implicit lyapunov functions and isochrones of linear systems lyapunov s direct method is based on a lyapunov function that explicitly depends on the system s state vector this article describes implicit lyapunov functions and corresponding stability theorems that are counterparts of the explicit case we also define isochrones of linear systems and describe their relationship to implicit lyapunov functions determining settling times is considered as an application

adaptive multiscale moment method ammm for analysis of scattering from perfectly conducting plates adaptive multiscale moment method ammm is presented for the analysis of scattering from a thin perfectly conducting plate this algorithm employs the conventional moment method and a special matrix transformation which is derived from the tensor products of the two one dimensional 1 d multiscale triangular basis functions that are used for expansion and testing functions in the conventional moment method the special feature of these new basis functions introduced through this transformation is that they are orthogonal at the same scale except at the initial scale and not between scales from one scale to another scale the initial estimate for the solution can be predicted using this multiscale technique hence the compression is applied directly to the solution and the size of the linear equations to be solved is reduced thereby improving the efficiency of the conventional moment method the basic difference between this methodology and the other techniques that have been presented so far is that we apply the compression not to the impedance matrix but to the solution itself directly using an iterative solution methodology the extrapolated results at the higher scale thus provide a good initial guess for the iterative method typically when the number of unknowns exceeds a few thousand unknowns the matrix solution time exceeds generally the matrix fill time hence the goal of this method is directed in solving electrically larger problems where the matrix solution time is of concern two numerical results are presented which demonstrate that the ammm is a useful method to analyze scattering from perfectly conducting plates

a periodic fmm for maxwell s equations in 3d and its applications to problems related to photonic crystals this paper presents an fmm fast multipole method for periodic boundary value problems for maxwell s equations in 3d the effect of periodicity is taken into account with the help of the periodised moment to local expansion m2l transformation formula which includes lattice sums we verify the proposed method by comparing the obtained numerical results with analytic solutions for models of the multi layered dielectric slab we then apply the proposed method to scattering problems for periodic two dimensional arrays of dielectric spheres and compare the obtained energy transmittances with those from the previous studies we also consider scattering problems for woodpile crystals where we find a passband related to a localised mode through these numerical tests we conclude that the proposed method is efficient and accurate

acceleration of fast multipole method for large scale periodic structures with finite sizes using sub entire domain basis functions an acceleration technique to the fast multipole method fmm has been proposed to handle large scale problems of periodic structures in free space with finite sizes based on the accurate sub entire domain basis functions in the proposed algorithm only nine or 27 elements in the whole impedance matrix are required to be computed and stored for a two dimensional or three dimensional periodic structure and the matrix vector multiply can be performed efficiently using the combination of fast fourier transform and fmm the theoretical analysis and numerical results show that both the memory requirement and computational complexity are only of the order of o n with small constants where n is the total number of unknowns

technical communique a fast nonlinear control method for linear systems with input saturation we present a novel fast saturating nonlinear feedback law for single input systems with linear dynamics and input saturation it is fast in the sense that it yields a better performance than a saturating linear control law the control law is based on implicit soft variable structure control a convex optimization procedure for the controller synthesis based on linear matrix inequalities lmis is derived at the price of some conservatism as an example we consider the control of a submarine

an efficient perfectly matched layer based multilevel fast multipole algorithm for large planar microwave structures an efficient multilevel fast multipole algorithm mlfma formalism to model radiation and scattering by from large planar microwave structures is presented the technique relies on an electric field integral equation efie formulation and a series expansion for the green dyadic based on the use of perfectly matched layers pml in this way a new pml mlfma is developed to efficiently evaluate matrix vector multiplications arising in the iterative solution of the scattering problem the computational complexity of the new algorithm scales down to o n for electrically large structures the theory is validated by means of several illustrative numerical examples

a nonlinear controller for input amplitude and rate constrained linear systems this technical note presents a nonlinear state feedback controller for systems with linear dynamics subject to an amplitude and rate limited actuator the nonlinear state feedback facilitates faster convergence compared to linear state feedback while guaranteeing domains of attraction of similar size the parametrization of the controller is done solving a convex optimization problem based on linear matrix inequalities lmis finally an example illustrates that the controller achieves large stability regions and short settling times

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

simulation of near ground long distance radiowave propagation over terrain using nystrom method with phase extraction technique and fmm acceleration a 2d surface integral equation based nystroumlm solver in which a phase extraction technique is utilized to reduce the number of surface unknowns is described as forward scattering is the dominant mechanism for the near ground wave propagation scenario the associated rapidly varying phase components of the integral equation kernel and solution unknowns are deduced and isolated in advance and subsequently built into the solver it is shown that by applying this method when combining with an adaptive surface segmentation routine as few as one to two average unknowns per wavelength is adequate in obtaining accurate solutions this significantly reduces the memory storage and computational expense for the simulation of long distance propagation effects the efficiency of this method is further improved by incorporating it into the framework of the fast multipole scheme the full details of the algorithm are discussed along with performance comparisons of the new solver to a regular nystroumlm solver for terrain surfaces in terms of solution convergence

regular article a fast adaptive multipole algorithm in three dimensions we present an adaptive fast multipole method for the laplace equation in three dimensions it uses both new compression techniques and diagonal forms for translation operators to achieve high accuracy at a reasonable cost

improved impedance matrix localization method em problems moment method calculations have the well known limitations of requiring excessive storage and execution times for even modestly large electromagnetics problems the impedance matrix localization iml method was introduced as a modification to standard moment method calculations to ease these limitations it utilizes a matrix transformation which effectively changes the basis testing functions into ones resembling traveling waves an improved method that uses an orthogonal transformation to generate standing wave like basis functions is presented here remarkable improvements are achieved in the numerical stability of the method and in its compatibility with iterative solvers furthermore the correspondence of the large elements in this matrix to geometrical theory of diffraction gtd terms is strengthened as is the possibility of further increasing the speed of iterative solutions by constructing preconditioners based on the pattern of nonzero matrix elements

fast and accurate wide band analysis of antennas mounted on conducting platform using aim and asymptotic waveform evaluation technique the adaptive integral method aim in conjunction with the asymptotic waveform evaluation awe technique is presented for wide band analysis of antennas in the presence of electrically large conducting platforms in the awe technique the pade approximation solution obtained by matching the coefficients of the taylor series namely moments is utilized to achieve fast frequency sweeping besides the calculation and storage of the high order frequency derivatives of impedance matrices the awe technique requires repeatedly solving the linear system for the moments thus the aim is employed to reduce matrix storage and to accelerate all the matrix vector multiplications in both the linear system for the moments and the iterative solver furthermore a localized self box inclusion sbi preconditioner is used to accelerate the solution procedure of the linear system for the moments finally three numerical examples are given and discussed the input admittance and return loss of the antennas over a given frequency band are obtained by aim and aim awe method respectively the good agreements show that the proposed hybrid technique can greatly reduce the computation time without loss of accuracy

iterative solution of high order boundary element method for acoustic impedance boundary value problems abstract a high order boundary element method for time harmonic acoustic impedance boundary value problems is presented the method is based on the galerkin type formulation of the burton miller integral equation bmie with high order polynomial basis and testing functions this formulation has several important advantages it is free of the interior resonance problem the hypersingular integral operator of the traditional bmie formulation can be avoided it leads to faster convergence in terms of the number of unknowns than the low order methods and it shows a good performance with iterative solvers to avoid the numerical difficulties associated to the implementation of the singular surface integral equations the singularity extraction technique is applied to evaluate the integrals in the singular and near singular cases the resulting matrix equation is solved iteratively with the generalized minimal residual method gmres and a simple preconditioner based on the incomplete lu factorization is applied to expedite the convergence numerical results indicate that the bmie formulation with galerkin method and high order basis functions has good convergence properties for various geometries and boundary conditions on a wide frequency range when the gmres method is applied to solve the matrix equation iteratively this in turn indicates that the formulation is well suited for an efficient application of fast solution procedures such as the fast multipole method

solution of arbitrarily dimensional matrix equation in computational electromagnetics by fast lifting wavelet like transform a new wavelet matrix transform wmt operated by lifting wavelet like transform lwlt is applied to the solution of matrix equations in computational electromagnetics the method can speedup the wmt without allocating auxiliary memory for transform matrices and can be implemented with the absence of the fast fourier transform furthermore to handle the matrix equation of arbitrarily dimension a new in space preprocessing technique based on lwlt is constructed to eliminate the limitation in matrix dimension complexity analysis and numerical simulation show the superiority of the proposed algorithm in saving cpu time numerical simulations for scattering analysis of differently shaped objects are considered to validate the effectiveness of the proposed method in particular due to its generality the proposed preprocessing technique can be extended to other engineering areas and therefore can pave a broad way for the application of the wmt

dual adaptive model predictive control abstract we present an adaptive dual model predictive controller dmpc that uses current and future parameter estimation errors to minimize expected output error by optimally combining probing for uncertainty reduction with control of the nominal model our novel approach relies on orthonormal basis function models to derive expressions for the predicted distributions for the output and unknown parameters conditional on the future input sequence propagating the exact future statistics enables reformulating the original stochastic problem into a deterministic equivalent that illustrates the dual nature of the optimal control but is nonlinear and nonconvex we further reformulate the nonlinear deterministic problem to pose an equivalent quadratically constrained quadratic programming qcqp problem that state of the art algorithms can solve efficiently providing the exact solution to the probabilistically constrained finite horizon dual control problem the adaptive dmpc solves this qcqp at each sampling time on a receding horizon the adaptation is a result of updating the parameter estimates used by the dmpc to decide the control input the paper demonstrates the application of dmpc to a single input single output siso system with unknown parameters in the simulation example the parameter estimates converge quickly and the probing vanishes with increasing accuracy and precision of the estimates improving the future control performance

controller design for a class of nonlinear systems with input saturation using convex optimization abstract in this paper we propose a new design strategy for nonlinear systems with input saturation the resulting nonlinear controllers are locally asymptotically stabilizing the origin the proposed methodology is based on exact feedback linearization which is used to reformulate the nonlinear system as a linear system having state dependent input saturation linear saturating state feedback controllers and soft variable structure controllers are developed based on this system formulation the resulting convex optimization problems can be written in terms of linear matrix inequalities and sum of squares conditions for which efficient solvers exist polynomial approximation based on legendre polynomials is used to extend the methodology to a more general class of nonlinear systems to demonstrate the benefit of this design method a stabilizing controller for a single link manipulator with flexible joint is developed

electromagnetic scattering from a rough layer propagation inside layer expansion method combined to an updated bmia cag approach an efficient method is developed to calculate the bistatic scattering coefficient bsc from a stack of two one dimensional rough interfaces separating homogeneous media the propagation inside layer expansion pile method recently published by dechamps was efficient with a complexity o n2 n being the number of samples per interface to reduce this complexity a fast method valid for a single rough surface the banded matrix iterative approach canonical grid bmia cag is combined to the pile method furthermore the calculation of the coupling interactions between both interfaces are also accelerated using a new method similar to the bmia cag the pile method reaches then a complexity of only o nlogn a study of the convergence of the pile is done and compared to another efficient method the forward backward

on stabilizing linear systems with input saturation via soft variable structure control laws abstract a large number of control methods deal with stabilizing single input linear systems with input saturation the linear full state feedback is one of the most used yielding either nonsaturating or high gain controls whereby the saturating effects of the latter are reduced by means of anti windup structures among the nonlinear controls the time optimal control in this case a bang bang type control yields the fastest time response but its switching surface is generally not characterizable related to the speed of the time response is the convergence rate which can be determined using invariant sets the most used ones are the ellipsoidal sets since they can be analyzed using powerful tools such as the lyapunov equation and designed via convex optimization for this reason they are also used for designing soft variable structure controls the paper presents a nonconservative design method for a stabilizing control of this type employing implicit lyapunov functions ilf a nonsaturating control law is given including some infinitely densely nested and contractive invariant sets of the equilibrium state the control law is then optimized by maximizing the ilf based lower bound of the convergence rate the maximal convergence control is shown to be of bang bang type with a parameter dependent switching scheme to overcome possible difficulties of a switching controller a saturating high gain control is also presented

a fast high order solver for problems of scattering by heterogeneous bodies a new high order integral algorithm for the solution of scattering problems by heterogeneous bodies is presented here a scatterer is described by a continuously or discontinuously varying refractive index n x within a two dimensional 2d bounded region solutions of the associated helmholtz equation under given incident fields are then obtained by high order inversion of the lippmann schwinger integral equation the algorithm runs in o nlog n operations where n is the number of discretization points a wide variety of numerical examples provided include applications to highly singular geometries high contrast configurations as well as acoustically electrically large problems for which supercomputing resources have been used recently our method provides highly accurate solutions for such problems on small desktop computers in cpu times of the order of seconds

a wideband fast multipole accelerated boundary integral equation method for time harmonic elastodynamics in two dimensions summary this article presents a wideband fast multipole method fmm to accelerate the boundary integral equation method for two dimensional elastodynamics in frequency domain the present wideband fmm is established by coupling the low frequency fmm and the high frequency fmm that are formulated on the ingenious decomposition of the elastodynamic fundamental solution developed by nishimura s group for each of the two fmms we estimated the approximation parameters that is the expansion order for the low frequency fmm and the quadrature order for the high frequency fmm according to the requested accuracy considering the coexistence of the derivatives of the helmholtz kernels for the longitudinal and transcendental waves in the burton muller type boundary integral equation of interest in the numerical tests the error resulting from the fast multipole approximation was monotonically decreased as the requested accuracy level was raised also the computational complexity of the present fast boundary integral equation method agreed with the theory that is nlog n where n is the number of boundary elements in a series of scattering problems the present fast boundary integral equation method is promising for simulations of the elastic systems with subwavelength structures as an example the wave propagation along a waveguide fabricated in a finite size phononic crystal was demonstrated copyright 2012 john wiley sons ltd

the fast multipole method we study integral methods applied to the resolution of the maxwell equations where the linear system is solved using an iterative method which requires only matrix vector products the fast multipole method fmm is one of the most efficient methods used to perform matrix vector products and accelerate the resolution of the linear system a problem involving n degrees of freedom may be solved in cniternlogn floating operations where c is a constant depending on the implementation of the method in this article several techniques allowing one to reduce the constant c are analyzed this reduction implies a lower total cpu time and a larger range of application of the fmm in particular new interpolation and anterpolation schemes are proposed which greatly improve on previous algorithms several numerical tests are also described these confirm the efficiency and the theoretical complexity of the fmm

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

a fast integral equation approach to acoustic scattering from three dimensional objects using a natural basis set boundary value integral equations and the moment method solution technique provide a succinct and elegant strategy for the solution of acoustic surface scattering problems this paper explores the application of a subdomain basis set based on the phase of the incident radiation which is used to solve for the unknown normal pressure gradient on the surface of the scatterer using the moment method the advantage of this basis set lies in the fact that it can accurately represent the fast phase character of the pressure gradient on the surface of the scatterer this allows for far fewer discretizations basis elements in the moment method formulation and therefore significantly reduces the density of unknowns that must be numerically computed the main contribution of this paper is to show how to efficiently employ this natural basis and to explore the physical justification for using this approach the method is compared with other techniques including the kirchhoff solution technique high frequency single scattering techniques the nussenzveig fock technique and the parabolic equation approximation unlike these methods no approximation to the physical system need be introduced

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

dual control of an integrator with unknown gain the dual control law for an integrator with constant but unknown gain is computed numerical problems associated with the solution of the bellman equation are reviewed properties of the dual control law are discussed a representation which makes it easy to compare dual control with certainty equivalence and cautious control is also introduced

the hybridization of fast multipole method with asymptotic waveform evaluation for the fast monostatic rcs computation the fast multipole method hybridized with the asymptotic waveform evaluation is presented in this paper to efficiently calculate the scattering from electrically large objects a novel interpolation method for the hybridization is proposed which provides a more accurate result for the scattering pattern calculation than the original extrapolation method the accuracy and efficiency of this proposed hybrid method are examined through numerical examples

a fast multi level boundary element method for the helmholtz equation abstract most recently we have developed a novel multi level boundary element method mlbem for the solution of the steady heat diffusion equation involving asymptotically decaying non oscillatory log singular and strongly singular kernels this hierarchical approach generalizes the pioneering work of brandt and lubrecht on multi level multi integration mlmi and c cycle multi grid to the broader class of mixed boundary value problems the result is a fast accurate and efficient boundary element method the present paper extends this new computational methodology to the solution of the helmholtz equation involving oscillatory log singular and strongly singular kernels for two dimensional problems we consider a direct boundary element formulation and due to the nature of the fundamental solutions split the corresponding boundary integral equation into real and imaginary parts then we introduce double noded corners to facilitate a patch by patch application of the mlmi algorithm for fast matrix vector and matrix transpose vector multiplications within bi conjugate gradient methods the performance of the proposed fast mlbem is investigated using a numerical example that possesses an exact solution for wave numbers 20 and below we demonstrate that the fast mlbem algorithm for the helmholtz equation is robust accurate and exceptionally efficient

incomplete lu preconditioning for large scale dense complex linear systems from electromagnetic wave scattering problems we consider the preconditioned iterative solution of large dense linear systems where the coefficient matrix is a complex valued matrix arising from discretizing the integral equation of electromagnetic scattering for some scattering structures this matrix can be poorly conditioned the main purpose of this study is to evaluate the efficiency of a class of incomplete lu ilu factorization preconditioners for solving this type of matrices we solve the electromagnetic wave equations using the bicg method with an ilu preconditioner in the context of a multilevel fast multipole algorithm mlfma the novelty of this work is that the ilu preconditioner as constructed using the near part block diagonal submatrices generated from the mlfma experimental results show that the ilu preconditioner reduces the number of bicg iterations substantially compared to the block diagonal preconditioner the preconditioned iteration scheme also maintains the computational complexity of the mlfma and consequently reduces the total cpu time

scheduled controllers for linear systems with bounded actuators state and output feedback controllers are designed for disturbance attenuation in linear systems with bounded actuators the controller is scheduled according to the proximity to the origin of the state of the plant in the state feedback case and the compensator state in the case of output feedback this procedure yields a linear parameter varying structure for the controller that allows higher gain and hence higher performance controllers as the states move closer to the origin the main results give sufficient conditions for the satisfaction of a parameter dependent performance measure without violating the saturation bounds linear splines are used to obtain solutions that can be obtained by standard lmi software examples including an open loop unstable system highlight the application of the results

a fast direct solver for the integral equations of scattering theory on planar curves with corners we describe an approach to the numerical solution of the integral equations of scattering theory on planar curves with corners it is rather comprehensive in that it applies to a wide variety of boundary value problems here we treat the neumann and dirichlet problems as well as the boundary value problem arising from acoustic scattering at the interface of two fluids it achieves high accuracy is applicable to large scale problems and perhaps most importantly does not require asymptotic estimates for solutions instead the singularities of solutions are resolved numerically the approach is efficient however only in the low and mid frequency regimes once the scatterer becomes more than several hundred wavelengths in size the performance of the algorithm of this paper deteriorates significantly we illustrate our method with several numerical experiments including the solution of a neumann problem for the helmholtz equation given on a domain with nearly 10000 corner points

volumetric fast multipole method for modeling schrodinger s equation a volume integral equation method is presented for solving schrodinger s equation for three dimensional quantum structures the method is applicable to problems with arbitrary geometry and potential distribution with unknowns required only in the part of the computational domain for which the potential is different from the background two different green s functions are investigated based on different choices of the background medium it is demonstrated that one of these choices is particularly advantageous in that it significantly reduces the storage and computational complexity solving the volume integral equation directly involves o n2 complexity in this paper the volume integral equation is solved efficiently via a multi level fast multipole method mlfmm implementation requiring o nlogn memory and computational cost we demonstrate the effectiveness of this method for rectangular and spherical quantum wells and the quantum harmonic oscillator and present preliminary results of interest for multi atom quantum phenomena

multistep and multistage convolution quadrature for the wave equation algorithms and experiments we describe how a time discretized wave equation in a homogeneous medium can be solved by boundary integral methods the time discretization can be a multistep runge kutta or a more general multistep multistage method the resulting convolutional system of boundary integral equations belongs to the family of convolution quadratures of lubich the aim of this work is twofold it describes an efficient robust and easily parallelizable method for solving the semidiscretized system the resulting algorithm has the main advantages of time stepping methods and of fourier synthesis at each time step a system of linear equations with the same system matrix needs to be solved yet computations can easily be done in parallel the computational cost is almost linear in the number of time steps and only the laplace transform of the time domain fundamental solution is needed the new aspect of the algorithm is that all this is possible without ever explicitly constructing the weights of the convolution quadrature this approach also readily allows the use of modern data sparse techniques to efficiently perform computation in space we investigate theoretically and numerically to which extent hierarchical matrix mathcal h matrix techniques can be used to speed up the space computation the second aim of this article is to perform a series of large scale 3d experiments with a range of multistep and multistage time discretization methods the backward difference formula of order 2 bdf2 the trapezoid rule and the 3 stage radau iia methods are investigated in detail one of the conclusions of the experiments is that the radau iia method often performs overwhelmingly better than the linear multistep methods especially for problems with many reflections yet in connection with hyperbolic problems bdfs have so far been predominant in the literature on convolution quadrature

on improving the performance with bounded continuous feedback laws we present controller design methods to smooth the discontinuity resulting from a piecewise linear control law which was proposed to improve the convergence performance for systems with input constraints the continuous control laws designed in this paper are explicit functions of the state and are easily implementable we also show that the convergence performance can be further improved by using a saturated high gain feedback law the efficiency of the proposed methods is illustrated with the puma 560 robot model

adaptive multiscale moment method ammm for analysis of scattering from three dimensional perfectly conducting structures the adaptive multiscale moment method ammm is presented for the analysis of scattering from three dimensional 3d perfectly conducting bodies this algorithm employs the conventional moment method mm using the subsectional triangular patch basis functions and a special matrix transformation which is derived from solving the fredholm equation of the first kind by the multiscale technique this methodology is more suitable for problems where the matrix solution time is much greater than the matrix fill time the widely used triangular patch vector basis functions developed by rao et al 1982 are used for expansion and testing functions in the conventional mm the objective here is to compress the unknowns in existing mm codes which solves for the currents crossing the edges of the triangular patch basis functions by use of a matrix transformation the currents source terms and impedance matrix can be arranged in the form of different scales from one scale to another scale the initial guess for the solution can be predicted according to the properties of the multiscale technique ammm can reduce automatically the size of the linear equations so as to improve the efficiency of the conventional mm the basic difference between this methodology and the other wavelet based techniques that have been presented so far is that we apply the compression not to the impedance matrix but to the solution itself directly in an iterative fashion even though it is an unknown two numerical results are presented which demonstrate that the ammm is a useful method for analysis of electromagnetic scattering from arbitrary shaped 3d perfectly conducting bodies

on the numerical evaluation of the singular integrals of scattering theory in a previous work the authors introduced a scheme for the numerical evaluation of the singular integrals which arise in the discretization of certain weakly singular integral operators of acoustic and electromagnetic scattering that scheme is designed to achieve high order algebraic convergence and high accuracy when applied to operators given on smoothly parameterized surfaces this paper generalizes the approach to a wider class of integral operators including many defined via the cauchy principal value operators of this type frequently occur in the course of solving scattering problems involving boundary conditions on tangential derivatives the resulting scheme achieves high order algebraic convergence and approximately 12 digits of accuracy

scattering from planar structures containing small features using the adaptive integral method aim fast integral equation algorithms such as the adaptive integral method aim have been demonstrated to reduce memory and execution time associated with moment method solutions for arbitrarily shaped three dimensional 3 d geometries in this paper we examine the efficiency of aim in modeling planar structures that contain small and intricate details as is the case with spirals and slot antennas such geometries require high tessellation due to the inclusion of very small features resulting in a large number of unknowns aim with its capability to translate the original grid to an equivalent sparser uniform grid is uniquely suited for the analysis of such geometries in the latter part of the paper we demonstrate the application of aim in connection with a finite element boundary integral formulation for cavity backed antennas

numerical accuracy of a pade type non reflecting boundary condition for the finite element solution of acoustic scattering problems at high frequency the present text deals with the numerical solution of two dimensional high frequency acoustic scattering problems using a new high order and asymptotic pade type artificial boundary condition the pade type condition is easy to implement in a galerkin least squares iterative finite element solver for arbitrarily convex shaped boundaries the method accuracy is investigated for different model problems and for the scattering problem by a submarine shaped scatterer as a result relatively small computational domains optimized according to the shape of the scatterer can be considered while yielding accurate computations for high frequencies copyright 2005 john wiley sons ltd

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

truncation error analysis of multipole expansion the multilevel fast multipole algorithm is based on the multipole expansion which has numerical error sources such as truncation of the addition theorem numerical integration and interpolation anterpolation of these we focus on the truncation error and discuss its control precisely the conventional selection rule fails when the buffer size is small compared to the desired numerical accuracy we propose a new approach and show that the truncation error can be controlled and predicted regardless of the number of buffer sizes

piecewise linear lq control for systems with input constraints abstract a piecewise linear control plc law based on lq theory is derived ths law raises an lq gain as the controlled error converges towards the origin it can be computed off line and it guarantees that input bounds are never exceeded without causing input saturation a succession of positively invariant sets are defined of diminishing size and associated with each is the corresponding highest lq gain possible in the presence of the input bounds the formulation gives rise to an iteration function whose solution is a fixed point fp the fp defines the optimal gain and the invariant set which comprise ellipsoids fp existence uniqueness and convergence properties are proven we explain the algorithms for the generation and subsequent implementation of the plc law the notion of a switching function is introduced consideration is given to the computational aspects of the fp the plc scheme is demonstrated for the linearized dynamics of the simple pendulum and the puma 560 robot a discrete time plc law can also be derived using the discrete time algebraic riccati equation

fast computation of angular responses of large scale three dimensional electromagnetic wave scattering many applications in electromagnetic engineering require predicting the currents induced by a wide range of incident plane waves on a given object this paper proposes a way to efficiently and accurately compute the angular responses for electrically large targets since the targets of concern are electrically large we have employed the newly developed non conformal domain decomposition method ddm as the direct maxwell equation solver the proposed fast angular sweep algorithm is then applied in conjunction with the ddm solver to produce wide range of angular responses there are basically three main ingredients in the proposed fast angular sweep algorithm the use of fourier harmonics to interpolate the right hand sides rhss over a given angular range the number of independent coefficient vectors in the fourier harmonics can be further reduced through the application of singular value decomposition svd and finally the matrix solution of multiple rhss can be solved efficiently using a recently proposed krylov recycling method gcro dr three numerical results are presented and compared to measurements and direct computations to validate the numerical solutions and to illustrate the effectiveness of the proposed approach

multipoint galerkin asymptotic waveform evaluation for model order reduction of frequency domain fem electromagnetic radiation problems in this paper a model order reduction technique is presented this technique known as galerkin asymptotic waveform evaluation gawe or multipoint galerkin asymptotic waveform evaluation mgawe if multiple expansion points are considered simultaneously can be used to reduce matrices describing electromagnetic em phenomena generated through the finite element method fem to a smaller space while still accurately approximating the characteristics of the original responses the resulting solution procedure of using gawe or mgawe to solve fem equations allows for wideband frequency simulations with a reduction in total computation time numerical simulations using these methods are shown along with traditional methods such as using an lu decomposition at each frequency point of interest and asymptotic waveform evaluation awe comparisons in accuracy as well as computation time are also given

tuning an adaptive controller using a robust control approach this article proposes a new technique for the tuning of a discrete adaptive controller that is designed based on lyapunov stability concepts the tuning is based on the minimisation of a performance index that can be calculated from a generalised eigenvalue problem gevp using lmi s linear matrix inequalities the proposed technique results in an adaptive controller with time varying tuning gains the solution is based on an approximation of the optimal dual adaptive control problem the tuning technique was used to perform on line control of a first order system and an isothermal and a non isothermal cstr the results show that the proposed approach provides better performance than an adaptive algorithm with the same structure but with constant adaptation gains also the proposed algorithm is shown to be superior to an adaptive controller based on a recursive least squares rls estimator during sudden changes in model parameters

stabilizing block diagonal preconditioners for complex dense matrices in electromagnetics abstract preconditioning techniques are widely used to speed up the convergence of iterative methods for solving large linear systems with sparse or dense coefficient matrices for certain application problems however the standard block diagonal preconditioner makes the krylov iterative methods converge more slowly or even diverge to handle this problem we apply diagonal shifting and stabilized singular value decomposition svd to each diagonal block which is generated from the multilevel fast multiple algorithm mlfma to improve the stability and efficiency of the block diagonal preconditioner our experimental results show that the improved block diagonal preconditioner maintains the computational complexity of mlfma converges faster and also reduces the cpu cost

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

application of volume integrals to the solution of partial differential equations abstract a group of algorithms for the numerical solution of elliptic partial differential equations is presented the differential equation is reduced to a fredholm equation of the second kind which in turn is discretized by means of the nystrom algorithm leading to a dense large scale system of linear algebraic equations this linear system is solved by means of the generalized conjugate residual algorithm which requires that the matrix of the system be applied to a sequence of recursively generated vectors since applying a dense matrix to a vector is a process of order n 2 where n is the dimension of the system the resulting algorithms are usually not competitive with finite differences and finite elements in terms of cpu time requirements however it turns out that the matrices of linear systems resulting from many partial differential equations can be applied to vectors in a fast manner i e for the cost proportional to n in some cases and to n log n or n log n 2 in others resulting in extremely efficient algorithms for the solution of certain elliptic partial differential equations the performances of several such algorithms are illustrated by numerical examples

fast inverse scattering solutions using the distorted born iterative method and the multilevel fast multipole algorithm the distorted born iterative method dbim computes iterative solutions to nonlinear inverse scattering problems through successive linear approximations by decomposing the scattered field into a superposition of scattering by an inhomogeneous background and by a material perturbation large or high contrast variations in medium properties can be imaged through iterations that are each subject to the distorted born approximation however the need to repeatedly compute forward solutions still imposes a very heavy computational burden to ameliorate this problem the multilevel fast multipole algorithm mlfma has been applied as a forward solver within the dbim the mlfma computes forward solutions in linear time for volumetric scatterers the typically regular distribution and shape of scattering elements in the inverse scattering problem allow the method to take advantage of data redundancy and reduce the computational demands of the normally expensive mlfma setup additional benefits are gained by employing kaczmarz like iterations where partial measurements are used to accelerate convergence numerical results demonstrate both the efficiency of the forward solver and the successful application of the inverse method to imaging problems with dimensions in the neighborhood of ten wavelengths