors of many orders of magnitude when compared to uniform grids of equivalent resolution

machine precision evaluation of singular and nearly singular potential integrals by use of gauss quadrature formulas for rational functions a new technique for machine precision evaluation of singular and nearly singular potential integrals with 1 r singularities is presented the numerical quadrature scheme is based on a new rational expression for the integrands obtained by a cancellation procedure in particular by using library routines for gauss quadrature of rational functions readily available in the literature this new expression permits the exact numerical integration of singular static potentials associated with polynomial source distributions the rules to achieve the desired numerical accuracy for singular and nearly singular static and dynamic potential integrals are presented and discussed and several numerical examples are provided

evaluation of 4 d reaction integrals in the method of moments coplanar element case recently the benefits of simultaneously treating source and testing integrals in the numerical evaluation of 4 d reaction integrals have been reported the reported schemes usually first transform the reaction integral to parametric coordinates and some combination of radial angular and or line segment integrals is then used to treat coincident edge adjacent or vertex adjacent triangular source and test element pairs however advantages of the reported approaches are tempered by their lack of generality and severely degraded performance on poorly shaped elements the latter caused primarily by the parametric transformations severe distortion of the kernel s circularly concentric level contours here for coplanar element pairs and kernels with 1 r singularities we apply the surface divergence theorem twice to obtain a novel formula for 4 d reaction integrals generalizing earlier schemes while retaining their benefits and without distorting the original configuration space numerical results illustrate the method s efficiency which is improved by employing appropriate transformations to further smooth the resulting integrands and hence accelerate their convergence the reaction integral formula can be extended to noncoplanar elements

high order finite elements applied to the discrete boltzmann equation a discontinuous galerkin approach for solving the discrete boltzmann equation is presented allowing to compute approximate solutions for fluid flow problems based on a two dimensional high order finite element and an explicit euler time stepping scheme the d2q9 model is discretized and the results are compared to the exact solution of the navier stokes equation four numerical examples are considered including stationary and instationary problems with curved boundaries it is demonstrated that the proposed method allows to obtain the desired highly efficient exponential convergence copyright 2006 john wiley sons ltd

a self adaptive co ordinate transformation for efficient numerical evaluation of general boundary element integrals almost all general purpose boundary element computer packages include a curved geometry modelling capability thus numerical quadrature schemes play an important role in the efficiency of programming the technique the present work discusses this problem in detail and introduces efficient means of computing singular or nearly singular integrals currently found in two dimensional axisymmetric and three dimensional applications emphasis is given to a new third degree polynomial transformation which was found greatly to improve the accuracy of gaussian quadrature scheme s within the near singularity range the procedure can easily be implemented into existing be codes and presents the important feature of being self adaptive i e it produces a variable lumping of the gauss stations toward the singularity depending on the minimum distance from the source point to the element the self adaptiveness of the scheme also makes it inactive when not useful large source distances which makes it very safe for general usage

theoretical and numerical treatment of surface integrals involving the free space green s function this paper deals with the problem of the calculation of surface integrals for electromagnetic scattering in the case of the widely popular double triangular basis functions first introduced by rao wilton and glisson 1982 an entire set of formulas is obtained which overrides the difficulties inherent to the singularity of the integrands and results showing the stability accuracy and efficiency of the methods developed are reported in an application of the method of moments to the case of perfectly conducting surfaces and computation of near field in domains including the surface itself furthermore the authors provide insight as regards the capability of triangular basis functions to model near field patterns

a two dimensional thin film transistor simulation using adaptive computing technique abstract in this paper an adaptive computational technique is applied to solve a set of two dimensional 2d drift diffusion dd equations together with nonlinear trap model in thin film transistors tfts different from the conventional dd equations in metal oxide semiconductor field effect transistors the nonlinear trap model depending on the potential energy accounts for the effect of grain boundary on the electrical characteristics of low temperature polycrystalline silicon ltps tfts our adaptive computing technique is mainly based on gummel s decoupling method a finite volume fv approximation a monotone iterative mi method a posteriori error estimation and an 1 irregular meshing scheme applying gummel s decoupling method to the set of dd equations firstly each decoupled partial differential equation pde is then approximated with fv method over 1 irregular mesh instead of conventional newton s iterative method the corresponding system of nonlinear algebraic equations is solved with mi method variations of the computed solutions such as potential and electron density are captured and a posteriori error estimation scheme is adopted to assess the quality of the computed solutions the mesh is adaptively refined accordingly the numerical method converges monotonically in both mi and gummel s iteration loops respectively various cases of simulation have been verified for a typical ltps tft to demonstrate the accuracy and robustness of the method

static and dynamic potential integrals for linearly varying source distributions in two and three dimensional problems a technique for the evaluation of static and dynamic potentials due to source distributions defined on domains with simple shape is presented the domains considered are polyhedral regions and in two dimensional problems plane polygons on which uniform or linearly varying source distributions are defined it is shown how three dimensional two dimensional potential integrals are always reducible to surface line integrals with nonsingular kernel by use of a nonlinear transformation for the integration variables that permits analytic integration in the static case the integration on the boundary is performed analytically and closed form results are given in the dynamic case the expressions of the boundary integrals are given in a form suitable for numerical integration the use of matrix notation allows for very compact expressions readily translatable into computer programs

numerical evaluation via singularity cancellation schemes of near singular integrals involving the gradient of helmholtz type potentials in this paper we present a purely numerical procedure to evaluate strongly near singular integrals involving the gradient of helmholtz type potentials for observation points at finite arbitrarily small distances from the source domain in the proposed approach the source domain is subdivided into a disc plus truncated subtriangles and proper variable transformations are applied in each integration domain to exactly cancel the kernel singularity a novel feature of the proposed angular transform is that required discrete values of the inverse transform which is transcendental are determined via a root finding procedure the same idea can also be applied to other transforms that arise in singularity cancellation methods the resulting integral may then evaluated via a low order gauss legendre quadrature scheme

stability and convergence of nonconforming hp finite element methods the stability and convergence of nonconforming hp finite element methods in par ticular the mortar finite element method and its variants are established based on a new stability measure for these methods using a generalized eigenvalue analysis estimates for this measure are computed numerically our numerical results demonstrate that these nonconforming methods prove to be good candidates for hp implementation and also behave ss well as conforming finite element methods the discussion here ls primarily in two dimensions but some extensions to three dimensions

quadrature over a pyramid or cube of integrands with a singularity at a vertex a simple transformation is introduced which facilitates the evaluation of integrals over certain square based pyramids or cubes in cases where the integrand has a singularity at a vertex

adaptive multiresolution antenna modeling using hierarchical mixed order tangential vector finite elements hierarchical mixed order tangential vector finite elements tvfes for tetrahedra are attractive for accurate and efficient finite element or hybrid finite element boundary integral fe bi simulation of complicated electromagnetic problems they provide versatility in the geometrical modeling of physical structures guarantee solutions free of spurious modes and allow a local increase of resolution by combination of mixed order tvfes of different orders within a computational domain regions with higher order mixed order tvfes can be selected a priori or be found adaptively via methods for a posteriori error estimation or indication this paper demonstrates the merits of various explicit residual methods for a posteriori error indication via adaptive refinement of fe bi solutions of electromagnetic radiation problems using hierarchical mixed order tvfes for tetrahedra

on the direct evaluation of weakly singular integrals in galerkin mixed potential integral equation formulations weakly singular integrals over coincident triangles arising in the galerkin discretization of mixed potential integral equation formulations are calculated using a direct evaluation method the proposed method utilizes a series of coordinate transformations together with a re ordering of the integrations in order to reduce the dimensionality of the original four dimensional 4d weakly singular integrals into 1d numerical integrations of smooth functions the final formulas can be easily evaluated with a standard gaussian quadrature rule resulting in a scheme with great accuracy and efficiency properties numerical results for the comparison of the proposed method with both singularity subtraction and singularity cancellation methods often used for the evaluation of multidimensional singular integrals are presented indicating the superior overall performance of the direct evaluation scheme

on weak residual error estimation a general framework for weak residual error estimators applying to various types of boundary value problems in connection with finite element and finite volume approximations is developed basic ideas commonly shared by various applications in error estimation and adaptive computation are presented and illustrated some numerical results are given to show the effectiveness and efficiency of the estimators

stable fft jvie solvers for fast analysis of highly inhomogeneous dielectric objects abstract a stable volume integral equation formulation based on equivalent volumetric currents is presented for modeling electromagnetic scattering of highly inhomogeneous dielectric objects the proposed formulation is numerically solved by means of galerkin method of moments on uniform grids allowing for acceleration of the matrix vector products associated with the iterative solver with the help of fft in addition the pertinent volume volume galerkin inner products are reduced to purely surface surface integrals with smoother kernels allowing for highly accurate and fast computation by readily available sophisticated cubatures numerical results demonstrate the convergence properties of the algorithm for scatterers with high dielectric contrast in addition we describe a road map for magnetic resonance specific volume integral equations fast solvers based on the proposed algorithm

xfem with hanging nodes for two phase incompressible flow this study develops the h version of the extended finite element method xfem applied to the simulation of two fluid incompressible flow in two and three dimensions a multilevel adaptive mesh refinement realized via hanging nodes on 1 irregular meshes is employed in the vicinity of the two fluid interface the sign enrichment is used for the xfem approximation which accurately accounts for the jump in the pressure field the level set method is used for the implicit representation of the interface the laplace beltrami technique is employed for the modelling of the surface tension which avoids the explicit computation of the curvature an emphasis of this work is on how the interplay between the interface movement in terms of a time dependent level set function the adaptive refinement and the enriched xfem approximations is realized this study also demonstrates that the approximation of the normal vector to the interface required for the computation of the surface tension can have a significant impact on the accuracy of the solver several two and three dimensional test cases are investigated

singularity extraction technique for integral equation methods with higher order basis functions on plane triangles and tetrahedra a numerical solution of integral equations typically requires calculation of integrals with singular kernels the integration of singular terms can be considered either by purely numerical techniques e g duffy s method polar co ordinate transformation or by singularity extraction in the latter method the extracted singular integral is calculated in closed form and the remaining integral is calculated numerically this method has been well established for linear and constant shape functions in this paper we extend the method for polynomial shape functions of arbitrary order we present recursive formulas by which we can extract any number of terms from the singular kernel defined by the fundamental solution of the helmholtz equation or its gradient and integrate the extracted terms times a polynomial shape function in closed form over plane triangles or tetrahedra the presented formulas generalize the singularity extraction technique for surface and volume integral equation methods with high order basis functions numerical experiments show that the developed method leads to a more accurate and robust integration scheme and in many cases also a faster method than for example duffy s transformation copyright 2003 john wiley sons ltd

singularity subtraction technique for high order polynomial vector basis functions on planar triangles in this paper a singularity subtraction technique is developed for computing the impedance matrix elements of various electromagnetic surface integral equation formulations with the galerkin method and high order basis functions analytical closed form formulas for computing surface integrals with r r sup n n spl ges 3 singularities times polynomial nodal shape functions of arbitrary order on a planar triangle are presented

analytical shape derivatives of the mfie system matrix discretized with rwg functions an analytical formula for the shape derivative of the magnetic field integral equation mfie method of moments mom system matrix or impedance matrix is derived and validated against finite difference formulas the motivation for computing the shape derivatives stems from adjoint variable methods avm the galerkin system matrix is constructed by means of rao wilton glisson rwg basis and testing functions the shape derivative formula yields an integral representation which is of same singularity order as the integrals appearing in the traditional mfie system matrix

duffy method for evaluation of weakly singular sie potential integrals over curved quadrilaterals with higher order basis functions a duffy method for singularity cancellation is proposed for evaluation of weakly singular potential integrals defined on generalized curved parametric quadrilateral patches with polynomial basis functions such integrals arise in evaluation of galerkin matrix elements in method of moments analysis of antennas and scatterers in cases of coincident source and test elements examples demonstrate that the proposed duffy method is more accurate more rapidly converging with the increase of orders of gauss legendre integration formulas and faster to execute than four other methods for singularity treatment considered in the study

numerical evaluation of singular and near singular potential integrals a simple and efficient numerical procedure using a singularity cancellation scheme is presented for evaluating singular and near singular potential integrals with 1 r singularities the procedure not only has several advantages over singularity subtraction methods but also improves on some aspects of other singularity cancellation methods such as polar and duffy transformations a theoretical analysis is presented for triangles quadrilaterals tetrahedrons bricks and prisms and numerical results are presented for triangles and prisms

higher order frequency domain computational electromagnetics a review of the higher order computational electromagnetics cem for antenna wireless and microwave engineering applications is presented higher order cem techniques use current field basis functions of higher orders defined on large e g on the order of a wavelength in each dimension curvilinear geometrical elements which greatly reduces the number of unknowns for a given problem the paper reviews all major surface volume integral and differential equation electromagnetic formulations within a higher order computational framework focusing on frequency domain solutions with a systematic and unified review of generalized curved parametric quadrilateral triangular hexahedral and tetrahedral elements and various types of higher order hierarchical and interpolatory vector basis functions in both divergence and curl conforming arrangements a large number of actual higher order techniques representing various combinations of formulations elements bases and solution procedures are identified and discussed the examples demonstrate the accuracy efficiency and versatility of higher order techniques and their advantages over low order discretizations the most important one being a much faster higher order convergence of the solution it is demonstrated that both components of the higher order modeling namely higher order geometrical modeling and higher order current field modeling are essential for accurate and efficient cem analysis of general antenna scattering and microwave structures

hp submeshing via non conforming finite element methods abstract non conformity in the hp version can involve incompatibility in both the degrees and the meshes between adjoining subdomains in this paper we show how the mortar finite element method m0 and two new variants m1 m2 can be used to join together such incompatible hp sub discretizations our results show optimality of the resulting non conforming method for various h p and hp discretizations including the case of exponential hp convergence over geometric meshes we also present numerical results for the lagrange multiplier when the method is implemented via a mixed method three dimensional considerations suggest that our methods m1 m2 are easier to generalize to arbitrary meshes than m0

an explicit a posteriori error indicator for electromagnetic finite element boundary integral analysis within the finite element method fem there is always an error associated with the solution quantifying this error is a very important aspect of fe analysis since it can increase confidence in a solution and can be used to drive adaptive refinements of the discretization optimizing the quality of the solution relative to the number of degrees of freedom and in turn reducing computational cost this paper presents an a posteriori error indicator for time harmonic electromagnetic analysis in three dimensions when using a galerkin fe approach with curl conforming elements and including a nonlocal boundary integral boundary condition as well as a dominant mode port boundary condition the error indicator is residual based of an explicit nature and constitutes a bound on an error energy measure the error indicator is evaluated by presenting results relating to common microwave engineering applications which shows that it can be used successfully to estimate the relative error distribution and that it can successfully serve within an adaptive algorithm

complete semi analytical treatment of weakly singular integrals on planar triangles via the direct evaluation method keywords galerkin inner products method of moments mixed potential integral equations weakly singular integrals linear source distributions surface integrals potential integrals electromagnetic scattering numerical evaluation greens function shape transformation quadrature equations reference lema article 2010 007doi 10 1002 nme 2877view record in web of science record created on 2010 01 20 modified on 2016 08 08

higher order conformal decomposition fem cdfem abstract a higher order accurate finite element method is proposed which uses automatically generated meshes based on implicit level set data for the description of boundaries and interfaces in two and three dimensions the method is an alternative for fictitious domain and extended finite element methods the domain of interest is immersed in a background mesh composed by higher order elements the zero level sets are identified and meshed followed by a decomposition of the cut background elements into conforming sub elements adaptivity is a crucial ingredient of the method to guarantee the success of the mesh generation it ensures the successful decomposition of cut elements and enables improved geometry descriptions and approximations it is confirmed that higher order accurate results with optimal convergence rates are achieved with the proposed conformal decomposition finite element method cdfem

potential integrals for uniform and linear source distributions on polygonal and polyhedral domains formulas for the potentials due to uniform and linearly varying source distributions defined on simply shaped domains are systematically developed and presented domains considered are infinite planar strips infinite cylinders of polygonal cross sections planar surfaces with polygonal boundaries and volumetric regions with polyhedral boundaries the expressions obtained are compact in form and their application in the numerical solution of electromagnetics problems by the method of moments is illustrated

the h p and h p versions of the finite element method in 1 dimension this paper is the first one in the series of three which are addressing in detail the properties of the three basic versions of the finite element method in the one dimensional setting the main emphasis is placed on the analysis when the exact solution has singularity of x type the first part analyzes thep version the second theh version and generalh p version and the final third part addresses the problems of the adaptiveh p version

a hierarchical iterative procedure for the analysis of composite laminates a multilevel recursively defined preconditioner for use with the preconditioned conjugate gradient pcg algorithm is developed and applied to solve thin and thick laminated plate problems the preconditioner is constructed from a sequence of hierarchical vector spaces arising from the p version of the finite element fe method numerical studies have been conducted using quadrilateral elements for two dimensional problems up to p 8 and serendipity brick elements for three dimensional problems up to p 5 the efficiency of the iterative procedure is illustrated using bending response of laminated plates the effects of element span ratios convergence tolerance polynomial order material properties and plate span ratios on the number of iterations required for convergence has been investigated results indicate that the preconditioner developed herein can be used to produce an efficient iterative solver for two and three dimensional problems in structural mechanics

application of hp adaptive be fe methods to elastic scattering abstract the investigation focuses on the development of hp adaptive methods for simulation of acoustical scattering problems the present formulation is based on steady state linear elasticity equations coupled with the burton miller integral equation representing the behavior of a surrounding acoustical medium the highlights of the proposed approach include a mathematically consistent variational formulation of the problem an hp adaptive fe be approximation based on standard galerkin methods an element by element solver a residual based a posteriori error estimate an hp adaptive strategy particular attention is given to asymptotic convergence and to a comparison of theory and numerical simulations

the h p adaptive finite element method for the numerical simulation of compressible flow an h p adaptive finite element method is presented for the numerical simulation of compressible fluid flow in addition to refining the mesh in regions where the estimated error is large the polynomial degree of the elements is increased it is shown that by using high order polynomials highly accurate approximations are obtained to a regularized form of the equations governing viscous compressible flow

on the numerical integration of the linear shape functions times the 3 d green s function or its gradient on a plane triangle formulas for the static and dynamic potentials due to linearly varying source distributions defined on a planar triangle are presented the general linear variation of the source is represented in terms of three linear basis functions each one associated with a different vertex of the triangular domain the singular kernels considered are given by the 3 d green s function and its gradient both for the static and dynamic case in the static case the evaluation of potentials is performed analytically and compact form results are given in the dynamic case the results are given in a form suited for numerical integration

exact results for kinetics of catalytic reactions the kinetics of an irreversible catalytic reaction on substrate of arbitrary dimension is examined in the limit of infinitesimal reaction rate reaction controlled limit we solve the dimer dimer surface reaction model or voter model exactly in arbitrary dimension d the density of reactive interfaces is found to exhibit a power law decay for d 2 and a slow logarithmic decay in two dimensions we discuss the relevance of these results for the monomer monomer surface reaction model

a new 3d finite element for adaptive h refinement in 1 irregular meshes a new finite element viable for use in the three dimensional simulation of transient physical processes with sharply varying solutions is presented the element is intended to function in adaptive h refinement schemes as a versatile transition between regions of different refinement levels ensuring interelement continuity by constructing a piecewise linear solution at the element boundaries and retaining all degrees of freedom in the solution phase construction of the element shape functions is described and a numerical example is presented which illustrates the advantages of using such an element in an adaptive refinement problem the new element can be used in moving front problems such as those found in reservoir engineering and groundwater flow applications

higher order hierarchical legendre basis functions for electromagnetic modeling this paper presents a new hierarchical basis of arbitrary order for integral equations solved with the method of moments mom the basis is derived from orthogonal legendre polynomials which are modified to impose continuity of vector quantities between neighboring elements while maintaining most of their desirable features expressions are presented for wire surface and volume elements but emphasis is given to the surface elements in this case the new hierarchical basis leads to a near orthogonal expansion of the unknown surface current and implicitly an orthogonal expansion of the surface charge in addition all higher order terms in the expansion have two vanishing moments in contrast to existing formulations these properties allow the use of very high order basis functions without introducing ill conditioning of the resulting mom matrix numerical results confirm that the condition number of the mom matrix obtained with this new basis is much lower than existing higher order interpolatory and hierarchical basis functions as a consequence of the excellent condition numbers we demonstrate that even very high order mom systems e g tenth order can be solved efficiently with an iterative solver in relatively few iterations

an accurate method for the calculation of singular integrals arising in time domain integral equation analysis of electromagnetic scattering an accurate method for the evaluation of the cauchy principal value integrals arising in time domain electromagnetic wave scattering is presented this is applied to a boundary integral equation bie method employing quadratic curvilinear surface elements where such singularities do not vanish as they generally do when simpler but less accurate discretizations are employed the technique involves weakening the singularity in the original kernel to a degree where conventional integration methods may be employed and transforming the strong singularity to a line integral in a form which allows cancellation of its singular components the effectiveness of the method is demonstrated by scattering calculations on a variety of targets and the computational cost of the approach is trivial

adaptive singularity cancellation for efficient treatment of near singular and near hypersingular integrals in surface integral equation formulations a proposed singularity cancellation technique for fully numerical evaluation of method of moments integrals in surface integral equation solutions produces reasonably accurate results with few quadrature points for singular and hypersingular integrals however for near singular and near hypersingular integrals time consuming computations need to be repeatedly performed over unnecessary regions outside the actual integration domain for a more efficient treatment of these integrals an adaptive singularity cancellation technique is proposed as such the source triangular domain is subdivided in a way that all sample points remain inside the desired integration domain and unnecessary computations are avoided second the accuracy of results in existing singularity cancellation transformations is greatly affected by variations in height of observation point above the plane of source domain this drawback has been removed in the adaptive singularity cancellation transformations additionally an optimum selection criterion for the distribution of quadrature samples is presented the criterion enables run time selection of optimum number of samples in different directions by consideration of the instantaneous geometry of the transformed integration domain

free vibration analysis of membranes using the h p version of the finite element method abstract the h p version of the finite element method is applied to the vibration of membranes this is accomplished using a polynomially enriched triangular element new simple expressions of hierarchical c 0 shape functions for triangles are given in terms of the shifted legendre orthogonal polynomials the h p version of the finite element method marries both the concepts of the conventional h version and the p version the accuracy of the solution is sought by simultaneously refining the mesh and increasing the polynomial order in each element results of frequency calculations are found for triangular and l shaped membranes using a number of meshes and polynomial orders it is shown that the h p version of the finite element method is always convergent from above and produces a high accuracy with few degrees of freedom

a family of augmented duffy transformations for near singularity cancellation quadrature a new family of systematically constructed near singularity cancellation transformations is presented yielding quadrature rules for integrating near singular kernels over triangular surfaces this family results from a structured augmentation of the well known duffy transformation the benefits of near singularity cancellation quadrature are that no analytical integral evaluations are required and applicability in higher order basis function and curvilinear settings six specific transformations are constructed for near singularities of orders one two and three two of these transformations are found to be equivalent to existing ones the performance of the new schemes is thoroughly assessed and compared with that of existing schemes results for the gradient of the scalar green function are also presented for simplicity static kernel results are shown the new schemes are competitive with and in some cases superior to the existing schemes considered

double higher order method of moments for surface integral equation modeling of metallic and dielectric antennas and scatterers a novel double higher order galerkin type method of moments based on higher order geometrical modeling and higher order current modeling is proposed for surface integral equation analysis of combined metallic and dielectric antennas and scatterers of arbitrary shapes the technique employs generalized curvilinear quadrilaterals of arbitrary geometrical orders for the approximation of geometry metallic and dielectric surfaces and hierarchical divergence conforming polynomial vector basis functions of arbitrary orders for the approximation of electric and magnetic surface currents within the elements the geometrical orders and current approximation orders of the elements are entirely independent from each other and can be combined independently for the best overall performance of the method in different applications the results obtained by the higher order technique are validated against the analytical solutions and the numerical results obtained by low order moment method techniques from literature the examples show excellent accuracy flexibility and efficiency of the new technique at modeling of both current variation and curvature and demonstrate advantages of large domain models using curved quadrilaterals of high geometrical orders with basis functions of high current approximation orders over commonly used small domain models and low order techniques the reduction in the number of unknowns is by an order of magnitude when compared to low order solutions

locking free mixed hp finite element methods for curvilinear domains mixed hp finite element methods fems are robust with respect to poisson ratio locking when straight sided quadrilateral elements are used for the p version which uses fixed and generally large elements curved elements are necessary to represent curved domains accurately we show that mixed hp curved quadrilateral elements retain the robustness of their straight sided counterparts provided degenerate elements are avoided we also show that hp version triangles are robust we use these concepts to develop a locking free fem for geometrically nonlinear elasticity

recent progress on application of hp adaptive be fe methods to elastic scattering summary several new issues related to the projcct described in references 1 3 are reported the presented problems include i sensitivity of p convergence results to geometric parametrizations and an idea of a new mesh generation for lip approximations 2 a posteriori error estimation for the coupled problem 3 a better understanding of the meaning of the asymptotic convergence a few typical numerical examples conclude the presentation

two and three dimensional transition element families for adaptive refinement analysis of elasticity problems in this paper new enhanced assumed strain eas and hybrid stress transition element families are developed for 2d and 3d adaptive refinement analysis of elasticity problems the eas element families are based on some existing incompatible transition element families by using the eas method and the previous incompatible modes the b matrix columns associated with the eas modes can be directly designed such that their domain integrals vanish automatically and they can be computed more efficiently for 2d hybrid stress transition element families it is possible to derive different stress fields that lead to rank sufficient transition elements however the task becomes intractable for 3d hybrid stress transition elements in which many combinations of mid side and mid face nodes are possible this paper proposes to use hybrid stress transition element families in which the assumed stress fields are linearly complete the new 2d element family is more accurate than the 2d rank sufficient element family the new 3d element family is more accurate than the one with additional bilinear stress modes numerical examples reveal that the most accurate transition element families are the newly developed hybrid stress families followed by the eas families the incompatible families and then the compatible families copyright 2008 john wiley sons ltd