material state remapping in computational solid mechanics a computational procedure for remapping material state information from one finite element mesh to another is described the procedure is useful in connection with evolving meshes for inelastic problems as for example occur in the context of fracture simulation and adaptive mesh refinement the proposed method is based on weak enforcement of equality between corresponding fields on the two meshes where piecewise constant fields on both meshes are generalized from the quadrature point values the essential algorithmic problem is that of calculating the volume partition of an arbitrary convex region with respect to a covering set of disjoint convex regions instead of geometrically resolving the associated intersections the problem is herein approximated by a constrained optimization problem which may be readily and efficiently solved computationally this formulation is a main contribution of the paper computational examples are given that illustrate the effectiveness of the proposed procedure copyright 2002 john wiley sons ltd

on a conjecture of voisin on the gonality of very general abelian varieties abstract we study orbits for rational equivalence of zero cycles on very general abelian varieties by adapting a method of voisin to powers of abelian varieties we deduce that for k at least 3 a very general abelian variety of dimension at least 2 k 2 has covering gonality greater than k this settles a conjecture of voisin we also discuss how upper bounds for the dimension of orbits for rational equivalence can be used to provide new lower bounds on other measures of irrationality in particular we obtain a strengthening of the alzati pirola bound on the degree of irrationality of abelian varieties

on the stability of the finite difference time domain method in this paper we give a necessary and sufficient condition for the stability of the finite difference time domain method fdtd method this is an explicit time stepping method that is used for solving transient electromagnetic field problems a necessary but not a sufficient condition for its stability is usually obtained by requiring that discrete fourier modes defined on the fdtd grid remain bounded as time stepping proceeds here we follow a different approach we rewrite the basic fdtd equations in terms of an iteration matrix and study the eigenvalue problem for this matrix from the analysis a necessary and sufficient condition for stability of the fdtd method follows moreover we show that for a particular time step the 2 norm of the fdtd iteration matrix is equal to the golden ratio

optimization based remap and transport a divide and conquer strategy for feature preserving discretizations this paper examines the application of optimization and control ideas to the formulation of feature preserving numerical methods with particular emphasis on the conservative and bound preserving remap constrained interpolation and transport advection of a single scalar quantity we present a general optimization framework for the preservation of physical properties and specialize it to a generic optimization based remap obr of mass density the latter casts remap as a quadratic program whose optimal solution minimizes the distance to a suitable target quantity subject to a system of linear inequality constraints the approximation of an exact mass update operator defines the target quantity which provides the best possible accuracy of the new masses without regard to any physical constraints such as conservation of mass or local bounds the latter are enforced by the system of linear inequalities in so doing the generic obr formulation separates accuracy considerations from the enforcement of physical properties we proceed to show how the generic obr formulation yields the recently introduced flux variable flux target fvft 1 and mass variable mass target mvmt 2 formulations of remap and then follow with a formal examination of their relationship using an intermediate flux variable mass target fvmt formulation we show the equivalence of fvft and mvmt optimal solutions to underscore the scope and the versatility of the generic obr formulation we introduce the notion of adaptable targets i e target quantities that reflect local solution properties extend fvft and mvmt to remap on the sphere and use obr to formulate adaptable conservative and bound preserving optimization based transport algorithms for cartesian and latitude longitude coordinate systems a selection of representative numerical examples on two dimensional grids demonstrates the computational properties of our approach

regular article on a class of pade finite volume methods a class of pade finite volume methods providing an improved spectral resolution is presented and compared with well known methods the formulation is based on the sliding averages of the variables and allows the computation of derivatives of all orders using the fourier analysis these methods are examined with respect to i order of accuracy ii spectral resolution iii boundary conditions and iv stability

scaling symmetric positive definite matrices to prescribed row sums we give a constructive proof of a theorem of marshall and olkin that any real symmetric positive definite matrix can be symmetrically scaled by a positive diagonal matrix to have arbitrary positive row sums we give a slight extension of the result showing that given a sign pattern there is a unique diagonal scaling with that sign pattern and we give upper and lower bounds on the entries of the scaling matrix

a synchronous and iterative flux correction formalism for coupled transport equations many problems of fluid dynamics involve the coupled transport of several density like dependent variables for instance densities of mass and momenta in elastic flows in this paper a conservative and synchronous flux corrected transport fct formalism is developed which aims at a consistent transport of such variables the technique differs from traditional fct algorithms in two respects first the limiting of transportive fluxes of the primary variables e g mass and momentum does not derive from smooth estimates of the variables but it derives from analytic constraints implied by the lagrangian form of the governing continuity equations which are imposed on the specific mixing ratios of the variables e g velocity components second the traditional fct limiting based on sufficiency conditions is augmented by an iterative procedure which approaches the necessity requirements this procedure can also be used in the framework of traditional fct schemes and a demonstration is provided that it can significantly reduce some of the pathological behaviors of fct algorithms although the approach derived is applicable to the transport of arbitrary conserved quantities it is particularly useful for the synchronous transport of mass and momenta in elastic flows where it assures intrinsic stability of the algorithm regardless of the magnitude of the mass density variable this latter property becomes especially important in fluids with large density variations or in models with a material vertical coordinate e g geophysical hydrostatic stratified flows in isopycnic isentropic coordinates where material surfaces can collapse to zero mass layers admitting therefore arbitrarily large local courant numbers

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

perfectly matched layer for the time domain finite element method a new perfectly matched layer pml formulation for the time domain finite element method is described and tested for maxwell s equations in particular we focus on the time integration scheme which is based on galerkin s method with a temporally piecewise linear expansion of the electric field the time stepping scheme is constructed by forming a linear combination of exact and trapezoidal integration applied to the temporal weak form which reduces to the well known newmark scheme in the case without pml extensive numerical tests on scattering from infinitely long metal cylinders in two dimensions show good accuracy and no signs of instabilities for a circular cylinder the proposed scheme indicates the expected second order convergence toward the analytic solution and gives less than 2 root mean square error in the bistatic radar cross section rcs for resolutions with more than 10 points per wavelength an ogival cylinder which has sharp corners supporting field singularities shows similar accuracy in the monostatic rcs

toward an oscillation free mass conservative eulerian lagrangian transport model ten numerical schemes to reduce spurious oscillations in transport simulations were implemented and tested in a eulerian lagrangian control volume finite element model the schemes included both new and existing flux corrected transport fct algorithms and nonlinear filters the ability of the methods to eliminate numerical oscillations while preserving mass and minimizing the introduction of numerical diffusion was compared in 2d tests of varying complexity the application of local mass correction algorithms was shown to be vital to avoid the introduction of mass errors by fct while none of the methods emerged as optimal for all cases a new fct method with a local mass correction scheme and a nonlinear filter can be recommended as the best approaches in general the method of choice depends on the problem being solved in particular on the concentration gradients and on the grid resolution

generalized scalings satisfying linear equations abstract we unify and generalize a broad class of problems referred in the literature as scaling problems by extending the applicability of a formulation suggested recently by bapat and raghavan specifically let a r n b r m and c r m n be given where a is strictly positive a c scaling of the vector a is defined to be a vector a r n with a i a i m k 1 u c kj k for some strictly positive vector u r m the problem of finding a c scaling of the vector a which satisfies the linear system cx b will be called a generalized scaling problem in this paper it is shown that previously studied matrix scaling problems e g finding scalings with prespecified row sums and column sums or finding scalings with row sums equaling the corresponding column sums or finding scalings of multidimensional matrices with prespecified margins are special instances of generalized scaling problems generalized scaling problems are reduced to convex optimization problems and the reduction is used to characterize solutions to develop necessary and sufficient conditions for their existence to establish uniqueness results and to characterize approximate solutions

multidimensional upwind methods for hyperbolic conservation laws abstract we present a class of second order conservative finite difference algorithms for solving numerically time dependent problems for hyperbolic conservation laws in several space variables these methods are upwind and multidimensional in that the numerical fluxes are obtained by solving the characteristic form of the full multidimensional equations at the zone edge and that all fluxes are evaluated and differenced at the same time in particular operator splitting is not used correct behavior at discontinuities is obtained by the use of solutions to the riemann problem and by limiting some of the second order terms numerical results are presented which show that the methods described here yield the same high resolution as the corresponding operator split methods

compatible fluxes for van leer advection application of the standard second order upstream centered advection method of van leer to a coupled transport equation system of the form t a a u 0 can produce artificial extrema in the ratiot a even thoughtsatisfies a simple advection equation and is expected to preserve monotonicity hereuis velocity is mass density andais a conserved quantity such as momentum density energy density or chemical species density thustis a mass specific transport quantity such as velocity energy per unit mass temperature or species mass fraction a new flux formulation and gradient limiting procedure is presented here which eliminates these artificial extrema preserves the second order accuracy and preserves the monotone character of the van leer method even in the limit of vanishing mass density such a formulation is calledcompatible the method is noniterative i e explicit and can be employed in a general finite volume framework sample results for the transport of a square wave in one and two dimensions are provided

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

hybrid time domain solvers for the maxwell equations in 2d numerical simulation is an important tool in understanding the electromagnetic field and how it interacts with the environment different topics for time domain finite difference fdtd and finite element fetd methods for maxwell s equations are treated in this thesis subcell models are of vital importance for the efficient modeling of small objects that are not resolved by the grid a novel model for thin sheets using shell elements is proposed this approach has the advantage of taking into account discontinuities in the normal component of the electric field unlike previous models based on impedance boundary conditions ibcs several results are presented to illustrate the capabilities of the shell element approach waveguides are of fundamental importance in many microwave applications for example in antenna feeds the key issues of excitation and truncation of waveguides are addressed a complex frequency shifted form of the uniaxial perfectly matched layer upml absorbing boundary condition abc in fetd is developed prism elements are used to promote automatic grid generation and enhance the performance results are presented where reflection errors below 70db are obtained for different types of waveguides including inhomogeneous cases excitation and analysis via the scattering parameters are achieved using waveguide modes computed by a general frequency domain mode solver for the vector helmholtz equation huygens surfaces are used in both fdtd and fetd for excitation in waveguide ports inverse problems have received an increased interest due to the availability of powerful computers an important application is non destructive evaluation of material a time domain minimization approach is presented where exact gradients are computed using the adjoint problem the approach is applied to a general form of maxwell s equations including dispersive media and upml successful reconstruction examples are presented both using synthetic and experimental measurement data parameter reduction of complex geometries using simplified models is an interesting topic that leads to an inverse problem gradients for subcell parameters are derived and a successful reconstruction example is presented for a combined dielectric sheet and slot geometry

implementation of the jacobian free newton krylov method for solving the first order ice sheet momentum balance we have implemented the jacobian free newton krylov jfnk method for solving the first order ice sheet momentum equation in order to improve the numerical performance of the glimmer community ice sheet model glimmer cism the land ice component of the community earth system model cesm our jfnk implementation is based on significant re use of existing code for example our physics based preconditioner uses the original picard linear solver in glimmer cism for several test cases spanning a range of geometries and boundary conditions our jfnk implementation is 1 8 3 6 times more efficient than the standard picard solver in glimmer cism importantly this computational gain of jfnk over the picard solver increases when refining the grid global convergence of the jfnk solver has been significantly improved by rescaling the equation for the basal boundary condition and through the use of an inexact newton method while a diverse set of test cases show that our jfnk implementation is usually robust for some problems it may fail to converge with increasing resolution as does the picard solver globalization through parameter continuation did not remedy this problem and future work to improve robustness will explore a combination of picard and jfnk and the use of homotopy methods

on the convergence of power scaled cesaro sums abstract power scaling is combined with cesaro summation and necessary and sufficient local conditions are given for the resulting matrix sequence j n t to converge it is shown that this convergence is closely related to path conditions on the one hand as well as suitable bilinear consistency conditions on the other hand

galois closure and lagrangian varieties abstract let x be a complex projective variety and consider the morphism k k h 0 x x 1 h 0 x x k we use galois closures of finite rational maps to introduce a new method for producing varieties such that k has non trivial kernel we then apply our result to the two dimensional case and we construct a new family of surfaces which are lagrangian in their albanese variety moreover we analyze these surfaces computing their chern invariants and proving that they are not fibred over curves of genus g 2 the topological index of these surfaces is negative and this provides a counterexample to a conjecture on lagrangian surfaces formulated in barja et al 2007 3

a conservative semi lagrangian multi tracer transport scheme cslam on the cubed sphere grid a conservative multi tracer transport algorithm on the cubed sphere based on the semi lagrangian approach cslam has been developed the scheme relies on backward trajectories and the resulting upstream cells polygons are approximated with great circle arcs biquadratic polynomial functions are used for approximating the density distribution in the cubed sphere grid cells the upstream surface integrals associated with the conservative semi lagrangian scheme are computed as line integrals by employing the gauss green theorem the line integrals are evaluated using a combination of exact integrals and high order gaussian quadrature the upstream cell trajectories information and computation of weights of integrals can be reused for each additional tracer the cslam scheme is extensively tested with various standard benchmark test cases of solid body rotation and deformational flow in both cartesian and spherical geometry and the results are compared with those of other published schemes the cslam scheme is accurate robust and moreover the edges and vertices of the cubed sphere discontinuities do not affect the overall accuracy of the scheme the cslam scheme exhibits excellent convergence properties and has an option for enforcing monotonicity the advantages of introducing cross terms in the fully two dimensional biquadratic density distribution functions are also examined in the context of cartesian as well as the cubed sphere grid which has six local sub domains with discontinuous edges and corners

on symmetric products of curves let c be a smooth complex projective curve of genus g and let c be its second symmetric product this paper concerns the study of some attempts at extending to c the notion of gonality in particular we prove that the degree of irrationality of c is at least g 1 when c is generic and that the minimum gonality of curves through the generic point of c equals the gonality of c in order to produce the main results we deal with correspondences on the k fold symmetric product of c with some interesting linear subspaces of p enjoying a condition of cayley bacharach type and with monodromy of rational maps as an application we also give new bounds on the ample cone of c when c is a generic curve of genus 6 g 8

adaptive moment of fluid method a novel adaptive mesh refinement amr strategy based on the moment of fluid mof method for volume tracking of evolving interfaces is presented moment of fluid method is a new interface reconstruction and volume advection method using volume fractions as well as material centroids the mesh refinement criterion is based on the deviation of the actual centroid obtained by interface reconstruction from the reference centroid given by moment advection process the centroid error indicator detects not only high curvature regions but also regions with complicated subcell structures like filaments a new lagrange remap scheme is presented for advecting moments which includes lagrangian backtracking polygon intersection based remapping and forward tracking to define the material centroid the effectiveness and efficiency of amr mof method is demonstrated with classical test problems such as zalesak s disk and reversible vortex problem the comparison with previously published results for these problems shows the superior accuracy of the amr mof method over other methods in addition two new test cases with severe deformation rates are introduced namely droplet deformation and s shape deformation problems for further demonstration of the capabilities of the amr mof method

field singularities at metal dielectric wedges the wedges discussed are the dielectric wedge the metallic 90 deg corner on a dielectric plane and the adjacent 90 deg metallic and dielectric corners the field components perpendicular to the edge may become infinite according to a law 1 r n numerical data are given for n and plots of lines of force of bar e or bar h are shown

a cell by cell anisotropic adaptive mesh ale scheme for the numerical solution of the euler equations in this paper a cell by cell anisotropic adaptive mesh technique is added to an existing staggered mesh lagrange plus remap finite element ale code for the solution of the euler equations the quadrilateral finite elements may be subdivided isotropically or anisotropically and a hierarchical data structure is employed an efficient computational method is proposed which only solves on the finest level of resolution that exists for each part of the domain with disjoint or hanging nodes being used at resolution transitions the lagrangian equipotential mesh relaxation and advection solution remapping steps are generalised so that they may be applied on the dynamic mesh it is shown that for a radial sod problem and a two dimensional riemann problem the anisotropic adaptive mesh method runs over eight times faster

a high order finite volume remapping scheme for nonuniform grids a hierarchy of one dimensional high order remapping schemes is presented and their performance with respect to accuracy and convergence rate investigated the schemes are also compared based on remapping experiments in closed domains the piecewise quartic method pqm is presented based on fifth order accurate piecewise polynomials and is motivated by the need to significantly improve hybrid coordinate systems of ocean climate models which require the remapping to be conservative monotonic and highly accurate a limiter for this scheme is fully described that never decreases the polynomial degree except at the location of extrema we assess the use of high order explicit and implicit i e compact estimates for the edge values and slopes needed to build the piecewise polynomials in both piecewise parabolic method ppm and pqm it is shown that all limited pqm schemes perform significantly better than limited ppm schemes and that pqm schemes are much more cost effective

on complexity of matrix scaling abstract line sun scaling problem for a nonnegative matrix a is to find positive definite diagonal matrices y z which result in prescribed row and column sums of the scaled matrix yaz the matrix balancing problem for a nonnegative square matrix a is to find a positive definite diagonal matrix x such that the row sums in the scaled matrix xax are equal to the corresponding column sums we demonstrate that versions of both these problems same as those of other scaling problems for non negative multiindex arrays can be reduced to a specific geometric programming problem for the latter problem we develop a polynomial time algorithm thus deriving polynomial time solvability of a number of generic scaling problems for nonnegative multiindex arrays our results extend those previously known for the problems of matrix balancing 3 and of double stochastic scaling of a square nonnegative matrix 2

a hybrid time domain technique that combines the finite element finite difference and method of moment techniques to solve complex electromagnetic problems this paper describes a hybrid technique directly operating in time domain that combines the finite element time domain fetd the finite difference time domain fdtd and the integral equation based method of moments in the time domain momtd techniques to analyze complex electromagnetic problems involving thin wire antennas radiating in the presence of inhomogeneous dielectric bodies whose shape can be arbitrary the method brings together the ability of the fdtd scheme to deal with arbitrary material properties the versatility of the fetd to accurately model curved geometries and that of the mom to analyze thin wire structures working in the time domain provides wide band information from a single execution of the marching on in time procedure and simplifies the interfacing of the fe and mom methods with the fdtd an approach specifically designed for time domain analysis numerical results that validate the hybrid method and show its capabilities are presented in the paper

the repair paradigm new algorithms and applications to compressible flow the repair paradigm leads to several algorithms for redistributing mass momentum and energy while adhering to local maximum principles as an adjunct to the remapping step in certain compressible flow codes that use remapping such as arbitrary lagrangian eulerian codes or for just redistributing mass in advection codes in the case of advection of a concentration repair keeps the newly computed concentration in a cell between the maximum and minimum concentrations in neighboring old cells thus guaranteeing at least that the new concentration is between zero and one for compressible flow density velocity and internal energy are similarly constrained while maintaining conservation of mass momentum and total energy in this way positive density and internal energy are achieved as a side effect we propose a new algorithm combining both local and global repair that maintains causality and is efficient in a parallel computational setting the local global algorithm is independent of the order in which the distribution is performed and it maintains 1d symmetry this is applied to advection in two dimensions and to among others the leblanc problem the sedov problem and an interacting 2d blast wave problem the latter is done with a lagrangian code for which rezoning remapping and repair are essential

compatible energy conserving bounds preserving remap of hydrodynamic fields for an extended ale scheme abstract from the very origins of numerical hydrodynamics in the lagrangian work of von neumann and richtmyer 83 the issue of total energy conservation as well as entropy production has been problematic because of well known problems with mesh deformation lagrangian schemes have evolved into arbitrary lagrangian eulerian ale methods 39 that combine the best properties of lagrangian and eulerian methods energy issues have persisted for this class of methods we believe that fundamental issues of energy conservation and entropy production in ale require further examination the context of the paper is an ale scheme that is extended in the sense that it permits cyclic or periodic remap of data between grids of the same or differing connectivity the principal design goals for a remap method then consist of total energy conservation bounded internal energy and compatibility of kinetic energy and momentum we also have secondary objectives of limiting velocity and stress in a non directional manner keeping primitive variables monotone and providing a higher than second order reconstruction of remapped variables in particular the new contributions fall into three categories associated with energy conservation and entropy production reconstruction and bounds preservation of scalar and tensor fields and conservative remap of nonlinear fields the paper presents a derivation of the methods details of implementation and numerical results for a number of test problems the methods requires volume integration of polynomial functions in polytopal cells with planar facets and the requisite expressions are derived for arbitrary order

constrained interpolation remap of divergence free fields abstract a novel constrained interpolation algorithm for remapping of solenoidal face finite element vector fields is presented the algorithm is based on explicit recovery postprocessing and interpolation of a potential for the original vector field and a subsequent application of a curl operator to obtain the desired divergence free finite element field on the new mesh the use of interpolation instead of advection in the remap process offers valuable computational advantages old and new meshes are neither required to have the same connectivity nor to be close to each other slope limiting and upwinding which can be sensitive to grid structure are avoided and replaced by local optimization to control energy of the remapped field the new method is validated using a suite of cyclic remap problems on random and tensor product mesh sequences a comparison with a local remapper based on a constrained transport advection algorithm is also included

fractional sylvester gallai theorems we prove fractional analogs of the classical sylvester gallai theorem our theorems translate local information about collinear triples in a set of points into global bounds on the dimension of the set specifically we show that if for every points v in a finite set there are at least v other points u v for which the line through v u contains a third point in v then the v resides in a 13 2 dimensional affine subspace of this result which is one of several variants we study is motivated by questions in theoretical computer science and in particular from the area of error correcting codes our proofs combine algebraic analytic and combinatorial arguments a key ingredient is a new lower bound for the rank of design matrices specified only by conditions on their zero non zero pattern

conservative multimoment transport along characteristics for discontinuous galerkin methods a set of algorithms based on characteristic discontinuous galerkin methods is presented for tracer transport on the sphere the algorithms are designed to reduce message passing interface communica

brunn minkowski inequalities for contingency tables and integer flows we establish approximate log concavity for a wide family of combinatorially defined integer valued functions examples include the number of non negative integer matrices contingency tables with prescribed row and column sums margins as a function of the margins and the number of integer feasible flows in a network as a function of the excesses at the vertices as a corollary we obtain approximate log concavity for the kostant partition function of type a we also present an indirect evidence that at least some of the considered functions might be genuinely log concave

a theoretical study of the stability criteria for hybridized fdtd algorithms for multiscale analysis in this paper we propose two new hybrid two dimensional generalized finite difference time domain algorithms formulated by using the cell method and designed to analyze objects with fine details without using very small time steps dictated by the courant condition a detailed analysis of the stability of the proposed algorithms is presented with special attention devoted to the phenomenon of late time instabilities finally some rules are provided that would ensure the stability of the proposed algorithms

a multistep flux corrected transport scheme a multistep flux corrected transport mfct scheme is developed to achieve conservative and monotonic tracer transports for multistep dynamical cores mfct extends zalesak two time level scheme to any multistep time differencing schemes by including multiple high order fluxes in the antidiffusive flux while computing the two time level low order monotone solution the multistep time differencing scheme used in this study is the third order adams bashforth ab3 scheme implemented in a finite volume icosahedral shallow water model the accuracy of ab3 mfct is quantified by the shape preserving advection experiments in non divergent flow as well as a cosine bell whose shape changes during advection in shear flow ab3 mfct has been shown to be insensitive to time step size this make ab3 mfct an attractive transport scheme for explicit high resolution model applications with small time step mfct is tested in shallow water model simulations to demonstrate that the use of mfct maintains positive definite tracer transport while at the same time conserving both fluid mass and tracer mass within round off errors in the ab3 dynamic core

on irrationality of surfaces in p3 abstract the degree of irrationality irr x of a n dimensional complex projective variety x is the least degree of a dominant rational map x p n it is a well known fact that given a product x p m or a n dimensional variety y dominating x their degrees of irrationality may be smaller than the degree of irrationality of x in this paper we focus on smooth surfaces s p 3 of degree d 5 and we prove that irr s p m irr s for any integer m 0 whereas irr y irr s occurs for some y dominating s if and only if s contains a rational curve

incremental remapping as a transport advection algorithm there are two fundamentally different strategies for solving the standard transport or continuity equation corresponding to whether it is expressed as a partial differential equation or as an integral statement of conservation the more common approach is to discretize the partial differential equation and to march the solution forward in time the alternative method is to project cell volumes along lagrangian trajectories as far forward or backward in time as desired and then to remap the resulting density distribution onto some target mesh this latter approach is known as remapping remapping has many advantages not the least of which is that the time step is limited only by accuracy considerations but it tends to be expensive and complex in this paper we show that if the time step is made sufficiently short such that trajectories are confined to the nearest neighbor cells then the remapping may be written as a flux form transport algorithm and it becomes nearly as simple and efficient as standard transport schemes the resulting method called incremental remapping retains most of the advantages of general remapping these include a geometric basis for transport b compatibility of associated tracer transport with simple tracer advection i e retention of tracer monotonicity properties and c efficient handling of multiple tracers since each additional tracer adds only a relatively small incremental cost

the monotonic quartic spline method qsm for conservative transport problems a quartic spline based remapping algorithm is developed and illustrative tests of it are presented herein to ensure mass conservation the scheme solves an integral form of the transport equation rather than the differential form the integrals are computed from reconstructed quartic splines with mass conservation constraints for higher dimensions this remapping can be used within a standard directional splitting methodology or within the flow dependent cascade splitting approach a high order grid and sub grid based monotonic filter is also incorporated into the overall scheme this filter is independent of the underlying spline representation adopted here and is of more general application

existence of matrices with prescribed off diagonal block element maxima abstract necessary and sufficient conditions are proven for the existence of a real square matrix such that for every principal submatrix the maximal or minimal value of an element in the row complement of the submatrix is prescribed the problem is solved in the cases where the positions of the nonzero elements of a are contained in a given set of positions where the positions of the nonzero elements of a are all given and where there is no restriction on the positions of the nonzero elements of a the uniqueness of the solution is studied as well

a subcell remapping method on staggered polygonal grids for arbitrary lagrangian eulerian methods we describe a new remapping algorithm for use in arbitrary lagrangian eulerian ale simulations the new features of this remapper are designed to complement a staggered mesh lagrangian phase in which the cells may be general polygons in two dimensions and which uses subcell discretizations to control unphysical mesh distortion and hourglassing our new remapping algorithm consists of three stages a gathering stage in which we interpolate momentum internal energy and kinetic energy to the subcells in a conservative way a subcell remapping stage in which we conservatively remap mass momentum internal and kinetic energy from the subcells of the lagrangian mesh to the subcells of the new rezoned mesh a scattering stage in which we conservatively recover the primary variables subcell density nodal velocity and cell centered specific internal energy on the new rezoned mesh we prove that our new remapping algorithm is conservative reversible and satisfies the debar consistency condition we also demonstrate computationally that our new remapping method is robust and accurate for a series of test problems in one and two dimensions

a finite volume eulerian lagrangian localized adjoint method for solution of the advection dispersion equation a new mass conservative method for solution of the one dimensional advection dispersion equation is derived and discussed test results demonstrate that the finite volume eulerian lagrangian localized adjoint method fvellam outperforms standard finite difference methods in terms of accuracy and efficiency for solute transport problems that are dominated by advection for dispersion dominated problems the performance of the method is similar to that of standard methods like previous ellam formulations fvellam systematically conserves mass globally with all types of boundary conditions fvellam differs from other ellam approaches in that integrated finite differences instead of finite elements are used to approximate the governing equation this approach in conjunction with a forward tracking scheme greatly facilitates mass conservation the mass storage integral is numerically evaluated at the current time level and quadrature points are then tracked forward in time to the next level forward tracking permits straightforward treatment of inflow boundaries thus avoiding the inherent problem in backtracking as used by most characteristic methods of characteristic lines intersecting inflow boundaries fvellam extends previous ellam results by obtaining mass conservation locally on lagrangian space time elements details of the integration tracking and boundary algorithms are presented test results are given for problems in cartesian and radial coordinates

penalized maximum likelihood estimation the baum welch algorithm diagonal balancing of symmetric matrices and applications to training acoustic data we study penalized maximum likelihood estimation methods for nonparametric density estimation and propose their use in training acoustic models for speech recognition several algorithms for the numerical solution of the optimization problems that we encounter are proposed and analyzed

reprint of atmospheric models used for practical climate simulation must be capable handling the transport of hundreds of tracers for computational efficiency conservative multi tracer semi lagrangian type transport schemes are appropriate global models based on high order galerkin approach employ highly non uniform spectral element grids and semi lagrangian transport is a challenge on those grids a conservative semi lagrangian scheme spelt spectral element lagrangian transport employing a multi moment compact reconstruction procedure is developed for non uniform quadrilateral grids the scheme is based on a characteristic semi lagrangian method that avoids complex and expensive upstream area computations the spelt scheme has been implemented in the high order method modeling environment homme which is based on a cubed sphere grid with spectral element spatial discretization additionally we show the strong scalability and multi tracer efficiency using several benchmark tests the spelt solution can be made monotonic positivity preserving by combining the flux corrected transport algorithm which is demonstrated on a uniform resolution grid in particular spelt can be efficiently used for non uniform grids and provides accurate and stable results for high resolution meshes

optimization based mesh correction with volume and convexity constraints we consider the problem of finding a mesh such that 1 it is the closest with respect to a suitable metric to a given source mesh having the same connectivity and 2 the volumes of its cells match a set of prescribed positive values that are not necessarily equal to the cell volumes in the source mesh this volume correction problem arises in important simulation contexts such as satisfying a discrete geometric conservation law and solving transport equations by incremental remapping or similar semi lagrangian transport schemes in this paper we formulate volume correction as a constrained optimization problem in which the distance to the source mesh defines an optimization objective while the prescribed cell volumes mesh validity and or cell convexity specify the constraints we solve this problem numerically using a sequential quadratic programming sqp method whose performance scales with the mesh size to achieve scalable performance we develop a specialized multigrid based preconditioner for optimality systems that arise in the application of the sqp method to the volume correction problem numerical examples illustrate the importance of volume correction and showcase the accuracy robustness and scalability of our approach

stability of explicit implicit hybrid time stepping schemes for maxwell s equations an improved version of the stable fem fdtd hybrid method t rylander and a bondeson comput phys commun 125 75 2000 for maxwell s equations is presented the new formulation has a modified time stepping scheme and is rigorously proven to be stable for time steps up to the stability limit for the fdtd the new scheme gives less reflection at the boundary between the structured and unstructured grids than the original formulation the hybrid method is compared to the fdtd with staircasing for scattering from a conducting sphere the discretization errors of the hybrid show quadratic dependence on mesh size while the scaling is less clear for the fdtd the fdtd gives errors that are 5 60 times higher than that of the hybrid depending on resolution and staircasing strategy

tracer transport within an unstructured grid ocean model using characteristic discontinuous galerkin advection abstract in a previous article a characteristic discontinuous galerkin cdg advection scheme was presented for tracer transport lee et al 2016 the scheme is conservative unconditionally stable with respect to time step and scales sub linearly with the number of tracers being advected here we present the implementation of the cdg advection scheme for tracer transport within mpas ocean a boussinesque unstructured grid ocean model with an arbitrary lagrangian eulerian vertical coordinate the scheme is implemented in both the vertical and horizontal dimensions and special care is taken to ensure that the scheme remains conservative in the context of moving vertical layers consistency is ensured with respect to the dynamics by a renormalization of the fluxes with respect to the volume fluxes derived from the continuity equation for spherical implementations the intersection of the flux swept regions and the eulerian grid are determined for great circle arcs and the fluxes and element assembly are performed on the plane via a length preserving projection solutions are presented for a suite of test cases and comparisons made to the existing flux corrected transport scheme in mpas ocean

a forward trajectory global semi lagrangian transport scheme a forward trajectory semi lagrangian scheme for advection on the surface of the sphere is proposed the advection scheme utilizes the forward downstream trajectory originating at eulerian grid points and cascade interpolation a sequence of 1d interpolations to transfer data from the downstream lagrangian points to the eulerian points a new and more accurate algorithm determines pole values the resulting forward trajectory semi lagrangian scheme can easily incorporate high order trajectory integration methods this avoids the standard iterative process in a typical backward trajectory scheme two third order accurate schemes and a second order accurate scheme are presented a mass conservative version of the forward trajectory semi lagrangian scheme is also derived within the cascade interpolation framework mass from a lagrangian cell is transferred to the corresponding eulerian cell with two 1d remappings through an intermediate cell system mass in the polar region is redistributed by way of an efficient local approximation the resulting scheme is globally conservative but restricted to meridional courant number c 1

a finite volume formulation of compact central schemes on arbitrary structured grids in the present paper a formulation allowing the use of compact schemes in the finite volume context on arbitrary meshes is presented the proposed formulation is based on the use of an implicit formula to evaluate the fluxes on the cell faces a series of numerical experiments for a 2d model convection equation a flat plate a subsonic vortical problem as well as the les simulation of channel flow has been carried out the results indicate an important improvement in obtained accuracy compared to a standard central finite volume formulation

implementation of the jacobian free newton krylov method for solving the for solving the first order ice sheet momentum balance we have implemented the jacobian free newton krylov jfnk method for solving the rst order ice sheet momentum equation in order to improve the numerical performance of the community ice sheet model cism the land ice component of the community earth system model cesm our jfnk implementation is based on signicant re use of existing code for example our physics based preconditioner uses the original picard linear solver in cism for several test cases spanning a range of geometries and boundary conditions our jfnk implementation is 1 84 3 62 times more efficient than the standard picard solver in cism importantly this computational gain of jfnk over the picard solver increases when rening the grid global convergence of the jfnk solver has been signicantly improved by rescaling the equation for the basal boundary condition and through the use of an inexact newton method while a diverse set of test cases show that our jfnk implementation is usually robust for some problems it may fail to converge with increasing resolution as does the picard solver globalization through parameter continuation did not remedy this problem and future work to improve robustness will explore a combination of picard and jfnk and the use of homotopy methods

a newton krylov solver for remapping based volume of fluid methods a new conservative remapping method is presented here for generating multi dimensional fluxes used for the time integration of hyperbolic equations through single stage unsplit advection a solution to the lagrangian mesh location is generated that converges the volumes of all remapped flux definitions to the volumes of equivalent one dimensional flux definitions at their corresponding cell faces the method is most feasible within localized subdomains of an eulerian solution domain the main utility of the method is the generation of fluxes in the vicinity of discontinuities and sharp gradients that does not introduce physically spuriously extrema while locally conserving mass in generating solutions to lagrangian mesh location by solving a nonlinear equation system the new remap requires the anchoring of the lagrangian mesh removal of degrees of freedom to make the problem definite the method is based on characteristic tracing along trajectories assumed to be linear this paper investigates the convergence and sensitivity of the lagrangian mesh solver to mesh and timestep size in assessing its merit for application in transient cfd codes for single stage unsplit advection volume of fluid methods the new remap suppresses the introduction of undershoots overshoots and wisps in combination with a conservative remapping phase the new method for fixing the location of the lagrangian mesh eliminates the need for heuristic redistribution or clipping procedures for spurious extrema removal

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

on simplifying incremental remap based transport schemes the flux form incremental remapping transport scheme introduced by dukowicz and baumgardner 1 converts the transport problem into a remapping problem this involves identifying overlap areas between quadrilateral flux areas and regular square grid cells which is non trivial and leads to some algorithm complexity in the simpler swept area approach originally introduced by hirt et al 2 the search for overlap areas is eliminated even if the flux areas overlap several regular grid cells the resulting simplified scheme leads to a much simpler and robust algorithm we show that for sufficiently small courant numbers approximately cfl 1 2 the simplified or swept area scheme can be more accurate than the original incremental remapping scheme this is demonstrated through a von neumann stability analysis an error analysis and in idealized transport test cases on the sphere using the incremental remapping based scheme called ff cslam flux form version of the conservative semi lagrangian multi tracer scheme on the cubed sphere

scalings of matrices which have prespecified row sums and column sums via optimization abstract the problem of scaling a matrix so that it has given row and column sums is transformed into a convex minimization problem in particular we use this transformation to characterize the existence of such scaling or corresponding approximations we obtain new results as well as new streamlined proofs of known results

scalings of matrices satisfying line product constraints and generalizations abstract a scaling of a nonnegative matrix a is a matrix having the form a uav where u and v are square diagonal matrices which have positive diagonal elements if the matrix a is square and v u 1 we call a a symmetric scaling of a we consider two problems the first concerns the identification of a scaling of a given nonnegative matrix with prescribed row and column products the second concerns the problem of finding a symmetric scaling of a given nonnegative square matrix whose row products equal the corresponding column products for each of these two scaling problems we characterize the solutions in terms of a nonlinear convex optimization problem we use the characterization to demonstrate that feasibility of either scaling problem is equivalent to the existence of a matrix satisfying the target property and having the same pattern as the given matrix we establish uniqueness of solutions to either scaling problem whenever it is feasible and we develop algorithms for computing the desired unique scalings in the cases where the problem are feasible

a fast high resolution algorithm for linear convection problems particle transport method the paper is devoted to a novel explicit technique the particle transport method ptm for solving linear convection problems while being a lagrangian characteristic based method ptm has the advantage of eulerian methods to represent the solution on a fixed mesh the proposed approach belongs to the class of monotone high resolution numerical schemes possesses the property of unconditional stability and works with structured and unstructured meshes it is also demonstrated that the method has a linear computational complexity the performance of the presented algorithm is tested on one and two dimensional benchmark problems the numerical results confirm that the method has the 2nd order spatial accuracy and can be significantly faster than the grid based methods of the same order copyright 2006 john wiley sons ltd

order independence and factor convergence in iterative scaling abstract we prove two results concerning iterative scaling which have been claimed but not proved by other authors in the field iterative scaling is a procedure which begins with a probability measure q on a finite set x and a finite set of partition constraints on x it produces a sequence of iterates p0 q p1 pt in which each pt t 62 0 is an adjustment scaling of pt 1 to fit a single set of prescribed partition constraints under fairly general hypotheses the iterates pt converge to the unique probability p which simultaneously satisfies the given constraints and is exponentially equivalent to the starting measure q or equivalently which minimizes the i divergence d p q over all probabilities p on x which satisfy the constraints the first main result theorem 3 1 states that the convergence of iterative scaling to the unique limit is independent of the order in which the adjustments for the prescribed partition constraints are made provided each adjustment is made infinitely many times the second main result theorem 4 2 is that under certain commonly satisfied conditions each factor of the exponential form being built up within the algorithm one factor for each partition constraint converges separately a third group of results sections 5 6 provides an account of the relationship between the probability measures which satisfy all of the constraints and those which are exponentially equivalent to q

electric and magnetic losses modeled by a stable hybrid with explicit implicit time stepping for maxwell s equations a stable hybridization of the finite element method fem and the finite difference time domain fdtd scheme for maxwell s equations with electric and magnetic losses is presented for two dimensional problems the hybrid method combines the flexibility of the fem with the efficiency of the fdtd scheme and it is based directly on ampere s and faraday s law the electric and magnetic losses can be treated implicitly by the fem on an unstructured mesh which allows for local mesh refinement in order to resolve rapid variations in the material parameters and or the electromagnetic field it is also feasible to handle larger homogeneous regions with losses by the explicit fdtd scheme connected to an implicitly time stepped and lossy fem region the hybrid method shows second order convergence for smooth scatterers the bistatic radar cross section rcs for a circular metal cylinder with a lossy coating converges to the analytical solution and an accuracy of 2 is achieved for about 20 points per wavelength the monostatic rcs for an airfoil that features sharp corners yields a lower order of convergence and it is found to agree well with what can be expected for singular fields at the sharp corners a careful convergence study with resolutions from 20 to 140 points per wavelength provides accurate extrapolated results for this non trivial test case which makes it possible to use as a reference problem for scattering codes that model both electric and magnetic losses

second order accurate volume tracking based on remapping for triangular meshes this paper presents a second order accurate piecewise linear volume tracking based on remapping for triangular meshes this approach avoids the complexity of extending unsplit second order volume of fluid algorithms advection methods on triangular meshes the method is based on lagrangian eulerian le methods therefore it does not deal with edge fluxes and corner fluxes flux corrections as is typical in advection algorithms the method is constructed of three parts a lagrangian phase a reconstruction phase and a remapping phase in the lagrangian phase the original eulerian grid is projected along trajectories to obtain lagrangian grids in practice this projection is handled through the time integration of velocity field for grid vertices at each time step the reconstruction is based on truncating the volume material polygon for each lagrangian mixed grid since in piecewise linear approximation the interface is represented by a segment line the polygon material truncation is mainly finding the segment interface finding the segment interface is calculating the line normal and line constant at each multi fluid cell details of applying two normal calculation methods differential and geometric least squares gls methods are given while the gls method exhibits second order accurate approximation in reproducing circular interfaces the differential least squares dls method results in a first order accurate representation of the interface the last part of the algorithm which is remapping of the volume materials from the lagrangian grid to the original one is performed by a series of polygon intersection procedures the behavior of the algorithm is investigated for flow fields with constant interface topology and flow fields inducing large interfacial stretching and tearing second order accuracy is obtained if the velocity integration as well as the reconstruction steps are at least second order accurate

matrix scaling entropy minimization and conjugate duality i existence conditions abstract we have four primary objectives in this paper first we introduce a problem called truncated matrix scaling that generalizes two well studied matrix scaling problems diagonal similarity scaling and fixed row column equivalence scaling second we derive necessary and sufficient conditions for the attainment of the infimum in the fenchel dual of a class of convex optimization problems third we show that existence of a solution for truncated matrix scaling is equivalent to the attainment of the infimum in a corresponding dual optimization problem we thereby derive necessary and sufficient conditions for the existence of a solution for truncated matrix scaling fourth we derive known existence conditions for similarity and equivalence scaling from the conditions for truncated matrix scaling

an improved finite element flux corrected transport algorithm an improved finite element flux corrected transport fe fct method for the numerical solution of hydrodynamic conservation equations is described based on the method developed by lohner and his collaborators to solve conservation equations in fluid mechanics and its application is extended to gas discharge problems the high and low order schemes used are the ones proposed by lohner who adds diffusion to the high order scheme by subtracting the lumped mass matrix from the consistent mass matrix to give the low order scheme the diffusion coefficient is adjusted globally a variable diffusion coefficient is introduced it is assumed to be constant in each element and is shown to transform the high order solution to a scheme equivalent to an upwind scheme which has minimal diffusion but ensures positive results this avoids the complexity of upwinding in fe especially in two dimensions it is also shown that the correct amount of real diffusion may be easily added to the algorithm when required for example for electrons results are presented which show that the high order scheme reduces to the upwind difference scheme when the new diffusion is used the proposed fct scheme is shown to give similar results in comparison with a fourth order fd fct algorithm finally the new method is applied to a streamer propagation problem in one dimension and the results obtained are shown to agree well with previously published results

the repair paradigm and application to conservation laws repair is a conservative post processing procedure to be used in numerical methods for hyperbolic conservation laws in order to preserve certain qualitative characteristics of the numerical solution such as positivity of density and internal energy by means of redistribution of conserved quantities such as mass momentum and total energy among the cells of the mesh in this paper we describe the repair paradigm and prove several theorems which form a theoretical foundation for the repair procedures we consider two applications of repair and present corresponding numerical results the first application deals with improving properties of the remapping conservative interpolation stage of arbitrary lagrangian eulerian ale methods for the gas dynamics equations in which the solution is conservatively transferred from one mesh to another one requirement for remapping is that the interpolated density and internal energy on the new mesh have to stay positive another desirable property is that the remapping procedure should not create new extrema for the velocity field for various reasons these properties may not be satisfied especially for high order methods repair plays a supplemental role by bringing gas dynamics quantities into physically justified bounds another application of repair is to improve the quality of numerical methods for advection of some scalar tracer field with prescribed divergence free velocity field in which case the advection equation can be written as a conservation law and therefore the total amount of tracer is conserved we show how the repair procedure allows us to reduce oscillations in a numerical solution obtained by a formally high order method repair offers an alternative to more classical methods of reducing oscillations and maintaining positivity

a semi lagrangian discontinuous galerkin method for scalar advection by incompressible flows a new conservative semi lagrangian formulation is proposed for the discretization of the scalar advection equation in flux form the approach combines the accuracy and conservation properties of the discontinuous galerkin dg method with the computational efficiency and robustness of semi lagrangian sl techniques unconditional stability in the von neumann sense is proved for the proposed discretization in the one dimensional case a monotonization technique is then introduced based on the flux corrected transport approach this yields a multi dimensional monotonic scheme for the piecewise constant component of the computed solution that is characterized by a smaller amount of numerical diffusion than standard dg methods the accuracy and stability of the method are further demonstrated by two dimensional tracer advection tests in the case of incompressible flows the comparison with results obtained by standard sl and dg methods highlights several advantages of the new technique

an extension of a theorem of darroch and ratcliff in loglinear models and its application to scaling multidimensional matrices abstract let c c ij be an m n matrix with real entries let b be any nonzero m vector let k c b 0 be bounded let x x 1 x 2 x n y y 1 y 2 y n be two nonnegative vectors with y k and x j 0 y j 0 for any coordinate j then it is shown that there exists a k and positive numbers z 1 z 2 z m such that j x j m i 1 z c ij i for all j th theorem slightly generalizes a theorem of darroch and ratcliff in loglinear models with a completely different proof technique the proof relies on an extension of a topological theorem of kronecker to set valued maps and the duality theorem of linear programming many theorems in scaling of matrices and multidimensional matrices are direct consequences of this theorem the main idea is to associate a suitable zero one matrix of transportation with any multidimensional matrix some motivations for scaling applications are also discussed

on the complexity of general matrix scaling and entropy minimization via the ras algorithm given an n m nonnegative matrix a a ij and positive integral vectors r e n and c e m having a common one norm h the r c scaling problem is to obtain positive diagonal matrices x and y if they exist such that xay has row and column sums equal to r and c respectively the entropy minimization problem corresponding to a is to find an n m matrix z z ij having the same zero pattern as a the sum of whose entries is a given number h its row and column sums are within given integral vectors of lower and upper bounds and such that the entropy function consisting of the sum of the terms z ij ln z ij a ij is minimized when the lower and upper bounds coincide matrix scaling and entropy minimization are closely related in this paper we present several complexity bounds for the e approximate r c scaling problem polynomial in n m h 1 e and ln v v where v and v are the largest and the smallest positive entries of a respectively these bounds although not polynomial in ln 1 1 e not only provide alternative complexities for the polynomial time algorithms but could result in better overall complexities in particular our theoretical analysis supports the practicality of the well known ras algorithm in our analysis we obtain bounds on the norm of scaling vectors which will be used in deriving not only some of the above complexities but also a complexity for square nonnegative matrices having positive permanent in particular our results extend nontrivially many bounds for the doubly stochastic scaling of square nonnegative matrices previously given by kalantari and khachiyan to the case of general r c scaling finally we study a more general entropy minimization problem where row and column sums are constrained to lie in prescribed intervals and the sum of all entries is also prescribed balinski and demange described an ras type algorithm for its continuous version but did not analyze its complexity we show that this algorithm produces an 1 e approximate solution within complexity polynomial in n m h v v and 1 1 e

fast optimization based conservative remap of scalar fields through aggregate mass transfer abstract we develop a fast efficient and accurate optimization based algorithm for the high order conservative and local bound preserving remap constrained interpolation of a scalar conserved quantity between two close meshes with the same connectivity the new formulation is as robust and accurate as the flux variable flux target optimization based remap fvft obr 1 2 yet has the computational efficiency of an explicit remapper the coupled system of linear inequality constraints resulting from the flux form of remap is the main efficiency bottleneck in fvft obr while advection based remappers use the flux form to directly enforce mass conservation the optimization setting allows us to treat mass conservation as one of the constraints to take advantage of this fact we consider an alternative mass variable mass target mvmt obr formulation in which the optimization variables are the net mass updates per cell and a single linear constraint enforces the conservation of mass in so doing we change the structure of the obr problem from a global linear inequality constrained qp to a singly linearly constrained qp with simple bounds using the structure of the mvmt obr problem and the fact that in remap the old and new grids are close we are able to develop a simple efficient and easily parallelizable optimization algorithm for the primal mvmt obr qp numerical studies on a variety of affine and non affine grids confirm that mvmt obr is as accurate and robust as fvft obr but has the same computational cost as the explicit state of the art fcr

a second order accurate material order independent interface reconstruction technique for multi material flow simulations a new second order accurate volume conservative material order independent interface reconstruction method for multi material flow simulations is presented first materials are located in multi material computational cells using a piecewise linear reconstruction of the volume fraction function these material locator points are then used as generators to reconstruct the interface with a weighted voronoi diagram that matches the volume fractions the interfaces are then improved by minimizing an objective function that smoothes interface normals while enforcing convexity and volume constraints for the pure material subcells convergence tests are shown demonstrating second order accuracy static and dynamic examples are shown illustrating the superior performance of the method over existing material order dependent methods

second invariant preserving remap of the 2d deviatoric stress tensor in ale methods abstract for numerical simulations of impact problems or fluid solid interactions the ale arbitrary lagrangian eulerian approach is a useful tool due to its ability to keep the computational mesh smooth and moving with the fluid the elastic plastic extension of the compressible fluid model requires tensor variables for the description of non volumetric deviatoric mechanical stress while lagrangian numerical schemes based on the evolution equation of the stress tensor are well developed tensor remap is still a relatively unexplored territory we propose a new approach to deviatoric stress remapping where the second invariant j 2 a conservative scalar quantity related to the strain energy is remapped independently of the tensor components these are re scaled to match the remapped invariant value effectively using only the principal directions and eigenvalue ratio from the component wise remap this approach is frame invariant preserves j 2 invariant bounds and conserves the total invariant we compare our method with component based remapping using a simple synchronized limiter or a specialized stress tensor limiter described in the literature

a lax wendroff type theorem for unstructured quasi uniform grids a well known theorem of lax and wendroff states that if the sequence of approximate solutions to a system of hyperbolic conservation laws generated by a conservative consistent numerical scheme converges boundedly a e as the mesh parameter goes to zero then the limit is a weak solution of the system moreover if the scheme satisfies a discrete entropy inequality as well the limit is an entropy solution the original theorem applies to uniform cartesian grids this article presents a generalization for quasi uniform grids with lipschitz boundary cells uniformly continuous inhomogeneous numerical fluxes and nonlinear inhomogeneous sources the added generality allows a discussion of novel applications like local time stepping grids with moving vertices and conservative remapping a counterexample demonstrates that the theorem is not valid for arbitrary non quasi uniform grids

matrix scaling a geometric proof of sinkhorn s theorem abstract matrix scaling problems have been extensively studied since sinkhorn established in 1964 the following result any positive square matrix of order n is diagonally equivalent to a unique doubly stochastic matrix of order n and the diagonal matrices which take part in the equivalence are unique up to scalar factors we present a new elementary proof of the existence part of sinkhorn s theorem which is based on well known geometrical interpretations of doubly stochastic matrices and left and right multiplication by diagonal matrices

a class of deformational flow test cases for linear transport problems on the sphere a class of new benchmark deformational flow test cases for the two dimensional horizontal linear transport problems on the sphere is proposed the scalar field follows complex trajectories and undergoes severe deformation during the simulation however the flow reverses its course at half time and the scalar field returns to its initial position and shape this process makes the exact solution available at the end of the simulation and facilitates assessment of the accuracy of the underlying transport scheme a procedure to eliminate possible cancellations of errors when the flow reverses is proposed the test suite consists of four cases three are based on non divergent flow fields and one on a divergent flow the initial conditions are prescribed in terms of regular latitude longitude spherical coordinates and are easy to implement the divergent flow is specifically aimed for conservative global transport schemes to test for conservation consistency and monotonicity or positivity of limiters filters in a challenging flow environment in the context of semi lagrangian schemes the time varying flow fields can be used to test trajectory algorithms where the exact trajectories do not follow great circle arcs the characteristics of the test cases are demonstrated with two different transport schemes

matrix scaling entropy minimization and conjugate duality ii the dual problem we present a matrix scaling problem calledtruncated scaling and describe applications arising in economics urban planning and statistics we associate a dual pair of convex optimization problems to the scaling problem and prove that the existence of a solution for the truncated scaling problem is characterized by the attainment of the infimum in the dual optimization problem we show that optimization problems used by bacharach 1970 bachem and korte 1979 eaves et al 1985 marshall and olkin 1968 and rothblum and schneider 1989 to study scaling problems can be derived as special cases of the dual problem for truncated scaling we present computational results for solving truncated scaling problems using dual coordinate descent thereby showing that truncated scaling provides a framework for modeling and solving large scale matrix scaling problems

a new stable hybrid three dimensional generalized finite difference time domain algorithm for analyzing complex structures in this paper we propose a new stable hybrid three dimensional 3 d generalized finite difference time domain algorithm formulated by using of the cell method cm a finite volumes type method designed to analyze objects with fine details without using very small time steps dictated by the courant condition the new algorithm is an extension to the 3 d cases of an analogous hybrid two dimensional algorithm also formulated by the cm and presented earlier by the authors in a previous publication we carry out a detailed analysis of the stability of the proposed algorithm paying special attention to the phenomenon of late time instabilities finally the results of some numerical tests are provided to show the absence of instabilities and the efficiency of the hybrid algorithm

a conservative multi tracer transport scheme for spectral element spherical grids atmospheric models used for practical climate simulation must be capable handling the transport of hundreds of tracers for computational efficiency conservative multi tracer semi lagrangian type transport schemes are appropriate global models based on high order galerkin approach employ highly non uniform spectral element grids and semi lagrangian transport is a challenge on those grids a conservative semi lagrangian scheme spelt spectral element lagrangian transport employing a multi moment compact reconstruction procedure is developed for non uniform quadrilateral grids the scheme is based on a characteristic semi lagrangian method that avoids complex and expensive upstream area computations the spelt scheme has been implemented in the high order method modeling environment homme which is based on a cubed sphere grid with spectral element spatial discretization additionally we show the strong scalability and multi tracer efficiency using several benchmark tests the spelt solution can be made monotonic positivity preserving by combining the flux corrected transport algorithm which is demonstrated on a uniform resolution grid in particular spelt can be efficiently used for non uniform grids and provides accurate and stable results for high resolution meshes

on the suppression of numerical oscillations using a non linear filter the idea of using a non linear filtering algorithm to eliminate numerically generated oscillations is investigated a detailed study is conducted to follow the development of numerical oscillations and their interaction with the filter a relaxation procedure is also proposed to enhance the effectiveness of the filter three model problems a 2d steady state scalar convection diffusion equation a 1d unsteady gas dynamics flow with shock and a 1d linear wave equation have been designed to test the performance of the filtering algorithm the effectiveness of the filter is assessed for convection schemes of different dispersive and diffusive characteristics demonstrating that it is effective in eliminating oscillations with short wavelength but oscillations of longer wavelengths are virtually unaffected it is concluded that a proper combination of non linear filter and dispersive numerical scheme is a viable alternative to dissipative schemes in resolving flows with sharp gradients and discontinuities

hybrid finite difference time domain modeling of curved surfaces using tetrahedral edge elements a hybrid finite difference time domain fdtd method is proposed for solving transient electromagnetic problems associated with structures of curved surfaces the method employs the conventional fdtd method for most of the regular region but introduces the tetrahedral edge based finite element scheme to model the region near the curved surfaces without any interpolation for the fields on the curved surface nor any additional stability constraint due to the finer division near the curved surfaces the novel finite element scheme is found to have second order accuracy unconditional stability programming ease and computational efficiency the hybrid method is applied to solve the electromagnetic scattering of three dimensional 3 d arbitrarily shaped dielectric objects to demonstrate its superior performance