capacity constraints across nests in assortment optimization under the nested logit model we consider assortment optimization problems when customers choose according to the nested logit model and there is a capacity constraint limiting the total capacity consumption of all products offered in all nests when each product consumes one unit of capacity our capacity constraint limits the cardinality of the offered assortment for the cardinality constrained case we develop an efficient algorithm to compute the optimal assortment when the capacity consumption of each product is arbitrary we give an algorithm to obtain a 4 approximate solution we show that we can compute an upper bound on the optimal expected revenue for an individual problem instance by solving a linear program in our numerical experiments we consider problem instances involving products with arbitrary capacity consumptions comparing the expected revenues from the assortments obtained by our 4 approximation algorithm with the upper bounds on the optimal expected revenues our numerical results indicate that the 4 approxim

maximally orthogonalized higher order bases over generalized wires quadrilaterals and hexahedra this paper presents a general theory of maximally orthogonalized div and curl conforming higher order basis functions hobfs over generalized wires quadrilaterals and hexahedra in particular all elements of such bases necessary for fast and easy implementation are listed up to order n 8 numerical results given for div conforming bases applied in an iterative method of moments solution of integral equations show that the condition number and the number of iterations are a much lower than in the case of other hobfs of polynomial type and b practically not dependent on the applied expansion order

revenue utility tradeoff in assortment optimization under the multinomial logit model with totally unimodular constraints we examine the revenue utility assortment optimization problem with the goal of finding an assortment that maximizes a linear combination of the expected revenue of the firm and the expected utilit

numerical characterization of divergence conforming constrained basis functions for surface integral equations this paper presents an algebraic method of generating arbitrary order basis functions suitable for use in moment methods the basis functions are constructed by enforcing a set of suitable constraints on a more general set of functions leading to a matrix representation of the constraint condition the desired bases are then found through use of the singular value decomposition divergence conforming constrained bases are presented for quadrilateral meshes for use in electric and magnetic field integral equations appropriate constraints for enforcing normal continuity at cell boundaries are discussed a variety of problems are analyzed using the constrained bases and results show that the constrained bases exhibit exponential convergence for smooth structures and produce systems whose condition numbers grow relatively slowly with increasing basis order

a surface patch model for polygonal plates a method of moments surface patch model for polygon plates is presented three methods for segmenting polygon plates are considered also the choice between full surface testing and point matching is discussed as it affects the efficiency and generality of the solution numerical results are compared with measurements and independent calculations for polygonal plates of three different shapes including a wire to plant junction

higher order interpolatory vector bases on pyramidal elements in the numerical solution of three dimensional 3 d electromagnetic field problems the regions of interest can be discretized by elements having tetrahedral brick or prismatic shape however such different shape elements cannot be linked to form a conformal mesh to this purpose pyramidal elements are required in this paper we define interpolatory higher order curl and divergence conforming vector basis functions on pyramidal elements with extension to curved pyramids and discuss their completeness properties a general procedure to obtain vector bases of arbitrary polynomial order is given and bases up to second order are explicitly reported these new elements ensure the continuity of the proper vector components across adjacent elements of equal order but different shape results to confirm the faster convergence of higher order functions on pyramids are presented

a hybrid fem mom method for 3 d electromagnetic scattering in layered medium accurate and efficient prediction of electromagnetic scattering from inhomogeneous objects in layered medium is one of the most challenging issues in engineering applications this paper presents the first 3 d higher order hybrid finite element method fem and method of moments mom for the accurate modeling of inhomogeneous dielectric objects in multilayered medium the main challenges of this paper include 1 the integration of these algorithms for layered medium and 2 the higher order computational approach involved in layered medium for high efficiency in the proposed method the mom with the layered medium dyadic green s function is used as the exact radiation boundary condition in an inhomogeneous background and the fem is applied to model the inhomogeneous objects furthermore the higher order maximally orthogonal basis functions with curl conforming and divergence conforming properties are used in the fem and mom respectively to improve the modeling capability of this algorithm for 3 d inhomogeneous objects scattering in multilayered medium this new method requires a much more tightly truncated simulation domain than the traditional fem and provides much higher flexibility than the pure surface integral equation method finally some numerical results are provided to validate the accuracy efficiency and flexibility of this method

volume surface integral equation method based on higher order hierarchical vector basis functions for em scattering and radiation from composite metallic and dielectric structures this paper presents a novel galerkin type method of moments solution of the volume surface integral equation vsie which is developed for the analysis of electromagnetic scattering and radiation from composite metallic and dielectric structures our new scheme utilizes curved tetrahedral elements and curved triangular patches for geometric modeling and the associated higher order hierarchical vector hohv basis functions for volume surface current modeling in contrast to the previous studies on higher order vsie our scheme which is reported for the first time in vsie is much more flexible in comparison with the conventional low order scheme our scheme requires much less memory and computational time for the same accuracy level numerical results are provided to demonstrate the accuracy efficiency and flexibility of our scheme

divergence conforming constrained basis functions for hexahedral volume elements this communication presents an algebraic method for constructing arbitrary order divergence conforming basis functions on hexahedral volume elements the appropriate constraints within and on the boundaries of elements are provided in particular the handling of faces where quantities are discontinuous is discussed the resulting bases are numerically characterized in terms of error convergence and system conditioning for a moment method discretization of the electric field volume integral equation for dielectric scatterers results show the accuracy of the proposed method as well as the low system matrix condition number that can be maintained as the basis order and mesh discretization are increased

combining the moment method with geometrical modelling by nurbs surfaces and bezier patches induced current distributions on conducting bodies of arbitrary shape modelled by nurbs non uniform rational b splines surfaces are obtained by using a moment method approach to solve an electric field integral equation efie the nurbs surfaces are expanded in terms of bezier patches by applying the cox de boor transformation algorithm this transformation is justified because bezier patches are numerically more stable than nurbs surfaces new basis functions have been developed which extend over pairs of bezier patches these basis functions can be considered as a generalization of rooftop functions the method is applied to obtain rcs values of several objects modelled with nurbs surfaces good agreement with results from other methods is observed the method is efficient and versatile because it uses geometrical modelling tools that are quite powerful

curl conforming hierarchical vector bases for triangles and tetrahedra a new family of hierarchical vector bases is proposed for triangles and tetrahedra these functions span the curl conforming reduced gradient spaces of nedelec the bases are constructed from orthogonal scalar polynomials to enhance their linear independence which is a simpler process than an orthogonalization applied to the final vector functions specific functions are tabulated to order 6 5 preliminary results confirm that the new bases produce reasonably well conditioned matrices

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

approximation algorithms for combinatorial fractional programming problems we are concerned with a combinatorial optimization problem which has the ratio of two linear functions as the objective function this type of problems can be solved by an algorithm that uses an auxiliary problem with a parametrized linear objective function because of its combinatorial nature however it is often difficult to solve the auxiliary problem exactly in this paper we propose an algorithm which assumes that the auxiliary problems are solved only approximately and prove that it gives an approximate solution to the original problem of which the accuracy is at least as good as that of approximate solutions to the auxiliary problems it is also shown that the time complexity is bounded by the square of the computation time of the approximate algorithm for the auxiliary problem as an example of the proposed algorithm we present a fully polynomial time approximation scheme for the fractional 0 1 knapsack problem

efficient scalable parallel higher order direct mom sie method with hierarchically semiseparable structures for 3 d scattering a novel fast scalable parallel algorithm is proposed for the solution of large 3 d scattering problems based on 1 the double geometrical and current approximation higher order dho method of moments mom in the surface integral equation sie formulation and 2 a direct solver for dense linear systems utilizing hierarchically semiseparable hss structures namely an hss matrix representation is used for compression factorization and solution of the system matrix in addition a rank revealing qr decomposition for memory compression is used with a stopping criterion in terms of the relative rank tolerance value a method for geometrical preprocessing of the scatterers based on the cobblestone distance sorting technique is employed in order to enhance the hss algorithm accuracy and parallelization numerical examples show how the accuracy of the dho hss mom sie method is easily controllable by using the relative tolerance for the matrix compression moreover the examples demonstrate low memory consumption as well as much faster simulation time when compared to the direct lu decomposition the method enables dramatically faster monostatic scattering computations than iterative solvers and reduced number of unknowns when compared to low order discretizations finally great scalability of the algorithm is demonstrated on more than one thousand processes

the maximal subgroups of the baby monster i abstract in this paper we describe the completion of the determination of the maximal subgroups of the baby monster simple group our results are proved using computer calculations with matrix generators for the group the full details of the calculations will appear elsewhere

approximating a class of combinatorial problems with rational objective function in the late seventies megiddo proposed a way to use an algorithm for the problem of minimizing a linear function a 0 a 1 x 1 a n x n subject to certain constraints to solve the problem of minimizing a rational function of the form a 0 a 1 x 1 a n x n b 0 b 1 x 1 b n x n subject to the same set of constraints assuming that the denominator is always positive using a rather strong assumption hashizume et al extended megiddo s result to include approximation algorithms their assumption essentially asks for the existence of good approximation algorithms for optimization problems with possibly negative coefficients in the linear objective function which is rather unusual for most combinatorial problems in this paper we present an alternative extension of megiddo s result for approximations that avoids this issue and applies to a large class of optimization problems specifically we show that if there is an approximation for the problem of minimizing a nonnegative linear function subject to constraints satisfying a certain increasing property then there is an approximation 1 approximation for the problem of minimizing maximizing a nonnegative rational function subject to the same constraints our framework applies to covering problems and network design problems among others

high order divergence conforming constrained bases for triangular cells this paper presents an algebraic technique for generating arbitrary order divergence conforming bases for curvilinear triangular cells the bases are constructed by enforcing appropriate constraints on a linear combination of general functions and then extracting the desired bases using singular value decompositions koornwinder dubiner polynomials are chosen as the general function set basic constraints are presented to obtain divergence conforming bases and additional constraints are presented to further enforce the bases to be nedelec results from a variety of problems are given to show that the bases exhibit high order convergence and also produce systems that are relatively well conditioned compared to other basis sets

higher order interpolatory vector bases for computational electromagnetics low order vector basis functions compatible with the nedelec 1980 representations are widely used for electromagnetic field problems higher order functions are receiving wider application but their development is hampered by the complex procedures used to generate them and lack of a consistent notation for both elements and bases in this paper fully interpolatory higher order vector basis functions of the nedelec type are defined in a unified and consistent manner for the most common element shapes it is shown that these functions can be obtained as the product of zeroth order nedelec representations and interpolatory polynomials with specially arranged arrays of interpolation points the completeness properties of the vector functions are discussed and expressions for the vector functions of arbitrary polynomial order are presented sample numerical results confirm the faster convergence of the higher order functions

persistency model and its applications in choice modeling given a discrete maximization problem with a linear objective function where the coefficients are chosen randomly from a distribution we would like to evaluate the expected optimal value and the marginal distribution of the optimal solution we call this the persistency problem for a discrete optimization problem under uncertain objective and the marginal probability mass function of the optimal solution is named the persistence value in general this is a difficult problem to solve even if the distribution of the objective coefficient is well specified in this paper we solve a subclass of this problem when the distribution is assumed to belong to the class of distributions defined by given marginal distributions or given marginal moment conditions under this model we show that the persistency problem maximizing the expected objective value over the set of distributions can be solved via a concave maximization model the persistency model solved using this formulation can be used to obtain important qualitative insights to the behavior of stochastic discrete optimization problems we demonstrate how the approach can be used to obtain insights to problems in discrete choice modeling using a set of survey data from a transport choice modeling study we calibrate the random utility model with choice probabilities obtained from the persistency model numerical results suggest that our persistency model is capable of obtaining estimates that perform as well if not better than classical methods such as logit and cross nested logit models we can also use the persistency model to obtain choice probability estimates for more complex choice problems we illustrate this on a stochastic knapsack problem which is essentially a discrete choice problem under budget constraint

on the compatibility of nested logit models with utility maximization abstract the paper examines the relationship between the nested multinomial logit nmnl model and rational consumer behavior we show that the daly zachary mcfadden dzm condition of the validity of stochastic utility maximization in nmnl models is unnecessarily strong and leads too often to rejection of nmnl models with large dissimilarity parameters in many cases the distribution of the stochastic utility components in the nmnl model can be modified in a way that preserves the nmnl choice probabilities on a subset of ri where i is the number of alternatives in the choice set on this subset the dzm condition can be violated without violating the restrictions of stochastic utility maximization

hierarchical curl conforming nedelec elements for quadrilateral and brick cells new curl conforming hierarchical vector basis functions are developed for quadrilateral and hexahedral cells these bases are constructed from orthogonal polynomials and are shown to maintain superior linear independence as their polynomial order is increased the procedure for constructing these basis functions is described and general expressions are provided for an arbitrary order

on chevalley groups acting on projective planes in io hcring introduced the concept of a strongly irreducible collineation group let n be a projective plane k a collineation group of n k is said to be strongly irreducible iff k fixes no points lines triangles or subplanes of n if k is a finite group acting strongly irreducible on 71 generated by perspectivities then hering shows in 10 that k is either an extension of a 3 group with a subgroup of the automorphismgroup or there is a normal subgroup g in k g a nonabelian finite simple group such that k aut g the aim of this paper is to prove the following theorem

double higher order large domain volume surface integral equation method for analysis of composite wire plate dielectric antennas and scatterers a novel double higher order large domain galerkin type method of moments based on higher order geometrical modeling and higher order current modeling is proposed for analysis of composite dielectric and metallic radiation scattering structures combining the volume integral equation vie approach for dielectric parts and the surface integral equation sie approach for metallic parts of the structure the technique employs lagrange type interpolation generalized hexahedra and quadrilaterals of arbitrary geometrical mapping orders for the approximation of geometry and hierarchical divergence conforming polynomial vector basis functions of arbitrary expansion orders for the approximation of currents within the elements the double higher order vsie vie sie method is extensively validated and evaluated against the analytical solutions and the numerical results obtained by alternative higher order methods

a general framework for designing approximation schemes for combinatorial optimization problems with many objectives combined into one in this paper we present a general framework for designing approximation schemes for combinatorial optimization problems in which the objective function is a combination of more than one function examples of such problems include those in which the objective function is a product or ratio of two linear functions parallel machine scheduling problems with the makespan objective robust versions of weighted multiobjective optimization problems and assortment optimization problems with logit choice models the main idea behind our approximation schemes is the construction of an approximate pareto optimal frontier of the functions that constitute the given objective using this idea we give the first fully polynomial time approximation schemes for the max min resource allocation problem with a fixed number of agents combinatorial optimization problems in which the objective function is the sum of a fixed number of ratios of linear functions or the product of a fixed number of linear functions and assor

approximation algorithms for the m dimensional 0 1 knapsack problem worst case and probabilistic analyses abstract we describe a polynomial approximation scheme for an m constraint 0 1 integer programming problem m fixed based on the use of the dual simplex algorithm for linear programming we also analyse the asymptotic properties of a particular random model

multiproduct price optimization and competition under the nested logit model with product differentiated price sensitivities we study firms that sell multiple substitutable products and customers whose purchase behavior follows a nested logit model of which the multinomial logit model is a special case customers make purchasing decisions sequentially under the nested logit model they first select a nest of products and subsequently purchase one within the selected nest we consider the multiproduct pricing problem under the general nested logit model with product differentiated price sensitivities and arbitrary nest coefficients we show that the adjusted markup defined as price minus cost minus the reciprocal of price sensitivity is constant for all the products within a nest at optimality this reduces the problem s dimension to a single variable per nest we also show that the adjusted nest level markup is nest invariant for all the nests which further reduces the problem to maximizing a single variable unimodal function under mild conditions we also use this result to simplify the oligopolistic multiproduct price competition and characterize the nash equilibrium we also consider more general attraction functions that include the linear utility and the multiplicative competitive interaction models as special cases and we show that similar techniques can be used to significantly simplify the corresponding pricing problems

saa regularized methods for multiproduct price optimization under the pure characteristics demand model utility based choice models are often used to determine a consumer s purchase decision among a list of available products to provide an estimate of product demands and when data on purchase decisions or market shares are available to infer consumers preferences over observed product characteristics these models also serve as a building block in modeling firms pricing and assortment optimization problems we consider a firm s multiproduct pricing problem in which product demands are determined by a pure characteristics model a sample average approximation saa method is used to approximate the expected market share of products and the firm profit we propose an saa regularized method for the multiproduct price optimization problem we present convergence analysis and numerical examples to show the efficiency and the effectiveness of the proposed method

volume integral equation with higher order hierarchical basis functions for analysis of dielectric electromagnetic scattering an efficient method of moments mom solution of volume electric field integral equation v efie with a kind of higher order basis functions is presented to model scattering from a dielectric object with arbitrary shapes and inhomogenuity this method is based on both higher order geometrical modeling and higher order current modeling which is realized using a family of higher order hierarchical vector hhov basis functions to expand the equivalent volume electric currents within curvilinear volume elements this higher order scheme of mom results in a significant reduction in meshing density and number of unknowns leading to a remarkable reduction of memory and cpu time in comparison with conventional low order mom while the accuracy of the solution remains at a comparable level numerical results agree with analytical solutions or with simulation results obtained by commercial software demonstrating the accuracy convergence efficiency flexibility and adaptability of the new approach

a simplified expression for the self mutual impedance between coplanar and parallel surface monopoles a simplified expression that is valid both for the self and mutual impedances between two coplanar and parallel piecewise sinusoidal pws surface monopoles is presented in contrast to the currently existing two dimensional integral form the present expression involves only a one dimensional integral further the integrand remains regular even for the case of self impedance and does not involve any special functions such as the exponential integral it is in a form suitable for efficient implementation on a computer the expressions are valid when the two surface monopoles are of the same size comparison is made with literature to demonstrate the validity of the expression

affine planes admitting a collineation group with a transitive action on the line at infinity abstract the affine planes admitting a collineation group with a transitive action on the line at infinity are investigated and an essentially complete classification is achieved when the group is almost simple a rather deep result is also obtained when the action on the line at infinity is faithful and primitive

mutual impedance of parallel and perpendicular coplanar surface monopoles one dimensional integral formulas are derived for mutual impedance of arbitrary size coplanar parallel and perpendicular surface monopoles the integrals in formulas are expressed as exponential integrals where possible the mutual impedance expression for parallel monopoles is a summation of exponential integrals and one dimensional integrals for perpendicular monopoles the mutual impedance is in closed form containing exponential integrals only the final expressions are in a form suitable for numerical computation since the expressions contain at most one dimensional integrals they can be utilized to reduce the matrix filling time in the moment method formulations especially when inhomogeneous sectioning is preferred additionally they can be used in rectangular surface patch modeling of conducting surfaces with edges which are at an angle to the surface patches providing the angle is small to this end the expressions were utilized in the moment method analysis of linearly tapered slot antennas very good accuracy was obtained with a reduction in computer time

a new algorithm for the complex exponential integral in the method of moments this paper presents a new algorithm for the rapid and accurate calculation of the complex exponential integral associated with the mutual impedance of sinusoidal basis and testing functions in the method of moments the new algorithm uses leibniz s theorem to calculate taylor series expansions of the integral instead of integrating expansions of the integrand as is often done this results in an algorithm which is twice as fast as and is valid over a wider range than previous algorithms this technique can be applied to many other integrals encountered in computational electromagnetics as well

on the locally continuous formulation of surface doublets exact locally continuous formulation of doublets and particularly rooftop basis functions based on unitary vector concept are presented basic properties of such a formulation are examined showing many advantages when compared with classical approximate formulation in particular in the case of rooftop basis functions based on exact formulation the shape quality factor is defined and optimal shapes of quadrilateral patches are determined if such quadrilaterals are used for modeling of general structures the number of unknowns needed in the analysis is almost halved when compared with modeling by triangular doublets

a column generation algorithm for choice based network revenue management during the past few years there has been a trend to enrich traditional revenue management models built upon the independent demand paradigm by accounting for customer choice behavior this extension involves both modeling and computational challenges one way to describe choice behavior is to assume that each customer belongs to a segment which is characterized by a consideration set i e a subset of the products provided by the firm that a customer views as options customers choose a particular product according to a multinomial logit criterion a model widely used in the marketing literature in this paper we consider the choice based deterministic linear programming model cdlp of gallego et al 2004 gallego g g iyengar r phillips a dubey 2004 managing flexible products on a network technical report corc tr 2004 01 department of industrial engineering and operations research columbia university new york and the follow up dynamic programming decomposition heuristic of van ryzin and liu 2008 van ryzin g j q liu 2008 on the choice based linear programming model for network revenue management manufacturing service oper management10 2 288 310 we focus on the more general version of these models where customers belong to overlapping segments to solve the cdlp for real size networks we need to develop a column generation algorithm we prove that the associated column generation subproblem is indeed np hard and propose a simple greedy heuristic to overcome the complexity of an exact algorithm our computational results show that the heuristic is quite effective and that the overall approach leads to high quality practical solutions

development and application of a novel class of hierarchical tangential vector finite elements for electromagnetics tangential vector finite elements tvfes overcome most of the shortcomings of node based finite elements for electromagnetic simulations for a triangular element this paper proposes a class of hierarchical tvpes that differ from traditional tvfes the hierarchical nature of the proposed tvfes makes them ideally suited for employing an efficient selective field expansion the lowest order tvfe employed within part of the computational domain and a higher order tvfe employed within the remaining part of the computational domain this is an attractive feature not shared by nonhierarchical tvfes for which a more traditional approach the same tvfe employed throughout the computational domain must be applied for determining the scattering by composite cylinders this paper argues that the performance in terms of accuracy memory and in most cases cpu time of the proposed class of hierarchical tvfes when applying selective field expansion is superior to that of the lowest order tvfe and a traditional nonhierarchical tvfe this is the case when an artificial absorber as well as a boundary integral is used for truncating the computational domain a guideline is given as to how lowest and higher order tvfes shall be combined for optimal performance of the proposed class of hierarchical tvfes

dynamic assortment optimization with a multinomial logit choice model and capacity constraint we consider an assortment optimization problem where a retailer chooses an assortment of products that maximizes the profit subject to a capacity constraint the demand is represented by a multinomial logit choice model we consider both the static and dynamic optimization problems in the static problem we assume that the parameters of the logit model are known in advance we then develop a simple algorithm for computing a profit maximizing assortment based on the geometry of lines in the plane and derive structural properties of the optimal assortment for the dynamic problem the parameters of the logit model are unknown and must be estimated from data by exploiting the structural properties found for the static problem we develop an adaptive policy that learns the unknown parameters from past data and at the same time optimizes the profit numerical experiments based on sales data from an online retailer indicate that our policy performs well

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

maximally orthogonal high order basis functions have a well conditioned gram matrix recently a novel high order finite element space for wires quadrilaterals and hexahedrons was presented 1 numerical results have shown a very favorable behavior of the condition number of the gram matrix of this finite element space as a function of the polynomial degree in this paper this high order finite element space is recognized to be expressible in terms of jacobi polynomials which can be easily computed using a three term recurrence in addition the condition number of the gram matrix of the one dimensional finite element space is rigorously analyzed for the general case of a piecewise smooth possibly curved geometry an explicit upper bound for the condition number in terms of the mesh quality is proved this bound implies that the one dimensional finite element space is stable for arbitrarily high polynomial degree numerical results corroborate the theoretical results and show that the basis can be used to perform hp refinement leading to an accurate handling of both large smooth regions and corners

maximally orthogonalized higher order basis functions in large domain finite element modeling in electromagnetics curl conforming max ortho basis functions mobfs are coupled with higher order large domain curved finite elements fes the performance of the functions is compared with that of the classical and near ortho basis functions through numerical experiments it is shown that max ortho fes yield highly orthogonal mass matrices for practically arbitrarily high orders of polynomial field approximations this facilitates the usage of iterative solvers and it significantly increases their efficiency accurate and fast computation of mobfs of arbitrarily high orders is enabled by the proposed two term recurrent formula

nonconformal discretization of electric current volume integral equation with higher order hierarchical vector basis functions a nonconformal discretization of the electric current volume integral equation jvie is presented for the electromagnetic scattering analysis of inhomogeneous dielectric objects this jvie is based on higher order geometrical and current modeling where curved tetrahedral elements and higher order hierarchical vector hohv basis functions are adopted in order to implement the nonconformal discretization the half face based hohv basis function is introduced to address the nonconformal volumetric elements compared to the conventional low order conformal nonconformal vie our nonconformal hohv based jvie has the advantage of improving the computational efficiency and accuracy compared to the previous vie discretized by other higher order functions our nonconformal jvie is based on the higher order geometric modeling and the hohv bases in order to improve the efficiency the basis expansion and recombination technique is introduced to significantly accelerate the matrix filling moreover the flexibility of basis order selection is further enhanced by the mixed order schemes numerical results are given to demonstrate its accuracy efficiency and flexibility

a scheme to analyze conducting plates of resonant size using the conjugate gradient method and the fast fourier transform a scheme for analyzing electrodynamic problems involving conducting plates of resonant size using the conjugate gradient cg method and the fast fourier transform fft is presented in detail the problems are analyzed by solving their corresponding electric field integral equation the procedure is made easy and systematic by using a sampling process with rooftop functions to represent the induced current and pulses to average the fields these functions have been widely used in moment method mm applications the scheme is an efficient numerical tool benefiting from the good convergence and low memory requirements of the cg and the low cpu time consumed in performing convolutions with the fft in comparison with the mm the scheme avoids the storage of large matrices and reduces the computer time by an order of magnitude several results are presented and compared with analytical numerical or measured values that appear in the literature