global attractor for the kirchhoff type equation with a strong dissipation abstract the paper studies the longtime behavior of the kirchhoff type equation with a strong dissipation u t t m u 2 u u t h u t g u f x it proves that the related continuous semigroup s t possesses in the phase space with low regularity a global attractor which is connected and an example is shown

long time dynamics of kirchhoff wave models with strong nonlinear damping we study well posedness and long time dynamics of a class of quasilinear wave equations with a strong damping we accept the kirchhoff hypotheses and assume that the stiffness and damping coefficients are functions of the l2 norm of the gradient of the displacement we prove the existence and uniqueness of weak solutions and study their properties for a wide class of nonlinearities which covers the case of possible degeneration or even negativity of the stiffness coefficient and the case of a supercritical source term our main results deal with global attractors for strictly positive stiffness factors we prove that in the natural energy space endowed with a partially strong topology there exists a global finite dimensional attractor in the non supercritical case this attractor is strong in this case we also establish the existence of a fractal exponential attractor and give conditions that guarantee the existence of a finite number of determining functionals

application of analytical retarded time potential expressions to the solution of time domain integral equations recently exact closed form expressions of the electric and magnetic fields and potentials due to impulsively excited rao wilton glisson basis functions have been presented in this work the application of these expressions in the solution of the combined field integral equation cfie is presented solutions via analytical expressions of the electric and magnetic fields are verified and compared with the conventional marching on in time mot algorithm solutions that employ numerical basis integrations it is shown that the accuracy and stability of the solutions obtained with the proposed analytical approach are better when compared to those obtained with the conventional numerical method in addition a discussion section about the effect of the proposed approach in solving the electric field integral equation efie is added in this section it is demonstrated that the dependency of the solution via analytical expressions of the fields are less sensitive to the time step size in comparison to the conventional solution and that the increase in accuracy is a necessary but not sufficient condition for stability

a novel scheme for the solution of the time domain integral equations of electromagnetics a new method to numerically solve time domain integral equations pertinent to electromagnetic surface scattering phenomena is presented the method uses approximate prolate spheroidal wave functions and standard rao wilton glisson basis functions to effect the temporal and spatial discretization of the integral equations respectively because the temporal basis functions are noncausal an extrapolation scheme is used to construct a system of equations that can be solved by marching on in time numerical results show that the proposed method is stable and that its solutions converge exponentially fast with the time bandwidth product of the approximate prolate spheroidal wave functions to results from a frequency domain method of moments solver that uses spatial basis functions and integration rules identical to those in the time domain solver

longtime behavior of the kirchhoff type equation with strong damping on rn abstract the paper studies the longtime behavior of the kirchhoff type equation with strong damping on r n u t t m u 2 u u t u u t g x u f x it shows that the related continuous semigroup s t possesses a global attractor which is connected and has finite fractal and hausdorff dimension

a time domain volume integral equation and its marching on in degree solution for analysis of dispersive dielectric objects a marching on in degree mod based scheme for analyzing transient electromagnetic scattering from three dimensional dispersive dielectric objects is proposed a time domain volume integral equation tdvie for the electric flux density throughout the object is first formulated and then solved using the mod scheme with the use of weighted laguerre polynomials as entire domain temporal basis functions the convolution of the electric flux density and the medium susceptibility and its derivatives can be handled analytically by employing the galerkin temporal testing procedure the time variable is eliminated in the resultant recursive matrix equation so that the proposed algorithm overcomes the late time instability problem that may occur in the conventional marching on in time mot approach some complex dispersive media such as the debye lorentz and drude media are simulated to illustrate the validity of the tdvie mod algorithm

attractors for the degenerate kirchhoff wave model with strong damping existence and the fractal dimension abstract in this paper we study the long time behavior of the kirchhoff type wave equation in the space h 0 1 l 2 we prove the existence of the global attractor for the equation which covers the case of possible generation of the stiffness coefficient we also consider the geometrical property of the global attractor by means of the z 2 index we provide under suitable assumptions the fractal dimension of the global attractor is infinite

a global attractor for the elastic waveguide model in rn abstract this paper studies the longtime behavior of solutions to the elastic waveguide model in r n u t t u u t t 2 u u t u t u g x u f x it proves that when the space dimension n 5 under rather mild conditions on g and f the related solution semigroup possesses in phase space with low regularity x h 2 h 1 h 2 h with 0 1 a global attractor which is connected

global attractor for a nonlinear wave equation arising in elastic waveguide model abstract the paper studies the longtime behavior of solutions to the initial boundary value problem ibvp for a nonlinear wave equation arising in an elastic waveguide model u t t u u t t 2 u u t g u f x it proves that when the space dimension n 5 under rather mild conditions the dynamical system associated with the above mentioned ibvp possesses a global attractor which is connected and has finite fractal and hausdorff dimension

numerical methods for high dimensional probability density function equations in this paper we address the problem of computing the numerical solution to kinetic partial differential equations involving many phase variables these types of equations arise naturally in many different areas of mathematical physics e g in particle systems liouville and boltzmann equations stochastic dynamical systems fokker planck and dostupov pugachev equations random wave theory malakhov saichev equations and coarse grained stochastic systems mori zwanzig equations we propose three different classes of new algorithms addressing high dimensionality the first one is based on separated series expansions resulting in a sequence of low dimensional problems that can be solved recursively and in parallel by using alternating direction methods the second class of algorithms relies on truncation of interaction in low orders that resembles the bogoliubov born green kirkwood yvon bbgky framework of kinetic gas theory and it yields a hierarchy of coupled probability density function equations the third class of algorithms is based on high dimensional model representations e g the anova method and probabilistic collocation methods a common feature of all these approaches is that they are reducible to the problem of computing the solution to high dimensional equations via a sequence of low dimensional problems the effectiveness of the new algorithms is demonstrated in numerical examples involving nonlinear stochastic dynamical systems and partial differential equations with up to 120 variables

existence of a global attractor for the parabolic equation with nonlinear laplacian principal part in an unbounded domain abstract in this paper we study the long time behavior of solutions for the parabolic equation with non linear laplacian principal part in r n we prove the existence of a global l 2 r n l r n attractor when n p and the existence of a global l 2 r n l n p n p r n attractor when n p

a fast time domain integral equation based scheme for analyzing scattering from dispersive objects a fast integral equation based scheme for analyzing transient scattering from inhomogeneous dispersive bodies is presented a time domain integral equation in terms of the electric flux inside the body is constructed by invoking the volume equivalence principle i e by equating the sum of the incident electric field and that radiated by equivalent volume polarization currents to the total electric field the proposed algorithm for solving this time domain integral equation incorporates a recursive convolution scheme that updates the polarization current from knowledge of the electric flux to reduce the computational cost and memory requirement of the resulting marching on in time scheme it is augmented with the plane wave time domain algorithm numerical results that validate the proposed approach and demonstrate its accuracy are presented

stable electric field tdie solvers via quasi exact evaluation of mot matrix elements prior theoretical studies and experience confirm that the stability of marching on in time mot solvers pertinent to the analysis of scattering from free standing three dimensional perfect electrically conducting surfaces hinges on the accurate evaluation of mot matrix elements resulting from a galerkin discretization of the underlying time domain integral equation tdie unfortunately the accurate evaluation of the four dimensional spatial integrals involved in the expressions for these matrix elements is prohibitively expensive when performed by computational means here a method that permits the quasi exact evaluation of mot matrix elements is presented specifically the proposed method permits the analytical evaluation of three out of the four spatial integrations leaving only one integral to be evaluated numerically since the latter has finite range and a piecewise smooth integrand it can be evaluated to very high accuracy using standard quadrature rules as a result the proposed method permits the fast evaluation of mot matrix elements with arbitrary user specified accuracy extensive numerical experiments show that an mot solver for the electric field tdie that uses the proposed quasi exact method is stable for a very wide range of time step sizes and yields solutions that decay exponentially after the excitation vanishes

finite dimensional attractors for the kirchhoff equation with a strong dissipation abstract the paper studies the existence of the finite dimensional global attractors and exponential attractors for the dynamical system associated with the kirchhoff type equation with a strong dissipation u t t m u 2 u u t h u t g u f x it proves that the above mentioned dynamical system possesses a global attractor which has finite fractal dimension and an exponential attractor for application the fact shows that for the concerned viscoelastic flow the permanent regime global attractor can be observed when the excitation starts from any bounded set in phase space and the dimension of the attractor that is the number of degree of freedom of the turbulent phenomenon and thus the level of complexity concerning the flow is finite

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

time domain adaptive integral method for surface integral equations an efficient marching on in time mot scheme is presented for solving electric magnetic and combined field integral equations pertinent to the analysis of transient electromagnetic scattering from perfectly conducting surfaces residing in an unbounded homogenous medium the proposed scheme is the extension of the frequency domain adaptive integral pre corrected fast fourier transform fft method to the time domain fields on the scatterer that are produced by space time sources residing on its surface are computed 1 by locally projecting for each time step all sources onto a uniform auxiliary grid that encases the scatterer 2 by computing everywhere on this grid the transient fields produced by the resulting auxiliary sources via global multilevel blocked space time ffts 3 by locally interpolating these fields back onto the scatterer surface as this procedure is inaccurate when source and observer points reside close to each other and 4 near fields are computed classically albeit pre corrected for errors introduced through the use of global ffts the proposed scheme has a computational complexity and memory requirement of o n sub t n sub s log sup 2 n sub s and o n sub s sup 3 2 when applied to quasiplanar structures and of o n sub t n sub s sup 3 2 log sup 2 n sub s and o n sub s sup 2 when used to analyze scattering from general surfaces here n sub s and n sub t denote the number of spatial and temporal degrees of freedom of the surface current density these computational cost and memory requirements are contrasted to those of classical mot solvers which scale as o n sub t n sub s sup 2 and o n sub s sup 2 respectively a parallel implementation of the scheme on a distributed memory computer cluster that uses the message passing interface is described simulation results demonstrate the accuracy efficiency and the parallel performance of the implementation

asymptotic behavior of solutions for initial boundary value problems for strongly damped nonlinear wave equations abstract we study initial boundary value problems for strongly damped nonlinear wave equations by using improved integral estimates it is proven that the solutions of the problems decay to zero exponentially as time t approaches infinity under a very simple and general assumption regarding the nonlinear term

parallel pwtd accelerated explicit solution of the time domain electric field volume integral equation a parallel plane wave time domain pwtd accelerated explicit marching on in time mot scheme for solving the time domain electric field volume integral equation td efvie is presented the proposed scheme leverages pulse functions and lagrange polynomials to spatially and temporally discretize the electric flux density induced throughout the scatterers and a finite difference scheme to compute the electric fields from the hertz electric vector potentials radiated by the flux density the flux density is explicitly updated during time marching by a predictor corrector pc scheme and the vector potentials are efficiently computed by a scalar pwtd scheme the memory requirement and computational complexity of the resulting explicit pwtd pc efvie solver scale as o n s log n s and o n s n t respectively here n s is the number of spatial basis functions and n t is the number of time steps a scalable parallelization of the proposed mot scheme on distributed memory cpu clusters is described the efficiency accuracy and applicability of the resulting parallelized pwtd pc efvie solver are demonstrated via its application to the analysis of transient electromagnetic wave interactions on canonical and real life scatterers represented with up to 25 million spatial discretization elements

long time behavior of strongly damped nonlinear wave equations abstract we consider the long time behavior of a strongly damped nonlinear wave equation we will show that the initial boundary value problem has a global solution and that there exists a compact global attractor with finite dimension

attractors for reaction diffusion equations in unbounded domains abstract in this paper we study the asymptotic behaviour of solutions for parabolic non linear evolution equations in r n we prove the asymptotic compactness of the solutions and then establish the existence of the global attractor in l 2 r n

stability of attractors for the kirchhoff wave equation with strong damping and critical nonlinearities abstract the paper investigates longtime dynamics of the kirchhoff wave equation with strong damping and critical nonlinearities u t t 1 u 2 u u t h u t g u f x with 0 1 the well posedness and the existence of global and exponential attractors are established and the stability of the attractors on the perturbation parameter is proved for the ibvp of the equation provided that both nonlinearities h s and g s are of critical growth

global attractors and their hausdorff dimensions for a class of kirchhoff models this paper studies the existence regularity and hausdorff dimensions of global attractors for a class of kirchhoff models arising in elastoplastic flow utt div u m 1 u ut 2u h ut g u f x it proves that under rather mild conditions the dynamical system associated with above mentioned models possesses in phase space x a global attractor which has further regularity in x 1 x and has finite hausdorff dimension for application the fact shows that for the concerned elastoplastic flow the permanent regime global attractor can be observed when the excitation starts from any bounded set in phase space and the dimension of the attractor that is the number of degree of freedom of the turbulent phenomenon and thus the level of complexity concerning the flow is finite

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

existence and exponential decay for a kirchhoff carrier model with viscosity abstract in this work we study the existence of global solutions and exponential decay for the following nonlinear problem formula where m is a c 1 function m 0 0 0

longtime dynamics of the kirchhoff equations with fractional damping and supercritical nonlinearity abstract the paper investigates the global well posedness and the longtime dynamics of the kirchhoff equations with fractional damping and supercritical nonlinearity u t t m u 2 u u t f u g x with 1 2 1 the main results are focussed on the relationships among the growth exponent p of the nonlinearity f u the global well posedness and the longtime dynamics of the equations we show that i even if p is up to the supercritical range that is 1 p n 4 n 4 the well posedness and the longtime behavior of the solutions of the equation are of the characters of the parabolic equation ii when n 4 n 4 p n 4 n 4 the corresponding subclass g of the limit solutions exists and possesses a weak global attractor

efficient evaluation of double surface integrals in time domain integral equation formulations a new integration approach is presented for accurately calculating time domain efie mfie and cfie matrix elements over triangular domains it mainly consists of a radial integration scheme for handling weakly singular and near hypersingular inner integrals and some new smoothing techniques for treating outer two dimensional 2 d integrals the proposed approach has sufficient generality and efficiency for solving time domain integral equations tdie with arbitrary types of temporal basis functions and temporal discretization schemes such as marching on in time mot marching on in degree mod and finite difference delay modeling convolution quadrature fddm cq etc the numerical results for calculating some typical integrals are given to demonstrate its capability with high accuracy and rapid convergence rate achieved

a space time discretization criterion for a stable time marching solution of the electric field integral equation numerical techniques based on a time domain recursive solution of the electric field integral equation efie may exhibit instability phenomena induced by the joint space time discretization the above problem is addressed with specific reference to the evaluation of electromagnetic scattering from perfectly conducting bodies of arbitrary shape we analyze a particular formulation of the method of moments which relies on a triangular patch geometrical model of the exterior surface of the scattering body and operates according to a marching on in time scheme whereby the surface current distribution at a given time step is recursively evaluated as a function of the current distribution at previous steps a heuristic stability condition is devised which allows us to define a proper time step as well as a geometrical discretization criterion ensuring convergence of the numerical procedure and therefore eliminating insurgence of late time oscillations the stability condition is discussed and validated by means of a few working examples

statistical analysis and simulation of random shocks in stochastic burgers equation we study the statistical properties of random shock waves in stochastic burgers equation subject to random space time perturbations and random initial conditions by using the response excitation probability density function pdf method and the mori zwanzig mz formulation of irreversible statistical mechanics we derive exact reduced order equations for the one point and two point pdfs of the solution field in particular we compute the statistical properties of random shock waves in the inviscid limit by using an adaptive shock capturing discontinuous galerkin method in both physical and probability spaces we consider stochastic flows generated by high dimensional random initial conditions and random additive forcing terms yielding multiple interacting shock waves collapsing into clusters and settling down to a similarity state we also address the question of how random shock waves in space and time manifest themselves in probability space the proposed new mathematical framework can be applied to different conservation laws potentially leading to new insights into high dimensional stochastic dynamical systems and more efficient computational algorithms

decay estimate of solutions to the sixth order damped boussinesq equation abstract in this paper we consider the initial value problem for the sixth order damped boussinesq equation we prove the global existence and asymptotic behavior of solutions for all space dimensions n 1 provided that the initial value is suitably small moreover we show that the solution can be approximated by the linear solution as time tends to infinity for n 2 the result slightly improves the result obtained by wang 2012 3

global attractor for a class of kirchhoff models the paper studies the longtime behavior of solutions to the initial boundary value problem ibvp for a class of kirchhoff models arising in elastoplastic flow utt div u m 1 u ut 2u h ut g u f x by combining the decomposition idea with the operate technique it proves that under rather mild conditions the dynamical system associated with above mentioned ibvp possesses in different phase spaces a global attractor which is connected respectively for application the fact shows that for the concerned elastoplastic flow the permanent regime global attractor can be observed when the excitation starts from any bounded set in phase space

adaptive discontinuous galerkin method for response excitation pdf equations evolution equations of the joint response excitation probability density function repdf generalize the existing pdf evolution equations and enable us to compute the pdf of the solution of stochastic systems driven by colored random noise this paper aims at developing an efficient numerical method for this evolution equation of repdf by considering the response and excitation spaces separately for the response space a nonconforming adaptive discontinuous galerkin method is used to resolve both local and discontinuous dynamics while a probabilistic collocation method is used for the excitation space we propose two fundamentally different adaptive schemes for the response space using either the local variance combined with the boundary flux difference or using particle trajectories the effectiveness of the proposed new algorithm is demonstrated in two prototype applications dealing with randomly forced nonlinear oscillators we first study the stochastic pendulum problem and compare the resulting pdf

time domain integral equation analysis of scattering from composite bodies via exact evaluation of radiation fields a novel marching on in time and poggio miller chang harrington wu tsai pmchwt based time domain integral equation solver for analyzing transient scattering from composite multiregion structures comprising homogeneous penetrable volumes and perfectly conducting surfaces is presented to render the marching on in time procedure stable observer and source integrals are approximated via multipoint collocation and evaluated in closed form the proposed scheme avoids the costly evaluation of five dimensional integrals required in full space time galerkin schemes and proves to be stable for all targets investigated including coated perfect electrically conducting surfaces and multiregion penetrable volumes

finite dimensional attractors for the quasi linear strongly damped wave equation abstract we present a new method of investigating the so called quasi linear strongly damped wave equations t 2 u t x u x u f u x x u g in bounded 3d domains this method allows us to establish the existence and uniqueness of energy solutions in the case where the growth exponent of the non linearity is less than 6 and f may have arbitrary polynomial growth rate moreover the existence of a finite dimensional global and exponential attractors for the solution semigroup associated with that equation and their additional regularity are also established in a particular case 0 which corresponds to the so called semi linear strongly damped wave equation our result allows to remove the long standing growth restriction f u c 1 u 5

explicit solution of the time domain volume integral equation using a stable predictor corrector scheme an explicit marching on in time mot scheme for solving the time domain volume integral equation is presented the proposed method achieves its stability by employing at each time step a corrector scheme which updates corrects fields computed by the explicit predictor scheme the proposed method is computationally more efficient when compared to the existing filtering techniques used for the stabilization of explicit mot schemes numerical results presented in this paper demonstrate that the proposed method maintains its stability even when applied to the analysis of electromagnetic wave interactions with electrically large structures meshed using approximately half a million discretization elements

stability properties of the time domain electric field integral equation using a separable approximation for the convolution with the retarded potential the state of art of time domain integral equation tdie solvers has grown by leaps and bounds over the past decade during this time advances have been made in i the development of accelerators that can be retrofitted with these solvers and ii understanding the stability properties of the electric field integral equation as is well known time domain electric field integral equation solvers have been notoriously difficult to stabilize research into methods for understanding and prescribing remedies have been on the uptick the most recent of these efforts are i lubich quadrature and ii exact integration in this paper we re examine the solution to this equation using i the undifferentiated form of the time domain electric field integral equation tdefie and ii a separable approximation to the spatio temporal convolution the proposed scheme can be constructed such that the spatial integrand over the source and observer domains is smooth and integrable as several numerical results will demonstrate the proposed scheme yields stable results for long simulation times and a variety of targets both of which have proven extremely challenging in the past

global existence and asymptotic behavior of solutions to a nonlinear wave equation of fourth order in this paper we focus on the cauchy problem for a nonlinear wave equation of fourth order in n dimensional space n 1 the decay structure of which is of regularity loss property based on the decay estimate of solutions to the linear problem we introduce a set of time weighted sobolev spaces by using the contraction mapping theorem we obtain the global in time existence and the optimal decay estimates of solutions to the cauchy problem under smallness assumption on the initial data

on a backward problem for the kirchhoff s model of parabolic type abstract we study for the first time the backward problem for nonlocal nonlinear boundary value problem of kirchhoff s model of parabolic type first we show that the problem is severely ill posed in the sense of hadamard we propose two methods the fourier truncation method for stabilizing the problem with homogeneous source and the quasi reversibility method for regularizing the problem with nonlinear source under some priori assumptions on the exact solution we establish some stability estimates in the h 0 1 norm

global existence and asymptotic behavior of solutions for a semi linear wave equation abstract in this paper we investigate the initial value problem for a semi linear wave equation in n dimensional space based on the decay estimate of solutions to the corresponding linear equation we define a set of time weighted sobolev spaces under small condition on the initial value we prove the global existence and asymptotic behavior of the solution in the corresponding sobolev spaces by the contraction mapping principle

robust solution of time domain integral equations using loop tree decomposition and bandlimited extrapolation a stabilization method that eradicates low frequency instabilities in the solution of the time domain integral equations of electromagnetic scattering is presented the method uses the loop tree decomposition originally suggested for the solution of low frequency scattering problems via the method of moments specifically a temporally differentiated form of the pertinent integral equation is tested using tree basis functions and the undifferentiated form is tested using solenoidal basis functions the underlying solution method uses bandlimited interpolation functions blifs and the higher order divergence conforming vector bases of graglia et al for the temporal and spatial discretization of the integral equations respectively an extrapolation technique has been implemented to overcome the noncausality introduced into the system by the blifs numerical results will demonstrate the stability and accuracy of the proposed technique

existence of a global attractor for semilinear dissipative wave equations on rn abstract we consider the semilinear hyperbolic problem utt ut x u f u x x r n t 0 with the initial conditions u x 0 u0 x and ut x 0 u1 x in the case where n 3 and x 1 g x lies in ln 2 r n the energy space x 0 d 1 2 r n l2g r n is introduced to overcome the difficulties related with the noncompactness of operators which arise in unbounded domains we derive various estimates to show local existence of solutions and existence of a global attractor in x 0 the compactness of the embedding d 1 2 r n l2g r n is widely applied

attractors for partly dissipative reaction diffusion systems in rn in this paper we study the asymptotic behavior of solutions for the partly dissipative reaction diffusion equations in n we prove the asymptotic compactness of the solutions and then establish the existence of the global attractor in 2 n 2 n l l 2000 academic press

a dc stable and large time step well balanced td efie based on quasi helmholtz projectors the marching on in time mot solution of the time domain electric field integral equation td efie has traditionally suffered from a number of issues including the emergence of spurious static currents dc instability and ill conditioning at large time steps low frequencies in this contribution a space time galerkin discretization of the td efie is proposed which separates the loop and star components of both the equation and the unknown judiciously integrating or differentiating these components with respect to time leads to an equation which is free from dc instability by choosing the correct temporal basis and testing functions for each of the components a stable mot system is obtained furthermore the scaling of these basis and testing functions ensure that the system remains well conditioned for large time steps the loop star decomposition is performed using quasi helmholtz projectors to avoid the explicit transformation to the unstable bases of loops and stars or trees and to avoid the search for global loops which is a computationally expensive operation

limiting behavior for strongly damped nonlinear wave equations in this paper we investigate both the existence and the limiting behavior for the equation utt aut au t u ut where a is a sectorial operator is periodic in t and satisfies certain regularity and growth assumptions in most results on limiting behavior we will assume a has compact resolvent we consider the equation as an abstract ode defined on a paired space x x 0 1 with regard to the limiting behavior one of our principal results will be to show that if there is a bounded set in one of the spaces considered for which all points or trajectories enter into and remain then there is a set j consisting of very smooth functions defined on all of the spaces considered which is the maximum compact invariant set uniformly asymptotically stable connected and having very strong attractivity properties in all these spaces we will often show it attracts all points in a bounded set uniformly we will give a few sharper results for the case where a the work is motivated by recent papers of webb and fitzgibbon and applies techniques found in recent papers by the author

a stable marching on in time scheme for solving the time domain electric field volume integral equation on high contrast scatterers a time domain electric field volume integral equation td efvie solver is proposed for characterizing transient electromagnetic wave interactions on high contrast dielectric scatterers the td efvie is discretized using the schaubert wilton glisson swg and approximate prolate spherical wave apsw functions in space and time respectively the resulting system of equations cannot be solved by a straightforward application of the marching on in time mot scheme since the two sided apsw interpolation functions require the knowledge of unknown future field samples during time marching causality of the mot scheme is restored using an extrapolation technique that predicts the future samples from known past ones unlike the extrapolation techniques developed for mot schemes that are used in solving time domain surface integral equations this scheme trains the extrapolation coefficients using samples of exponentials with exponents on the complex frequency plane this increases the stability of the mot td efvie solver significantly since the temporal behavior of decaying and oscillating electromagnetic modes induced inside the scatterers is very accurately taken into account by this new extrapolation scheme numerical results demonstrate that the proposed mot solver maintains its stability even when applied to analyzing wave interactions on high contrast scatterers

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

longtime dynamics of the kirchhoff equation with strong damping and critical nonlinearity on rn abstract the paper studies the longtime dynamics of the kirchhoff equation with strong damping and critical nonlinearity on r n u t t u t m u 2 u u t g x u f x we establish the well posedness the existence of the global and exponential attractors in natural energy space h h 1 r n l 2 r n in critical nonlinearity case these results improve not only the recent ones achieved by yang 2007 32 but also ones achieved by conti pata and squassina 2005 9 to some extent