an ale formulation for implicit time integration of quasi steady state wear problems abstract a fully coupled implicit scheme is developed for quasi steady state wear problems the formulation admits finite configuration changes due to both deformation and wear the unconditionally stable implicit backward euler scheme is used for time integration of the shape evolution problem thus the solution may proceed with large time increments contrary to the commonly used explicit forward euler scheme in which the time increment is restricted by the stability condition this comes at the cost that the shape transformation mapping constitutes an additional unknown as a result a kind of an arbitrary lagrangian eulerian ale formulation is obtained in which the problem is solved simultaneously for the nodal positions and displacements the incremental coupled problem is solved using the newton method which leads to a highly efficient computational scheme as illustrated by two and three dimensional numerical examples

the mixed order bcgs fft method for the scattering of three dimensional inhomogeneous anisotropic magnetodielectric objects this paper presents the first fft based fast volume integral equation solver for inhomogeneous anisotropic magnetodielectric objects the volume integral equations are formulated by employing mixed order basis functions that expand the flux densities and vector potentials in the coupled field integral equations in terms of different sets of basis functions with different orders volumetric roof top basis functions are used for flux densities whereas second order curl conforming basis functions are used for vector potentials a fast volume integral equations solver namely the bcgs fft method is then applied to accelerate the solution of this mixed order weak form formulation examples show that the mixed order bcgs fft method has high accuracy compared to both analytical and numerical solutions examples also show the mixed order bcgs fft method has high computational efficiency compared to commercial software

a fast combined field volume integral equation solution to em scattering by 3 d dielectric objects of arbitrary permittivity and permeability a fast solution to the combined field volume integral equation cfvie for electromagnetic scattering by large three dimensional dielectric bodies of arbitrary permittivity and permeability is presented the cfvie is formulated in the region of the scatterers by expressing the total fields as the sum of the incident wave and the radiated wave due to both the electric and magnetic polarization currents the resultant integral equation is solved using the method of moments mom then the precorrected fast fourier transform p fft method is applied to reduce the memory requirement and accelerate the matrix vector multiplication in the mom solution in the implementation of the p fft method two sets of projection operators are constructed respectively for the projections of the electric sources and magnetic sources in addition two sets of interpolation operators are also applied respectively for the computation of the vector scalar potentials and the curl of the vector potentials in the support of the testing functions the resultant method has a memory requirement of o n and a computational complexity of o nlogn respectively where n denotes the number of unknowns

an efficient hybrid mlfma fft solver for the volume integral equation in case of sparse 3d inhomogeneous dielectric scatterers electromagnetic scattering problems involving inhomogeneous objects can be numerically solved by applying a method of moments discretization to the volume integral equation for electrically large problems the iterative solution of the resulting linear system is expensive both computationally and in memory use in this paper a hybrid mlfma fft method is presented which combines the fast fourier transform fft method and the high frequency multilevel fast multipole algorithm mlfma in order to reduce the cost of the matrix vector multiplications needed in the iterative solver the method represents the scatterers within a set of possibly disjoint identical cubic subdomains which are meshed using a uniform cubic grid this specific mesh allows for the application of ffts to calculate the near interactions in the mlfma and reduces the memory cost considerably since the aggregation and disaggregation matrices of the mlfma can be reused additional improvements to the general mlfma framework such as an extention of the fft interpolation scheme of sarvas et al from the scalar to the vectorial case in combination with a more economical representation of the radiation patterns on the lowest level in vector spherical harmonics are proposed and the choice of the subdomain size is discussed the hybrid method performs better in terms of speed and memory use on large sparse configurations than both the fft method and the hf mlfma separately and it has lower memory requirements on general large problems this is illustrated on a number of representative numerical test cases

a comparison of acceleration procedures for the two dimensional periodic green s function alternate acceleration procedures are evaluated for the two dimensional free space periodic green s function two of these techniques yield exponential convergence rates and are preferable if high accuracies are required numerical aspects of these procedures are described

solving the volume integral equations of electromagnetic scattering time harmonic electromagnetic scattering by inhomogeneous three dimensional structures within a free space environment can be described by electric and magnetic field volume integral equations involving the free space green function a comprehensive set of galerkin projection formulations also known as moment methods for the numerical solution of these equations is presented together with comparative numerical results such formulations are widely used for particle scattering analysis optical near field calculation etc results are obtained with higher order divergence and curl conforming basis functions on iso parametric tetrahedral meshes the results demonstrate that all formulations converge with similar accuracy in the case of an analytically solvable test problem when modeling flux densities as solution variables it is argued that solenoidal function spaces should be used rather than the standard divergence conforming function spaces this assertion is supported by the results some of the formulations involve solving for curl conforming fields such fields can be discretized with fewer unknowns than divergence conforming ones implying lower computational costs additionally some formulations yield system matrices which are approximately halfway sparse meaning that computational costs will be down by a factor of 2 when iterative solvers are employed which is the case for the widely used fast methods

broadband muller mlfma for electromagnetic scattering by dielectric objects the multilevel fast multipole algorithm mlfma is very efficient for solving large scale electromagnetic scattering problems however at low frequencies or when the discretization is small compared with the wavelength both the mlfma and the underlying integral equation formulation typically suffer from a subwavelength breakdown for the electromagnetic scattering from a homogeneous dielectric object we obtain a stable and well conditioned surface integral formulation using a variant of the classical muumlller formulation and linear basis functions to overcome the subwavelength breakdown of the mlfma we use both propagating and evanescent plane waves to represent the fields the implementation is based on a combination of the spectral representation of the green s function and rokhlin s translation formula we also present a new interpolation scheme for the evanescent part which significantly improves the error controllability of the mlfma implementation several numerical results verify both the error controllability and scalability of the proposed algorithm

weak form quadrature element method for accurate free vibration analysis of thin skew plates in this paper a novel weak form quadrature element method qem is proposed for accurate free transverse vibration analysis of thin isotropic skew plates with general boundary conditions in the formulation of the stiffness matrix the first and second order derivatives of the shape functions at integration points are computed explicitly by using the differential quadrature rule this leads to a great simplicity in formulating an n n node quadrature plate element and a large reduction of programming effort different from the existing weak form quadrature element method or differential quadrature finite element method the element nodes can be either the same or different from the integration points convergence studies are performed free vibration of skew thin plates with various skew angles and different combinations of boundary conditions is analyzed it is shown that although the assumed displacement field does not explicitly consider the bending moment singularities at the obtuse angles the proposed qem can yield accurate frequencies even for the thin isotropic skew plate with large skew angles

an efficient numerical evaluation of the green s function for the helmholtz operator on periodic structures abstract numerical methods which are based on boundary integral formulations require the numerical evaluation of the green s function associated with the problem in the case of periodic structures the green s function is often an infinite series this infinite series may converge slowly making numerical evaluation expensive here we present a practical computer implementation of a technique which dramatically speeds up the convergence of the infinite series green s function associated with the helmholtz operator to show the consequences of using this technique we include some numerical examples

on the computation of power in volume integral equation formulations we present simple and stable formulas for computing power including absorbed radiated scattered and extinction power in current based volume integral equation formulations the proposed formulas are given in terms of vector matrix vector products of quantities found solely in the associated linear system in addition to their efficiency the derived expressions can guarantee the positivity of the computed power we also discuss the application of poynting s theorem for the case of sources immersed in dissipative materials the formulas are validated against results obtained both with analytical and numerical methods for scattering and radiation benchmark cases

current based volume integral equation formulation for bianisotropic materials the electric and magnetic current volume integral equation formulation is developed for the electromagnetic scattering analysis of arbitrarily shaped 3 d bianisotropic objects the eigenvalue spectrum of the operator is derived and analyzed in the case of bi isotropic media the effect of inhomogeneity and bianisotropy on the spectrum and convergence of iterative solutions is investigated numerically

efficient nystrom solutions of electromagnetic scattering by composite objects with inhomogeneous anisotropic media analysis of electromagnetic em scattering by composite objects with inhomogeneous or anisotropic media requires an efficient solution of volume integral equations vies or volume surface integral equations vsies in the integral equation approach the traditional method of moments mom with the rao wilton glisson rwg basis function and the schaubert wilton glisson swg basis function may not be convenient because the basis functions are defined over a triangular or tetrahedral element pairs and the swg basis function could cause a surface charge density on the common faces separating dissimilar media in this work we develop an efficient nystrom scheme as an alternative to solve the vies or vsies for those objects the advantages of nystrom method include the simple mechanism of implementation allowance of nonconforming meshes and removal of basis or testing function making the method more suitable for solving such problems numerical examples for em scattering by typical objects are presented to demonstrate the method

generalized volume surface integral equation for modeling inhomogeneities within high contrast composite structures numerical solutions of volume integral equations with high contrast inhomogeneous materials require extremely fine discretization rates making their utility very limited given the application of such materials for antennas and metamaterials it is extremely important to explore computationally efficient modeling methods in this paper we propose a novel volume integral equation technique where the domain is divided into different material regions each represented by a corresponding uniform background medium coupled with a variation together representing the overall inhomogeneity this perturbational approach enables us to use different green s functions for each material region hence the resulting volume surface integral equation alleviates the necessity for higher discretizations within the higher contrast regions with the incorporation of a junction resolution algorithm for the surface integral equations defined on domain boundaries we show that the proposed volume surface integral equation formulation can be generalized to model arbitrary composite structures incorporating conducting bodies as well as highly inhomogeneous material regions

design of simple low order finite elements for large strain analysis of nearly incompressible solids a simple four node quadrilateral and an eight node hexahedron for large strain analysis of nearly incompressible solids are proposed based on the concept of deviatoric volumetric split and the replacement of the compatible deformation gradient with an assumed modified counterpart the formulation developed is applicable to arbitrary material models the closed form of the corresponding exact tangent stiffnesses which have a particularly simple structure is derived it ensures asymptotically quadratic rates of convergence of the newton raphson scheme employed in the solution of the implicit finite element equilibrium equations from a practical point of view the incorporation of the proposed elements into existing codes is straightforward it requires only small changes in the routines of the standard displacement based 4 node quadrilateral and 8 node brick a comprehensive set of numerical examples involving hyperelasticity as well as multiplicative elasto plasticity is provided it illustrates the performance of the proposed elements over a wide range of applications including strain localisation problems metal forming simulation and adaptive analysis

a faster aggregation for 3d fast evanescent wave solvers using rotations a novel technique to accelerate the aggregation and disaggregation stages in evanescent plane wave methods is presented the new method calculates the six plane wave radiation patterns from a multipole expansion aggregation and calculates the multipole expansion of an incoming field from the six plane wave incoming field patterns it is faster than the direct approach for multipole orders larger than one and becomes six times faster for large multipole orders the method relies on a connection between the discretizations of the six integral representations and on the fact that the wigner d matrices become diagonal for rotations around the z axis the proposed technique can also be extended to the vectorial case in two different ways one of which is very similar to the scalar case the other method relies on a beltrami decomposition of the fields and is faster than the direct approach for any multipole order this decomposition is also not limited to evanescent wave solvers but can be used in any vectorial multilevel fast multipole algorithm

fast analysis of transient electromagnetic scattering phenomena using the multilevel plane wave time domain algorithm the computational complexity of classical marching on in time mot methods for solving time domain integral equations tdies pertinent to the analysis of transient scattering phenomena involving perfectly conducting targets grows as o n sub t n sub s sup 2 n sub t and n sub s denote the number of temporal and spatial degrees of freedom dof of the electric current on the target this scaling law impedes the application of these schemes to the analysis of large scale scattering phenomena the recently developed plane wave time domain pwtd algorithm permits the rapid evaluation of transient wave fields generated by temporally bandlimited sources and hence the acceleration of marching on in time based tdie solvers previously we described a two level pwtd enhanced tdie solver for analyzing electromagnetic scattering from perfectly conducting targets the computational complexity of this algorithm scales as o n sub t n sub s sup 1 5 logn sub s here a multilevel pwtd scheme for rapidly evaluating electric fields due to temporally bandlimited electric current sources is described in addition a multilevel pwtd enhanced tdie solver for analyzing electromagnetic scattering from perfectly conducting scatterers using o n sub t n sub s log sup 2 n sub s cpu resources is outlined last the accuracy and cpu memory efficiency of this solver are demonstrated by analyzing transient scattering from electrically large bodies

differential quadrature element analysis using extended differential quadrature abstract the extended differential quadrature edq has been proposed a certain order derivative or partial derivative of the variable function with respect to the coordinate variables at an arbitrary discrete point is expressed as a weighted linear sum of the values of function and or its possible derivatives at all grid nodes the grid pattern can be fixed while the selection of discrete points for defining discrete fundamental relations is flexible this method can be used to the differential quadrature element and generalized differential quadrature element analyses

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

modified spherical wave functions with anisotropy ratio application to the analysis of scattering by multilayered anisotropic shells we describe a novel and rigorous vector eigenfunction expansion of electric type green s dyadics for radially multi layered uniaxial anisotropic media in terms of the modified spherical vector wave functions which can take into account the effects of anisotropy ratio systematically in each layer the material constitutions e and epsiv macrmu macr are tensors and distribution of sources is arbitrary both the unbounded and scattering dyadic green s functions dgfs for rotationally uniaxial anisotropic media are derived in spherical coordinates r thetas phi the coefficients of scattering dgfs based on the coupling recursive algorithm satisfied by the coefficient matrix are derived and expressed in a compact form with these dgfs obtained the electromagnetic fields in each layer are straightforward once the current source is known a specific model is proposed for the scattering and absorption characteristics of multilayered uniaxial anisotropic spheres and some novel performance regarding anisotropy effects is revealed

spherical wave operators and the translation formulas translational formulas for both scalar and vector spherical wave solutions of the helmholtz equation are developed in a straightforward manner using differential operator representations for the modal functions and well known expressions for the scalar and dyadic free space green s functions the expansion coefficients are given in compact integral or differential operator forms useful for analytic investigation

electromagnetic scattering by an inhomogeneous gyroelectric sphere using volume integral equation and orthogonal dini type basis functions the electromagnetic scattering by an inhomogeneous gyroelectric sphere is studied in this work the solution is constructed using the well known electric field volume integral equation efvie the kernel that incorporates the green s function is expanded in spherical vector wave functions and the unknown electric field and electric displacement is expanded in spherical vector wave functions using fully orthogonal dini type basis functions the permittivity tensor of the spherical object supports a continuously varying radial inhomogeneity while its permeability is that of free space this approach allows a fully analytical computation of the unknown matrix coefficients in special cases of homogeneous permittivity tensors the validation of our method is performed by comparisons with published results in the literature new numerical results are given for various continuously varying permittivity tensors

large deformation frictional contact mechanics continuum formulation and augmented lagrangian treatment absract a complete methodology for the formulation and solution of unilateral contact problem with non associated threshold friction between solids undergoing large deformations is presented the approach includes a continuum contact mechanics model combined with an augmented lagrangian method for treating the contact and friction inequality constraints the main developments are a precise statement of the incremental contact minimization problem the exact computations of the first and second variations of the normal gap and the tangential slip velocity and an extension of the augmented lagrangian formulation for frictional contact problems from the discrete to the continuum framework the corresponding saddle point functional first variation mixed virtual work and second variation exact linearization are given the development are illustrated by numerical simulations of frictional contact problems between rigid elastic and elastoplastic bodies a new severe benchmark for large slip frictional contact elements is also proposed

an efficient volume integral equation solution to em scattering by complex bodies with inhomogeneous bi isotropy a generalized volume integral equation method is formulated for electromagnetic scattering by arbitrarily shaped complex bodies with inhomogeneous bi isotropy based on the volume equivalence principle the integral equations are represented in terms of a pair of coupled bi isotropic polarized volume electric and magnetic flux densities reduction of the integral equations into the corresponding matrix equations is obtained using the method of moments mom combined with the tetrahedral mesh in the mom solution the three dimensional solenoidal function is incorporated as the basis function defined over each tetrahedral element and the details of implementation particularly the treatment of integral singularities will be elucidated the efficiency and accuracy of the proposed method are validated by illustratively supported examples

broadband multilevel fast multipole algorithm based on an approximate diagonalization of the green s function we present a broadband multilevel fast multipole algorithm mlfma for fast and efficient solutions of three dimensional multiscale problems involving large objects with dense discretizations the proposed solver is based on the approximate diagonalization of the green s function using scaled spherical and plane waves leading to stable interaction computations for arbitrarily short distances in terms of wavelength despite contradictory requirements on the scaling factor that limit the accuracy of the diagonalization the resulting low frequency scheme is extremely stable and easy to plug into conventional mlfma implementations by simply extending built in tree structures converting them into broadband solvers without needing dense programming efforts accuracy and efficiency of the broadband mlfma are demonstrated on canonical problems as well as on multiscale problems that cannot be solved efficiently via standard implementations of mlfma

rapid solution of integral equations of classical potential theory an algorithm is described for rapid solution of classical boundary value problems dirichlet an neumann for the laplace equation based on iteratively solving integral equations of potential theory cpu time requirements for previously published algorithms of this type are proportional to n2 where n is the number of nodes in the discretization of the boundary of the region the cpu time requirements for the algorithm of the present paper are proportional to n making it considerably more practical for large scale problems

integral equation based analysis of scattering from 3 d inhomogeneous anisotropic bodies this paper presents an integral equation based scheme to analyze scattering from inhomogeneous bodies with anisotropic electromagnetic properties both the permittivity and permeability are assumed to be generalized tensors requisite integral equations are derived using volume equivalence theorem with the electric and magnetic flux densities being the unknown quantities matrix equations are derived by discretizing these unknowns using three dimensional rao wilton glisson basis functions reduction of the integral equation to a corresponding matrix equation is considerably more involved due to the presence of anisotropy and the use of vector basis function methods for evaluation of the integrals involved in the construction of this matrix is elucidated in detail the method of moments technique is augmented with the fast multipole method and a compression scheme the latter two enable large scale analysis finally several numerical results are presented and compared against analytical solutions to validate the proposed scheme an appendix provides analytical derivations for the formulae that are used to validate numerical method and the necessary formulae that extends the approach presented herein to the analysis of scattering bianisotropic bodies

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

explicit time marching schemes for solving the magnetic field volume integral equation a method for constructing explicit marching on in time mot schemes to solve the time domain magnetic field volume integral equation td mfvie on inhomogeneous dielectric scatterers is proposed the td mfvie is cast in the form of an ordinary differential equation ode and the unknown magnetic field is expanded using curl conforming spatial basis functions inserting this expansion into the td mfvie and spatially testing the resulting equation yield an ode system with a gram matrix this system is integrated in time for the unknown time dependent expansion coefficients using a linear multistep method the gram matrix is sparse and well conditioned for galerkin testing and consists of only four diagonal blocks for point testing the resulting explicit mot schemes which call for the solution of this matrix system at every time step are more efficient than their implicit counterparts which call for inversion of a fuller matrix system at lower frequencies numerical results compare the efficiency accuracy and stability of the explicit mot schemes and their implicit counterparts for low frequency excitations the results show that the explicit mot scheme with point testing is significantly faster than the other three solvers without sacrificing from accuracy

on volume integral equations the focus of this paper is on the volume integral representations to be used in constructing integral equations for composite volume media the major thrust of the paper is to identify where derivatives of a discontinuous function arise in the derivation of the volume representation three different derivation methods are presented resulting in identical representation independent of the derivation method these representations agree with some in the existing literature and disagree with others when an electric field formulation is considered the source of disagreement manifests itself only when magnetic materials are present likewise for the dual situation the inconsistency appears for a magnetic field formulation of dielectric materials this paper identifies the sources of error in the incorrect representations and its major contribution is the rigorously correct derivation of the representations to be used in volume integral equations we also present numerical results for an integral equation derived from our representation the numerical results employ only the e field as the unknown and the singularity is handled in a manner analogous to a standard numerical treatment of the electric field integral equation

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

volume integral equations for electromagnetic scattering in two dimensions we study the strongly singular volume integral equation that describes the scattering of time harmonic electromagnetic waves by a penetrable obstacle we consider the case of a cylindrical obstacle and fields invariant along the axis of the cylinder which allows the reduction to two dimensional problems with this simplification we can refine the analysis of the essential spectrum of the volume integral operator started in a previous paper costabel et al 2012 and obtain results for non smooth domains that were previously available only for smooth domains it turns out that in the transverse electric te case the magnetic contrast has no influence on the fredholm properties of the problem as a byproduct of the choice that exists between a vectorial and a scalar volume integral equation we discover new results about the symmetry of the spectrum of the double layer boundary integral operator on lipschitz domains

efficient fast multipole method for low frequency scattering the solution of the helmholtz and maxwell equations using integral formulations requires to solve large complex linear systems a direct solution of those problems using a gauss elimination is practical only for very small systems with few unknowns the use of an iterative method such as gmres can reduce the computational expense most of the expense is then computing large complex matrix vector products the cost can be further reduced by using the fast multipole method which accelerates the matrix vector product for a linear system of size n the use of an iterative method combined with the fast multipole method reduces the total expense of the computation to n log n there exist two versions of the fast multipole method one which is based on a multipole expansion of the interaction kernel exp ikr r and which was first proposed by v rokhlin and another based on a plane wave expansion of the kernel first proposed by w c chew in this paper we propose a third approach the stable plane wave expansion spw fmm which has a lower computational expense than the multipole expansion and does not have the accuracy and stability problems of the plane wave expansion the computational complexity is n log n as with the other methods

scattering from 3 d inhomogeneous chiral bodies of arbitrary shape by the method of moments a method of moments mom solution is presented for the problem of electromagnetic scattering by a three dimensional 3d inhomogeneous chiral scatterer illuminated by an arbitrary incident field the volume equivalence principle was used to obtain coupled integral equations for equivalent volume currents these integral equations were then solved numerically using mom the volume of the scatterer was modeled by tetrahedral cells and face based expansion functions were used to approximate the equivalent currents computed results are in very good agreement with exact data or other published data

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

meshfree solutions of volume integral equations for electromagnetic scattering by anisotropic objects volume integral equations vies are indispensable for solving inhomogeneous or anisotropic electromagnetic em problems by integral equation approach the solution of vies strongly relies on the discretization of volume integral domains and tetrahedral elements in discretization are usually preferred for arbitrary geometric shapes unlike discretizing a surface domain discretizing a volume domain is very inconvenient in practice and special commercial software is needed in general even for a simple and regular geometry to release the burden of descretizing volume domains especially to remove the constraint of mesh conformity in the traditional method of moments mom we propose a novel meshfree scheme for solving vies in this paper the scheme is based on the transformation of volume integrals into boundary integrals through the green gauss theorem when integral kernels are regularized by excluding a small cylinder enclosing the observation node the original integral domain represented by the object is also expanded to a cylindrical domain circumscribing the object to facilitate the evaluation of boundary integrals the singular integrals over the small cylinder are specially handled with singularity subtraction techniques numerical examples for em scattering by inhomogeneous or anisotropic objects are presented to illustrate the scheme and good results are observed

a discontinuous galerkin volume integral equation method for scattering from inhomogeneous objects a discontinuous galerkin volume integral equation dgvie method is proposed for scattering from inhomogeneous objects it is shown that this dgvie has several advantages over other volume integral methods first the dgvie can be used for nonconformal meshes second the order of the singularity in dgvie has been reduced from 1 r text 3 to 1 r and the implementation of dgvie becomes simple third the proposed dgvie converges faster than the traditional vie methods especially for objects with high permittivity numerical results validate the accuracy and efficiency of the proposed dgvie

analytical and numerical results for vibration analysis of multi stepped and multi damaged circular arches this paper investigates the in plane linear dynamic behaviour of multi stepped and multi damaged circular arches under different boundary conditions cracked cross sections are modelled as massless elastic rotational hinges in damaged configuration cracks can be located both at the interface between two adjacent portions as well as inside the portion itself for each arch portion bounded by two cracks the differential equations of motion have been established considering axial extension transverse shear effects and rotatory inertia the equilibrium equations of arch portions are combined in the coupled fundamental system in terms of radial displacement tangential displacement and rotation analytical and numerical solutions for multi stepped arches in undamaged as well as in damaged configurations are proposed the analytical solution is based on the euler characteristic exponent procedure involving the roots of characteristic polynomials while the numerical method is focused on the generalized differential quadrature gdq method and the generalized differential quadrature element gdqe technique numerical results are shown in terms of the first 10 analytical and numerical frequencies of multi stepped and multi damaged arches with different boundary conditions finally convergence and stability characteristics of the gdqe procedure are investigated the convergence rate of the natural frequencies is shown to be very fast and the stability of the numerical procedure is very good

a generalized differential quadrature element method abstract the generalized differential quadrature element method gdqem has been proposed the element weighting coefficients are generated by a generic differential quadrature gdq with which the element weighting coefficients for elements having arbitrary configurations can be straightly generated by using this gdq technique the governing differential or partial differential equations defined on all elements the transition conditions on the inter element boundary of two adjacent elements and the boundary conditions can be discretized a global algebraic equation system can be obtained by assembling all of the discretized equations this method can convert a generic engineering or scientific problem having an arbitrary domain configuration into a computer algorithm without adopting the mapping technique

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

on optimal contact shapes generated by wear the optimal shape design of contacting surfaces has usually been aimed at controlling the contact pressure distribution however a much wider class of contact optimization problems can be formulated by maximizing contact force or displacement torsional moment or minimizing the friction dissipation the special classes of optimization problems are considered namely minimization of generalized wear volume rate minimization of generalized friction dissipation power and minimization of the generalized wear dissipation power depending on both normal pressure and slip velocity the specific wear rule was assumed and the optimality conditions are derived they generate optimal contact pressure distribution and the corresponding optimal wear rate the optimization problems are reduced to non linear programming problems and for their solution a special iteration process is used the wear process is analysed in two specific cases first when the relative sliding velocity between bodies is constant and the second case when one of bodies rotates with respect to another body for rotational motion the problem of minimization of friction dissipation power is considered by applying the technique of control of contact pressure distribution and minimization of the generalized friction dissipation power with a new control parameter q it is demonstrated that the wear dissipation power at the contact surface is minimal in the steady state of wear process and in many cases corresponds to the uniform wear rate the illustrative examples for rotating bodies demonstrate the evolution of wear process toward a steady state the minimization of the generalized wear volume rate and of generalized friction dissipation power does not induce the steady state of wear process in the rotation motion the identification procedure is proposed to specify the wear parameters copyright 2005 john wiley sons ltd

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

iterative forward and inverse algorithms based on domain integral equations for three dimensional electric and magnetic objects an iterative approach to full vector three dimensional inverse scattering problems where the unknown objects can have conductivity permittivity and permeability different from the known background medium is discussed since this problem involves a large number of unknowns it has to be solved effectively and efficiently so that the results can be obtained in timely manner the forward modeling is based on a domain integral equation approach formulated in terms of the electric and magnetic contrast sources normalized with the characteristic impedance of the background medium our numerical tests indicate that this formulation is prerequisite in order to arrive at a forward solution within an acceptable number of iterations and hence it is also of significant importance in the optimization process of the inverse problem the inverse scattering problem is attacked using the multiplicative regularized contrast source inversion method as known in the literature the complexity of this inverse method is approximately equal to the complexity of two equivalent forward algorithms of the conjugate gradient type furthermore this inverse method has been armed with a weighted l2 norm regularizer which has been included as a multiplicative constraint some representative numerical testings will be presented to illustrate the ability of the our numerical algorithms

analysis of volume integral equation formulations for scattering by high contrast penetrable objects the volume integral equation method is applied in electromagnetic scattering from arbitrarily shaped three dimensional inhomogeneous objects the properties of the volume electric and magnetic field integral equations vefie and vmfie are investigated numerical experiments show that if the galerkin s method with the lowest mixed order basis functions is used to discretize the equations the accuracy of the vmfie can be significantly poorer than the accuracy of the vefie in particular for high contrast objects at high frequencies the accuracy of the vmfie can be essentially improved with full first order linear basis functions the linear basis functions are found to be useful also when a single volume integral equation is used to model a general scatterer where both permittivity and permeability differ from the background

performing interpolation and anterpolation entirely by fast fourier transform in the 3 d multilevel fast multipole algorithm the fast multipole methods are used for solving a scalar acoustic or vector electromagnetic wave equation by integral equation methods with a large number of unknowns in this paper a new method is presented for performing interpolation and anterpolation in both spherical coordinates theta and phi by fft in the three dimensional 3 d multilevel fast multipole algorithm mlfma the key idea is to approximate functions on the unit sphere by truncated fourier series in two variables rather than by the usual spherical harmonics the proposed method is exact in interpolating and anterpolating and has the high numerical efficiency of fft the method is numerically compared to the method of performing interpolation and anterpolation using lagrangian interpolation which presently is probably the fastest method for those operations and the results suggest that the proposed new method is equally or more efficient depending on the desired accuracy

sensitivity analysis for frictional contact problems in the augmented lagrangian formulation direct differentiation method of sensitivity analysis is developed for frictional contact problems as a result of the augmented lagrangian treatment of contact constraints the direct problem is solved simultaneously for the displacements and lagrange multipliers using the newton method the main purpose of the paper is to show that this formulation of the augmented lagrangian method is particularly suitable for sensitivity analysis because the direct differentiation method leads to a non iterative exact sensitivity problem to be solved at each time increment the approach is applied to a general class of three dimensional frictional contact problems and numerical examples are provided involving large deformations multibody contact interactions and contact smoothing techniques

optimal interpolation of radiated fields over a sphere an optimal sampling interpolation algorithm is developed that allows the accurate recovery of scattered or radiated fields over a sphere from a minimum number of samples using the concept of the field equivalent spatial bandwidth a central interpolation scheme is developed to compute the field in theta phi coordinates starting from its samples the maximum allowable sample spacing and error upper bounds are also rigorously derived several simulated examples of pattern reconstruction are presented for both the cases of field and power pattern interpolation the interpolation error as a function of the retained sample number has been also evaluated and compared with the theoretical upper bounds the algorithm stability versus randomly distributed errors added to the exact samples is demonstrated

a mixed form fast multipole algorithm the fast multipole algorithm manifests in two very different forms at low frequencies and at mid frequencies each can operate in their respective regimes but are not tenable in the other regimes the paper reports on a way to factorize the green s function for fast algorithm using a mixed form the low frequency fast multipole algorithm lf fma will be used at low frequencies or the long wavelength regime and the multilevel fast multipole algorithm mlfma will be used for the mid frequencies or the shorter wavelength regime for object modeling where both long wavelength and wave physics are important we propose a mixed form fast multipole algorithm mf fma this algorithm has no low frequency break down and it can work seamlessly from static where circuit physics is important to dynamic where wave physics is important

application of bem and optimization technique to wear problems in this paper a new method for solving wear problems using the boundary element method bem is proposed the proposed method uses a shape optimization technique for rapid calculation of the maximum wear depth and the final geometry of the bodies in contact after a specified service period the optimization method solves the wear problem directly without using increments of the sliding distance as in the classical methods the bem is used for modelling both bodies in contact treating the problem as a multi region problem the material loss is presented in terms of the applied load and the sliding distance and is modelled using a linear wear model the proposed method is shown to be robust as it requires only few iterations to achieve a converged solution the reduction in computational effort as compared to the classical incremental method becomes more significant as the sliding distance increases

extended gdq and related discrete element analysis methods for transient analyses of continuum mechanics problems abstract the extended gdq proposed by the author is used to develop solution algorithms for solving the discrete transient equation system of a continuum mechanics problem it is a direct integration approach two integration methods are developed they are time element by time element method and stages by stages method these two time integration algorithms can be used to solve a generic discrete transient equation system of an originally discrete system or a discrete system resulting from the discretization of a transient system of continuum mechanics problems by using a certain discretization technique such as the dqem fem fdm etc

the ale formulation of bodies in rolling contact theoretical foundations and finite element approach abstract numerical methods for the analysis of rolling contact problems are of high importance for the optimization of the components car tires for example today finite element methods for the computation of stationary rolling contact have been developed for industrial use however from a review of the scientific literature it has been concluded that the theoretical foundations of the relative kinematic description i e an arbitrary lagrangian eulerian ale formulation seems to be not well understood in detail this presentation is aimed to close this gap starting from the basic kinematic description of the ale formulation of rolling the weak form of the equations of motion are developed by this careful analysis an additional flux contribution is derived which has not been recognized in the scientific literature so far the contact problem is described for the treatment of two deformable bodies in rolling contact within the framework of well established methods for the numerical treatment of contact in the lagrangian picture in general essential differences between the lagrangian description and the ale description of rolling are shown up and discussed in detail for a comprehensive presentation the finite element discretization is restricted to the case of a deformable wheel rolling on a rigid plane surface however the sketched algorithmic approach is valid in general the efficiency of the numerical algorithms developed so far are discussed by the analysis of a simple three dimensional example critical remarks and an outlook to further research in this field concludes this presentation

broadband multilevel fast multipole algorithm for electric magnetic current volume integral equation a volume integral equation method given in terms of the equivalent electric and magnetic volume currents and discretized using non conforming element wise constant approximations is applied to electromagnetic scattering analysis of inhomogeneous and anisotropic objects a broadband version of the multilevel fast multipole algorithm mlfma combining low frequency stable planewave expansion technique with the high frequency mlfma and utilizing global interpolators based on trigonometric polynomials is used to accelerate the computations

the development of irregular elements for differential quadrature element method steady state heat conduction analysis abstract a new numerical approach for solving steady state heat conduction problems by using the irregular elements of the differential quadrature element method dqem is proposed the mapping technique is used to transform the governing partial differential equation the natural transition condition of two adjacent elements and the newmann boundary condition defined on the irregular physical element into the parent space the differential quadrature technique is used to discretize the transformed relation equations defined on the regular element in the parent space various techniques for selecting and implementing the constraint conditions at element corners are proposed a global algebraic equation system can be obtained by assembling all of the discretized relation equations numerical procedures are summarized and the related computer code is developed numerical results are presented they demonstrate the developed dqem steady state heat conduction analysis model

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 diagonalized multilevel fast multipole method with spherical harmonics expansion of the k space integrals diagonalization of the fast multipole method fmm for the helmholtz equation is usually achieved by expanding the multipole representation in propagating plane waves the resulting k space integral over the ewald sphere is numerically evaluated storing the k space quadrature samples of the method of moments mom basis functions constitutes a large portion of the overall memory requirements of the resulting algorithm for solving the integral equations of scattering and radiation problems in this paper it is proposed to expand the k space representation of the basis functions by spherical harmonics in order to reduce the sampling redundancy introduced by numerical quadrature rules aggregations plane wave translations and disaggregations in the realized multilevel fast multipole method mlfmm are carried out using the k space samples of a numerical quadrature rule however the incoming plane waves on the finest mlfmm level are expanded in spherical harmonics again thus due to the orthonormality of spherical harmonics the testing integrals for the individual testing functions are simplified into series over products of spherical harmonics expansion coefficients overall the resulting mlfmm can save a considerable amount of memory without compromising accuracy and numerical speed

rapid solution of integral equations of scattering theory in two dimensions abstract the present paper describes an algorithm for rapid solution of boundary value problems for the helmholtz equation in two dimensions based on iteratively solving integral equations of scattering theory cpu time requirements of previously published algorithms of this type are of the order n 2 where n is the number of nodes in the discretization of the boundary of the scatterer the cpu time requirements of the algorithm of the present paper are n 4 3 and can be further reduced making it considerably more practical for large scale problems

a fast spherical filter with uniform resolution this paper introduces a fast algorithm for obtaining a uniform resolution representation of a function known at a latitude longitude grid on the surface of a sphere equivalent to a triangular isotropic truncation of the spherical harmonic coefficients for the function the proposedspectral truncation method which is based on the fast multipole method and the fast fourier transform projects the function to a space with uniform resolution while avoiding surface harmonic transformations the method requireso n2logn operations foro n2 grid points as opposed too n3 operations for the standard spectral transform method providing a reduced complexity spectral method obviating the pole problem in the integration of time dependent partial differential equations on the sphere the filter s performance is demonstrated with numerical examples

two volume integral equations for the inhomogeneous and anisotropic forward problem in electroencephalography abstract this work presents two new volume integral equations for the electroencephalography eeg forward problem which differently from the standard integral approaches in the domain can handle heterogeneities and anisotropies of the head brain conductivity profiles the new formulations translate to the quasi static regime some volume integral equation strategies that have been successfully applied to high frequency electromagnetic scattering problems this has been obtained by extending to the volume case the two classical surface integral formulations used in eeg imaging and by introducing an extra surface equation in addition to the volume ones to properly handle boundary conditions numerical results corroborate theoretical treatments showing the competitiveness of our new schemes over existing techniques and qualifying them as a valid alternative to differential equation based methods