conformal deformation of a riemannian metric to a scalar flat metric with constant mean curvature on the boundary one of the most celebrated theorems in mathematics is the riemann mapping theorem it says that an open simply connected proper subset of the plane is conformally diffeomorphic to the disk in higher dimensions very few regions are conformally diffeomorphic to the ball however we can still ask whether a domain is conformally diffeomorphic to a manifold that resembles the ball in two ways namely it has zero scalar curvature and its boundary has constant mean curvature in this paper we generalize the riemann mapping theorem to higher dimensions in that sense

vector finite element formulation for scattering from two dimensional heterogeneous bodies a formulation is proposed for electromagnetic scattering from two dimensional heterogeneous structures that illustrates the combination of the curl curl form of the vector helmholtz equation with a local radiation boundary condition rbc to eliminate spurious nonzero eigenvalues in the spectrum of the matrix operator vector basis functions incorporating the nedelec constraints are employed basis functions of linear and quadratic order are presented and approximations made necessary by the use of the local rbc are discussed results obtained with linear tangential quadratic normal vector basis functions exhibit excellent agreement with exact solutions for layered circular cylinder geometries and demonstrate that abrupt jump discontinuities in the normal field components at material interfaces can be accurately modeled the vector 2d formulation illustrates the features necessary for a general three dimensional implementation

on the positivity of the effective action in a theory of random surfaces it is shown that the functional s eta frac 1 24 pi int left frac 1 2 left nabla eta right 2 2 eta right d mu 0 defined onc functions on the two dimensional sphere satisfies the inequalitys 0 if is subject to the constraint int e eta 1 d mu 0 0 the minimums 0 is attained at the solutions of the euler lagrange equations the proof is based on a sharper version of moser trudinger s inequality due to aubin which holds under the additional constraint int e eta xd mu 0 0 this condition can always be satisfied by exploiting the invariance ofs under the conformal transformations ofs2 the result is relevant for a recently proposed formulation of a theory of random surfaces

spectral super elements for wave propagation in structures with local non uniformities the spectral element method for the analysis of wave propagation in structures is extended by the introduction of a super element concept to handle local regions of non uniformity the region of interest is meshed with conventional finite elements and its stiffness and mass matrices dynamically condensed leaving only the connection degrees of freedom these are further condensed to just waveguide connectivities thus making the element suitable for assembly with other spectral elements the formulation is verified by comparison with 2 d finite element solutions examples of its use in waveguides with cracks holes and extended joints are demonstrated

compact isospectral sets of surfaces on etudie des ensembles de surfaces qui sont isospectrales par rapport a l operateur de laplace beltrami

modelling turbulence induced vibration of pipes with a spectral finite element method the vibration of pipes is studied here using the arnold warburton theory for thin shells and a simplified theory valid in a lower frequency regime the vibrational response is described numerically with the spectral finite element method sfem which uses the exact solutions of the equations of motion as basis functions for turbulence excitation the set of basis functions was extended to include particular solutions which model a spatially distributed excitation an efficient numerical solution to homogeneous random excitation is presented and the results compare favourably with wind tunnel measurements

finite element implementation of maxwell s equations for image reconstruction in electrical impedance tomography traditionally image reconstruction in electrical impedance tomography eit has been based on laplace s equation however at high frequencies the coupling between electric and magnetic fields requires solution of the full maxwell equations in this paper a formulation is presented in terms of the maxwell equations expressed in scalar and vector potentials the approach leads to boundary conditions that naturally align with the quantities measured by eit instrumentation a two dimensional implementation for image reconstruction from eit data is realized the effect of frequency on the field distribution is illustrated using the high frequency model and is compared with laplace solutions numerical simulations and experimental results are also presented to illustrate image reconstruction over a range of frequencies using the new implementation the results show that scalar vector potential reconstruction produces images which are essentially indistinguishable from a laplace algorithm for frequencies below 1 mhz but superior at frequencies reaching 10 mhz

mixed finite elements for electromagnetic analysis the occurrence of spurious solutions is a well known limitation of the standard nodal finite element method when applied to electromagnetic problems the two commonly used remedies that are used to address this problem are i the addition of a penalty term with the penalty factor based on the local dielectric constant and which reduces to a helmholtz form on homogeneous domains regularized formulation ii a formulation based on a vector and a scalar potential both these strategies have some shortcomings the penalty method does not completely get rid of the spurious modes and both methods are incapable of predicting singular eigenvalues in non convex domains some non zero spurious eigenvalues are also predicted by these methods on non convex domains in this work we develop mixed finite element formulations which predict the eigenfrequencies including their multiplicities accurately even for nonconvex domains the main feature of the proposed mixed finite element formulation is that no ad hoc terms are added to the formulation as in the penalty formulation and the improvement is achieved purely by an appropriate choice of finite element spaces for the different variables we show that the formulation works even for inhomogeneous domains where double noding is used to enforce the appropriate continuity requirements at an interface for two dimensional problems the shape of the domain can be arbitrary while for the three dimensional ones with our current formulation only regular domains which can be nonconvex can be modeled since eigenfrequencies are modeled accurately these elements also yield accurate results for driven problems c 2014 elsevier ltd all rights reserved

new spectral lanczos decomposition method for induction modeling in arbitrary 3 d geometry traditional resistivity tools are designed to function in vertical wells in horizontal well environments the interpretation of resistivity logs becomes much more difficult because of the nature of 3 d effects such as highly deviated bed boundaries and invasion the ability to model these 3 d effects numerically can greatly facilitate the understanding of tool response in different formation geometries three dimensional modeling of induction tools requires solving maxwell s equations in a discrete setting either finite element or finite difference the solutions of resulting discretized equations are computationally expensive typically on the order of 30 to 60 minutes per log point on a workstation this is unacceptable if the 3 d modeling code is to be used in interpreting induction logs in this paper we propose a new approach for solutions to maxwell s equations the new method is based on the spectral lanczos decomposition method sldm with krylov subspaces generated from the inverse powers of th

a high order mixed vector finite element method for solving the time dependent maxwell equations on unstructured grids we present a mixed vector finite element method for solving the time dependent coupled ampere and faraday laws of maxwell s equations on unstructured hexahedral grids that employs high order discretization in both space and time the method is of arbitrary order accuracy in space and up to 4th order accurate in time making it well suited for electrically large problems where grid anisotropy and numerical dispersion have plagued other methods in addition the method correctly models both the jump discontinuities and the divergence free properties of the electric and magnetic fields is charge and energy conserving conditionally stable and free of spurious modes several computational experiments are performed to demonstrate the accuracy efficiency and benefits of the method

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

from ginzburg landau to hilbert einstein via yamabe abstract in this paper based on some mathematical results obtained by yamabe osgood phillips and sarnak we demonstrate that in dimensions three and higher the famous ginzburg landau equations used in the theory of phase transitions can be obtained without any approximations by minimization of the riemannian type hilbert einstein action functional for pure gravity in the presence of cosmological term we use this observation in order to bring to completion the work by lifshitz done in 1941 on group theoretical refinements of the landau theory of phase transitions in addition this observation allows us to develop a systematic extension to higher dimensions of known string theoretic path integral methods developed for calculation of observables in two dimensional conformal field theories

sharp sobolev inequalities on the sphere and the moser trudinger inequality where de denotes normalized surface measure v is the conformal gradient and q 2n n 2 a modern folklore theorem is that by taking the infinitedimensional limit of this inequality one obtains the gross logarithmic sobolev inequality for gaussian measure which determines nelson s hypercontractive estimates for the hermite semigroup see 8 one observes using conformal invariance that the above inequality is equivalent to the sharp sobolev inequality on rn for which boundedness and extremal functions can be easily calculated using dilation invariance and geometric symmetrization the roots here go back to hardy and littlewood the advantage of casting the problem on the sphere is that the role of the constants is evident and one is led immediately to the conjecture that this inequality should hold whenever possible for example 2 q 0o if n 2 this is in fact true and will be demonstrated in section 2 a clear question at this point is what is the situation in dimension 2 two important arguments 25 26 27 dealt with this issue both motivated by geometric variational problems because q goes to infinity for dimension 2 the appropriate function space is the exponential class responding in part

correlation functions in liouville theory we show that after integrating over the zero mode in liouville correlation functions the remaining functional integral resembles a free theory and may be evaluated by formally continuing the central charge we apply this technique to the unitary minimal models coupled to gravity on the sphere computing a number of three point functions after taking into account the normalizations of operators and the functional integral we find exact agreement between the liouville three point functions and the results from matrix models

nodal finite element de rham complexes we construct 2d and 3d finite element de rham sequences of arbitrary polynomial degrees with extra smoothness some of these elements have nodal degrees of freedom and can be considered as generalisations of scalar hermite and lagrange elements using the nodal values the number of global degrees of freedom is reduced compared with the classical nedelec and brezzi douglas marini finite elements and the basis functions are more canonical and easier to construct our finite elements for h mathrm div with regularity r 2 coincide with the nonstandard elements given by stenberg numer math 115 1 131 139 2010 we show how regularity decreases in the finite element complexes so that they branch into known complexes the standard de rham complexes of whitney forms and their higher order version can be regarded as the family with the lowest regularity the construction of the new families is motivated by finite element systems

a global approach to the rankin selberg convolution for 3 we discuss the rankin selberg convolution on gl 3 z in the classical language of symmetric spaces and automorphic forms introduction study of the rankin selberg convolution of two automorphic forms on gl 2 has yielded many interesting number theoretic applications recently this construction has been extended to automorphic forms on gl n by jacquet piatetskii shapiro and shalika see 8 for the local results their methods generalize those of jacquet langlands in particular they make considerable use of the representation theory over local fields as developed by bernstein zelevinsky and others in this paper we shall give a discussion of their results in a classical nonadelic language in the simplest higher rank situation that of two automorphic forms on gl 3 z we must emphasize that most of the ideas in this paper are not really new but simply restatements in this more classical language of those of jacquet piatetskiishapiro anid shalika further a classical sketch of the rankin selberg method has been given by jacquet 7 however we are able to sharpen these results at the archimedean place by giving the precise gamma factors at infinity and also the behavior of the convolution at its poles see also 10 these are of particular interest because of two applications which require this precise version of the convolution the first noted by moreno shahidi 30 and serre 17 see also 14 obtains the coefficient bound ia p i pl 5 p 1 5 for the size of the fourier coefficient of a gl 2 maass wave form which is also a hecke eigenform here the normalization is such that the ramanujan petersson conjecture predicts la p l 2 this follows by combining the convolution with the gelbart jacquet lifting 3 from gl 2 to gl 3 and a result of chandrasekharannarasimhan 2 on the order of partial l series the second is given in the thesis of received by the editors february 25 1985 and in revised form april 10 1986 1980 mathematics subject classification 1985 revision primary 10d05 iod20 iod24 secondary 12a67

a fast higher order time domain finite element boundary integral method for 3 d electromagnetic scattering analysis a novel hybrid time domain finite element boundary integral method for analyzing three dimensional 3 d electromagnetic scattering phenomena is presented the method couples finite element and boundary integral field representations in a way that results in a sparse system matrix and solutions that are devoid of spurious modes to accurately represent the unknown fields the scheme employs higher order vector basis functions defined on curvilinear tetrahedral elements to handle problems involving electrically large objects the multilevel plane wave time domain algorithm is used to accelerate the evaluation of the boundary integrals numerical results demonstrate the accuracy and versatility of the proposed scheme

on a finite element method for solving the three dimensional maxwell equations abstract the aim of this paper is to present a method for solving the time domain three dimensional maxwell equations which can be coupled with a particle solver for this purpose maxwell s equations are reformulated as a constrained wave equation system with lagrange multipliers associated to the conditions 0 and e e 0 we approximate both the fields and the lagrange multipliers with a finite element method using a taylor hood element

a hybrid pstd adi cfdtd method for mixed scale electromagnetic problems we propose a hybrid technique combining the pseudospectral time domain pstd method with the alternating direction implicit conformal finite difference time domain adi cfdtd method to solve 3 d mixed scale problems in computational electromagnetics a mixed scale problem contains both electrically large and relatively homogeneous regions and electrically small fine details thus poses a significant computational challenge to any single computational method if it is utilized alone in particular the adi cfdtd method is an unconditionally stable time domain method with second order spatial accuracy and allows the time step to be increased beyond the courant friedrichs levy limit it is suitable for electrically small problem structure details much smaller than a wavelength but is inefficient and suffers from large numerical errors for electrically large scale regions the pstd method on the other hand is accurate and efficient for regions with large relatively homogeneous materials but loses its efficiency for electrically small structures the hybrid pstd adi cfdtd method overcomes these disadvantages and is potentially more useful than the individual solvers the implementation details and numerical accuracy of this hybrid method are examined numerical examples demonstrate the advantages of the hybrid pstd adi cfdtd method

classification of prime 3 manifolds with σ invariant greater than rp 3 in this paper we compute the invariants sometimes also called the smooth yamabe invariants of rp 3 and rp 2 s 1 which are equal and show that the only prime 3 manifolds with larger invariants are s 3 s 2 s 1 and s 2 s 1 the nonorientable s 2 bundle over s 1 more generally we show that any 3 manifold with invariant greater than rp 3 is either s 3 a connect sum with an s 2 bundle over s 1 or has more than one nonorientable prime compo

a fast time domain finite element boundary integral method for electromagnetic analysis a time domain finite element boundary integral fe bi method is presented for analyzing electromagnetic em scattering from two dimensional 2 d inhomogeneous objects the scheme s finite element component expands transverse fields in terms of a pair of orthogonal vector basis functions and is coupled to its boundary integral component in such a way that the resultant finite element mass matrix is diagonal and more importantly the method delivers solutions that are free of spurious modes the boundary integrals are computed using the multilevel plane wave time domain algorithm to enable the simulation of large scale scattering phenomena numerical results demonstrate the capabilities and accuracy of the proposed hybrid scheme

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

least squares finite element method and preconditioned conjugate gradient solution a least squares variational procedure for first order systems of differential equations and an approximate formulation based on finite elements are developed error estimates a condition number bound and analysis of weighting factors are given steepest descent and conjugate gradient solution procedures are examined and an appropriate preconditioner constructed which is demonstrated to yield rapid convergence and to be insensitive to problem size numerical studies of rates of convergence for a test problem are given

time domain integration of the maxwell equations on finite elements an explicit time domain integration scheme is developed for finite element spatial discretization of the maxwell equations a generalized wave equation is used in weak form which is free of vector parasites when discretized on single c sup 0 elements the use of integral lumping renders the mass matrix diagonal with no necessary degradation in accuracy the explicit method which results combines the economy of established finite difference techniques with the geometric flexibility of finite elements test problems representative of practical hyperthermia applications show agreement with analytic and frequency domain finite element methods and confirm scaling arguments on run time and memory

energy flow models from finite element analysis computationally efficient methods are described by which the results of a finite element analysis of a system may be post processed to form energy flow models yielding time and perhaps frequency average subsystem energies as well as input and dissipated powers the methods are particularly efficient for excitation which is spatially distributed or broadband e g rain on the roof or if the frequency average response is required first a method based on a global finite element analysis is presented this involves a global modal decomposition and a reordering of the subsequent numerical calculations the properties of the distribution of the excitation and the system s mass and stiffness lead to subsystem force distribution mass distribution and stiffness distribution matrices the response is given by a sum of terms involving the interaction of a pair of global modes the contribution of each pair depending on the appropriate elements of the distribution matrices frequency averaging is performed by separating the resulting frequency dependent terms and integrating in most practical cases this integration can be done analytically next an alternative method involving component mode synthesis is described in this individual finite element analyses are performed for each subsystem using here the fixed interface method these are then assembled to perform a global modal analysis with the order of the model being much reduced the consequent results are then post processed in the same way finally a system comprising three coupled plates is presented as a numerical example

dynamic behaviour of structures in large frequency range by continuous element methods abstract the continuous element method is presented in the context of the harmonic response of beam assemblies a general formulation is described from the displacement solution of the elementary problem a direct computation of elementary dynamic stiffness matrices is presented in the present formulation distributed loadings are taken into account in the case of more complex geometries for which many coupling phenomena occur an explicit formulation is no more conceivable in this case a numerical approach is presented this approach allows an algorithmic computation of exact dynamic stiffness matrices this method called numerical continuous element allows one to consider the coupled vibrations of curved beams and those of helical beams the validation of this numerical method is achieved by comparisons with the harmonic response of various beams obtained by a finite element approach finally a comparison between eigenfrequencies obtained experimentally and numerically for a straight beam and a helical beam has been made to evaluate the performances of the method

invariants of conformal laplacians the conformal laplacian d d d n 2 s 4 n 1 acting on functions on a riemannian manifold mn with scalar curvature s is a conformally invariant operator in this paper we will use d to construct new conformal invariants one of these is a pointwise invariant one is the integral of a local expression and one is a nonlocal spectral invariant derived from functional determinants we begin in 1 by describing the laplacian d and its green function in the context of conformal geometry we then derive a basic formula giving the variation in the heat kernel of d this formula is strikingly simpler than the corresponding formula for the ordinary laplacian given by ray and singer 15 the heat kernel of d has an asymptotic expansion k t x x 4 t n 2 ak x tk in 2 we prove that a n 2 2 is a pointwise conformal invariant of weight 2 i e it satisfies a n 2 2 x 2g 2a n 2 2 x g where g is the metric and is any smooth positive function in particular this shows the existence of a nontrivial locally computable conformally invariant density naturally associated to the conformal structure of an even dimensional manifold the key to the proof is to consider the parametrix of the green s function which is obtained from the heat kernel by an integral transform one finds that a n 2 2 occurs as the coefficient of the first log term in this parametrix and its conformal invariance then follows directly from the conformal invariance of the green s function in 3 we show that an 2 is a global conformal invariant the calculations in 4 show that it is not a pointwise invariant the proof is a direct calculation of the invariant of an 2 using equation 1 10

elimination of spurious modes in finite element analysis abstract a common cause of spurious non physical modes that arise in either finite difference or finite element derived eigenvalue problems is identified it is shown that these modes are the result of an excessively flexible system the flexibility is removed by constraining the problem an analogy is drawn between electromagnetic wave propagation and acoustic wave propagation in liquids to show that the spurious modes encountered in both cases are due to fundamentally the same cause results are presented to show that constraining the problem yields a significant reduction in the number of spurious modes a big improvement in the quality of the eigenvector of the physical modes and only a marginal increase in the error in the eigenvalue for the low order modes

the origin of spurious solutions in computational electromagnetics it is commonly believed that the divergence equations in the maxwell equations are redundant for transient and timeharmonic problems therefore most of the numerical methods in computational electromagnetics solve only two first order curl equations or the second order curl curl equations this misconception is the true origin of spurious modes and inaccurate solutions in computational electromagnetics by studying the div curl system this paper clarifies that the first order maxwell equations are not overdetermined and the divergence equations must always be included to maintain the ellipticity of the system in the space domain to guarantee the uniqueness of the solution and the accuracy of the numerical methods and to eliminate the infinitely degenerate eigenvalue this paper shows that the common derivation and usage of the second order curl curl equations are incorrect and that the solution of helmholtz equations needs the divergence condition to be enforced on an associated part of the boundary the div curl method and the least squares method introduced in this paper provide rigorous derivation of the equivalent second order maxwell equations and their boundary conditions the node based least squares finite element method lsfem is recommended for solving the first order full maxwell equations directly examples of the numerical solutions by lsfem are given to demonstrate that the lsfem is free of spurious solutions

critical points of the determinant of the laplace operator abstract the determinant of the laplace operator det is a function on the set of metrics on a compact manifold generalizing the work of osgood phillips and sarnak on surfaces we consider one parameter variations of metrics of fixed volume in the conformal class of given metric by calculating the derivative of log det with respect to such variations we find the condition for a metric to be a critical point of the determinant function homogeneous manifolds satisfy this condition but we exhibit examples of locally homogeneous manifolds which are not critical points in dimensions 3 for 3 dimensional manifolds we derive a formula for the second derivative of log det with respect to such a variation at a critical point using this formula we show that the standard metric on the sphere s 3 and some flat metrics on three dimensional tori are local maxima of the determinant function

a two dimensional dispersion analysis of selected methods for solving the linearized shallow water equations abstract the accuracy and cost of three finite element methods for solving the linearized two dimensional shallow water equations are compared with a traditional explicit finite difference technique accuracy is determined by comparing numerical and analytic plane wave solutions cost is measured as the number of computations per unit of real time and per unit of model area two of the finite element methods are shown to be cost competitive and as accurate as the chosen explicit finite difference technique though not comprehensive the finite element analyses also suggest that meshes composed of equilateral triangles most accurately represent phase and group velocity

perfectly matched layer mesh terminations for nodal based finite element methods in electromagnetic scattering the perfectly matched layer pml concept introduced by berenger 1994 is implemented for nodal based finite element frequency domain methods starting from a scalar vector potential framework anisotropic media equivalent gauge conditions are developed for both coupled and uncoupled i e direct field scalar vector field formulations the resulting discrete system of equations are shown to be identical for both the anisotropic and stretched coordinate viewpoints of pml mesh termination on node based finite elements reaching this equivalency requires that special attention be paid to the basis weighting functions used within the pml region specifically a material dependency is found to be essential the alternative but identical stretched coordinate approach provides the perspective needed to realize a scheme for generalizing the pml to non cartesian mesh terminations which are more natural in the finite element context several benchmark problems and associated numerical results are presented to demonstrate the performance of the pml on node based finite elements

spectral finite elements for vibrating rods and beams with random field properties the classical stochastic helmholtz equation grasps through the random field of the refraction index the spatial variability in the mass density but not the variability in elastic moduli or geometric parameters in contradistinction to this restriction the present analysis accounts for the spatial randomness of mass density as well as those of elastic properties and cross sectional geometric properties of rods undergoing longitudinal vibrations and of timoshenko beams in flexural vibrations all the material variabilities are described here by random fourier series with a typical average characteristic size of inhomogeneity d which is either smaller comparable to or larger than the wavelength the third length scale entering the problem but kept constant is the rod or beam length we investigate the relative effects of random noises in all the material parameters on the spectral stiffness matrices associated with rods and beams for a very wide range of frequencies

extremals of determinants of laplacians on etudie le determinant associe au laplacien en fonction de la metrique sur une surface donnee et en particulier ses valeurs extremes quand la metrique est bien restreinte

three dimensional computer modeling of electromagnetic fields a global lookback lattice truncation scheme abstract a new lattice truncation scheme for the finite difference time domain approach to the solution of maxwell s equations has been developed the problem space is truncated near the sources and the field components on its boundary are generated from those field values known at retarded times on an interior surface one cell from it with an integral representation of the electromagnetic field the numerical implementation of this global lookback scheme is discussed examples which have been used to determine its characteristics and its validity are given

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

conformal invariants for determinants of laplacians on riemann surfaces for a riemann surface with smooth boundaries conformal weyl invariant quantities proportional to the determinant of the scalar laplacian operator are constructed both for dirichlet and neumann boundary conditions the determinants are defined by zeta function regularization the other quantities in the invariants are determined from metric properties of the surface as applications explicit representations for the determinants on the flat disk and the flat annulus are derived

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

time domain finite element methods various time domain finite element methods for the simulation of transient electromagnetic wave phenomena are discussed detailed descriptions of test trial spaces explicit and implicit formulations nodal and edge facet element basis functions are given along with the numerical stability properties of the different methods the advantages and disadvantages of mass lumping are examined finally the various formulations are compared on the basis of their numerical dispersion performance

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

response variance prediction in the statistical energy analysis of built up systems in the statistical energy analysis sea of high frequency noise and vibration a complex engineering structure is represented as an assembly of subsystems the response of the system to external excitation is expressed in terms of the vibrational energy of each subsystem and these energies are found by employing the principle of power balance strictly the computed energy is an average taken over an ensemble of random structures and for many years there has been interest in extending the sea prediction to the variance of the energy a variance prediction method for a general built up structure is presented here closed form expressions for the variance are obtained in terms of the standard sea parameters and an additional set of parameters alpha k that describe the nature of the power input to each subsystem k and alpha ks that describe the nature of the coupling between subsystems k and s the theory is validated by comparison with monte carlo simulations of plate networks and structural acoustic systems

extremal metrics of zeta function determinants on 4 manifolds in conformal geometry the sobolev inequality at a critical exponent has received much attention in particular the determination of the best constants has played a crucial role in the yamabe problem in dimension two the analogous problem deals with the moser trudinger inequality on a compact riemann surface m2 there exists a constant c c m so that f e47w2 c m if f ivw12 1 and f w 0 the connection of this inequality with geometry comes through the zeta functional determinant of the laplacian as defined by ray singer for a riemannian metric g let 0 a1 a2 be the spectrum

a posteriori error indicators for maxwell s equations abstract in this paper we shall analyze a class of a posteriori error indicators for an electromagnetic scattering problem for maxwell s equations in the presence of a bounded inhomogeneous and anisotropic scatterer problems of this type arise when computing the interaction of electromagnetic radiation with biological tissue we briefly recall existence and uniqueness theory associated with this problem then we show how a posteriori error indicators can be derived using an adjoint equation approach the error indicators use both the jump in normal and tangential components of the field across faces in the mesh

finite element analysis of controlled source electromagnetic induction using coulomb gauged potentials a 3 d finite element solution has been used to solve controlled source electromagnetic em induction problems in heterogeneous electrically conducting media the solution is based on a weak formulation of the governing maxwell equations using coulomb gauged em potentials the resulting sparse system of linear algebraic equations is solved efficiently using the quasi minimal residual method with simple jacobi scaling as a preconditioner the main aspects of this work include the implementation of a 3 d cylindrical mesh generator with high quality local mesh refinement and a formulation in terms of secondary em potentials that eliminates singularities introduced by the source these new aspects provide quantitative induction log interpretation for petroleum exploration applications examples are given for 1 d 2 d and 3 d problems and favorable comparisons are presented against other previously published multidimensional em induction codes the method is general and can also be adapted for controlled so

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

a note on mass lumping in the finite element time domain method mass lumping has been used to produce explicit time integration schemes for the finite element time domain method in this paper we show that a specific choice in the lumping procedure can produce a scheme that is equivalent to the finite difference time domain method if lumping is done in the time integration process one can show that it can be equivalent to the newmark beta method

moduli space heights and isospectral sets of plane domains let q be a plane domain of finite connectivity n with smooth boundary and choose a fixed domain 2 of the same type then there exists a flat metric g on 2 such that q is isometric with 29g in what follows we do not distinguish between isometric domains by the spectrum of 29 we mean the spectrum of the laplace beltrami operator ag on 29 with dirichlet boundary conditions the height h eg log det ag is a spectral invariant and plays a central role in this paper among all suitably normalized flat metrics on 2 conformal to a given metric g there is a unique flat metric for which the height is a minimum this metric is characterized by the fact that d 2 has constant geodesic curvature we call such a metric uniform and denote it by u the set of all such metrics is denoted by u 2 we can therefore identify with the moduli space 2 of conformal structures on e for n 3 we introduce a special parametrization for mu 2 by means of which we show that h u oo as u approaches the boundary of fu 2 using this along with the heat invariants for the laplacian we then show that any isospectral set of plane domains is compact in the c topology similar results hold for n 1 and 2

critical metrics for the determinant of the laplacian in odd dimensions let m be a closed compact n dimensional manifold with n odd we calculate the first and second variations of the zeta regularized determinants det a and det l as the metric on m varies where a denotes the laplacian on functions and l denotes the conformal laplacian we see that the behavior of these functionals depends on the dimension indeed every critical metric for 1 n 1 2det a or 1 n 1 21 det l has finite index consequently there are no local maxima if n 4rm 1 and no local minima if n 4m 3 we show that the standard 3 sphere is a local maximum for det a while the standard 4m 3 sphere with m 1 2 is a saddle point by contrast for all odd n the standard n sphere is a local extremal for det l an important tool in our work is the canonical trace on odd class operators in odd dimensions this trace is related to the determinant by the formula det q tr log q and we prove some basic results on how to calculate this trace

resonant beam vibration a wave evolution analysis abstract in an attempt to verify the concept of wave mode duality and to understand the wave train closure principle in resonant beam vibration an elastically supported beam subjected to a swept sinusoidal force is investigated through a simulation of wave evolution from initial to final steady state response wave evolution is simulated in the superposition and the degenerate states according to the nature of wave reflection at the boundaries of the beam from the results resonance condition is established and the natural frequencies and mode shapes are calculated using a simply supported beam and a cantilever beam as examples the concept of wave mode duality at resonance is verified an examination of the wave train closure principle shows that although the frequency equations obtained by using the principle are identical to those derived from the wave evolution results the principle does not describe the realistic process of the formulation of vibration modes in general the waves described in the wave train closure principle are not physical but virtual waves that represent final steady state waves which can only be asymptotically approached in reality the principle can be used as a convenient technique to obtain vibration modes from the point of view of wave propagation

least square finite element method for electromagnetic fields in 2 d abstract a least squares finite element approximation scheme for electromagnetic fields in two dimensional domains is discussed considering the magnetic field strength lsh ls and the vector of the current density lsj ls as unknowns we describe maxwell s equation as a time dependent form in three dimensions then reduce it into two dimensional steady problems of two categories based on the first order system of partial differential equations the least squares method is applied to the finite element method the rates of convergence for both lsh ls and lsj ls achieve optimal order this method creates an easy way to develop computer software

conjugate direction methods for helmholtz problems with complex valued wavenumbers the convergence behaviour of conjugate direction methods for helmholtz problems with complex valued wavenumbers is studied the model problem is a galerkin discretization of the scalar helmholtz equation on square arrays of 2d and 3d c linear elements a series of controlled experiments is performed which use the dimensionless wavenumber and the algebraic size of the system of equations to completely characterize the iterative performance of the solvers the effects of algebraic size are examined as functions of both mesh refinement and mesh extension within the limits of present day workstation computing environments a comparison is drawn between the conjugate direction methods investigated and the equivalent time domain solution obtained through explicit time stepping

a general approach for the stability analysis of the time domain finite element method for electromagnetic simulations this paper presents a general approach for the stability analysis of the time domain finite element method tdfem for electromagnetic simulations derived from the discrete system analysis the approach determines the stability by analyzing the root locus map of a characteristic equation and evaluating the spectral radius of the finite element system matrix the approach is applicable to the tdfem simulation involving dispersive media and to various temporal discretization schemes such as the central difference forward difference backward difference and newmark methods it is shown that the stability of the tdfem is determined by the material property and by the temporal and spatial discretization schemes the proposed approach is applied to a variety of tdfem schemes which include 1 time domain finite element modeling of dispersive media 2 time domain finite element boundary integral method 3 higher order tdfem and 4 orthogonal tdfem numerical results demonstrate the validity of the proposed approach for stability analysis

three dimensional orthogonal vector basis functions for time domain finite element solution of vector wave equations three dimensional 3 d orthogonal vector basis functions are developed for the time domain finite element solution of vector wave equations these basis functions enforce both the tangential continuity of the electric field and the normal continuity of the electric flux the stability of the resulting time domain finite element schemes is investigated and demonstrated to be guaranteed the use of the proposed basis functions completely eliminates the matrix solution at each time step required by the time domain finite element solution of vector wave equations the computational cost thereby scales as o n sub t n with n sub t and n denoting the number of time steps and the number of unknowns respectively defined over tetrahedral elements the proposed basis functions increase the solution efficiency without compromising the geometry modeling flexibility both numerical results and comparison with traditional vector basis functions demonstrate the accuracy as well as the efficiency of the proposed three dimensional orthogonal vector bases

finite element solution of maxwell s equations for hyperthermia treatment planning abstract a general galerkin formulation is given for the periodic form of maxwell s equations on a bounded inhomogeneous medium the formulation conserves energy exactly and its dispersion relation is studied solutions for test problems representative of hyperthermia applications show good agreement with analytic solutions a representative clinical example is shown

a hybrid method for the vibration analysis of complex structural acoustic systems a new method is presented for the analysis of complex dynamic systems which is based on partitioning the system degrees of freedom into a global set and a local set the global equations of motion are formulated and solved in a standard deterministic manner although due account is taken of the presence of the local degrees of freedom via an approach which is analogous to fuzzy structure theory the local equations of motion are formulated and solved by using statistical energy analysis sea with due account being taken of power input from the global degrees of freedom the method can be considered to encompass a number of existing analysis techniques and to form a flexible framework within which a number of detailed modeling strategies can be devised a simple rod system provides an initial application and it is shown that the method yields very good results from low to high frequency excitation