on analysis of exponentially decaying pulse signals using stochastic volatility model part ii student t distribution the authors have recently demonstrated how the stochastic volatility model incorporating the exponential power distribution can be used to retrieve the instant of initiation of an exponentially decaying pulse and its decay constants in the presence of background noises in the present study the student t distribution which can be expressed in a two stage scale mixtures representation is adopted in the stochastic volatility model it is found that the corresponding performance is comparable to that for the case of the exponential power distribution when the signal to noise ratio is larger than or equal to 3db the performance deteriorates quickly when the signal to noise ratio drops below 0db

preconditioning technique in the interpolative decomposition multilevel fast multipole algorithm the potential of the interpolative decomposition multilevel fast multipole algorithm id mlfma on developing an effective preconditioning technique for multiscale dynamic electromagnetic problems are analyzed the preconditioner based on multilevel inverse based ilu is developed for id mlfma the proposed preconditioning technique is investigated by numerical experiments on complex targets

a rational function preconditioner for indefinite sparse linear systems this paper introduces a rational function preconditioner for linear systems with indefinite sparse matrices a by resorting to rational functions of a the algorithm decomposes the spectrum of a into two disjoint regions and approximates the restriction of a 1 on these regions separately we show a systematic way to construct these rational functions so that they can be applied stably and inexpensively an attractive feature of the proposed approach is that the construction and application of the preconditioner can exploit two levels of parallelism moreover the proposed preconditioner can be modified at a negligible cost into a preconditioner for a nearby matrix of the form a ci which can be useful in some applications the efficiency and robustness of the proposed preconditioner are demonstrated on a few tests with challenging model problems including problems arising from the helmholtz equation in three dimensions

symmetric permutations for i matrices to delay and avoid small pivots during factorization in this article we present several new permutations for i matrices making these more suitable for incomplete lu factorization preconditioners used in solving linear systems by iterative methods a general matrix can be transformed by row permutation as well as row and columns scaling into an i matrix i e a matrix having elements of modulus 1 on the diagonal and elements of modulus of no more than 1 elsewhere reordering rows and columns by the same permutation clearly preserves i matrices in this article we consider such reordering techniques which make the permuted matrix more suitable for an incomplete lu factorization preconditioner than the original i matrix we use a multilevel iluc an incomplete lu factorization preconditioner using crout s implementation of gaussian elimination without pivoting to test these reorderings the combination of i matrix preprocessing with the various algorithms presented here and the multilevel incomplete lu factorizations forms a powerful preconditioning method for unsymmetric highly indefinite problems the c code has been made available in the software package ilu

a robust and efficient ilu that incorporates the growth of the inverse triangular factors in this paper we present a new ilu decomposition which is based on an existing sparse direct solver in contrast to many incomplete lu decompositions this ilu incorporates information about the inverse factors l 1 and u 1 which have direct influence on the dropping strategy we demonstrate in several large scale examples that this implementation constructs a robust preconditioner

preconditioning highly indefinite and nonsymmetric matrices standard preconditioners like incomplete factorizations perform well when the coefficient matrix is diagonally dominant but often fail on general sparse matrices we experiment with nonsymmetric permutations and scalings aimed at placing large entries on the diagonal in the context of preconditioning for general sparse matrices the permutations and scalings are those developed by olschowka and neumaier linear algebra appl 240 1996 pp 131 151 and by duff and koster siam j matrix anal appl 20 1999 pp 889 901 tech report ral tr 99 030 rutherford appleton laboratory chilton uk 1999 we target highly indefinite nonsymmetric problems that cause difficulties for preconditioned iterative solvers our numerical experiments indicate that the reliability and performance of preconditioned iterative solvers are greatly enhanced by such preprocessing

existence uniqueness and causality theorems for wave propagation in stratified temporally dispersive complex media a mixed initial boundary value problem for a nonlocal hyperbolic equation is analyzed with respect to unique solubility and causality the regularity of the step response and impulse response the green functions is investigated and a wave front theorem is proved the problem arises e g at time varying electromagnetic plane wave excitation of stratified temporally dispersive bi isotropic or anisotropic slabs concluding the problem is uniquely solvable strict causality holds and a well defined wave front speed exists this speed is independent of dispersion and excitation and depends on the nondispersive properties of the medium only

an electromagnetic inverse problem for dispersive media the dispersion of transient electromagnetic waves in a homogeneous medium can be characterized by expressing either the complex permittivity as a function of frequency or the susceptibility kernel as a function of time in this paper a time domain technique is used to derive a nonlinear integrodifferential equation which relates the susceptibility kernel for a one dimensional homogeneous slab to the reflection operator for the medium thus the susceptibility kernel which is a function of time can be determined from reflection data a numerical implementation of this technique is shown the more general case of a medium consisting of a stack of homogeneous dispersive layers is also addressed

robust statistical modeling using the t distribution abstract the t distribution provides a useful extension of the normal for statistical modeling of data sets involving errors with longer than normal tails an analytical strategy based on maximum likelihood for a general model with multivariate t errors is suggested and applied to a variety of problems including linear and nonlinear regression robust estimation of the mean and covariance matrix with missing data unbalanced multivariate repeated measures data multivariate modeling of pedigree data and multivariate nonlinear regression the degrees of freedom parameter of the t distribution provides a convenient dimension for achieving robust statistical inference with moderate increases in computational complexity for many models estimation of precision from asymptotic theory and the bootstrap is discussed and graphical methods for checking the appropriateness of the t distribution are presented

transient wave propagation in reciprocal bi isotropic media at oblique incidence in this paper a new wave splitting is suggested that simplifies the analysis of wave propagation in reciprocal bi isotropic media two different methods to solve the scattering problem are analyzed the invariant imbedding and the green function approach the medium is modeled by constitutive relations in the time domain time convolutions and the slab is assumed to be inhomogeneous with respect to the depth it is shown that the cross polarized contribution to the reflected field at normal incidence is zero for the general reciprocal inhomogeneous slab moreover the rotation and the attenuation of the wave front are calculated explicitly in the general inhomogeneous slab case special attention is paid to normal incidence and to the homogeneous semi infinite medium

numerical solution of an extended white metzner model for eccentric taylor couette flow in this study we have developed a new numerical approach to solve differential type viscoelastic fluid models for a commonly used benchmark problem namely the steady taylor couette flow between eccentric cylinders the proposed numerical approach is special in that the nonlinear system of discretized algebraic flow equations is solved iteratively using a newton krylov method along with an inverse based incomplete lower upper preconditioner the numerical approach has been validated by solving the benchmark problem for the upper convected maxwell model at a large deborah number excellent agreement with the numerical data reported in the literature has been found in addition a parameter study was performed for an extended white metzner model a large eccentricity ratio was chosen for the cylinder system in order to allow flow recirculation to occur we detected several interesting phenomena caused by the large eccentricity ratio of the cylinder system and by the viscoelastic nature of the fluid encouraged by the results of this study we intend to investigate other polymeric fluids having a more complex microstructure in an eccentric annular flow field

on analysis of exponentially decaying pulse signals using stochastic volatility model a stochastic volatility model incorporating the exponential power distributions is adopted in the present study to analyze exponentially decaying pulses in the presence of background noises of various magnitudes the discussions are focused on its effectiveness in the determination of the instant of the pulse initiation and the decay constant the results are compared with those obtained by the conventional short time fourier transform it is found that the present stochastic volatility model can retrieve the instant of the pulse initiation and the decay constant within engineering tolerance even when the noise is slightly stronger that the pulse amplitude its performance is substantially better than that of the fourier transform when the frequency of the decay pulse fluctuates

multilevel preconditioners constructed from inverse based ilus this paper analyzes dropping strategies in a multilevel incomplete lu decomposition context and presents a few strategies for obtaining related ilus with enhanced robustness the analysis shows that the incomplete lu factorization resulting from dropping small entries in gaussian elimination produces a good preconditioner when the inverses of these factors have norms that are not too large as a consequence a few strategies are developed whose goal is to achieve this feature a number of templates for enabling implementations of these factorizations are presented numerical experiments show that the resulting ilus offer a good compromise between robustness and efficiency

multilevel ilu with reorderings for diagonal dominance this paper presents a preconditioning method based on combining two sided permutations with a multilevel approach the nonsymmetric permutation exploits a greedy strategy to put large entries of the matrix in the diagonal of the upper leading submatrix the method can be regarded as a complete pivoting version of the incomplete lu factorization this leads to an effective incomplete factorization preconditioner for general nonsymmetric irregularly structured sparse linear systems

factorized approximate inverses with adaptive dropping this paper presents a new approach to constructing factorized approximate inverses for a symmetric and positive definite matrix a the proposed strategy is based on adaptive dropping that reflects the quality of preserving the relation uz i between the direct factor u and the inverse factor z satisfying a u tu and a 1 zz t an important part of the approach is column pivoting used to minimize the growth of the condition number of leading principal submatrices of u that occurs explicitly in the dropping criterion numerical experiments demonstrate that the resulting approximate inverse factorization is robust as a preconditioner for solving large and sparse systems of linear equations

algebraic multilevel preconditioner for the helmholtz equation in heterogeneous media an algebraic multilevel ml preconditioner is presented for the helmholtz equation in heterogeneous media it is based on a multilevel incomplete ldl t factorization and preserves the inherent complex symmetry of the helmholtz equation the ml preconditioner incorporates two key components for efficiency and numerical stability symmetric maximum weight matchings and an inverse based pivoting strategy the former increases the block diagonal dominance of the system whereas the latter controls l 1 for numerical stability when applied recursively their combined effect yields an algebraic coarsening strategy similar to algebraic multigrid methods even for highly indefinite matrices the ml preconditioner is combined with a krylov subspace method and applied as a black box solver to a series of challenging two and three dimensional test problems mainly from geophysical seismic imaging the numerical results demonstrate the robustness and efficiency of the ml preconditioner even at higher frequency regimes

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

automatic basis function regularization for integral equations in the presence of ill shaped mesh elements bad meshes are a common problem in using computational electromagnetics codes often much of an engineer s or analyst s time ids wasted improving a mesh until the solver finally converges we investigate the problem as it comes up in integral equation methods and observe that its effects can be detected by analyzing the singular values of the electric field integral equation matrix armed with this information we automatically remove the undesirable degrees of freedom caused by the ill shaped mesh elements so that the iterative solver behaves as if they were not present all without any extra effort by the user an a posteriori error estimator is developed which verifies the improved accuracy for test problems and also suggests potential future applications in adaptive mesh refinement for integral equation methods further numerical examples demonstrate the improved solution convergence

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

high order fdtd methods for transverse magnetic modes with dispersive interfaces a new finite difference time domain fdtd algorithm is introduced to solve two dimensional 2d transverse magnetic tm modes with a straight dispersive interface driven by the consideration of simplifying interface jump conditions the auxiliary differential equation of the debye constitution model is rewritten to form a new debye maxwell tm system interface auxiliary differential equations are utilized to describe the transient changes in the regularities of electromagnetic fields across a dispersive interface the resulting time dependent jump conditions are rigorously enforced in the fdtd discretization by means of a matched interface and boundary scheme higher order convergences are numerically achieved for the first time in the literature in 2d fdtd simulations of dispersive inhomogeneous media

a new preconditioning technique for solving large sparse linear systems abstract a new sparse approximate triangular factorization technique for solving large sparse linear system by iterative methods is proposed the method is based on the description of the triangular factorization of a matrix as a product of elementary matrices and provides a general scheme for constructing incomplete preconditioners for the given matrix in particular the familiar incomplete choleski decomposition can be incorporated into this scheme the algorithm based on choice by value compares favorably with the incomplete choleski preconditioner and equipped with a user controlled parameter is able to tackle extremely ill conditioned problems arising in structural analysis semiconductor simulation oil reservoir modelling and other applications when applied to a positive definite symmetric matrix the algorithm produces a preconditioning matrix preserving that property

crout versions of ilu for general sparse matrices this paper presents an efficient implementation of the incomplete lu ilu factorization derived from the crout version of gaussian elimination at step k of the elimination the kth row of u and the kth column of l are computed using previously computed rows of u and columns of l the data structure and implementation borrow from already known techniques used in developing both sparse direct solution codes and incomplete cholesky factorizations this version of ilu can be computed much faster than standard threshold based ilu factorizations computed rowwise or columnwise in addition the data structure allows efficient implementations of more rigorous and effective dropping strategies