the robust h sub 2 control problem a worst case design the worst case effect of a disturbance system on the h sub 2 norm of the system is analyzed an explicit expression is given for the worst case h sub 2 norm when the disturbance system is allowed to vary over all nonlinear time varying and possibly noncausal systems with bounded l sub 2 induced operator norm an upper bound for this measure which is equal to the worst case h sub 2 norm if the exogeneous input is scalar is defined some further analysis of this upper bound is done and a method to design controllers which minimize this upper bound over all robustly stabilizing controllers is given the latter is done by relating this upper bound to a parameterized version of the auxiliary cost function studied in the literature

modeling of thermally assisted magnetodynamics thermomagnetic recording uses local heating of ferromagnetic media to locally decrease coercivity and change saturation magnetization of the material and alleviate magnetization reversal a modified landau lifshitz equation is proposed as a phenomenological model to allow for changes in magnetization magnitude and is studied both analytically and numerically

weak solutions of the landau lifshitz bloch equation abstract the landau lifshitz bloch llb equation is a formulation of dynamic micromagnetics valid at all temperatures treating both the transverse and longitudinal relaxation components important for high temperature applications we study llb equation in case the temperature raised higher than the curie temperature the existence of weak solution is showed and its regularity properties are also discussed in this way we lay foundations for the rigorous theory of llb equation that is currently not available

logarithmically improved regularity criterion for the harmonic heat flow and related equations abstract we use an interpolation inequality on besov spaces to show a logarithmically improved regularity criterion for the harmonic heat flow the landau lifshitz equations and the landau lifshitz maxwell system

stability and convergence of finite element approximation schemes for harmonic maps this article discusses stability and convergence of approximation schemes for harmonic maps a finite element discretization of an iterative algorithm due to f alouges is introduced and shown to be stable and convergent in general only on acute type triangulations an break a posteriori criterion is proposed which allows us to monitor sufficient conditions for weak convergence to a harmonic map on general triangulations and for adaptive mesh refinement numerical break experiments show that an adaptive strategy automatically refines triangulations in neighborhoods of typical point singularities and thereby underline its efficiency

regularity properties of the solutions to the 3d maxwell landau lifshitz system in weighted sobolev spaces this paper is concerned with special regularity properties of the solutions to the maxwell landau lifshitz mll system describing ferromagnetic medium besides the classical results on the boundedness of tm te and th in the spaces l i l 2 w and l 2 i w 1 2 w we derive also estimates in weighted sobolev spaces this kind of estimates can be used to control the taylor remainder when estimating the error of a numerical scheme

martingale weak solutions of the stochastic landau lifshitz bloch equation abstract the present paper studies the stochastic landau lifshitz bloch equation which is recommended as the only valid model at temperature around the curie temperature and is especially important for the simulation of heat assisted magnetic recording we study the stochastic landau lifshitz bloch equation in the case that the temperature is raised higher than the curie temperature the global existence of martingale weak solutions is proved by using a new argument and regularity properties of the weak solutions are discussed

iterative solution and preconditioning for the tangent plane scheme in computational micromagnetics abstract the tangent plane scheme is a time marching scheme for the numerical solution of the nonlinear parabolic landau lifshitz gilbert equation which describes the time evolution of ferromagnetic configurations exploiting the geometric structure of the equation the tangent plane scheme requires only the solution of one linear variational form per time step which is posed in the discrete tangent space determined by the nodal values of the current magnetization we develop an effective solution strategy for the arising constrained linear systems which is based on appropriate householder reflections we derive possible preconditioners which are essentially independent of the time step and prove linear convergence of the preconditioned gmres algorithm numerical experiments underpin the theoretical findings

large time asymptotics for a matrix spin drift diffusion model abstract the large time asymptotics of the density matrix solving a drift diffusion poisson model for the spin polarized electron transport in semiconductors is proved the equations are analyzed in a bounded domain with initial and dirichlet boundary conditions if the relaxation time is sufficiently small and the boundary data is close to the equilibrium state the density matrix converges exponentially fast to the spinless near equilibrium steady state the proof is based on a reformulation of the matrix valued cross diffusion equations using spin up and spin down densities as well as the perpendicular component of the spin vector density which removes the cross diffusion terms key elements of the proof are time uniform positive lower and upper bounds for the spin up and spin down densities derived from the de giorgi moser iteration method and estimates of the relative free energy for the spin up and spin down densities

current induced magnetization dynamics global existence of weak solutions abstract we consider a model of current induced magnetization dynamics described by the landau lifshitz gilbert llg equations of the magnetization in which an additional current dependent term is added two methods namely faedo galerkin penalty fgp method and hyperbolic regularization method are used to show the existence of finite energy global weak solutions

analysis of a coupled spin drift diffusion maxwell landau lifshitz system abstract the existence of global weak solutions to a coupled spin drift diffusion and maxwell landau lifshitz system is proved the equations are considered in a two dimensional magnetic layer structure and are supplemented with dirichlet neumann boundary conditions the spin drift diffusion model for the charge density and spin density vector is the diffusion limit of a spinorial boltzmann equation for a vanishing spin polarization constant the maxwell landau lifshitz system consists of the time dependent maxwell equations for the electric and magnetic fields and of the landau lifshitz gilbert equation for the local magnetization involving the interaction between magnetization and spin density vector the existence proof is based on a regularization procedure l 2 type estimates and moser type iterations which yield the boundedness of the charge and spin densities furthermore the free energy is shown to be nonincreasing in time if the magnetization spin interaction constant in the landau lifshitz equation is sufficiently small

geometrical integration of landau lifshitz gilbert equation based on the mid point rule landau lifshitz gilbert llg equation is the fundamental equation to describe magnetization vector field dynamics in microscale and nanoscale magnetic systems this equation is highly nonlinear in nature and for this reason it is generally solved by using numerical techniques in this paper the mid point rule time stepping technique is applied to the numerical time integration of llg equation and the relevant properties of the numerical scheme are discussed the mid point rule is an unconditionally stable and second order accurate scheme which preserves the fundamental geometrical properties of llg dynamics first it exactly preserves the llg property of conserving the magnetization magnitude at each spatial location second for constant in time applied fields it preserves the llg lyapunov structure namely the fact that the free energy is a decreasing function of time in addition in the case of zero damping the mid point rule preserves the conservation of the system free energy the above preservation properties are unconditionally valid i e they are fulfilled for any value of the time step finally the llg hamiltonian structure in the case of zero damping is preserved up to the third order terms with respect to the time step the main difficulty related to this scheme is the necessity of solving a large system of globally coupled nonlinear equations this problem has been circumvented by using special and reasonably fast quasi newton iterative technique the proposed numerical scheme is then tested on the standard micromagnetic problem no 4 in the numerical computations the spatial discretization is obtained by finite difference technique and the magnetostatic field is computed through the fast fourier transform method

robustness in the presence of mixed parametric uncertainty and unmodeled dynamics continuing the development of the structured singular value approach to robust control design the authors investigate the problem of computing mu in the case of mixed real parametric and complex uncertainty the problem is shown to be equivalent to a smooth constrained finite dimensional optimization problem in view of the fact that the functional to be maximized may have several local extrema an upper bound on mu whose computation is numerically tractable is established this leads to a sufficient condition of robust stability and performance a historical perspective on the development of the mu theory is included

adaptive techniques for landau lifshitz gilbert equation with magnetostriction in this paper we propose a time space adaptive method for micromagnetic problems with magnetostriction the considered model consists of coupled maxwell s landau lifshitz gilbert llg and elastodynamic equations the time discretization of maxwell s equations and the elastodynamic equation is done by backward euler method the space discretization is based on whitney edge elements and linear finite elements respectively the fully discrete llg equation reduces to an ordinary differential equation which is solved by an explicit method that conserves the norm of the magnetization

convergence of an implicit explicit midpoint scheme for computational micromagnetics abstract based on lowest order finite elements in space we consider the numerical integration of the landau lifschitz gilbert equation llg the dynamics of llg is driven by the so called effective field which usually consists of the exchange field the external field and lower order contributions such as the stray field the latter requires the solution of an additional partial differential equation in full space following bartels and prohl 2006 we employ the implicit midpoint rule to treat the exchange field however in order to treat the lower order terms effectively we combine the midpoint rule with an explicit adams bashforth scheme the resulting integrator is formally of second order in time and we prove unconditional convergence towards a weak solution of llg numerical experiments underpin the theoretical findings

improved first order approximation of eigenvalues and eigenvectors a method based on reduced basis approximation concepts is presented for improved first order approximation of eigenvalues and eigenvectors of modified structural dynamic systems the terms of a local approximation based on taylor or matrix power series are used as basis vectors for approximating the perturbed eigenparameters for each eigenmode a reduced eigensystem is generated by using the baseline eigenvector and the first order approximation term as ritz vectors the solution of the reduced eigensystem leads to two possible estimates of each perturbed eigenvalue and eigenvector criteria for selection of the best approximation are presented the zero and first order rayleigh quotient approximation can be directly recovered as special cases of the present method results are presented for approximate dynamic reanalysis of a 25 bar planar truss structure it is shown that high quality approximation of the perturbed eigenparameters can be obtained for moderate perturbations in the stiffness and mass matrices for very large local perturbations of the structure including deletion of some structural members it is shown that the present method yields reasonable quality approximations

a landau lifshitz type equation in studying thin film micromagnetics the paper is concerned with a landau lifshitz type equation which was first raised by desimone and otto etc when studying thin film micromagnetics we get the existence of a continuous solution using penalty approximation compensated compactness and commutator estimate

convergence result for the constraint preserving mid point scheme for micromagnetism an important progress was recently done in numerical approximation of weak solutions to a micromagnetic model equation the problem with the nonconvex side constraint of preserving the length of the magnetization was tackled by using reduced integration several schemes were proposed and their convergence to weak solutions was proved all schemes were derived from the landau lifshitz gilbert form of the micromagnetic equation however when the precessional term in the original landau lifshitz ll form of the micromagnetic equation tends to zero the above schemes become unusable we propose a scheme derived from the mid point rule for the ll form of the micromagnetic equation combined with the reduced integration we show convergence to a weak solution of the ll equation and demonstrate the usefulness of the proposed scheme to study the limit process when the precessional parameter of the micromagnetic equation goes to zero

mode localization phenomena in large space structures the possibility of localization or confinement of vibratory modes in large space structures is investigated theoretically and numerically these structures belong to a class of periodic structures that have recently been shown to be sensitive to periodicity b reaking disorder or imperfections when localization occurs the modal amplitude of a global mode becomes confined to a local region of the structure with serious implications for the control problem the results of this study indicate that mode localization is most likely to occur in structures consisting of a large number of weakly coupled substructures certain large space structures with high modal densities fall in this category and it is therefore important to include the effect of structural imperfections and disorder when designing control systems for shape or directional control of such structures k kh kw ku k k m m m n n p qi qt t u v w uf 8fj e 6

space discretization for the landau lifshitz gilbert equation with magnetostriction abstract we consider the conservation of momentum equation for the displacement vector together with a nonlinear dissipative magnetic law described by landau lifshitz gilbert llg equation this system describes the magnetostriction caused by an applied magnetic field we use a finite element approximation and we design a numerical scheme for computations we derive the error estimates for the approximation of the displacement vector and the magnetization

partial regularity to the landau lifshitz equation with spin accumulation abstract in this paper we consider a model for the spin magnetization system that takes into account the diffusion process of the spin accumulation this model consists of the landau lifshitz equation describing the precession of the magnetization coupled with a quasi linear parabolic equation describing the diffusion of the spin accumulation this paper establishes the global existence and uniqueness of weak solutions for large initial data in r 2 moreover partial regularity is shown in particular the solution is regular on r 2 0 with the exception of at most finite singular points

existence regularity and local uniqueness of the solutions to the maxwell landau lifshitz system in three dimensions abstract we study a model of ferromagnetism governed by maxwell s equations coupled with the non linear landau lifshitz equation of micromagnetism we are interested in the cases of space periodic solutions for 3d domains obtaining the regularity of the solution m in w per 2 2 space and of the solutions e h in w per 1 2 space we state the existence theorem finally we prove the local uniqueness of the solutions

convergence of an implicit constraint preserving finite element discretization of p harmonic heat flow into spheres we propose an implicit discretization of the p harmonic map heat flow into the sphere s 2 that enjoys a discrete energy inequality and converges under only a mild mesh constraint to a weak solution a fully practical iterative scheme that approximates the solution of the nonlinear system of equations in each time step is proposed and analyzed computational studies to motivate possible finite time blow up behavior of solutions for p 2 are included

analysis of a drift diffusion model with velocity saturation for spin polarized transport in semiconductors abstract a system of drift diffusion equations with electric field under dirichlet boundary conditions is analyzed the system of strongly coupled parabolic equations for particle density and spin density vector describes the spin polarized semi classical electron transport in ferromagnetic semiconductors the presence of a nonconstant and nonsmooth magnetization vector solution of the landau lifshitz equation causes the diffusion matrix to be dependent on space and time and to have in general poor regularity properties thus making the analysis challenging to partially overcome the analytical difficulties the velocity saturation hypothesis is made which results in a bounded drift velocity the global in time existence and uniqueness of weak solutions is shown by means of a semi discretization in time which yields an elliptic semilinear problem and a quadratic entropy inequality which allow for the limit of vanishing time step size the convergence of the weak solutions to the steady state under some restrictions on the parameters and data is shown finally the higher regularity of solutions for a smooth magnetization in two space dimensions is shown through a diagonalization argument which allows to get rid of the cross diffusion terms in the fluid equations and the iterative application of gagliardo nirenberg inequalities and a generalized version of aubin lemma

time average in micromagnetism abstract in this paper we study a model of ferromagnetic material governed by a nonlinear laudau lifschitz equation coupled with maxwell equations we prove the existence of weak solutions then we prove that all points of the limit set of any trajectories are solutions of the stationary model furthermore we derive rigourously the quasistatic model by an appropriate time average method

higher order regularity results in 3d for the landau lifshitz equation with an exchange field abstract we derive and prove higher order regularity results for the landau lifshitz ll equation describing the evolution of spin fields in continuum ferromagnets these results are based on the weight s min 1 s which helps to get nonlinear parts under control

a finite element approximation for the stochastic landau lifshitz gilbert equation abstract the stochastic landau lifshitz gilbert llg equation describes the behaviour of the magnetisation under the influence of the effective field containing random fluctuations we first transform the stochastic llg equation into a partial differential equation with random coefficients without the ito term the resulting equation has time differentiable solutions we then propose a convergent linear scheme for the numerical solution of the reformulated equation as a consequence we show the existence of weak martingale solutions to the stochastic llg equation a salient feature of this scheme is that it does not involve solving a system of nonlinear algebraic equations and that no condition on time and space steps is required when 1 2 1 numerical results are presented to show the applicability of the method

accurate discretization of a non linear micromagnetic problem abstract in this paper we propose a finite element discretization of the maxwell landau lifchitz gilbert equations governing the electromagnetic field in a ferromagnetic material our point of view is that it is desirable for the discrete problem to possess conservation properties similar to the continuous system we first prove the existence of a new class of liapunov functions for the continuous problem and then for a variational formulation of the continuous problem we also show a special continuous dependence result then we propose a family of mass lumped finite element schemes for the problem for the resulting semi discrete problem we show that magnetization is conserved and that semi discrete liapunov functions exist finally we show the results of some computations that show the behavior of the fully discrete liapunov functions

optimal stability criterion for a wall in a ferromagnetic wire in a magnetic field abstract in this paper we study a one dimensional asymptotic model of ferromagnetic nanowire submitted to a magnetic field we address the stability of the wall configuration for the landau lifschitz equation thus we determine the stability domain improving a result of carbou labbe

on the evolution of domain walls in hard ferromagnets we propose a sharp interface theory for the dynamics of domain walls in highly anisotropic hard ferromagnetic bodies starting from the gilbert equation we consider the asymptotic regime when the hardness parameter goes to infinity and we use the technique of matched expansions to derive a system of two evolution equations for the domain wall regarded as a smooth surface the first equation apart for a nonlocal forcing term has the standard form for a surface set in motion according to its mean curvature the second relates the normal velocity to the internal structure of the domain wall

asymptotic analysis for two joined thin slanting ferromagnetic films abstract starting from a 3 d non convex and nonlocal micromagnetic energy for ferromagnetic materials we determine via an asymptotic analysis the free energy of two joined ferromagnetic thin films we distinguish different regimes depending on the limit of the ratio between the small thickness of the two films

heat flow for the square root of the negative laplacian for unit length vectors abstract the paper is concerned with heat flow for the square root of the negative laplacian for unit length vectors motivated by the model of desimone kohn otto and muller we show the existence of weak solutions for the periodic case by means of the penalty approximation and commutator estimate

on a hyperbolic parabolic system arising in magnetoelasticity the evolution of a magnetoelastic material is described by a nonlinear hyperbolic parabolic system we introduce a simplified but nontrivial model and prove the existence of a unique solution to the corresponding initial boundary value problem

a convergent and precise finite element scheme for landau lifschitz gilbert equation in this paper we propose a new scheme for the numerical integration of the landau lifschitz gilbert llg equations in their full complexity in particular including stray field interactions the scheme is consistent up to order 2 in time and unconditionally stable it combines a linear inner iteration with a non linear renormalization stage for which a rigorous proof of convergence of the numerical solution toward a weak solution is given when both space and time stepsizes tend to 0 0 a numerical implementation of the scheme shows its performance on physically relevant test cases we point out that to the knowledge of the authors this is the first finite element scheme for the llg equations which enjoys such theoretical and practical properties

error estimates for a numerical scheme for ferromagnetic problems we propose a finite element method for approximating the nonlinear equations describing the electromagnetic field in a ferromagnetic material using energy arguments we prove an optimal convergence rate for the method assuming a sufficiently smooth electromagnetic field we also verify that the finite element solution satisfies various conservation conditions appropriate to the continuous problem finally we provide some numerical examples

hausdorff measure of the singular set of landau lifshitz equations with a nonlocal term this paper is concerned with the partial regularity of the stationary solutions to the landau lifshitz system of ferromagnetic spin chain with gilbert damping and a nonlocal term in 3 dimensions the hausdorff measure of the singular set is discussed

the gilbert equation with dry friction type damping a modified gilbert equation for micromagnetics is considered obtained by augmenting the standard viscous like dissipation with a rate independent term we prove existence of a weak solution both with and without viscous dissipation by scaling time we show that if the applied field varies very slowly then gyromagnetic effects and viscous dissipation become negligible in the infinitesimally slow loading limit the system thus becomes fully rate independent

a gauss seidel projection method for micromagnetics simulations abstract one of the main difficulties in micromagnetics simulation is the severe time step constraint introduced by the exchange field using standard explicit integrators leads to a physical time step of sub pico seconds which is often two orders of magnitude smaller than the fastest physical time scales direct implicit integrators require solving complicated coupled systems in this paper we introduce an implicit method whose complexity is comparable to solving the scalar heat equation implicitly this method is based on a combination of a gauss seidel implementation of a fractional step implicit solver for the gyromagnetic term and the projection method for the heat flow of harmonic maps this method allows us to carry out fully resolved calculations for the switching of the magnetization in micron sized elements

well posedness of the ferrimagnetic equations in this paper we show the existence of global weak solutions of the ferrimagnetic equations on compact riemannian manifold using the penalty method we also show the uniqueness of the solution and its well posedness by the energy estimates method in lower dimensions in particular when the space dimension is one we can prove that the problem is globally well posed

eigenvalue reanalysis of locally modified structures using a generalized rayleigh s method in this paper we introduce approximate reanalysis methods based on the generalized rayleigh s quotient with these methods the fundamental eigenvalue of a locally modified system can be computed readily using the fundamental mode as well as the static solution of the original system following a general development of theory several special cases of in terest in design are derived here and then tabulated numerical examples illustrate the accuracy of the new formulations

wong zakai approximation for the stochastic landau lifshitz gilbert equations abstract in this work we study stochastic landau lifshitz gilbert equations sllges in one dimension with non zero exchange energy only firstly by introducing a suitable transformation we convert the sllges to a highly nonlinear time dependent partial differential equation with random coefficients which is not fully parabolic we then prove that there exists a pathwise unique solution to this equation and that this solution enjoys the maximal regularity property following regular approximation of the brownian motion and using reverse transformation we show existence of strong solution of sllges taking values in a two dimensional unit sphere s 2 in r 3 the construction of the solution and its corresponding convergence results are based on wong zakai approximation

global smooth solutions for the one dimensional spin polarized transport equation abstract the existence of global smooth solutions of spin polarized transport equation in dimension one is studied we prove that for smooth initial data the equation admits a unique global smooth solution without smallness restriction when the gilbert damping term vanishes 0 refined a priori estimates are made and the global existence and uniqueness of smooth solutions are also obtained

robust control under parametric uncertainty via primal dual convex analysis a numerical method is proposed for optimal robust control synthesis the method applies to the case when the coefficients of the characteristic polynomial depend linearly on the uncertain parameters a primal dual pair of infinite dimensional convex problems is solved by successive finite dimensional approximations the primal dual pair has no duality gap and both upper and lower bounds produced by the approximations converge monotonically to the optimal value

homogenization of the demagnetization field operator in periodically perforated domains in this paper we study the homogenization of the demagnetization field operator in periodically perforated domains using the two scale convergence method as an application we homogenize the landau lifshitz equation in such domains we consider regular homothetic holes

numerical methods for the landau lifshitz equation we discuss numerical schemes for various forms of the landau lifshitz equation a new simple projection method is introduced and is shown to be unconditionally stable the advantages over other schemes are also demonstrated numerically

computational complexity of spl mu calculation the structured singular value spl mu measures the robustness of uncertain systems numerous researchers over the last decade have worked on developing efficient methods for computing spl mu this paper considers the complexity of calculating spl mu with general mixed real complex uncertainty in the framework of combinatorial complexity theory in particular it is proved that the spl mu recognition problem with either pure real or mixed real complex uncertainty is np hard this strongly suggests that it is futile to pursue exact methods for calculating spl mu of general systems with pure real or mixed uncertainty for other than small problems

maxwell s equations with vector hysteresis electromagnetic processes in magnetic materials are described by maxwell s equations in ferrimagnetic insulators assuming that d e e we have the equation

numerical scheme for augmented landau lifshitz equation in heat assisted recording the motivation of heat assisted recording is to improve the thermal stability of recorded data bits by increasing the strength of the uniaxial anisotropy during the recording process the medium is heated by a laser reducing the coercivity and allowing the head to write data bits we present a micromagnetic model based on the augmented landau lifshitz equation taking into account a phenomenological power law describing the dependence of the saturation magnetization on the temperature a full discrete numerical scheme is presented and the convergence of approximate solutions to a weak one is shown

estimating the conservatism of popov s criterion for real parametric uncertainties abstract we consider the problems of robust stability and performance analysis of linear systems subject to parametric uncertainties the popov criterion provides lower bounds of stability margins and upper bounds on robust performance in this paper we propose a method for obtaining upper bounds on stability margin or lower bounds on robust h2 performance based on the outcome of the lower bound computation for the stability problem or the upper bound computation for the h2 performance problem we make several numerical tests

global solutions of a dynamical equation in ferrimagnet abstract we consider global solutions of a dynamical equation in ferrimagnet we show that it admits a global weak solution by using the penalty method by the energy estimates method we show there exists a unique global smooth solution finally we establish the relationship between this equation and wave maps

the weak solutions to the evolution problems of harmonic maps on demontre l existence de solutions faibles globales a des problemes d evolution des applications harmoniques de varietes de riemann compactes sans bord dans des spheres

symplectic flow for the square root of the negative laplacian abstract the paper is concerned with symplectic flow for the square root of the negative laplacian which is motivated when studying a one dimensional model about ferromagnetic thin film without gilbert damping term only gyromagnetic term remained derived from the stationary model of a desimone r v kohn s muller and f otto existence of weak solution to the model is proved by viscosity approximation and commutator estimate

approximate eigensolution of laplacian matrices for locally modified graph products laplacian matrices and their spectrum are of great importance in algebraic graph theory there exist efficient formulations for eigensolutions of the laplacian matrices associated with a special class of graphs called product graphs in this paper the problem of determining a few approximate smallest eigenvalues and eigenvectors of large scale product graphs modified through the addition or deletion of some nodes and or members is investigated the eigenproblem associated with a modified graph model is reduced using the set of master eigenvectors and linear approximated slave eigenvectors from the original model implicitly restarted lanczos method is employed to obtain the required eigenpairs of the reduced problem examples of large scale models are included to demonstrate the efficiency of the proposed method compared to the direct application of the irl method

numerical analysis of an explicit approximation scheme for the landau lifshitz gilbert equation the landau lifshitz gilbert equation describes magnetic behavior in ferromagnetic materials construction of numerical strategies to approximate weak solutions for this equation is made difficult by its top order nonlinearity and nonconvex constraint in this paper we discuss necessary scaling of numerical parameters and provide a refined convergence result for the scheme first proposed by alouges and jaisson 2006 as an application we numerically study discrete finite time blowup in two dimensions

numerical methods of lyapunov function construction and their application to the absolute stability problem the minimax approach is used to study numerical selection of a lyapunov function from a multiparameter class of functions a numerical method is suggested for plotting an absolute stability region in the space of system gains for a control system with several nonstationary nonlinearities

a convergent finite element approximation for the quasi static maxwell landau lifshitz gilbert equations we propose a q linear scheme for the numerical solution of the quasi static maxwell landau lifshitz gilbert mllg equations despite the strong nonlinearity of the landau lifshitz gilbert equation the proposed method results in a linear system at each time step we prove that as the time and space steps tend to zero with no further conditions when email protected 12 1 the finite element solutions converge weakly to a weak solution of the mllg equations numerical results are presented to show the applicability of the method

smooth solution to the one dimensional inhomogeneous non automorphic landau lifshitz equation using the differential difference method and viscosity vanishing approach we obtain the existence and uniqueness of the global smooth solution to the periodic initial value problem of the inhomogeneous non automorphic landau lifshitz equation without gilbert damping terms in one dimension to establish the uniform estimates we use some identities resulting from the fact jz x t jz 1 and the fact that the vectors fz z x z z xg form an orthogonal base of the space r 3

optimal error estimates of a linearized backward euler fem for the landau lifshitz equation we present a fully discrete linearized backward euler finite element method for the landau lifshitz equation in which a new linearization is proposed for the gyromagnetic term optimal almost unconditional error estimates of the scheme in l 2 and h 1 norms are proved i e when the stepsizes h and tau are smaller than given constants the analysis relies on the new linearization and an error splitting argument proposed by li and sun int j numer anal model 10 2013 pp 622 633 and siam j numer anal 51 2013 pp 1959 1977 numerical results in both two and three dimensional spaces are provided to confirm our theoretical analysis and show the unconditional stability convergence of the scheme

a lanczos based method for structural dynamic reanalysis problems in this paper a new solution method for the modified eigenvalue problem with specific application to structural dynamic reanalysis is presented the method which is based on the block lanczos algorithm is developed for multiple low rank modifications to a system and calculates a few selected eigenpairs given the solution to the original system ax x procedures are developed for the modified standard eigenvalue problem a a x x where 1 a jbsjbt where sj s p p p n and b n p is constant for all the perturbations sj 2 a i jbisjbit where bi n p may vary with the pertubations sj the procedures are then extended for the reciprocal and generalized eigenvalue problems so that they are directly applicable to the structural dynamic reanalysis problem numerical examples are given to demonstrate the applications of the method

an iterative approximation scheme for the landau lifshitz gilbert equation a new iterative numerical scheme for a solution of the single landau lifshitz gilbert equation i e that the magnetic field is given is proposed the approach uses the fixed point technique for handling the nonlinearities at each time step the second order of convergence in the time is proved and also confirmed by an example with an exact solution

global weak solution for the landau lifshitz maxwell equation in three space dimensions abstract in this paper by using an a priori estimate and the galerkin method the global existence of a weak solution for the landau lifshitz maxwell equations in three dimension is proved

initial boundary value problems for anisotropic landau lifshitz equations in three or four space dimensions abstract in this paper we will show the existence of partially regular solutions to the initial boundary value problem for landau lifshitz equations with nonpositive anisotropy constants in three or four space dimensions the partial regularity is proved up to the boundary both for the dirichlet problem and for the neumann problem in addition for the neumann case a generalized stability condition which ensures the partial regularity is given for equations with positive or negative anisotropy coefficients we will give two results of existence and uniqueness for the solutions corresponding to ground states

global weak solutions of the fractional landau lifshitz maxwell equation abstract the fractional landau lifshitz maxwell equation is considered in this paper we show the global existence of suitable weak solutions by galerkin method and the vanishing viscosity method the main difficulties in this study are due to the loss of compactness of this system and the fact that the nonlinear term is nonlocal and of the same order of the equation to overcome these difficulties we introduce the commutator estimates and some cancellation properties to this equation which prove to be proper tools in the study of landau lifshitz type equations

partial regularity for harmonic maps and related problems via gauge theory we give a new proof of partial regularity for harmonic maps in dimensions m 3 into arbitrary targets this proof avoids the use of adapted frames and permits to consider targets of minimal c 2 regularity the proof we present moreover extends to a large class of elliptic systems of quadratic growth

analysis and synthesis of robust control systems via parameter dependent lyapunov functions in this paper the problem of robust stability of systems subject to parametric uncertainties is considered sufficient conditions for the existence of parameter dependent lyapunov functions are given in terms of a criterion which is reminiscent of but less conservative than popov s stability criterion an equivalent frequency domain criterion is demonstrated the relative sharpness of the proposed test and existing stability criteria is then discussed the use of parameter dependent lyapunov functions for robust controller synthesis is then considered it is shown that the search for robustly stabilizing controllers may be limited to controllers with the same order as the original plant a possible synthesis procedure and a numerical example are then discussed

convergence of an implicit finite element method for the landau lifshitz gilbert equation the landau lifshitz gilbert equation describes the dynamics of ferromagnetism where strong nonlinearity and nonconvexity are hard to tackle so far existing explicit schemes to approximate weak solutions suffer from severe time step restrictions in this paper we propose an implicit fully discrete scheme and verify unconditional convergence

properties of the mixed spl mu problem and its bounds upper and lower bounds for the mixed spl mu problem have recently been developed and here we examine the relationship of these bounds to each other and to spl mu a number of interesting properties are developed and the implications of these properties for the robustness analysis of linear systems and the development of practical computation schemes are discussed in particular we find that current techniques can only guarantee easy computation for large problems when spl mu equals its upper bound and computational complexity results prohibit this possibility for general problems in this context we present some special cases where computation is easy and make some direct comparisons between mixed spl mu and kharitonov type analysis methods

sparse matrix factor modification in structural reanalysis structural reanalysis problems such as in nonlinear finite element analysis or optimum design involve progressive changes in the global stiffness matrix and its matrix factors although many studies have been devoted to the subject of matrix factor modification most investigations have dealt with the problem separately from sparse matrix methods this paper introduces a graph theoretic model for the forward solution procedure which is applicable for identifying the modified entries of the matrix factors due to changes in the original matrix applications of this graph theoretic model to existing refactorization methods are presented the relation between substructuring and sparse matrix ordering strategies and their effects on reanalysis are discussed modification of a sparse matrix associated with an n n finite element grid ordered by the nested dissection scheme is analysed

a convergent implicit finite element discretization of the maxwell landau lifshitz gilbert equation we propose an implicit fully discrete scheme for the numerical solution of the maxwell landau lifshitz gilbert equation which is based on linear finite elements and satisfies a discrete sphere constraint as well as a discrete energy law as numerical parameters tend to zero solutions weakly accumulate at weak solutions of the maxwell landau lifshitz gilbert equation a practical linearization of the nonlinear scheme is proposed and shown to converge for certain scalings of numerical parameters computational studies are presented to indicate finite time blow up behavior and to study combined electromagnetic phenomena in ferromagnets for benchmark problems

a numerical scheme for a maxwell landau lifshitz gilbert system we consider maxwell s equations together with a nonlinear dissipative magnetic law described by the landau lifshitz gilbert equation the paper is devoted to the numerical study of this problem we introduce two algorithms for the time discretization the modulus of magnetization is conserved in both cases assuming a sufficiently smooth electromagnetic field we derive the error estimates for both approximation schemes

existence of partially regular weak solutions to landau lifshitz maxwell equations abstract in this paper the authors establish the existence of partially regular weak solutions to the landau lifshitz equations coupling with static maxwell systems in 3 dimensions by ginzburg landau approximation it is proved that the hausdorff measure of the singular set is locally finite this extends the similar results of ding and guo s ding b guo hausdorff measure of the singular set of landau lifshitz equations with a nonlocal term comm math phys 250 1 2004 95 117 from the stationary solutions to weak solutions and the results of wang c wang on landau lifshitz equations in dimensions at most four indiana univ math j 55 5 2006 1615 1644 from landau lifshitz equations to landau lifshitz maxwell equations

on the weak solutions to the maxwell landau lifshitz equations and to the hall magneto hydrodynamic equations in this paper we deal with weak solutions to the maxwell landau lifshitz equations and to the hall magneto hydrodynamic equations first we prove that these solutions satisfy some weak strong uniqueness property then we investigate the validity of energy identities in particular we give a sufficient condition on the regularity of weak solutions to rule out anomalous dissipation in the case of the hall magneto hydrodynamic equations we also give a sufficient condition to guarantee the magneto helicity identity our conditions correspond to the same heuristic scaling as the one introduced by onsager in hydrodynamic theory finally we examine the sign locally of the anomalous dissipations of weak solutions obtained by some natural approximation processes

partially regular solution to landau lifshitz maxwell equations in two dimensions abstract the present paper is concerned with the existence uniqueness and singularities of the landau lifshitz equation coupled with maxwell equations on riemannian manifold in two dimensions it is shown that there exists a weak solution which is regular with exception of at most finitely many singular points

the stability of localized solutions of landau lifshitz equations we study the landau lifshitz equation of ferromagnetism on r 2 with an easy axis anisotropy we establish the existence of topologically nontrivial periodic solutions and show they are stable against equivariant perturbations along the way we establish the global well posedness of the cauchy problem for a class of data with no size restriction

stabilization of solutions of nonlinear and degenerate evolution equations on etudie le comportement asymptotique des solutions bornees des equations de la forme u t u f x u dans r u x o u 0 x dans u x t u 1 x t dans r ou est un domaine borne de r n avec de classe c 2 0 1