fast sweeping algorithms for a class of hamilton jacobi equations we derive a godunov type numerical flux for the class of strictly convex homogeneous hamiltonians that includes h p q sqrt ap 2 bq 2 2cpq c 2 ab we combine our godunov numerical fluxes with simple gauss seidel type iterations for solving the corresponding hamilton jacobi hj equations the resulting algorithm is fast since it does not require a sorting strategy as found e g in the fast marching method in addition it providesa way to compute solutions to a class of hj equations for which the conventional fast marching method is not applicable our experiments indicate convergence after a few iterations even in rather difficult cases

transformation optics based local mesh refinement for solving maxwell s equations in this paper a novel local mesh refinement algorithm based on transformation optics to has been developed for solving the maxwell s equations of electrodynamics the new algorithm applies transformation optics to enlarge a small region so that it can be resolved by larger grid cells the transformed anisotropic maxwell s equations can be stably solved by an anisotropic fdtd method while other subgridding or adaptive mesh refinement fdtd methods require time space field interpolations and often suffer from the late time instability problem to avoid small time steps introduced by the transformation optics approach an additional application of the mapping of the material matrix to a dispersive material model is employed numerical examples on scattering problems of dielectric and dispersive objects illustrate the performance and the efficiency of the transformation optics based fdtd method

a viscosity solutions approach to shape from shading the problem of recovering a lambertian surface from a single two dimensional image may be written as a first order nonlinear equation which presents the disadvantage of having several continuous and even smooth solutions a new approach based on hamilton jacobi bellman equations and viscosity solutions theories enables one to study non uniqueness phenomenon and thus to characterize the surface among the various solutions a consistent and monotone scheme approximating the surface is constructed thanks to the dynamic programming principle and numerical results are presented

analysis of an exact fractional step method an exact fractional step or projection method for solving the incompressible navier stokes equations is analyzed the method is applied to both structured and unstructured staggered mesh schemes there are no splitting errors associated with the method it satisfies the incompressibility condition to machine precision and reduces the number of unknowns the exact projection technique is demonstrated on a two dimensional cavity flow and a multiply connected moving domain with a free surface its performance is compared directly to classic fractional step methods and shown to be roughly twice as efficient boundary conditions and the relationship of the method to streamfunction vorticity methods are discussed

simulations of multiphase flows with multiple length scales using moving mesh interface tracking with adaptive meshing in multiphase flows the length scales of thin regions such as thin films between nearly touching drops and thin threads formed during the interface pinch off are usually several orders of magnitude smaller than the size of the drops in this paper a number of extra length criteria for adaptive meshes are developed and implemented in the moving mesh interface tracking method to solve these multiple length scale problems with high fidelity a nominal length scale based on the solutions of laplace s equations with the unit normal vectors of surfaces as the boundary conditions is proposed for the adaptive mesh refinement in the thin regions for almost flat interfaces boundaries which are near to the thin regions the averaged length of the interior edges sharing the two nodes with the boundary edge is introduced for the mesh adaptation the averaged length of the interfacial edges is used for the interior elements near the interfaces but outside of the thin regions for the interior mesh away from the interfaces boundaries different averaged length scales based on the initial mesh are employed for the adaptive mesh refining and coarsening numerous cases are simulated to demonstrate the capability of the proposed schemes in handling multiple length scales which include the relaxation and necking of an elongated droplet droplet droplet head on approaching droplet wall interactions and a droplet pair in a shear flow the smallest length resolved for the thin regions is three orders of magnitude smaller than the largest characteristic length of the problem

artificial immune multi objective sar image segmentation with fused complementary features artificial immune systems ais are the computational systems inspired by the principles and processes of the vertebrate immune system ais based algorithms typically mimic the human immune system s characteristics of learning and adaptability to solve some complicated problems here an artificial immune multi objective optimization framework is formulated and applied to synthetic aperture radar sar image segmentation the important innovations of the framework are listed as follows 1 an efficient and robust immune multi objective optimization algorithm is proposed which has the features of adaptive rank clones and diversity maintenance by k nearest neighbor list 2 besides two conflicting fuzzy clustering validity indices are incorporated into this framework and optimized simultaneously and 3 moreover an effective fused feature set for texture representation and discrimination is constructed and researched which utilizes both the gabor filter s ability to precisely extract texture features in low and mid frequency components and the gray level co occurrence probability s glcp ability to measure information in high frequency two experiments with synthetic texture images and sar images are implemented to evaluate the performance of the proposed framework in comparison with other five clustering algorithms fuzzy c means fcm single objective genetic algorithm soga self organizing map som wavelet domain hidden markov models hmtseg and spectral clustering ensemble sce experimental results show the proposed framework has obtained the better performance in segmenting sar images than other five algorithms and behaves insensitive to the speckle noise

a vector finite element time domain method for solving maxwell s equations on unstructured hexahedral grids in this paper the vector finite element time domain vfetd method is derived analyzed and validated the vfetd method uses edge vector finite elements as a basis for the electric field and face vector finite elements as a basis for the magnetic flux density the galerkin method is used to convert maxwell s equations to a coupled system of ordinary differential equations the leapfrog method is used to advance the fields in time the method is shown to be stable and to conserve energy and charge for arbitrary hexahedral grids a numerical dispersion analysis shows the method to be second order accurate on distorted hexahedral grids several computational experiments are performed to determine the accuracy and efficiency of the method

a fast level set method for propagating interfaces a method is introduced to decrease the computational labor of the standard level set method for propagating interfaces the fast approach uses only points close to the curve at every time step we describe this new algorithm and compare its efficiency and accuracy with the standard level set approach

finite difference on grids with nearly uniform cell area and line spacing for the wave equation on complex domains a finite difference time dependent numerical method for the wave equation supported by recently derived novel elliptic grids is analyzed the method is successfully applied to single and multiple two dimensional acoustic scattering problems including soft and hard obstacles with complexly shaped boundaries the new grids have nearly uniform cell area j grids and nearly uniform grid line spacing email protected numerical experiments reveal the positive impact of these two grid properties on the scattered field convergence to its harmonic steady state the restriction imposed by stability conditions on the time step size is relaxed due to the near uniformity cell areas and grid line spacing as a consequence moderately large time steps can be used for relatively fine spatial grids resulting in greater accuracy at a lower computational cost also numerical solutions for wave problems inside annular regions of complex shapes are obtained the use of the new grids results in late time stability in contrast with other classical finite difference time dependent methods

a high order accurate parallel solver for maxwell s equations on overlapping grids a scheme for the solution of the time dependent maxwell s equations on composite overlapping grids is described the method uses high order accurate approximations in space and time for maxwell s equations written as a second order vector wave equation high order accurate symmetric difference approximations to the generalized laplace operator are constructed for curvilinear component grids the modified equation approach is used to develop high order accurate approximations that use only three time levels and have the same time stepping restriction as the second order scheme discrete boundary conditions for perfect electrical conductors and for material interfaces are developed and analyzed the implementation is optimized for component grids that are cartesian resulting in a fast and efficient method the solver runs on parallel machines with each component grid distributed across one or more processors numerical results in two and three dimensions are presented for the fourth order accurate version of the method these results demonstrate the accuracy and efficiency of the approach

a novel 3 d cpfdtd scheme for modeling grid nonconformally aligned transmitter structures in this paper a novel three dimensional 3 d subcell algorithm for modeling metallic objects which are nonconformally oriented within the finite difference time domain fdtd grid is proposed the generally applicable algorithm is based on the contour path cp technique and enables in combination with an enhanced nonconformally aligned source model a more accurate spatial representation of antenna structures than the common staircase approach to evaluate the performance of the new algorithm the simulation results are compared with the classical staircase approach for dipole antennas as well as for a generic phone significant improvements were achieved for all antenna parameters from the near and far field i e feedpoint impedance radiation pattern and field distributions

adaptive tetrahedral meshing in free surface flow an unstructured three dimensional moving mesh algorithm is developed for free surface flows with the capability of simulating large deformation a robust edge swapping algorithm and an optimization based mesh smoothing algorithm are used to improve mesh quality as the interface deforms the edge swapping algorithm uses an optimal swap sequence to transform configurations with several tetrahedra sharing a common edge the optimization based mesh smoothing relocates vertex position so that the minimum quality of the incident cells is maximized also edge contraction and bisection are used to adjust the mesh resolution according to surface curvature these local refinements effectively maintain good mesh quality and appropriate mesh size while avoiding global re meshing this scheme s robustness and accuracy are demonstrated with deforming liquid ligaments periodic jets and colliding droplets

time dependent numerical method with boundary conforming curvilinear coordinates applied to wave interactions with prototypical antennas a new unstaggered finite difference time dependent technique to accurately model scattring from prototypical 2d antenna structures is devised the unbounded boundary value problems defining these phenomena are redefined over bounded domains using appropriate radiation operators over finite artificial boundaries generalized curvilinear coordinates are generated such that physical boundaries correspond to coordinate lines a numerical procedure to generate almost orthogonal boundary conforming fine grids over these bounded regions is developed once the governing equations are written in terms of the new curvilinear coordinates a time dependent numerical method is applied to obtain time harmonic steady state solutions to these problems the electric field wave amplitude as well as the wave pattern inside the waveguide and the scattered field from the prototypical antennas are obtained accuracy and computational cost are compared when almost orthogonal and nonorthogonal grids are in use an optical theorem for a flanged waveguide antenna with perfect electrical conductor walls is derived it is verified that the approximate solutions obtained by application of the time dependent numerical method with boundary conforming curvilinear coordinates satisfy the optical theorem

high order essentially nonsocillatory schemes for hamilton jacobi equations hamilton jacobi h j equations are frequently encountered in applications e g in control theory and differential games h j equations are closely related to hyperbolic conservation laws in one space dimension the former is simply the integrated version of the latter similarity also exists for the multidimensional case and this is helpful in the design of difference approximations in this paper high order essentially nonoscillatory eno schemes for h j equations are investigated which yield uniform high order accuracy in smooth regions and sharply resolve discontinuities in the derivatives the eno scheme construction procedure is adapted from that for hyperbolic conservation laws the schemes are numerically tested on a variety of one dimensional and two dimensional problems including a problem related to control optimization and high order accuracy in smooth regions good resolution of discontinuities in the derivatives and convergence to viscosity solutions are observed

a lattice boltzmann scheme for incompressible multiphase flow and its application in simulation of rayleigh taylor instability in this paper we propose a new lattice boltzmann scheme for simulation of multiphase flow in the nearly incompressible limit the new scheme simulates fluid flows based on distribution functions the interfacial dynamics such as phase segregation and surface tension are modeled by incorporating molecular interactions the lattice boltzmann equations are derived from the continuous boltzmann equation with appropriate approximations suitable for incompressible flow the numerical stability is improved by reducing the effect of numerical errors in calculation of molecular interactions an index function is used to track interfaces between different phases simulations of the two dimensional rayleigh taylor instability yield satisfactory results the interface thickness is maintained at 3 4 grid spacings throughout simulations without artificial reconstruction steps

an explicit fourth order orthogonal curvilinear staggered grid fdtd method for maxwell s equations the explicit fourth order staggered finite difference time domain scheme previously proposed for a cartesian grid is extended to maxwell s equations in an orthogonal curvilinear coordinate system and applied to electromagnetic wave problems a simple technique is also presented for generating orthogonal curvilinear grids that conform to the material boundaries and interfaces of the problem numerical experiments are presented to illustrate the efficiency and accuracy of the method

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

a numerical method for solving incompressible flow problems with a surface of discontinuity a numerical method for solving problems in which a moving surface of discontinuity separates regions of incompressible flow is presented the method developed is notable in that it does not introduce any artificial smoothing of the change in fluid properties across the surface of discontinuity this results in an increase in accuracy relative to methods which introduce smoothing effects the method was also shown to be fairly versatile problems describing a free surface an immiscible fluid interface and a premixed flame discontinuity were solved there is a limitation however in that the method appears to be most suitable for application to inviscid problems the reason for this limitation and possible approaches toward resolving it are discussed

on hopf s formulas for solutions of hamilton jacobi equations soit h r n r on considere l equation de hamilton jacobi u t h du 0 dans r n 1 r n 0 on etudie les proprietes des formules de hopf pour les solutions

second order procedure for modeling dielectric material interfaces in structured nonorthogonal finite difference discretizations of maxwell s equations structured nonorthogonal finite difference discretizations of maxwell s equations are often employed to incorporate curved dielectric material interfaces as part of this process it is necessary to employ an adequate procedure to enforce the tangential field continuity conditions at the locations of the interfaces where the components of the permittivity tensor are discontinuous this contribution proposes a second order domain splitting procedure that can accomplish this task without assuming that the permittivity tensor components are piecewise constant or diagonal as explained this feature is needed to exploit the full geometrical flexibility of structured grid generation the proposed domain splitting procedure consistently yields a global error that is second order accurate even in extreme cases where the components of the permittivity tensor have a change of sign or a sharp jump

level set methods for the simulation of epitaxial phenomena we introduce a model for epitaxial phenomena based on the motion of island boundaries which is described by the level set method our model treats the growing film as a continuum in the lateral direction but retains atomistic discreteness in the growth direction an example of such an island dynamics model using the level set method is presented and compared with the corresponding rate equation description extensions of our methodology to more general settings are then discussed s1063 651x 98 50212 7

time domain method having a naturally diagonal mass matrix independent of element shape for general electromagnetic analysis 2 d formulations in this paper we present a new time domain method that has a naturally diagonal mass matrix and thereby a strict linear computational complexity per time step regardless of whether the discretization is a structured grid or an unstructured mesh this property is obtained independent of the element shape used for discretization no interpolations projections and mass lumping are required the accuracy and stability of the proposed method are both theoretically guaranteed in addition no dual mesh is needed and the tangential continuity of the fields is satisfied across the element interface the flexible framework of the proposed method also allows for a straightforward extension to higher order accuracy in both electric and magnetic fields numerical experiments have been conducted on a variety of unstructured triangular element meshes correlations with analytical solutions and the time domain finite element method have validated the accuracy and generality of the proposed new time domain method

ant intelligence inspired blind data detection for ultra wideband radar sensors given the computational complexity and sophisticated implementation of traditionally parametric channel estimators it has been gradually recognized that the existing data detection methodologies based on the finite impulse response fir propagation channel modeling may become infeasible for ultra wideband uwb radar sensors especially in some large scale distributed scenarios by exploiting the implicit information involved in the received signals in this investigation we present a non parametric uwb data detection scheme for the distributed radar sensor networks a novel characteristic representation is suggested first from a pattern classification point of view a group of quantitative features are then extracted by making full use of the inherent property of uwb propagations thus uwb data detection is formulated as a pattern classification problem in a multidimensional feature space by thoroughly utilizing the self similarity of the representative patterns the ant swarm intelligence inspired clustering algorithm with the new designed ant movement strategy is adopted to perform unsupervised data detections the developed scheme is independent of any a priori modeling information which essentially avoids the expensive parametric estimators and thus enables practically feasible realizations to alleviate the computational burden the principle component analysis pca is further employed to compress the feature space the simulation results validate the new algorithm which is superior to the other popular non parametric data analysis schemes

an analysis of finite volume finite element and finite difference methods using some concepts from algebraic topology in this paper we apply the ideas of algebraic topology to the analysis of the finite volume and finite element methods illuminating the similarity between the discretization strategies adopted by the two methods in the light of a geometric interpretation proposed for the role played by the weighting functions in finite elements we discuss the intrinsic discrete nature of some of the factors appearing in the field equations underlining the exception represented by the constitutive term the discretization of which is maintained as the key issue for numerical methods devoted to field problems we propose a systematic technique to perform this task present a rationale for the adoption of two dual discretization grids and point out some optimization opportunities in the combined selection of interpolation functions and cell geometry for the finite volume method finally we suggest an explanation for the intrinsic limitations of the classical finite difference method in the construction of accurate high order formulas for field problems

multicomponent flow calculations by a consistent primitive algorithm the dynamics of inviscid multicomponent fluids may be modelled by the euler equations augmented by one or more additional species equation s attempts to compute solutions for extended euler models in conservation form show strong oscillations and other computational inaccuracies near material interfaces these are due to erroneous pressure fluctuations generated by the conservative wave model this problem does not occur in single component computations and arises only in the presence of several species a nonconservative primitive euler formulation is proposed which results in complete elimination of the oscillations the numerical algorithm uses small viscous perturbations to remove leading order conservation errors and is conservative to the order of numerical approximation numerical experiments show clean monotonic solution profiles with acceptably small conservation error for shocks of weak to moderate strengths

accuracy of staircase approximations in finite difference methods for wave propagation while a number of increasingly sophisticated numerical methods have been developed for time dependent problems in electromagnetics the yee scheme is still widely used in the applied fields mainly due to its simplicity and computational efficiency a fundamental drawback of the method is the use of staircase boundary approximations giving inconsistent results usually experience of numerical experiments provides guidance of the impact of these errors on the final simulation result in this paper we derive exact discrete solutions to the yee scheme close to the staircase approximated boundary enabling a detailed theoretical study of the amplitude phase and frequency errors created furthermore we show how evanescent waves of amplitude o 1 o 1 occur along the boundary these characterize the inconsistencies observed in electromagnetic simulations and the locality of the waves explain why in practice the yee scheme works as well as it does the analysis is supported by detailed proofs and numerical examples

fdtd algorithm in curvilinear coordinates em scattering the finite difference time domain fdtd algorithm for the solution of electromagnetic scattering problems is formulated in generalized coordinates in two dimensions and implemented in a code with the lowest order bayliss turkel radiation boundary condition expressed in cylindrical coordinates it is shown that for a perfect conductor such a formulation leads to a stable well posed algorithm and that in regions where the curvature of the coordinate lines is not great the dispersion and anisotropy effects are negligible such effects become more pronounced in regions of high curvature leading to unphysical phase shifts the magnitude of such shifts and the amount of wavefront distortion is studied via numerical experiments using a cylindrical mesh near field results are given for two canonical shapes for each polarization the circular cylinder and cylinders of square and rectangular cross sections these results are compared with those obtained by exact eigenfunction expansion techniques with method of moments mm solutions and with solutions obtained from an alternate fdtd approach in each case agreement is excellent the propagation of a plane wave through a polar space in the absence of a scatterer is also examined and it is shown that the fdtd algorithm is capable of tracking the incident wave closely

a 3d moving mesh finite element method for two phase flows a 3d ale finite element method is developed to study two phase flow phenomena using a new discretization method to compute the surface tension forces the computational method is based on the arbitrary lagrangian eulerian formulation ale and the finite element method fem creating a two phase method with an improved model for the liquid gas interface an adaptive mesh update procedure is also proposed for effective management of the mesh to remove add and repair elements since the computational mesh nodes move according to the flow the ale description explicitly defines the two phase interface position by a set of interconnected nodes which ensures a sharp representation of the boundary including the role of the surface tension the proposed methodology for computing the curvature leads to accurate results with moderate programming effort and computational cost static and dynamic tests have been carried out to validate the method and the results have compared well to analytical solutions and experimental results found in the literature demonstrating that the new proposed methodology provides good accuracy to describe the interfacial forces and bubble dynamics this paper focuses on the description of the proposed methodology with particular emphasis on the discretization of the surface tension force the new remeshing technique and the validation results additionally a microchannel simulation in complex geometry is presented for two elongated bubbles c 2014 elsevier inc all rights reserved

numerical stability of nonorthogonal fdtd methods in this paper a sufficient test for the numerical stability of generalized grid finite difference time domain fdtd schemes is presented it is shown that the projection operators of such schemes must be symmetric positive definite without this property such schemes can exhibit late time instabilities the origin and the characteristics of these late time instabilities are also uncovered based on this study nonorthogonal grid fdtd schemes nfdtd and the generalized yee gy methods are proposed that are numerically stable in the late time for quadrilateral prism elements allowing these methods to be extended to problems requiring very long time simulations the study of numerical stability that is presented is very general and can be applied to most solutions of maxwell s equations based on explicit time domain schemes

a finite volume method for the approximation of maxwell s equations in two space dimensions on arbitrary meshes a new finite volume method is presented for discretizing the two dimensional maxwell equations this method may be seen as an extension of the covolume type methods to arbitrary possibly non conforming or even non convex n sided polygonal meshes thanks to an appropriate choice of degrees of freedom an equivalent formulation of the scheme is given in terms of discrete differential operators obeying discrete duality principles the main properties of the scheme are its energy conservation its stability under a cfl like condition and the fact that it preserves gauss law and divergence free magnetic fields second order convergence is demonstrated numerically on non conforming and distorted meshes

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

a stitching method for the generation of unstructured meshes for use with co volume solution techniques abstract the successful implementation of co volume time domain solution techniques requires the use of high quality smooth dual meshes the generation of delaunay voronoi diagrams with these properties for two dimensional domains of complicated geometrical shape is considered in the adopted approach near boundary regions are discretised according to prescribed criteria and the remainder of the computational domain is discretised using an ideal mesh the two meshes are stitched together to provide a consistent mesh for the complete domain after smoothing the resulting mesh is found to be of a quality which exceeds that of meshes produced by standard automatic unstructured mesh generation methods examples involving electromagnetic wave scattering are included to demonstrate the computational performance that can be achieved with a co volume time domain solution algorithm on these meshes

the finite difference time domain fdtd and the finite volume time domain fvtd methods in solving maxwell s equations the finite difference time domain fdtd and its current generalizations have been demonstrated to be useful and powerful tools for the calculation of the radar cross section rcs of complicated objects the radiation of antennas in the presence of other structures and other applications the mathematical techniques for conformal fdtd have matured the primary impediments to its implementation are the complex geometries and material properties associated with the problem even under these circumstances fdtd is more flexible to implement because it is based on first principles instead of a clever mathematical trick this paper gives an account of some new results on conformal fdtd obtained by the authors and their associates at lockheed martin space company since 1988 the emphasis is on nonsmooth boundary condition simulation

a stable and consistent generalization of the fdtd technique to nonorthogonal unstructured grids a new way to extend the finite difference time domain fdtd technique to nonorthogonal grids is described in this paper the method whose theoretical foundations are based on the finite integration technique and on recently extended affine theories can be proven to be both stable and consistent in order to show its benefits the nonorthogonal fdtd is applied to the analysis of a cylindrical cavity and to the characterization of biconical antennas for ultrawideband applications

a level set formulation of eulerian interface capturing methods for incompressible fluid flows a level set formulation is derived for incompressible immiscible navier stokes equations separated by a free surface the interface is identified as the zero level set of a smooth function eulerian finite difference methods based on this level set formulation are proposed these methods are robust and efficient and are capable of computing interface singularities such as merging and reconnection numerical experiments are presented to demonstrate the effectiveness of the methods

numerical study of wall effects on buoyant gas bubble rise in a liquid filled finite cylinder the wall effects on the axisymmetric rise and deformation of an initially spherical gas bubble released from rest in a liquid filled finite circular cylinder are numerically investigated the bulk and gas phases are considered incompressible and immiscible the bubble motion and deformation are characterized by the morton number mo eotvos number eo reynolds number re weber number we density ratio viscosity ratio the ratios of the cylinder height and the cylinder radius to the diameter of the initially spherical bubble h h d 0 r r d 0 bubble rise in liquids described by eo and mo combinations ranging from 1 0 01 to 277 5 0 092 as appropriate to various terminal state reynolds numbers re t and shapes have been studied the range of terminal state reynolds numbers includes 0 02 re t 70 bubble shapes at terminal states vary from spherical to intermediate spherical cap skirted the numerical procedure employs a front tracking finite difference method coupled with a level contour reconstruction of the front this procedure ensures a smooth distribution of the front points and conserves the bubble volume for the wide range of eo and mo examined bubble motion in cylinders of height h 8 and r 3 is noted to correspond to the rise in an infinite medium both in terms of reynolds number and shape at terminal state in a thin cylindrical vessel small r the motion of the bubble is retarded due to increased total drag and the bubble achieves terminal conditions within a short distance from release the wake effects on bubble rise are reduced and elongated bubbles may occur at appropriate conditions for a fixed volume of the bubble increasing the cylinder radius may result in the formation of well defined rear recirculatory wakes that are associated with lateral bulging and skirt formation the paper includes figures of bubble shape regimes for various values of r eo mo and re t our predictions agree with existing results reported in the literature

particle swarm optimization for determining fuzzy measures from data fuzzy measures and fuzzy integrals have been successfully used in many real applications how to determine fuzzy measures is the most difficult problem in these applications though there have existed some methodologies for solving this problem such as genetic algorithms gradient descent algorithms and neural networks it is hard to say which one is more appropriate and more feasible each method has its advantages and limitations therefore it is necessary to develop new methods or techniques to learn distinct fuzzy measures in this paper we make the first attempt to design a special particle swarm algorithm to determine a type of general fuzzy measures from data and demonstrate that the algorithm is effective and efficient furthermore we extend this algorithm to identify and revise other types of fuzzy measures to test our algorithms we compare them with the basic particle swarm algorithms gradient descent algorithms and genetic algorithms in literatures in addition for verifying whether our algorithms are robust in noisy situations a number of numerical experiments are conducted theoretical analysis and experimental results show that for determining fuzzy measures the particle swarm optimization is feasible and has a better performance than the existing genetic algorithms and gradient descent algorithms

fdtd simulations of tem horns and the implications for staircased representations two dimensional 2 d tem horns are modeled using the finite difference time domain fdtd method the boundary walls are perfect electric conductors and one wall which does not align with the cartesian grid is approximated using a staircased representation by carefully comparing the fdtd results to those of the analytic solution one can make conclusions about the coarseness with which a boundary can be represented it is found that staircasing errors are small when the staircase diagonal the hypotenuse of the right triangle created by the stairstep is smaller than half a wavelength at the highest significant frequency in the excitation this rule of thumb is put forward as a necessary condition for the discretization of general problems results are also provided for some simple fdtd schemes that are designed to reduce staircasing errors by using large aspect ratio cells a grid can be constructed that satisfies the rule of thumb given above while this approach eliminates general staircasing errors some errors persist owing to the presence of step discontinuities immediately adjacent to the horn feed these errors can be further reduced by using a cell splitting approach it is shown that the contour path fdtd technique can be used to eliminate nearly all staircasing errors while some additional improvement is shown to be provided by using a stabilized contour path fdtd approach finally a recently proposed conformal technique that permits simple implementation is shown to provide results comparable with those of the stabilized contour path approach

level set methods an overview and some recent results the level set method was devised by s osher and j a sethian 1988 j comput phys 79 12 49 as a simple and versatile method for computing and analyzing the motion of an interface in two or three dimensions bounds a possibly multiply connected region the goal is to compute and analyze the subsequent motion of under a velocity field v this velocity can depend on position time the geometry of the interface and the external physics the interface is captured for later time as the zero level set of a smooth at least lipschitz continuous function x t i e t x x t 0 is positive inside negative outside and is zero on t topological merging and breaking are well defined and easily performed in this review article we discuss recent variants and extensions including the motion of curves in three dimensions the dynamic surface extension method fast methods for steady state problems diffusion generated motion and the variational level set approach we also give a user s guide to the level set dictionary and technology and couple the method to a wide variety of problems involving external physics such as compressible and incompressible possibly reacting flow stefan problems kinetic crystal growth epitaxial growth of thin films vortex dominated flows and extensions to multiphase motion we conclude with a discussion of applications to computer vision and image processing

the immersed interface method for the navier stokes equations with singular forces abstract peskin s immersed boundary method has been widely used for simulating many fluid mechanics and biology problems one of the essential components of the method is the usage of certain discrete delta functions to deal with singular forces along one or several interfaces in the fluid domain however the immersed boundary method is known to be first order accurate and usually smears out the solutions in this paper we propose an immersed interface method for the incompressible navier stokes equations with singular forces along one or several interfaces in the solution domain the new method is based on a second order projection method with modifications only at grid points near or on the interface from the derivation of the new method we expect fully second order accuracy for the velocity and nearly second order accuracy for the pressure in the maximum norm including those grid points near or on the interface this has been confirmed in our numerical experiments furthermore the computed solutions are sharp across the interface nontrivial numerical results are provided and compared with the immersed boundary method meanwhile a new version of the immersed boundary method using the level set representation of the interface is also proposed in this paper

modeling merging and breakup in the moving mesh interface tracking method for multiphase flow simulations the three dimensional moving mesh interface tracking mmit method coupled with local mesh adaptations by quan and schmidt s p quan d p schmidt a moving mesh interface tracking method for 3d incompressible two phase flows j comput phys 221 2007 761 780 demonstrated the capability to accurately simulate multiphase flows to handle large deformation and also to perform interface pinch off for some specific cases however another challenge i e how to handle interface merging such as droplet coalescence has not been addressed in this paper we present a mesh combination scheme for interface connection and a more general mesh separation algorithm for interface breakup these two schemes are based on the conversion of liquid cells in one phase to another fluid by changing the fluid properties of the cells in the combination or separation region after the conversion the newly created interface is usually ragged and a local projection method is employed to smooth the interface extra mesh adaptation criteria are introduced to handle colliding interfaces with almost zero curvatures as the distance between the interfaces diminishes simulations of droplet pair collisions including both head on and off center coalescences show that the mesh adaptations are capable of resolving very small length scales and the mesh combination and mesh separation schemes can handle the topological transitions in multiphase flows the potential of our method to perform detailed investigations of droplet coalescence and breakup is also displayed

convergence analysis of a covolume scheme for maxwell s equations in three dimensions this paper contains error estimates for covolume discretizations of maxwell s equations in three space dimensions several estimates are proved first an estimate for a semi discrete scheme is given second the estimate is extended to cover the classical interlaced time marching technique third some of our unstructured mesh results are specialized to rectangular meshes both uniform and nonuniform by means of some additional analysis it is shown that the spatial convergence rate is one order higher than for the unstructured case

a boundary condition capturing method for poisson s equation on irregular domains interfaces have a variety of boundary conditions or jump conditions that need to be enforced the ghost fluid method gfm was developed to capture the boundary conditions at a contact discontinuity in the inviscid euler equations and has been extended to treat more general discontinuities such as shocks detonations and deflagrations and compressible viscous flows in this paper a similar boundary condition capturing approach is used to develop a new numerical method for the variable coefficient poisson equation in the presence of interfaces where both the variable coefficients and the solution itself may be discontinuous this new method is robust and easy to implement even in three spatial dimensions furthermore the coefficient matrix of the associated linear system is the standard symmetric matrix for the variable coefficient poisson equation in the absence of interfaces allowing for straightforward application of standard black box solvers

convergence analysis of fully discrete finite volume methods for maxwell s equations in nonhomogeneous media we will consider both explicit and implicit fully discrete finite volume schemes for solving three dimensional maxwell s equations with discontinuous physical coefficients on general polyhedral domains stability and convergence for both schemes are analyzed we prove that the schemes are second order accurate in time both schemes are proved to be first order accurate in space for the voronoi delaunay grids and second order accurate for nonuniform rectangular grids we also derive explicit expressions for the dependence on the physical parameters in all estimates

numerical simulation of 3d bubbles rising in viscous liquids using a front tracking method the rise of bubbles in viscous liquids is not only a very common process in many industrial applications but also an important fundamental problem in fluid physics an improved numerical algorithm based on the front tracking method originally proposed by tryggvason and his co workers has been validated against experiments over a wide range of intermediate reynolds and bond numbers using an axisymmetric model j hua j lou numerical simulation of bubble rising in viscous liquid j comput phys 22 2007 769 795 in the current paper this numerical algorithm is further extended to simulate 3d bubbles rising in viscous liquids with high reynolds and bond numbers and with large density and viscosity ratios representative of the common air water two phase flow system to facilitate the 3d front tracking simulation mesh adaptation is implemented for both the front mesh on the bubble surface and the background mesh on the latter mesh the governing navier stokes equations for incompressible newtonian flow are solved in a moving reference frame attached to the rising bubble specifically the equations are solved using a finite volume scheme based on the semi implicit method for pressure linked equations simple algorithm and it appears to be robust even for high reynolds numbers and high density and viscosity ratios the 3d bubble surface is tracked explicitly using an adaptive unstructured triangular mesh the numerical model is integrated with the software package paramesh a block based adaptive mesh refinement amr tool developed for parallel computing paramesh allows background mesh adaptation as well as the solution of the governing equations in parallel on a supercomputer further peskin distribution function is applied to interpolate the variable values between the front and the background meshes detailed sensitivity analysis about the numerical modeling algorithm has been performed the current model has also been applied to simulate a number of cases of 3d gas bubbles rising in viscous liquids e g air bubbles rising in water simulation results are compared with experimental observations both in aspect of terminal bubble shapes and terminal bubble velocities in addition we applied this model to simulate the interaction between two bubbles rising in a liquid which illustrated the model s capability in predicting the interaction dynamics of rising bubbles

divergence preserving discrete surface integral methods for maxwell s curl equations using non orthogonal unstructured grids abstract several new discrete surface integral methods for solving maxwell s equations in the time domain are presented these methods which allow the use of general non orthogonal mixed polyhedral unstructured grids are direct generalizations of the canonical staggered grid finite difference method these methods are conservative in that they locally preserve divergence or charge employing mixed polyhedral cells hexahedral tetrahedral etc these methods allow more accurate modeling of non rectangular structures and objects because the traditional stair stepped boundary approximations associated with the orthogonal grid based finite difference methods can be avoided numerical results demonstrating the accuracy of these new methods are presented

capturing the behavior of bubbles and drops using the variational level set approach we reproduce the general behavior of complicated bubble and droplet motions using the variational level set formulation introduced by the authors earlier our approach here ignores inertial effects thus the motion is only correct as an approximation for very viscous problems however the steady states are true equilibrium solutions inertial forces will be added in future work the problems include soap bubbles colliding and merging drops falling or remaining attached to a generally irregular ceiling and liquid penetrating through a funnel in both two and three dimensions each phase is identified with a particular level set function the zero level set of this function is that particular phase boundary the level set functions all evolve in time through a constrained gradient descent procedure so as to minimize an energy functional the functions are coupled through physical constraints and through the requirements that different phases do not overlap and vacuum regions do not develop both boundary conditions and inequality constraints are cast in terms of either local or global equality constraints the gradient projection method leads to a system of perturbed by curvature if surface tension is involved hamilton jacobi equations coupled through a constraint the coupling is enforced using the lagrange multiplier associated with this constraint the numerical implementation requires much of the modern level set technology in particular we achieve a significant speed up by using the fast localization algorithm of h k zhao m kang b merriman d peng and s osher

fuzzy clustering of time series in the frequency domain traditional and fuzzy cluster analyses are applicable to variables whose values are uncorrelated hence in order to cluster time series data which are usually serially correlated one needs to extract features from the time series the values of which are uncorrelated the periodogram which is an estimator of the spectral density function of a time series is a feature that can be used in the cluster analysis of time series because its ordinates are uncorrelated additionally the normalized periodogram and the logarithm of the normalized periodogram are also features that can be used in this paper we consider a fuzzy clustering approach for time series based on the estimated cepstrum the cepstrum is the spectrum of the logarithm of the spectral density function we show in our simulation studies for the typical generating processes that have been considered fuzzy clustering based on the cepstral coefficients performs very well compared to when it is based on other features

a boundary condition capturing method for incompressible flame discontinuities abstract in this paper we propose a new numerical method for treating two phase incompressible flow where one phase is being converted into the other e g the vaporization of liquid water we consider this numerical method in the context of treating discontinuously thin flame fronts for incompressible flow this method was designed as an extension of the ghost fluid method 1999 j comput phys 152 457 and relies heavily on the boundary condition capturing technology developed in liu et al 2000 j comput phys 154 15 for the variable coefficient poisson equation and in kang et al in press j comput phys for multiphase incompressible flow our new numerical method admits a sharp interface representation similar to the method proposed in helenbrook et al 1999 j comput phys 148 366 since the interface boundary conditions are handled in a simple and straightforward fashion the code is very robust e g no special treatment is required to treat the merging of flame fronts the method is presented in three spatial dimensions with numerical examples in one two and three spatial dimensions

a front tracking method for viscous incompressible multi fluid flows abstract a method to simulate unsteady multi fluid flows in which a sharp interface or a front separates incompressible fluids of different density and viscosity is described the flow field is discretized by a conservative finite difference approximation on a stationary grid and the interface is explicitly represented by a separate unstructured grid that moves through the stationary grid since the interface deforms continuously it is necessary to restructure its grid as the calculations proceed in addition to keeping the density and viscosity stratification sharp the tracked interface provides a natural way to include surface tension effects both two and three dimensional full numerical simulations of bubble motion are presented

conservative and bounded volume of fluid advection on unstructured grids abstract this paper presents a novel eulerian lagrangian piecewise linear interface calculation plic volume of fluid vof advection method which is three dimensional unsplit and discretely conservative and bounded the approach is developed with reference to a collocated node based finite volume two phase flow solver that utilizes the median dual mesh constructed from non convex polyhedra the proposed advection algorithm satisfies conservation and boundedness of the liquid volume fraction irrespective of the underlying flux polyhedron geometry which differs from contemporary unsplit vof schemes that prescribe topologically complicated flux polyhedron geometries in efforts to satisfy conservation instead of prescribing complicated flux polyhedron geometries which are prone to topological failures our vof advection scheme the non intersecting flux polyhedron advection nifpa method builds the flux polyhedron iteratively such that its intersection with neighboring flux polyhedra and any other unavailable volume is empty and its total volume matches the calculated flux volume during each iteration a candidate nominal flux polyhedron is extruded using an iteration dependent scalar the candidate is subsequently intersected with the volume guaranteed available to it at the time of the flux calculation to generate the candidate flux polyhedron the difference in the volume of the candidate flux polyhedron and the actual flux volume is used to calculate extrusion during the next iteration the choice in nominal flux polyhedron impacts the cost and accuracy of the scheme however it does not impact the methods underlying conservation and boundedness as such various robust nominal flux polyhedron are proposed and tested using canonical periodic kinematic test cases zalesak s disk and two and three dimensional deformation the tests are conducted on the median duals of a quadrilateral and triangular primal mesh in two dimensions and on the median duals of a hexahedral wedge and tetrahedral primal mesh in three dimensions comparisons are made with the adaptation of a conventional unsplit vof advection scheme to our collocated node based flow solver depending on the choice in the nominal flux polyhedron the nifpa scheme presented accuracies ranging from zeroth to second order and calculation times that differed by orders of magnitude for the nominal flux polyhedra which demonstrate second order accuracy on all tests and meshes the nifpa method s cost was comparable to the traditional topologically complex second order accurate vof advection scheme

hybrid multifluid algorithms extensions of many successful single component schemes to compute multicomponent gas dynamics suffer from oscillations and other computational inaccuracies near material interfaces that are caused by the failure of the schemes to maintain pressure equilibrium between the fluid components a new algorithm based on the compressible euler equations for multicomponent fluids augmented by the pressure evolution equation is presented the extended set of equations offers two alternative ways to update the pressure field i using the equation of state or ii using the pressure evolution equation in a numerical implementation these two procedures generally yield different answers the former is a standard conservative update but may produce oscillations near material interfaces the latter is nonconservative but becomes exact near interfaces and automatically maintains pressure equilibrium a hybrid scheme which selects from the two pressure update procedures is presented the scheme perfectly conserves total mass and momentum and conserves total energy everywhere except at a finite very small number of grid cells computed solutions exhibit oscillation free interfaces and have em negligible relative conservation errors in total energy even for very strong shocks the proposed hybrid approach and switching strategies are independent of the numerical implementation and may provide a simple framework within which to extend one s favourite scheme to solve multifluid dynamics

a front tracking method for the computations of multiphase flow direct numerical simulations of multiphase flows using a front tracking method are presented the method is based on writing one set of governing equations for the whole computational domain and treating the different phases as one fluid with variable material properties interfacial terms are accounted for by adding the appropriate sources as functions at the boundary separating the phases the unsteady navier stokes equations are solved by a conventional finite volume method on a fixed structured grid and the interface or front is tracked explicitly by connected marker points interfacial source terms such as surface tension are computed on the front and transferred to the fixed grid advection of fluid properties such as density is done by following the motion of the front the method has been implemented for fully three dimensional flows as well as for two dimensional and axisymmetric ones first the method is described for the flow of two or more isothermal phases the representation of the moving interface and its dynamic restructuring as well as the transfer of information between the moving front and the fixed grid are discussed applications and extensions of the method to homogeneous bubbly flows atomization flows with variable surface tension solidification and boiling are then presented

motion of curves in three spatial dimensions using a level set approach the level set method was originally designed for problems dealing with codimension one objects where it has been extremely succesful especially when topological changes in the interface i e merging and breaking occur attempts have been made to modify it to handle objects of higher codimension such as vortex filaments while preserving the merging and breaking property we present numerical simulations of a level set based method for moving curves in r3 the model problem for higher codimension that allows for topological changes a vector valued level set function is used with the zero level set representing the curve our results show that this method can handle many types of curves moving under all types of geometrically based flows while automatically enforcing merging and breaking

a moving mesh interface tracking method for 3d incompressible two phase flows an interface tracking method using an unstructured moving mesh has been developed for simulating three dimensional incompressible and immiscible two phase flows the interface mesh is moved in a lagrangian fashion a local mesh adaptation method is used to capture the changing interface curvature maintain good mesh quality and deal with large deformation the interface is of zero thickness so the jump and continuity conditions across the interface are implemented directly without any smoothing of the properties of the two fluids this is theoretically beneficial compared to other methods that allow the fluids properties to continuously vary in an interface region the curvature for interfacial tension calculation is geometrically computed by a least squares parabola fitting method a mesh separation scheme for interfacial flows is employed to handle topological transition the numerical technique is tested and validated by several cases which include a two layer couette flow an oscillating droplet surrounded by gas and a droplet in shear flow the results obtained from numerical simulations are found to be in excellent agreement with analytical solutions and experimental results a collapsing ligament in a quiescent gas flow and a modulated jet pinching are simulated to show the robustness of the method

interfacial dynamics for stokes flow theoretical and computational aspects of the method of interfacial dynamics for flow at vanishing reynolds number are considered the mathematical formulation relies on the boundary integral representation that expresses the flow in terms of distributions of stokes flow singularities over the interfaces the densities of the distributions are identified with the jump in the hydrodynamic traction due to interfacial in plane and transverse tensions the interfacial velocity or the strength of a hydrodynamic potential the numerical procedure involves describing the interfaces in terms of interfacial marker points that reproduce the evolving shapes of the interfaces by global or local interpolation solving integral equations of the second kind for the interfacial velocity or for the density of a hydrodynamic potential and computing the motion of the marker points while simultaneously updating interfacial fields relevant to the dynamics including the concentration of a surfactant and the position of interfacial point particles at an equilibrium configuration interfaces exhibiting isotropic tension elastic tensions viscous and incompressible behavior are considered the mathematical modeling of the tensions and bending moments developing over interfaces with a membrane like constitution is discussed in the context of the theory of thin shells to facilitate the numerical implementation the coupling of the interfacial mechanics to the hydrodynamics by means of interface force and torque balances is formulated in global cartesian coordinates recent progress in the implementation of boundary element methods is reviewed and areas for further research are identified

numerical dispersion and stability characteristics of time domain methods on nonorthogonal meshes the familiar finite difference time domain method for discretizing maxwell s curl equations on orthogonal grids has been extended to nonorthogonal grids by a number of researchers while it is difficult to determine the dispersion and stability characteristics of these methods when applied on arbitrary grids analysis of the idealized but representative case of a uniform skewed mesh proves to be quite tractable in 2 d this analysis demonstrates that numerical dispersion errors are small for well resolved spatial wavelengths and that these methods converge to the continuous space solution in the limit as the cell and time step sizes vanish grid anisotropy variations in wave propagation speed as a function of the propagation angle relative to the mesh coordinates increases as the mesh is skewed in spite of this there exist some angles where waves propagate through the skewed mesh with virtually no dispersion this analysis also provides a stability limit for the time step size in terms of geometrical mesh quantities

a novel ant based clustering algorithm using the kernel method a novel ant based clustering algorithm integrated with the kernel ack method is proposed there are two aspects to the integration first kernel principal component analysis kpca is applied to modify the random projection of objects when the algorithm is run initially this projection can create rough clusters and improve the algorithm s efficiency second ant based clustering is performed in the feature space rather than in the input space the distance between the objects in the feature space which is calculated by the kernel function of the object vectors in the input space is applied as a similarity measure the algorithm uses an ant movement model in which each object is viewed as an ant the ant determines its movement according to the fitness of its local neighbourhood the proposed algorithm incorporates the merits of kernel based clustering into ant based clustering comparisons with other classic algorithms using several synthetic and real datasets demonstrate that ack method exhibits high performance in terms of efficiency and clustering quality