global well posedness and analyticity of solutions to three dimensional hall mhd equations abstract in this paper suppose that the initial data is sufficiently small we study the global well posedness and analyticity of mild solutions to the three dimensional incompressible hall mhd equations

achieving minimum length scale in topology optimization using nodal design variables and projection functions a methodology for imposing a minimum length scale on structural members in discretized topology optimization problems is described nodal variables are implemented as the design variables and are projected onto element space to determine the element volume fractions that traditionally define topology the projection is made via mesh independent functions that are based upon the minimum length scale a simple linear projection scheme and a non linear scheme using a regularized heaviside step function to achieve nearly 0 1 solutions are examined the new approach is demonstrated on the minimum compliance problem and the popular simp method is used to penalize the stiffness of intermediate volume fraction elements solutions are shown to meet user defined length scale criterion without additional constraints penalty functions or sensitivity filters no instances of mesh dependence or checkerboard patterns have been observed copyright 2004 john wiley sons ltd

a remark on regularity criterion for the 3d hall mhd equations based on the vorticity in this paper we investigate the regularity criterion for the local in time classical solution to the three dimensional 3d incompressible hall magnetohydrodynamic equations hall mhd it is proved that the control of the vorticity alone can ensure the smoothness of the solution

global existence and asymptotic behavior for the 3d generalized hall mhd system abstract in this paper we consider the global existence for the 3d generalized hall mhd equations with fractional dissipative terms u and b under small initial data in the setting of sobolev norms with lower regularity for the global existence we enlarge the range of dissipative exponents from 1 7 6 to 1 3 2 which established in a recent work in addition the long time behavior and rates of decay for both the solutions and higher derivatives in different sobolev spaces are obtained by using the fourier splitting method which extends the previous work by chae and schonbek

spectral collocation solutions to multiparameter mathieu s system our main aim is the accurate computation of a large number of specified eigenvalues and eigenvectors of mathieu s system as a multiparameter eigenvalue problem mep the reduced wave equation for small deflections is solved directly without approximations introduced by the classical mathieu functions we show how for moderate values of the cut off collocation parameter the qr algorithm and the arnoldi method may be applied successfully while for larger values the jacobi davidson method is the method of choice with respect to convergence accuracy and memory usage

decay estimates of solutions for the equations of motion of compressible viscous and heat conductive gases in an exterior domain in ℝ3 we consider the equations of motion of compressible viscous and heat conductive gases in an exterior domain in 3 we give the l q l p estimates for solutions to the linearized equations and show an optimal decay estimate for solutions to the nonlinear problem

on global existence energy decay and blow up criteria for the hall mhd system in this paper we obtain global existence and energy decay for 3d hall magnetohydrodynamics hall mhd system with u and b besides the classical energy method and besov space techniques the interpolating inequalities are crucial in the proof of decay estimates then two osgood type blow up criteria are established our results improve the corresponding theorems in 3 and 4 in addition we establish two beale kato majda blow up criterion for the generalized version of hall mhd with u and b 1

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

boundary effects in a phase field approach to topology optimization a phase field based topology optimization approach is considered for the maximum stiffness or minimum compliance problem the objective functional to be minimized consists in addition to the compliance a cost for gray solutions and a cost for interfaces between void and full material since the interfaces between void and full material are penalized via a volume integral in the original phase field formulation there is no penalty associated with interfaces along the external boundaries in the present contribution an additional term representing the cost of interfaces at external boundaries is added to the functional subject to minimization it is shown that the new boundary term enters the optimization as a robin boundary condition the method is implemented in a finite element setting and numerical simulations of typical structures are considered the results indicate that the optimal designs are influenced by the cost of interfaces to a large less

global wellposedness for hall mhd equations abstract this paper concerns the wellposedness problem of hall mhd system the mild solution of hall mhd equations exists globally in the nonhomogeneous lei lin space setting provided that the initial data satisfies u 0 x 1 x 0 b 0 x 1 x 0 min 2 4 where is the viscosity of the fluid and is the magnetic diffusion coefficient our global existence result covers rougher initial data and improves the previous results

the beale kato majda criterion for the 3d magneto hydrodynamics equations we study the blow up criterion of smooth solutions to the 3d mhd equations by means of the littlewood paley decomposition we prove a beale kato majda type blow up criterion of smooth solutions via the vorticity of velocity only namely sup j in mathbb z int 0 t delta j nabla times u infty dt where j is the frequency localization operator in the littlewood paley decomposition

topology optimization using regularized intermediate density control abstract we consider topology optimization of elastic continua the elasticity tensor is assumed to depend linearly on the design function density as in the variable thickness sheet problem in order to get black white design pictures the intermediate density values are controlled by an explicit constraint this constraint is regularized by including a compact and linear operator s to guarantee existence of solutions a proof of convergence of the finite element fe discretized optimization problem s solutions to exact ones is also given so the method is not prone to numerical anomalies such as mesh dependence or checkerboards the procedure is illustrated in some minimum compliance examples where s is chosen to be a classical convolution type operator the fe discretized optimization problems are solved by sequential convex approximations

a class large solution of the 3d hall magnetohydrodynamic equations abstract in this paper we construct the global large solution to the three dimensional incompressible hall mhd equations with a class of initial data here the large solution means that the l norm can be arbitrarily large initially

global existence and temporal decay for the 3d compressible hall magnetohydrodynamic system abstract in this paper we are concerned with the 3d compressible hall magnetohydrodynamic system in the whole space we prove the global existence and temporal decay rates of the solutions to the system when the initial data are close to a stable equilibrium state by using a pure energy method

some convergence results in perimeter controlled topology optimization abstract the computation of optimal topologies of elastic continuum structures using a constraint on the perimeter is investigated predicting macroscopic black white topologies without the use of homogenization techniques this approach is presently one of the most attractive approaches in topology optimization mathematical justifications are given for both the relaxation of the discrete value constraint on the design variable and for the finite element discretizations it turns out that the way in which the perimeter has been calculated to date the numerical results will not approximate the intended original problem but one with a taxi cab perimeter which measures lengths of structural edges after projection onto the coordinate axes

topology optimization with implicit functions and regularization summary topology optimization is formulated in terms of the nodal variables that control an implicit function description of the shape the implicit function is constrained by upper and lower bounds so that only a band of nodal variables needs to be considered in each step of the optimization the weak form of the equilibrium equation is expressed as a heaviside function of the implicit function the heaviside function is regularized to permit the evaluation of sensitivities we show that the method is a dual of the bendshe kikuchi method the method is applied both to problems of optimizing single material and

existence theorem and blow up criterion of the strong solutions to the two fluid mhd equation in r3 abstract we first give the local well posedness of strong solutions to the cauchy problem of the 3d two fluid mhd equations and then study the blow up criterion of the strong solutions by means of the fourier frequency localization and bony s paraproduct decomposition it is proved that the strong solution u b can be extended after t t if either u l t q b p 0 with 2 q 3 p 1 and b l t 1 b 0 or j l t q b p 0 with 2 q 3 p 2 where t u denotes the vorticity of the velocity and j b stands for the current density

spectral collocation for multiparameter eigenvalue problems arising from separable boundary value problems in numerous science and engineering applications a partial differential equation has to be solved on some fairly regular domain that allows the use of the method of separation of variables in several orthogonal coordinate systems separation of variables applied to the helmholtz laplace or schrodinger equation leads to a multiparameter eigenvalue problem mep important cases include mathieu s system lame s system and a system of spheroidal wave functions although multiparameter approaches are exploited occasionally to solve such equations numerically meps remain less well known and the variety of available numerical methods is not wide the classical approach of discretizing the equations using standard finite differences leads to algebraic meps with large matrices which are difficult to solve efficiently the aim of this paper is to change this perspective we show that by combining spectral collocation methods and new efficient numerical methods for algebraic meps it is possible to solve such problems both very efficiently and accurately we improve on several previous results available in the literature and also present a matlab toolbox for solving a wide range of problems

on the blow up criterion and small data global existence for the hall magnetohydrodynamics abstract in this paper we establish an optimal blow up criterion for classical solutions to the incompressible resistive hall magnetohydrodynamic equations we also prove two global in time existence results of the classical solutions for small initial data the smallness conditions of which are given by the suitable sobolev and the besov norms respectively although the sobolev space version is already an improvement of the corresponding result in 4 the optimality in terms of the scaling property is achieved via the besov space estimate the special property of the energy estimate in terms of b 2 1 s norm is essential for this result contrary to the usual mhd the global well posedness in the 2 1 2 dimensional hall mhd is wide open

a regularity criterion for a generalized hall mhd system abstract this paper proves a regularity criterion for a 3d generalized hall mhd system in terms of velocity gradient in negative besov spaces

an enhanced genetic algorithm for structural topology optimization genetic algorithms gas have become a popular optimization tool for many areas of research and topology optimization an effective design tool for obtaining efficient and lighter structures in this paper a versatile robust and enhanced ga is proposed for structural topology optimization by using problem specific knowledge the original discrete black and white 0 1 problem is directly solved by using a bit array representation method to address the related pronounced connectivity issue effectively the four neighbourhood connectivity is used to suppress the occurrence of checkerboard patterns a simpler version of the perimeter control approach is developed to obtain a well posed problem and the total number of hinges of each individual is explicitly penalized to achieve a hinge free design to handle the problem of representation degeneracy effectively a recessive gene technique is applied to viable topologies while unusable topologies are penalized in a hierarchical manner an efficient fem based function evaluation method is developed to reduce the computational cost a dynamic penalty method is presented for the ga to convert the constrained optimization problem into an unconstrained problem without the possible degeneracy with all these enhancements and appropriate choice of the ga operators the present ga can achieve significant improvements in evolving into near optimum solutions and viable topologies with checkerboard free mesh independent and hinge free characteristics numerical results show that the present ga can be more efficient and robust than the conventional gas in solving the structural topology optimization problems of minimum compliance design minimum weight design and optimal compliant mechanisms design it is suggested that the present enhanced ga using problem specific knowledge can be a powerful global search tool for structural topology optimization copyright 2005 john wiley sons ltd

on the temporal decay for the hall magnetohydrodynamic equations abstract we establish temporal decay estimates for weak solutions to the hall magnetohydrodynamic equations with these estimates in hand we obtain algebraic time decay for higher order sobolev norms of small initial data solutions

on the regularity of weak solutions to the magnetohydrodynamic equations abstract in this paper we study the regularity of weak solution to the incompressible magnetohydrodynamic equations we obtain some sufficient conditions for regularity of weak solutions to the magnetohydrodynamic equations which is similar to that of incompressible navier stokes equations moreover our results demonstrate that the velocity field of the fluid plays a more dominant role than the magnetic field does on the regularity of solution to the magneto hydrodynamic equations

filters in topology optimization in this article a modified filtered version of the minimum compliance topology optimization problem is studied the direct dependence of the material properties on its pointwise density is replaced by a regularization of the density field by the mean of a convolution operator in this setting it is possible to establish the existence of solutions moreover convergence of an approximation by means of finite elements can be obtained this is illustrated through some numerical experiments the filtering technique is also shown to cope with two important numerical problems in topology optimization checkerboards and mesh dependent designs copyright 2001 john wiley sons ltd

global well posedness bkm blow up criteria and zero h limit for the 3d incompressible hall mhd equations abstract we consider the cauchy problem for the 3d incompressible hall mhd equations firstly we prove the global well posedness under some new conditions which improve the previous corresponding results in 3 4 24 then a beale kato majda bkm blow up criterion is established finally we show the explicit convergence rate of strong solutions from the hall mhd equations to the mhd equations as the hall coefficient h 0

constraints of distance from boundary to skeleton for the control of length scale in level set based structural topology optimization abstract a method is proposed for the control of minimum maximum length scale in the level set based structural topology optimization the minimum maximum length scale of structure is characterized by using the concept of smallest biggest maximal inscribable ball in order to prevent trivial zero minimum length scale the skeleton of structure is utilized and trimmed the control of length scale is realized by constraining the distance from boundary to skeleton and the distance is explicitly constructed by using the highly efficient fast marching method numerical examples in two dimensions are investigated

second root vectors for multiparameter eigenvalue problems of fredholm type a class of multiparameter eigenvalue problems involving generally non self adjoint and unbounded operators is studied a basis for the second root subspace at eigenvalues of fredholm type is computed in terms of the underlying multiparameter system a self adjoint version of this result is given under a weak definiteness condition and sturm liouville and finitedimensional examples are considered

on the well posedness of the ideal mhd equations in the triebel lizorkin spaces in this paper we prove the local well posedness for the ideal mhd equations in the triebel lizorkin spaces and obtain a blow up criterion of smooth solutions specifically we fill a gap in a step of the proof of the local well posedness part for the incompressible euler equation in chae comm pure appl math 55 654 678 2002

an improved regularity criterion for the 3d hall mhd equations via the vorticity abstract in this paper we consider the three dimensional incompressible hall magnetohydrodynamic equations and establish an improved regularity criterion of local in time classical solutions involving only the vorticity field consequently this improves the previous result

a level set method for structural topology optimization this paper presents a new approach to structural topology optimization we represent the structural boundary by a level set model that is embedded in a scalar function of a higher dimension such level set models are flexible in handling complex topological changes and are concise in describing the boundary shape of the structure furthermore a well founded mathematical procedure leads to a numerical algorithm that describes a structural optimization as a sequence of motions of the implicit boundaries converging to an optimum solution and satisfying specified constraints the result is a 3d topology optimization technique that demonstrates outstanding flexibility of handling topological changes fidelity of boundary representation and degree of automation we have implemented the algorithm with the use of several robust and efficient numerical techniques of level set methods the benefit and the advantages of the proposed method are illustrated with several 2d examples that are widely used in the recent literature of topology optimization especially in the homogenization based methods

nonlinear multiparameter eigenvalue problems linearised and nonlinearised solutions abstract the paper focuses on a nonlinear multiparameter eigenvalue problem called p this problem involves n spectral parameters and also depends on n 2 numerical parameters where n 2 is an integer if these numerical parameters vanish p degenerates into n linear one parameter eigenvalue problems called p i 0 i 1 n in connection with p one can consider another n nonlinear one parameter eigenvalue problems called p i the problems p i have eigenvalues with as well as without linear counterparts the paper suggests to consider p i as nonunperturbed instead of p i 0 using properties of eigenvalues of p i one manages to prove existence of eigentuples of p among the eigentuples found in this way there are eigetuples with as well as without linear counterparts results of the paper are found with a nonclassical approach applications of the found results to nonlinear optics are shown

fundamental relationship between bilateral filtering adaptive smoothing and the nonlinear diffusion equation in this paper the relationship between bilateral filtering and anisotropic diffusion is examined the bilateral filtering approach represents a large class of nonlinear digital image filters we first explore the connection between anisotropic diffusion and adaptive smoothing and then the connection between adaptive smoothing and bilateral filtering previously adaptive smoothing was considered to be an inconsistent approximation to the nonlinear diffusion equation we extend adaptive smoothing to make it consistent thus enabling a unified viewpoint that relates nonlinear digital image filters and the nonlinear diffusion equation

analytical and numerical solutions of the unsteady 2d flow of mhd fractional maxwell fluid induced by variable pressure gradient abstract the nonlocal property of the fractional derivative can supply more precise mathematical models for depicting flow dynamics of complex fluid which cannot be modelled appropriately by normal integer order differential equations this paper studies the analytical and numerical methods of unsteady 2d flow of magnetohydrodynamic mhd fractional maxwell fluid in a rectangular pipe driven by variable pressure gradient the governing equation is formulated with caputo time dependent fractional derivatives whose orders are distributed in interval 0 2 a challenge is to firstly obtain the exact solution by combining modified separation of variables method with mikusinski type operational calculus meanwhile the numerical solution is also obtained by the implicit finite difference method whose validity has been confirmed by the comparison with the exact solution constructed different to the most classical works both the stability and convergence analysis of two dimensional multi term time fractional momentum equation are derived based on numerical analysis the results show that the velocity increases with the rise of the fractional parameter and relaxation time while an increase in the values of hartmann number leads to a slower velocity in the rectangular pipe

radial basis functions and level set method for structural topology optimization level set methods have become an attractive design tool in shape and topology optimization for obtaining lighter and more efficient structures in this paper the popular radial basis functions rbfs in scattered data fitting and function approximation are incorporated into the conventional level set methods to construct a more efficient approach for structural topology optimization rbf implicit modelling with multiquadric mq splines is developed to define the implicit level set function with a high level of accuracy and smoothness a rbf level set optimization method is proposed to transform the hamilton jacobi partial differential equation pde into a system of ordinary differential equations odes over the entire design domain by using a collocation formulation of the method of lines with the mathematical convenience the original time dependent initial value problem is changed to an interpolation problem for the initial values of the generalized expansion coefficients a physically meaningful and efficient extension velocity method is presented to avoid possible problems without reinitialization in the level set methods the proposed method is implemented in the framework of minimum compliance design that has been extensively studied in topology optimization and its efficiency and accuracy over the conventional level set methods are highlighted numerical examples show the success of the present rbf level set method in the accuracy convergence speed and insensitivity to initial designs in topology optimization of two dimensional 2d structures it is suggested that the introduction of the radial basis functions to the level set methods can be promising in structural topology optimization

an operator splitting algorithm for tikhonov regularized topology optimization in this work we investigate a tikhonov type regularization scheme to address the ill posedness of the classical compliance minimization problem we observe that a semi implicit discretization of the gradient descent flow for minimization of the regularized objective function leads to a convolution of the original gradient descent step with the green s function associated with the modified helmholtz equation the appearance of filtering in this update scheme is different from the current density and sensitivity filtering techniques in the literature the next iterate is defined as the projection of this provisional density onto the space of admissible density functions for a particular choice of projection mapping we show that the algorithm is identical to the well known forward backward splitting algorithm an insight that can be further explored for topology optimization also of interest is that with an appropriate choice of the projection parameter nearly all intermediate densities are eliminated in the optimal solution using the common density material models we show examples of near binary solutions even for large values of the regularization parameter

multiparameter spectral theory and separation of variables multiparameter spectral theory generalizes the classical spectral theory of linear operators to n linear operators linked by n spectral parameters the spectral parameters arise as separation constants when for example separation of variables techniques are used to solve boundary value problems for partial differential equations in this paper we discuss some of the fundamental aspects of the theory such as solvability commutativity and abstract representation theory many of these concepts are of importance to modern developments in separation of variables techniques the ideas are illustrated in application to differential equations and special functions of mathematical physics

topology optimization of structures using meshless density variable approximants this paper proposes a new structural topology optimization method using a dual level point wise density approximant and the meshless galerkin weak forms totally based on a set of arbitrarily scattered field nodes to discretize the design domain the moving least squares mls method is used to construct shape functions with compactly supported weight functions to achieve meshless approximations of system state equations the mls shape function with the zero order consistency will degenerate to the well known shepard function while the mls shape function with the first order consistency refers to the widely studied mls shape function the shepard function is then applied to construct a physically meaningful dual level density approximant because of its non negative and range restricted properties first in terms of the original set of nodal density variables this study develops a nonlocal nodal density approximant with enhanced smoothness by incorporating the shepard function into the problem formulation the density at any node can be evaluated according to the density variables located inside the influence domain of the current node second in the numerical implementation we present a point wise density interpolant via the shepard function method the density of any computational point is determined by the surrounding nodal densities within the influence domain of the concerned point according to a set of generic design variables scattered at field nodes an alternative solid isotropic material with penalization model is thus established through the proposed dual level density approximant the lagrangian multiplier method is included to enforce the essential boundary conditions because of the lack of the kronecker delta function property of mls meshless shape functions two benchmark numerical examples are employed to demonstrate the effectiveness of the proposed method in particular its applicability in eliminating numerical instabilities copyright 2012 john wiley sons ltd

an extended level set method for shape and topology optimization in this paper the conventional level set methods are extended as an effective approach for shape and topology optimization by the introduction of the radial basis functions rbfs the rbf multiquadric splines are used to construct the implicit level set function with a high level of accuracy and smoothness and to discretize the original initial value problem into an interpolation problem the motion of the dynamic interfaces is thus governed by a system of coupled ordinary differential equations odes and a relatively smooth evolution can be maintained without reinitialization a practical implementation of this method is further developed for solving a class of energy based optimization problems in which approximate solution to the original hamilton jacobi equation may be justified and nucleation of new holes inside the material domain is allowed for furthermore the severe constraints on the temporal and spatial discretizations can be relaxed leading to a rapid convergence to the final design insensitive to initial guesses the normal velocities are chosen to perform steepest gradient based optimization by using shape sensitivity analysis and a bi sectioning algorithm a physically meaningful and efficient extension velocity method is also presented the proposed method is implemented in the framework of minimum compliance design and its efficiency over the existing methods is highlighted numerical examples show its accuracy convergence speed and insensitivity to initial designs in shape and topology optimization of two dimensional 2d problems that have been extensively investigated in the literature

structural optimization using sensitivity analysis and a level set method in the context of structural optimization we propose a new numerical method based on a combination of the classical shape derivative and of the level set method for front propagation we implement this method in two and three space dimensions for a model of linear or nonlinear elasticity we consider various objective functions with weight and perimeter constraints the shape derivative is computed by an adjoint method the cost of our numerical algorithm is moderate since the shape is captured on a fixed eulerian mesh although this method is not specifically designed for topology optimization it can easily handle topology changes however the resulting optimal shape is strongly dependent on the initial guess

some estimates of solutions for the equations of motion of compressible viscous fluid in the three dimensional exterior domain abstract we consider the equations of motion of compressible viscous fluid in an exterior domain in r 3 we give the l q l p estimates for solutions to the linearized equations and show an optimal decay estimate for solutions to the nonlinear problem in particular we shall give l 1 estimates which implies the diffusion wave of compressible navier stokes flow

a level set method for topology optimization of heat conduction problem under multiple load cases in this paper we present a numerical approach of topology optimization under multiple load cases for heat conduction problem this framework is based on the theories of topological derivative and shape derivative for elliptic system we employ level set model to implicitly represent geometric boundary of thermal conductive material introducing topological derivative will generate new topology in the design domain which suppresses the dependence of initial topology guess to some extent the shape optimization is obtained by combining shape derivative with level set method the functional of quadratic temperature gradient is taken as the objective function in our analysis which is subjected to the state equation of steady heat conduction and volume constrain the shape of material domain is treated as the design variable and the final result is achieved by updating level set function gradually we develop an effective numerical technique to implement the optimal design with multiple load cases for heat conduction problem numerical examples demonstrate that our proposed approach is effective and robust for topology optimization of heat conduction problem

bifurcation analysis of magnetic reconnection in hall mhd systems abstract the influence of the hall term on the width of the magnetic islands of the tearing mode is examined we applied the center manifold cmf theory to a magnetohydrodynamic mhd system the mhd system was chosen to be incompressible and includes in addition to viscosity the hall term in ohm s law for certain values of physical parameters the corresponding center manifold is two dimensional and therefore the original partial differential equations could be reduced to a two dimensional system of ordinary ones this amplitude equations exhibit a pitchfork bifurcation which corresponds to the occurrence of the tearing mode eigenvalue problems and linear equations due to the center manifold reduction were solved numerically with the arpack library an important result of this analysis is the growth of the tearing mode island width by increasing the hall parameter a feature which has been observed in recent numerical simulations of collisionless reconnection

topology optimization of non linear elastic structures and compliant mechanisms abstract a linear elastic response is assumed in most structural topology optimization problems while this assumption is valid for a wide variety of problems it is not valid for structures undergoing large displacements the elastic structural analysis used here accommodates geometric and material non linearities the material density field is filtered to enforce a length scale on the field variation and is penalized to remove less effective intermediate densities the filtering scheme is embedded in the structural analysis to resolve the non existent solution to the solid void topology problem in this way we know precisely what optimization problem is being solved the structural topology optimization formulation is also used to design compliant mechanisms

a moving superimposed finite element method for structural topology optimization level set methods are becoming an attractive design tool in shape and topology optimization for obtaining efficient and lighter structures in this paper a dynamic implicit boundary based moving superimposed finite element method s version fem or s fem is developed for structural topology optimization using the level set methods in which the variational interior and exterior boundaries are represented by the zero level set both a global mesh and an overlaying local mesh are integrated into the moving s fem analysis model a relatively coarse fixed eulerian mesh consisting of bilinear rectangular elements is used as a global mesh the local mesh consisting of flexible linear triangular elements is constructed to match the dynamic implicit boundary captured from nodal values of the implicit level set function in numerical integration using the gauss quadrature rule the practical difficulty due to the discontinuities is overcome by the coincidence of the global and local meshes a double mapping technique is developed to perform the numerical integration for the global and coupling matrices of the overlapped elements with two different co ordinate systems an element killing strategy is presented to reduce the total number of degrees of freedom to improve the computational efficiency a simple constraint handling approach is proposed to perform minimum compliance design with a volume constraint a physically meaningful and numerically efficient velocity extension method is developed to avoid the complicated pde solving procedure the proposed moving s fem is applied to structural topology optimization using the level set methods as an effective tool for the numerical analysis of the linear elasticity topology optimization problems for the classical elasticity problems in the literature the present s fem can achieve numerical results in good agreement with those from the theoretical solutions and or numerical results from the standard fem for the minimum compliance topology optimization problems in structural optimization the present approach significantly outperforms the well recognized ersatz material approach as expected in the accuracy of the strain field numerical stability and representation fidelity at the expense of increased computational time it is also shown that the present approach is able to produce structures near the theoretical optimum it is suggested that the present s fem can be a promising tool for shape and topology optimization using the level set methods copyright 2005 john wiley sons ltd

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

the method of moving asymptotes a new method for structural optimization a new method for non linear programming in general and structural optimization in particular is presented in each step of the iterative process a strictly convex approximating subproblem is generated and solved the generation of these subproblems is controlled by so called moving asymptotes which may both stabilize and speed up the convergence of the general process

a logarithmic improvement of regularity criterion for the mhd equations in terms of the pressure abstract in this paper we prove a logarithmic improvement of regularity criterion only in terms of the pressure in morrey campanato spaces for the cauchy problem to the incompressible mhd equations

bilateral filtering for structural topology optimization filtering has been a major approach used in the homogenization based methods for structural topology optimization to suppress the checkerboard pattern and relieve the numerical instabilities in this paper a bilateral filtering technique originally developed in image processing is presented as an efficient approach to regularizing the topology optimization problem a non linear bilateral filtering process leads to a suitable problem regularization to eliminate the checkerboard instability pronounced edge preserving smoothing characteristics to favour the 0 1 convergence of the mass distribution and computational efficiency due to its single pass and non iterative nature thus we show that the application of the bilateral filtering brings more desirable effects of checkerboard free mesh independence crisp boundary computational efficiency and conceptual simplicity the proposed bilateral technique has a close relationship with the conventional domain filtering and range filtering the proposed method is implemented in the framework of a power law approach based on the optimality criteria and illustrated with 2d examples of minimum compliance design that has been extensively studied in the recent literature of topology optimization and its efficiency and accuracy are highlighted copyright 2005 john wiley sons ltd

modelling topology optimization problems as linear mixed 0 1 programs this paper deals with topology optimization of discretized continuum structures it is shown that a large class of non linear 0 1 topology optimization problems including stress and displacement constrained minimum weight problems can equivalently be modelled as linear mixed 0 1 programs the modelling approach is applied to some test problems which are solved to global optimality