a hybrid finite element method for 3 d scattering using nodal and edge elements a hybrid finite element method for three dimensional scattering is presented and numerical examples shown this approach which couples finite element discretization with the method of moments is particularly well suited for monostatic radar cross section calculations the method is based on a scalar and vector potential formulation of maxwell s equations the use of nodal elements and a highly efficient body of revolution implementation of the method of moments combined nodal and edge elements are employed to accurately model fields around corners and edges a curvature based sampling criterion is derived and shown to ensure accurate answers for highly curved scatterers numerical results and cray computer timings are compared with published results for an edge element code using radiation boundary conditions

a highly robust and versatile finite element boundary integral hybrid code for scattering by bor objects a hybrid technique is presented that combines the finite element and boundary integral methods for simulating electromagnetic scattering from body of revolution bor objects this technique correctly models the boundary conditions along the axis of revolution in both the finite element and boundary integral formulations and yields highly accurate solutions because of the decoupled computations for the finite element and boundary integral equations the technique is highly efficient as compared to the method of moments especially for bors comprising layered or inhomogeneous materials it is applicable to a variety of complex large size bor objects consisting of perfect conductors anisotropic impedance surfaces anisotropic resistive surfaces and anisotropic inhomogeneous materials

modeling of electromagnetic absorption scattering problems using hp adaptive finite elements a model problem for the steady state form of maxwell s equations is considered the problem is formulated in a weak form using a lagrange multiplier laying down a foundation for a general class of novel hp adaptive fe approximations a convergence proof for affine elements is presented the proposed method is illustrated and verified with a series of 2d experiments including elements with curved boundaries and nonhomogeneous media

complementary operators a method to annihilate artificial reflections arising from the truncation of the computational domain in the solution of partial differential equations the ease and simplicity with which the finite difference time domain fdtd or the finite elements fe techniques can handle complex radiation or scattering problems have lead to a remarkable surge in the use of these methods while execution time is becoming less of an impediment when solving large problems the biggest constraint remains the memory needed to run the fdtd or the fe methods it is precisely this limitation that the article addresses a boundary operation is developed to minimize the artificial reflections that arise when truncating the computational domain of an open region scattering or radiation problem the method is based on the use of two boundary operators that are complementary in their action by solving the problem with each of the two operators and then averaging the two solutions the first order reflections that arise from the artificial boundary can be completely eliminated numerical results are presented to show that this new technique gives significant reduction in the error when compared to other widely used boundary conditions

hierarchal vector basis functions of arbitrary order for triangular and tetrahedral finite elements new vector finite elements are proposed for electromagnetics the new elements are triangular or tetrahedral edge elements tangential vector elements of arbitrary polynomial order they are hierarchal so that different orders can be used together in the same mesh and p adaption is possible they provide separate representation of the gradient and rotational parts of the vector field explicit formulas are presented for generating the basis functions to arbitrary order the basis functions can be used directly or after a further stage of partial orthogonalization to improve the matrix conditioning matrix assembly for the frequency domain curl curl equation is conveniently carried out by means of universal matrices application of the new elements to the solution of a parallel plate waveguide problem demonstrates the expected convergence rate of the phase of the reflection coefficient for tetrahedral elements to order 4 in particular the full order elements have only the same asymptotic convergence rate as elements with a reduced gradient space such as the whitney element however further tests reveal that the optimum balance of the gradient and rotational components is problem dependent

simulations of solitons using quadratic spline finite elements abstract a numerical solution to the korteweg de vries equation is obtained using the bubnov galerkin method with quadratic spline finite elements the element matrices are set up algebraically using reduce a linear stability analysis of the scheme shows the method to be unconditionally stable classical problems concerning the development motion and interaction of solitons are used to validate the method the numerical scheme is compared with published algorithms and shown to be both accurate and efficient

an amplitude finite element formulation for electromagnetic radiation and scattering electromagnetic radiation and scattering in an exterior domain within the context of a finite element method has traditionally involved imposing a suitable absorbing boundary condition on the truncation boundary of the numerical domain to inhibit reflection from it in this work based on the wilcox asymptotic expansion of the electric far field we propose an amplitude formulation within the framework of the nodal finite element method whereby the highly oscillatory radial part of the field is separated out a priori so that the standard lagrange interpolation functions that are used have to capture a relatively gently varying function since these elements can be used in the immediate vicinity of the radiator or scatterer with few exceptions which we enumerate it is more effective compared to methods that impose absorbing boundary conditions at the truncation boundary especially for high frequency problems the proposed method is based on the standard galerkin finite element formulation and uses standard lagrange interpolation functions standard gaussian quadrature and the same degrees of freedom as a conventional formulation we show the effectiveness of the proposed formulation on a wide variety of radiation and scattering problems involving both conducting and dielectric bodies and involving both convex and non convex domains with sharp corners

solitary waves induced by the boundary forced ew equation the development of a train of ew solitary waves induced by boundary forcing is studied using a petrov galerkin finite element scheme with shape functions taken as quadratic b spline functions a linear recurrence relationship for the numerical scheme is obtained via a crank nicholson approach involving a product approximation results are compared with those for the rlw and kdv equations

a new dual primal domain decomposition approach for finite element simulation of 3 d large scale electromagnetic problems a novel dual primal non overlapping domain decomposition method ddm for the finite element solution of three dimensional 3d large scale electromagnetic problems is proposed this method reduces the computational complexity from solving the original 3d problem to an equivalent interface problem by utilizing the idea of the dual primal finite element tearing and interconnecting feti dpem method the new method which is referred to as the feti dpem2 combines the dual primal idea with two lagrange multipliers and implements robin type transmission condition at the subdomain interfaces to significantly improve the convergence of the interface solution in the high frequency region similar to the original version a global coarse problem related to the degrees of freedom at the subdomain corner edges is designed to propagate the residual error to the whole computational domain at each iteration which further increases the convergence numerical examples are presented to demonstrate the validity and the capability of this method the results show that the proposed method produces fast solutions to large scale problems in any frequency band

a higher order multilevel fast multipole algorithm for scattering from mixed conducting dielectric bodies a higher order multilevel fast multipole algorithm mlfma is presented for computing electromagnetic scattering from three dimensional bodies comprising both conducting and dielectric objects the problem is formulated using the poggio miller chang harrington wu tsai 1973 1977 approach for multiple homogeneous dielectric objects and the combined field approach for conducting objects the resultant integral equations are discretized by the method of moments mom in which the conducting and dielectric surfaces interfaces are represented by curvilinear triangular patches and the unknown equivalent electric and magnetic currents are expanded using higher order vector basis functions such a discretization yields a highly accurate representation of the unknown currents without compromising the accuracy of geometrical modeling an implicit matrix filling scheme is employed to facilitate the treatment of complex scatterers having multiple junctions the resultant numerical system is then solved by mlfma which is tailored to accommodate the material properties of dielectric scatterers and the solution is accelerated using an incomplete lu decomposition preconditioner numerical examples are presented to demonstrate the accuracy and versatility of this approach in dealing with a wide array of scattering problems

eigenvalue approximation by a mixed method for resonant inhomogeneous cavities with metallic boundaries for an inhomogeneous cavity bounded by a perfect conductor we prove that the approximation of the eigenvalues for the maxwell problem leads to a second order rate of convergence when using mixed finite elements if the cavity has a disconnected boundary the problem has null eigenvalues we verify the existence of null eigenvalues for the approximate problem they do not mix with the others that still converge at the same rate

rigorous auxiliary variable based implementation of a second order abc for the vector fem the finite element method fem is commonly used for electromagnetic radiation and scattering analysis when an infinite free space exterior domain needs to be incorporated into the method a radiation boundary condition must be enforced an approach which has received considerable attention is to employ approximate conditions known as absorbing boundary conditions abcs that preserve the sparsity of the original fem system upon discretization in the case of time harmonic analysis based on the vector wave equation in three dimensions the symmetric spherical bayliss turkel type abcs of first and second orders are well established the second order version is expected to be more accurate however when using the standard curl conforming approach to fem discretization an implementation difficulty is encountered relating to successive derivatives being required of the nonconforming field components this issue is addressed here by introducing a scheme where the nonconforming first order derivatives are projected onto a suitably conforming auxiliary field of which another derivative can then be taken instead additional computational costs are minimal and the scheme retains the symmetry of the standard formulation numerical results demonstrate the superior performance of the rigorously implemented second order abc over its first order counterpart

parallel domain decomposition based algorithm of hybrid fe bi mlfma method for 3 d scattering by large inhomogeneous objects the hybrid method of the finite element boundary integral multilevel fast multipole algorithm fe bi mlfma has been recognized as one of the most powerful numerical methods for analyzing large inhomogeneous radiation scattering problems a domain decomposition algorithm dda of fe bi mlfma is presented in this paper by using the finite element tearing and interconnecting method feti the formulation of dda fe bi mlfma is presented and analyzed in detail the numerical performance of dda fe bi mlfma is investigated by numerical experiments from many aspects it includes the convergence speed versus types of domain decomposition number of subdomains types and inhomogeneity of dielectrics involving in solved problems and the scalability of dda fe bi mlfma the comparison of dda and previous algorithms of fe bi mlmfma is also carried out finally the capability of dda fe bi mlfma is shown for large inhomogeneous problems

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

influence of particle shape in the additive manufacturing process for ceramics abstract additive manufacturing am of ceramics through a vat photopolymerization vp process is a promising technique due to the high intrinsic resolution and the evanescence of stresses introduced during the layerwise additive manufacturing process compared to the regular vat photopolymerization process the addition of ceramic powder increases physical complexity hence large scale adoption and optimization of am for ceramics requires a thorough understanding of the underlying physics this work focuses on the light scattering introduced through a complex interplay between optical properties of different constituents and its effect on the photopolymerization the effect of the shape of the ceramic particle is investigated for isolated and multiple particle cases using a parametric analysis with regular convex polygons although the analysis of two dimensional isolated particle shapes indicates a preference for one shape over the other this difference vanishes in a multiple scattering situation a three dimensional analysis furthermore shows that a two dimensional approximation of the three dimensional scattering problem is relevant and can be used to further the process understanding of ceramic vp

edge based finite elements and vector abcs applied to 3 d scattering an edge based finite element formulation with vector absorbing boundary conditions is presented for scattering by composite structures having boundaries satisfying impedance and or transition conditions remarkably accurate results are obtained by placing the mesh a small fraction of a wavelength away from the scatterer

on the variational formulation of hybrid finite element boundary integral techniques for electromagnetic analysis this paper addresses the time harmonic electromagnetic analysis of a three dimensional inhomogeneous radiator scatterer in free space such analysis can be carried out by combining the finite element method fem with the method of moments mom which yields finite element boundary integral fe bi formulations a general framework is presented within which stationary fe bi formulations can be established variational boundary value problems which relate to equivalent underlying variational principles stationary functionals the formulations are shown to be accurate robust and computationally efficient they avoid the problem of interior resonances without resorting to the combined field integral equation and they result in symmetric system matrices which preserve reciprocity explicitly thus the stationary fe bi framework combines the fem and mom on the continuous level as opposed to the usual approach of hybridization after discretization which generally leads to asymmetric matrices the stationary fe bi framework allows one to solve either for the electric and magnetic fields on the volume of the problem domain or for one volume and one exterior surface field quantity with only marginal differences in computational cost the volume surface formulations have the same storage requirements as previous fe bi formulations and can be more efficiently solved the volume volume formulations provide simultaneous solutions of the electric and magnetic fields which could for instance be used to construct error estimators directly based on maxwell s equations

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

a theoretical and numerical analysis of the measured equation of invariance the measured equation of invariance mei has been previously introduced to efficiently and accurately handle the boundary truncation for finite methods the present authors give a theoretical analysis that provides several important insights into the capabilities of the mei from the numerical study they can explain why the mei works better than one would expect both the theoretical and the numerical analyses demonstrate that the accuracy of the solution is dependent on the electrical size of the geometry as well as the distance between the mesh boundary and the geometry from the analysis the authors propose a new set of metrons that is less sensitive to the excitation than the previously proposed sinusoidal metrons

a multilevel formulation of the finite element method for electromagnetic scattering multigrid techniques for three dimensional 3 d electromagnetic scattering problems are presented the numerical representation of the physical problem is accomplished via a finite element discretization with nodal basis functions a total magnetic field formulation with a vector absorbing boundary condition abc is used the principal features of the multilevel technique are outlined the basic multigrid algorithms are described and estimations of their computational requirements are derived the multilevel code is tested with several scattering problems for which analytical solutions exist the obtained results clearly indicate the stability accuracy and efficiency of the multigrid method

measured equation of invariance a new concept in field computations numerical computations of frequency domain field problems or elliptical partial differential equations may be based on differential equations or integral equations the new concept of field computation presented in this paper is based on the postulate of the existence of linear equations of the discretized nodal values of the fields different from the conventional equations but leading to the same solutions the postulated equations are local and invariant to excitation it is shown how the equations can be determined by a sequence of measures the measured equations are particularly useful at the mesh boundary where the finite difference methods fail the measured equations do not assume the physical condition of absorption so they are also applicable to concave boundaries using the measured equations one can terminate the finite difference mesh very close to the physical boundary and still obtain robust solutions it will definitely make a great impact on the way one applies finite difference and finite element methods in many problems computational results using the measured equations of invariance in two and three dimensions are presented

a non overlapping domain decomposition method with non matching grids for modeling large finite antenna arrays a non overlapping domain decomposition method ddm is proposed herein to solve maxwell equations in r 3 in this work the maxwell equations are discretized using a vector finite element method with hierarchical h curl vector basis functions there are two major ingredients in the proposed non overlapping ddm a a proper 1st order transmission condition to enforce field continuity across domain boundaries and b a cement technique to allow non matching grids for neighboring domains moreover a detail fourier analysis of the transmission condition for a canonical half space example is presented the analysis provides significant insights into the convergence behavior of the proposed non overlapping ddm for solving electromagnetic radiation problems such as the large finite antenna arrays particularly for the antenna arrays the proposed non overlapping ddm is extremely efficient since the formulation can easily incorporate geometrical repetitions exponentially tapered notch vivaldi antenna arrays with size up to 100x100 elements are solved on a common pc to validate the proposed non overlapping ddm

implementation and experiments of a hybrid algorithm of the mlfma enhanced fe bi method for open region inhomogeneous electromagnetic problems although the computational complexity of the finite element boundary integral fe bi method is significantly reduced by the multilevel fast multipole algorithm mlfma this mlfma enhanced fe bi solution experiences a very slow convergence for some complex inhomogeneous problems a hybrid algorithm combining direct methods with iterative methods is designed to speed up the rate of convergence of this mlfma enhanced fe bi solution this hybrid algorithm is efficiently implemented with the aid of a newly developed package superlu of the lu decomposition solver numerical experiments are performed for scattering by a coated northrop wing to demonstrate the efficiency of this hybrid algorithm more importantly the thorough investigation of the numerical experiments clearly shows the better accuracy stability and robustness of this hybrid algorithm over the conventional algorithms

an analytical characterization of the error in the measured equation of invariance in previous publications the authors have numerically shown that the measured equation of invariance mei is not invariant to excitation the major implication is that an appropriate set of metrons should be selected for each geometry and excitation in question an argument however can be raised against these findings one can claim that the mei is indeed invariant and that any discrepancies are entirely due to the mesh discretization error the authors disprove this claim by a counterexample they perform an analytical study of the mei as applied to a perfectly conducting circular cylinder with a fixed choice of metrons they then investigate the behavior of the mei when the electrical radius of the cylinder becomes large and when the nodal separation goes to zero they prove that even as the mei residual goes to zero the error in the mei solution remains finite and cannot be reduced below a certain limit

absorbing boundary conditions on arbitrary boundaries for the scalar and vector wave equations the solution of open region scattering problems involving inhomogeneous arbitrarily shaped objects may be performed through the use of partial differential equation techniques which require enclosing the scatterer by an outer boundary on which an absorbing boundary condition abc is applied in order to minimize the size of the domain to be meshed and consequently the number of unknowns if may be advisable to implement abc s devised for outer boundaries of arbitrary shapes such abc s are obtained for the 3d scalar and vector wave equations they incorporate most of existing boundary conditions when used in conjunction with a finite element technique the numerical results derived by using a simplified form of these abc s compare favourably to those obtained by using a rigorous hybrid finite element integral equation formulation these boundary conditions have been obtained in the frequency domain framework they may however be used in time domain calculations

comments on a theoretical and numerical analysis of the measured equation of invariance in the original paper see ibid vol 42 no 8 p 1097 1105 1994 the authors claimed to have found theoretical insights into the measured equations of invariance mei method their first insight was a proof that the postulate of invariance was wrong and their second insight led to the discovery of an optimum set of metrons metrons are considered to be possible induced current densities due to some unknown incident fields they also presented a series of computational results to highlight their theories this article points out the defects in the analyses and conclusions presented by the authors there are two things in the paper which are basically incorrect one is that the authors consider a zero in a numerical formulation to be an absolute zero the other is that they assume the invariance to excitations to be the same as the invariance to metrons based on these assumptions they have reached conclusions which are actually contradictory to their own calculations this article shows where the defects of their analyses occur and why their two insights are contradictory to each other

solitary waves of the regularized long wave equation abstract a finite element solution of the regularised long wave equation based on galerkin s method using cubic splines as element shape functions is set up a linear stability analysis shows the scheme to be unconditionally stable test problems including the migration and interaction of solitary waves are used to validate the method which is found to be accurate and efficient the three invariants of the motion are evaluated to determine the conservation properties of the algorithm the temporal evolution of a maxwellian initial pulse is then studied

accurate solutions of maxwell s equations around pec corners and highly curved surfaces using nodal finite elements a method is presented for computing accurate solutions of maxwell s equations in the presence of perfect electrical conductors pecs with sharp corners and highly curved surfaces using conventional nodal finite elements and a scalar vector s v potential formulation this technique approximates the pec with an impedance boundary condition ibc where the impedance is small critically it couples both potentials through this boundary condition rather than setting the scalar potential to zero this permits cancellation of the tangential components of the vector potential resulting in an accurate normal electric field the cause for the inaccuracies that nodal methods experience in the presence of sharp pec corners or highly curved pec surfaces is elucidated it is then shown how the inclusion of the scalar potential cures these deficiencies permitting accurate solutions spectral analysis of the resulting finite element matrices are shown validating the boundary conditions used examples are presented comparing a benchmark solution conventional pec and ibc boundary conditions and the new s v potential ibc on a pec wedge and pec ellipse in both cases the new s v ibc produces superior results

validity of the measured equation of invariance the measured equation of invariance mei is derived without any postulates it is shown that the coefficients of the mei are invariant to the field of excitation however the accuracy of the mei solution is closely related to the number of nodes in the mei coupling more nodes improves progressively the accuracy of the mei solution with increasing nodes the matrix problem for the determination of the mei coefficients becomes seriously ill conditioned and generally must be solved using multiple precision arithmetic the consequences of the ill conditioning phenomenon are discussed

phase accuracy comparisons and improved far field estimates for 3 d edge elements on tetrahedral meshes abstract edge element methods have proved very effective for 3 d electromagnetic computations and are widely used on unstructured meshes however the accuracy of standard edge elements can be criticised because of their low order this paper analyses discrete dispersion relations together with numerical propagation accuracy to determine the effect of tetrahedral shape on the phase accuracy of standard 3 d edge element approximations in comparison to other methods scattering computations for the sphere obtained with edge elements are compared with results obtained with vertex elements and a new formulation of the far field integral approximations for use with edge elements is shown to give improved cross sections over conventional formulations

continuous potential maxwell solutions on nodal based finite elements a nodal based finite element approach for computing electric fields in heterogeneous media is presented the primary calculation is formulated in terms of continuous potentials so that no special care is required on element assembly at dielectric interfaces the resulting galerkin weak form matrices exhibit the special helmholtz structure which guarantees the absence of parasitic solutions in driven problems with physically well posed boundary conditions the enhanced sparsity of the helmholtz form mitigates the extra coupling effort associated with introduction of a fourth degree of freedom relative to direct e solution e can be extracted from the computed potentials as a postprocessing step either at nodal positions or element centroids solutions obtained with this approach for several benchmark and practical problems are shown to be parasite free and essentially indistinguishable from previously reported direct e computations

a novel exact two point field equation 2pfe for solving electromagnetic scattering problems the finite difference fd method is a basic technique for solving differential equations the disadvantage of it for electromagnetic em problems of an open region is that the mesh needs to be terminated with the application of a proper boundary condition in this paper a novel exact two point field equation 2pfe is derived from rigorous analysis of the radiation field and it is proposed to be used as the termination boundary condition bc for solving em scattering problems in the open region by the iterative fd method this 2pfe bc approaches its exact solution through the iteration process and at the same time the scattered field and the induced current density approach their exact solutions the novel 2pfe is simple in concept and easy to apply the validity of the 2pfe and the iterative fd method has been tested several two dimensional 2 d scattering problems have been successfully solved the results agree very well with those obtained by method of moments mom or measured equation of invariance mei

a new family of mixed finite elements in ir 3 we introduce two families of mixed finite element on conforming inh div and one conforming inh curl these finite elements can be used to approximate the stokes system

an effective domain decomposition based preconditioner for the fe bi mlfma method for 3d scattering problems a domain decomposition based preconditioner ddp is presented for the hybrid finite element boundary integral multilevel fast multipole algorithm fe bi mlfma the formulation of fe bi is first approximated by the finite element method fem with absorbing boundary condition abc then this approximate fem abc formulation is solved by using the finite element tearing and interconnecting method feti finally an inner outer iterative algorithm with variable convergence threshold is designed for fe bi mlfma because of good numerical scalability of feti and good approximation of fem abc this ddp fe bi mlfma performs well even for large lossless objects

the finite element modeling of three dimensional electromagnetic fields using edge and nodal elements an efficient and accurate finite element method is presented for computing transient as well as time harmonic electromagnetic fields in three dimensional configurations containing arbitrarily inhomogeneous media that may be anisotropic to obtain accurate results with an optimum computational efficiency both consistently linear edge and consistently linear nodal elements are used for approximating the spatial distribution of the field compared with earlier work the formulation is generalized by adding a method for explicitly modeling the normal continuity along interfaces that are free of surface charge in addition the conditions for efficiently solving time harmonic problems using a code designed for solving transient problems are discussed a general and simple method for implementing arbitrary inhomogeneous absorbing boundary conditions for modeling arbitrary incident fields is introduced

interpolation extrapolation and application of the measured equation of invariance to scattering by very large cylinders using the conventional method of moment mom calculations a cylinder of circumferential dimension of 100 wavelengths is considered to be large using the measured equation of invariance mei approach a cylinder of 10000 wavelengths is within the storage capacity and numerical tolerance of a workstation although the mei has greatly reduced the storage and solution time of the matrix its overhead to generate the matrix elements is about the same order as that of the mom when the target is very large that overhead can be very time consuming this paper presents an interpolation and extrapolation technique such that the boundary equations of the mei for high frequencies may be predicted from those of low frequencies it is demonstrated that in the optical limit the same set of coefficients may be used for all frequencies which is consistent with the concept of geometric optics where the same rule is applied to all frequencies

nonconformal feti dp domain decomposition methods for fe bi mlfma the nonconformal domain decomposition methods ddms of the hybrid finite element boundary integral multilevel fast multipole algorithm fe bi mlfma are presented for computing large electromagnetic scattering radiation problems the numerical performance of different transmission conditions between finite element method fem subdomains and fem and bi domains is studied in this paper the dirichlet transmission condition dtc employed at the interface between fem and bi domains has faster convergence than the robin type transmission condition and this finding is different from the conclusions for the fem ddms published in the literature furthermore the cement element ce based dual primal finite element tearing and interconnecting feti dp ddm has faster convergence than the lagrange multiplier based feti dp method under the fe bi system and is also different from that under the system of the fem with the absorbing boundary condition fem abc it shows that the ddms of fe bi mlfma have some essential differences from those of fem abc the analysis of these numerical phenomena is presented in this paper further comparison between the ddms of fe bi mlfma and fem abc demonstrates that the ddms of fe bi mlmfa have essential advantages over those of fem abc various numerical experiments confirm the accuracy efficiency and flexibility of the nonconformal ddm of fe bi mlfma which is the ce based feti dp ddm with dtc connecting fem and bi

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

a difference analogue of the davey stewartson system discrete gram type determinant solution and lax pair we consider a difference difference davey stewartson system together with its bilinear structure we write some new gram type determinantal solutions taking into account a set of jacobi identities for determinants a bilinear backlund transformation is constructed and consequently a lax pair for the discrete system is derived

a dispersion analysis of finite element methods for maxwell s equations a dispersion analysis of six different finite element methods for approximating maxwell s equations in space is presented the study is limited to two space dimensions and triangular elements but all the methods considered can be generalised to three dimensions using prismatic elements spatial grids consisting of both equilateral and right triangles are considered

stabilized interior penalty methods for the time harmonic maxwell equations we propose stabilized interior penalty discontinuous galerkin methods for the indefinite time harmonic maxwell system the methods are based on a mixed formulation of the boundary value problem chosen to provide control on the divergence of the electric field we prove optimal error estimates for the methods in the special case of smooth coefficients and perfectly conducting boundary using a duality approach

theoretical modeling of cavity backed patch antennas using a hybrid technique a hybrid technique that combines the method of moments mom and the finite element method fem to analyze cavity backed patch antennas is presented this technique features the use of fem in solving the electromagnetic field distribution in the cavity and the use of mom in solving integral equations outside the cavity the results of mom and fem are combined through the continuity conditions on the boundary of the cavity due to the flexibility of fem complex cavities filled with inhomogeneous media can be analyzed by this technique the results obtained by this hybrid technique are compared to the finite difference time domain fdtd results and good agreement is found

discretized boundary equation method for two dimensional scattering problems a unified approach named discretized boundary equation dbe method is introduced for two dimensional 2 d scattering problems it is based on the discretization of field expressions for one or two components of the scattered field the dbes can be used either on the object surface to obtain the solution directly or on the truncation boundary of a finite difference fd or finite element fe mesh as termination conditions this paper describes the general theory of the dbe method and key points or limitations for its implementation a new on surface formulation for the solution of scattering by perfectly conducting cylinders is presented as an application of the two component version of the dbe method and validated through numerical examples mesh termination conditions for the fd or fe method are derived based on the one component formulation of the dbe method and their equivalence and difference to the measured equation of invariance are discussed in particular the dbe obtained with the minimum norm least squares solution is investigated thoroughly and its validity and features are demonstrated through numerical results generated together with the fd method for scattering by cylinders with various material properties

a taylor galerkin method for convective transport problems a method is described to derive finite element schemes for the scalar convection equation in one or more space dimensions to produce accurate temporal differencing the method employs forward time taylor series expansions including time derivatives of second and third order which are evaluated from the governing partial differential equation this yields a generalized time discretized equation which is successively discretized in space by means of the standard bubnov galerkin finite element method the technique is illustrated first in one space dimension with linear elements and euler leap frog and crank nicolson time stepping several interesting relations with standard galerkin and recently developed petrov galerkin methods emerge and the new taylor galerkin schemes are found to exhibit particularly high phase accuracy with minimal numerical damping the method is successively extended to deal with variable coefficient problems and multi dimensional situations

a novel boundary infinite element a new improved infinite element based on mapping is proposed for modelling unbounded domain problems mapping has previously been used in such problems not only for the entire domain but also for the infinite element itself the novelty of the present approach is the simplicity of the mapping and the retention of standard integration abscissae and weights the implementation of these elements is very straightforward and they are ideally suited for the analysis of infinite domain static problems in two and three dimensions

nonlinear differential difference equations as backlund transformations shows that the best known nonlinear differential difference equations associated with the discrete schrodinger spectral problem and also with the discrete zakharov shabat spectral problem can be interpreted as backlund transformations for some continuous nonlinear evolution equations

a vector dual primal finite element tearing and interconnecting method for solving 3 d large scale electromagnetic problems a lagrange multiplier based non overlapping domain decomposition method referred to as the dual primal finite element tearing and interconnecting feti dp is formulated for the finite element simulation of large three dimensional 3 d electromagnetic problems this formulation extends the feti dp for solving the scalar helmholtz equation to the solution of the vector curl curl wave equation using edge based finite elements it enforces the field continuity explicitly along the edges shared by more than two subdomains and implicitly at the interfaces between two subdomains through the use of lagrange multipliers with the aid of a direct sparse solver for each subdomain system the large global problem is reduced to a much smaller interface problem from which a neumann boundary condition is obtained at the interfaces between all the subdomains this neumann boundary condition is then used to calculate the field within each subdomain it is shown that the resulting feti dpem method is scalable with respect to the size of finite elements and the number of subdomains it is also scalable with respect to the size of the subdomains when the subdomains with its surfaces enclosed by perfect magnetic conductors cannot support any resonant modes the feti dpem method is applied to the electromagnetic simulation of array type structures where the geometrical redundancy is fully exploited to speedup the simulation and reduce the memory requirement numerical results for the simulation of finite antenna arrays and photonic bandgap devices are presented to demonstrate the application accuracy efficiency and capability of the feti dpem method

the post processing approach in the finite element method part 2 the calculation of stress intensity factors abstract in the context of a model problem the authors describe post processing techniques for the calculation of generalized stress intensity factors they discuss two broad classes of methods one involving an influence function and the other related to the well known energy release principle of fracture mechanics an error analysis is sketched and two numerical examples are given to illustrate the effectivity of the techniques this is the second in a series of three papers author

the adaptive computation of far field patterns by a posteriori error estimation of linear functionals this paper is concerned with the derivation of a priori and a posteriori error bounds for a class of linear functionals arising in electromagnetics which represent the far field pattern of the scattered electromagnetic field the a posteriori error bound is implemented into an adaptive finite element algorithm and a series of numerical experiments is presented

the bymoment method for two dimensional electromagnetic scattering the bymoment method is presented for analyzing two dimensional electromagnetic wave scattering in an unbounded region the method introduces a conforming surface to geometrically decouple the interior region containing the scatterer from the exterior region extending to infinity the solution in the interior is generated using the standard finite element solution of an interior dirichlet boundary value problem the interior solution is then coupled to the exterior using green s theorem in the unbounded exterior region the validity of the method and the associated computer program is demonstrated by comparing the results to those of other methods for scattering by various cylindrical geometries

the generalized finite element method for helmholtz equation theory computation and open problems in this paper we address the generalized finite element method for the helmholtz equation we obtain our method by employing the finite element method on cartesian meshes which may overlap the boundaries of the problem domain and by enriching the approximation by plane waves pasted into the finite element basis at each mesh vertex by the partition of unity method here we address the q convergence of the method where q is the number of plane waves added at each vertex for the class of smooth analytic solutions for which we get better than exponential convergence for sufficiently small h depending on p an important observation is that we can monitor the accuracy in any computed solution quantity of interest at negligible cost by using q extrapolation our results assume exact integration of all the employed integrals further studies are needed to analyze the effects of the numerical integrations and also the effect of the roundoff errors

an analysis of ne de lec s method for the spatial discretization of maxwell s equations abstract in 1980 nedelec developed a family of curl and divergence conforming finite elements in r 3 he proposed the use of these elements to discretize the time dependent maxwell equations noting that the elements have the advantage that the discrete magnetic displacement can be made exactly divergence free in this paper we shall analyze a slight generalization of nedelec s scheme and prove essentially optimal order convergence estimates in a variety of situations we also demonstrate that the nedelec method can be superconvergent at certain special points and we relate the method to yee s finite difference scheme a by product of our analysis will be a convergence proof for yee s method

choice of the perfectly matched layer boundary condition for frequency domain maxwell s equations solvers we show that the performance of frequency domain solvers of maxwell s equations is greatly affected by the kind of the perfectly matched layer pml used in particular we demonstrate that using the stretched coordinate pml sc pml results in significantly faster convergence speed than using the uniaxial pml upml such a difference in convergence behavior is explained by an analysis of the condition number of the coefficient matrices additionally we develop a diagonal preconditioning scheme that significantly improves solver performance when upml is used

a direct method for dromion solutions of the davey stewartson equations and their asymptotic properties a new direct approach to determining a class of solutions including the dromion solutions of the davey stewartson equations is presented the form of solution obtained allows a detailed asymptotic analysis of the dromion solutions and compact expression for the phase shifts and changes of amplitude as a result of interaction of the dromions to be determined a class of solutions describing dromion scattering is discussed and computer plots of the interactions of such solutions are presented

hermite infinite elements and graded quadratic b spline finite elements quadratic b spline finite elements are defined for a graded mesh hermite infinite elements are proposed to extend the applicability of these finite elements to unbounded regions test problems used to compare this technique with published procedures show that the quadratic b spline finite element solution has as expected lower error bounds than a linear element solution these experiments also demonstrate that the hermite infinite elements used to close the b spline finite element arrays lead to error norms comparable in size with other infinite element formulations the generation of solitary waves in a semi infinite shallow channel by boundary forcing is modelled by the korteweg de vries equation using an array of graded elements closed by a zero pole infinite element the resulting simulation of solitary wave motion across a non uniform mesh confirms existing work and illustrates the effectiveness of the present formulation

electrostatic solution for three dimensional arbitrarily shaped conducting bodies using finite element and measured equation of invariance differential equation techniques such as the finite element fe and finite difference fd have the advantage of sparse system matrices that have relatively small memory requirements for storage and relatively short central processing unit cpu time requirements for solving electrostatic problems however these techniques do not lend themselves as readily for use in open region problems as the method of moments mom because they require the discretization of the space surrounding the object where the mom only requires discretization of the surface of the object a relatively new mesh truncation method known as the measured equation of invariance mei is investigated augmenting the fe method for the solution of electrostatic problems involving three dimensional 3 d arbitrarily shaped conducting objects this technique allows truncation of the mesh as close as two node layers from the object the mei views sparse matrix numerical techniques as methods of determining the weighting coefficients between neighboring nodes and finds those weights for nodes on the boundary of the mesh by assuming viable charge distributions on the surface of the object and using green s function to measure the potentials at the nodes problems in the implementation of the fe mei are discussed and the method is compared against the mom for a cube and a sphere

coupling finite element and integral equation solutions using decoupled boundary meshes electromagnetic scattering a method is outlined for calculating scattered fields from inhomogeneous penetrable objects using a coupled finite element integral equation solution the finite element equation can efficiently model fields in penetrable and inhomogeneous regions while the integral equation exactly models fields on the finite element mesh boundary and in the exterior region by decoupling the interior finite element and exterior integral equation meshes considerable flexibility is found in both the number of field expansion points as well as their density only the nonmetal portions of the object need be modeled using a finite element expansion exterior perfect conducting surfaces are modeled using an integral equation with a single unknown field since e sub tan is identically zero on these surfaces numerical convergence accuracy and stability at interior resonant frequencies are studied in detail

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

the post processing approach in the finite element method part 1 calculation of displacements stresses and other higher derivatives of the displacements this is the first in a series of three papers in which we discuss a method for post processing a finite element solution to obtain high accuracy approximations for displacements stresses stress intensity factors etc rather than take the values of these quantities directly from the finite element solution we evaluate certain weighted averages of the solution over the entire region these yield approximations are of the same order of accuracy as the strain energy we obtain error estimates and also present some numerical examples to illustrate the practical effectiveness of the technique in the third paper of this series we address the matters of adaptive mesh selection and a posteriori error estimation

on the formulation of hybrid finite element and boundary integral methods for 3 d scattering this paper studies in detail a variety of formulations for the hybrid finite element and boundary integral fe bi method for three dimensional 3 d electromagnetic scattering by inhomogeneous objects it is shown that the efficiency and accuracy of the fe bi method depends highly on the formulation and discretization of the boundary integral equation bie used a simple analysis of the matrix condition number identifies the efficiency of the different fe bi formulations and an analysis of weighting functions shows that the traditional fe bi formulations cannot produce accurate solutions a new formulation is then proposed and numerical results show that the resulting solution has a good efficiency and accuracy and is completely immune to the problem of interior resonance finally the multilevel fast multipole algorithm mlfma is employed to significantly reduce the memory requirement and computational complexity of the proposed fe bi method

generalized finite element method for vector electromagnetic problems the generalized finite element method gfem as introduced by babuska is a partition of unity framework for solving scalar partial differential equations pdes to date they have been applied extensively to the solution of elliptic and parabolic pdes this technique can be interpreted as a unified prescription of a host of well known techniques such as classical finite element methods that are based on tessellation point cloud techniques and element free galerkin methods the focus of this paper is to extend this technique to solve vector electromagnetic problems however modification of gfem to address this problem poses a novel set of challenges i the vector nature of the problem and the different continuity requirements on each component imply that basis functions developed should share similar characteristics ii the basis functions have to be able to represent divergence free electromagnetic fields in a source free region when they themselves are not divergence free these have been the primary impediments to extension of this technique in this paper we propose a method that may be used to overcome these obstacles and will demonstrate h and p convergence characteristics of the proposed method for a range of problems finally we will demonstrate convergence characteristics of this technique for analyzing scattering from a sharp wedge when the basis functions include analytical local field representation

evaluation of a spherical pml for vector fem applications the implementation and evaluation of a spherical perfectly matched layer pml within a cartesian finite element method context using standard curl conforming elements is presented in this paper results are compared to the long standing 1st order absorbing boundary condition abc and a new rigorous implementation of a 2nd order abc for curl conforming elements the 4 and 8 layer spherical pmls are shown to offer very attractive levels of absorption with reflections on the order of 60 to 70db demonstrated numerical tests show that the guidelines for cartesian pml absorbers in terms of maximum conductivity also carry over to the spherical pml the 2nd order abc is also shown to offer very good performance finally coding issues for both the spherical pml and the analytical abcs are briefly addressed

modeling radiation with an efficient hybrid finite element integral equation waveguide mode matching technique a method is presented to model electromagnetic radiation combining the finite element technique in the penetrating portion of a three dimensional 3 d radiating structure with an integral equation on the outer surface of the computational domain and with a waveguide mode matching technique on a cross section of the feeding waveguide the antenna can be of general shape provided a portion of the surrounding medium up to a surface of revolution is chosen as part of the computational domain this truncation scheme and the accurate source representation are more general than those existing in the literature for radiation modeling an open ended waveguide and a waveguide with a choke ring are analyzed and their radiation patterns are obtained and compared with available measurements

a fast domain decomposition method for the solution of electromagnetic scattering by large objects a nonoverlapping domain decomposition method is proposed for the finite element solution of the scattering problem by electrically large inhomogeneous infinite cylinders of arbitrary cross section to minimize the size of the total computational domain a second order absorbing boundary condition abc is applied upon an outer boundary of arbitrary shape which may be conformal to the surface of the scatterer this domain is then partitioned into concentric subdomains circumscribing the object a second order transmission condition derived from the abc is prescribed upon the interfaces between two adjacent subdomains this particular configuration is responsible for the fast convergence of the domain decomposition iterative algorithm which is parallelizable numerical results obtained with a nonparallelized computer code are presented which emphasize the superiority of this technique in terms of memory storage requirements and computing times over the standard finite element approach as well as over the rigorous hybrid finite element integral equation formulation

discontinuous galerkin inspired framework for vector generalized finite element methods discontinuous galerkin methods have been extensively used in simulations of various electromagnetic problems in both time and frequency domains in this paper we exploit features of these methods to provide a framework that can be used to overcome a fundamental bottleneck in using as well as augmenting the capabilities of vector generalized finite element methods vgfem this approach permits the use of vgfem for analysis of piecewise inhomogeneous domains without defining additional constraints on basis functions and allows hybridization with other finite element formulations interior penalty discontinuous galerkin method ip dgm is used to enable communication among partitioned domains we will present several results that demonstrate applications of these hybrid methods as well as their convergence characteristics

nodal based finite element modeling of maxwell s equations weak forms are derived for maxwell s equations which are suitable for implementation on conventional c sup 0 elements with scalar bases the governing equations are expressed in terms of general vector and scalar potentials for the electric field intensity vector gauge theory is invoked to close the system and dictates the continuity requirements for the potentials at material interfaces as well as the blend of boundary conditions at exterior boundaries two specific gauges are presented both of which lead to helmholtz weak forms which are parasite free and enjoy simple physically meaningful boundary conditions a general and numerically efficient procedure for enforcing the jump discontinuities on the normal components of vector fields at dielectric interfaces and boundary conditions on curved surfaces is also given

implementation of the second order abc in the feti dpem method for 3d em problems the electromagnetic dual primal finite element tearing and interconnecting feti dpem method originally equipped with the first order absorbing boundary condition abc is combined with the second order abc implemented using auxiliary variables to enhance the accuracy of electromagnetic scattering and radiation simulations when the second order abc surface is partitioned by domain decomposition it is necessary to enforce an extra continuity condition on the auxiliary variables representing a continuous surface divergence for the electric field at the junctions of the subdomain interfaces and the truncation surface a simple approach to enforce such a continuity is proposed without altering the overall framework of the feti dpem method numerical examples are provided to demonstrate the accuracy improvement due to the use of the second order abc

a study of discretization error in the finite element approximation of wave solutions a dispersion analysis is used to study the errors caused by the spatial discretization of the finite element method for the two dimensional scalar helmholtz equation it is shown that the error can be determined analytically for a uniform mesh of infinite extent numerical results are presented to show the effects of several parameters on the error these parameters are the nodal density the electrical size of the mesh the direction of propagation of the incident wave the type of element and the type of boundary condition

further development of vector generalized finite element method and its hybridization with boundary integrals recently vector generalized finite element method vgfem was introduced for the solution of the vector helmholtz equation and its applicability was validated for canonical problems vgfem uses a local helmholtz decomposition to construct basis functions in overlapping local domains of some canonical shape while using a canonical shape for local domains adds flexibility to the method one needs to provide information regarding boundaries of domains inhomogeneities the need for surface information proves to be a bottleneck in using the method for a larger class of problems this paper is targeted towards overcoming these deficiencies here we will introduce the modifications to this method that permit interfacing with arbitrarily shaped local domains to facilitate interfacing with existing meshing software integrate this method with boundary integrals and provide a framework for studying dispersion as will be apparent the hybridization of the method with boundary integrals is not a simple adaptation of existing methods onto the vgfem framework likewise dispersion analysis is nontrivial due to the overlapping nature of vgfem basis functions a range of practical problems has been analyzed within the presented framework and results are compared either against measurements or existing fem data to validate the presented methodology

application of discrete periodic wavelets to measured equation of invariance recently the wavelet expansions have been applied in field computations in the frequency domain the application is focused on the thinning of matrices arising from the method of moment mom the thinning of matrices can best be done by the measured equation of invariance mei which provides sparsity almost without sacrificing accuracy in that the boundary equation it entails is convertible to that of the mom the real power of the wavelet expansions is to give high resolution in convolution integrals high resolution is also needed in the process of finding the mei coefficients which are obtained via an integration process almost identical to that of the mom in this paper it is shown that when the fast discrete periodic wavelets fdpw are used as metron currents in the mei method the resolutions of the mei coefficients are improved at high frequency computations or at geometric extremities the level of sparsity of the mei is much more favorable than that achievable by the thinning of mom matrix using the wavelet expansions the role of fdpw in the mei happens to be more fitting than its place in the mom

a convergence analysis of yee s scheme on nonuniform grids the yee scheme is the principal finite difference method used in computing time domain solutions of maxwell s equations on a uniform grid the method is easily seen to be second order convergent in space this paper shows that the yee scheme is also second order convergent on a nonuniform mesh despite the fact that the local truncation error is nodally only of first order

two coupled particle finite volume methods using delaunay voronoi meshes for the approximation of vlasov poisson and vlasov maxwell equations this paper deals with the approximation of vlasov poisson and vlasov maxwell equations we present two coupled particle finite volume methods which use the properties of delaunay voronoi meshes these methods are applied to benchmark calculations and engineering problems such as simulation of electron injector devices

a fem domain decomposition method for photonic and electromagnetic band gap structures this paper introduces an efficient domain decomposition algorithm for the solution of time harmonic electromagnetic fields arising in three dimensional finite size photonic band gap and electromagnetic band gap structures the method is based on the finite element approximation and a nonoverlapping domain decomposition method a set of cement unknowns on the inter domain interfaces has been explicitly introduced to enforce the appropriate field continuities the introduction of these extra unknowns allows for nonconforming nonmatching triangulations across domain eliminating the need for periodic mesh to ensure and improve the convergence of the outer iteration loop robin transmission condition is used to communicate information across interfaces the resulting system of equations is solved with a fast algorithm that loosely resembles the well known finite element tearing and interconnecting algorithm in this algorithm the method solves in the preprocessing step for the robin primal subdomain problems multiple times by exciting one dual unknown at a time this step generates an iteration matrix that is then used to update the dual unknowns in the outer loop iteration the present method becomes extremely efficient for problems with geometric repetitions such as photonic and electromagnetic band gap structures

a domain decomposition method with nonconformal meshes for finite periodic and semi periodic structures we present a domain decomposition method as a preconditioner for krylov type solvers to model complex electromagnetic problems containing periodicities the method reduces memory requirements by decomposing the original problem into several nonoverlapping sub domains the 1st order transmission condition is employed on interfaces between adjacent sub domains to enforce continuity of electromagnetic fields and to ensure the sub domain problems are well posed by following the spirit of duality paring a symmetric system is obtained to reduce the computational burdens of the present method the finite element tearing and interconnecting like algorithm is adopted this algorithm results in the computation of the so called numerical green s function which can be compressed efficiently via a rank revealing matrix factorization algorithm the final system matrix is solved by krylov solvers instead of classical stationary solvers to improve the convergence of iterative solvers several robust implementation details are discussed and the choice of some popular krylov subspace solvers is studied through numerical examples

a numerical study of iterative substructuring method for finite element analysis of high frequency electromagnetic fields this paper describes iterative methods for the high frequency electromagnetic analysis using the finite element method of maxwell equations including displacement current the conjugate orthogonal conjugate gradient method has been widely used to solve a complex symmetric system however the conventional method suffers from oscillating convergence histories in large scale analysis in this paper to solve large scale complex symmetric systems arising from the formulation of the e method an iterative substructuring method like the minimal residual method is presented and the performance of the convergence of the method is evaluated by numerical results as the result the proposed method shows a stable convergence behavior and a fast convergence rate compared to other iterative methods

numerical implementation of second and third order conformal absorbing boundary conditions for the vector wave equation a rigorous implementation in an edge based finite element formulation of second and third order conformal absorbing boundary conditions abcs is presented for the solution of three dimensional 3 d scattering problems when the boundary s terminating the mesh is the surface of a parallelepiped a special treatment is provided for the singularities edges of s a systematic numerical study is carried out that compares the performances of these abcs with those of the standard zero order abc as well as of a more simple though less rigorous implementation of the second order abc when s is separated from the scatterer by only one or two layers of elements the numerical results that are presented demonstrate the good level of numerical accuracy achieved when the second and third order abcs are employed and the singularities of s are appropriately dealt with

3 d electromagnetic scattering computation in free space with the feti fdp2 method the electromagnetic dual primal finite element tearing and interconnecting feti dpem method is a nonoverlapping domain decomposition method developed for the finite element analysis of large scale electromagnetic problems where the corner edges are globally numbered this paper presents an extension of the feti dpem2 method named feti full dual primal feti fdp2 where more flexible robin type boundary conditions are imposed on the inner interfaces between subdomains as well as on the corner edges leading to a new interface problem its capacities are tested in the framework of a three dimensional 3 d free space scattering problem with a scattered field formulation and a computational domain truncated by perfectly mathed layers pml first we compare its accuracy with respect to other feti dpem2 methods and to a complete resolution of the fem problem thanks to a direct sparse solver we show that the convergence of iterative solvers is affected by the presence of the pml and can be accelerated by means of a more accurate approximation between adjacent subdomains of the dirichlet to neumann dtn operator the effectiveness of the iterative solvers are also considered for different test cases the advantages of the proposed feti fdp2 method combined with the associated dtn approximation is numerically demonstrated regardless the chosen working frequency or the iterative solvers