poisson nernst planck equations for simulating biomolecular diffusion reaction processes i finite element solutions in this paper we developed accurate finite element methods for solving 3 d poisson nernst planck pnp equations with singular permanent charges for simulating electrodiffusion in solvated biomolecular systems the electrostatic poisson equation was defined in the biomolecules and in the solvent while the nernst planck equation was defined only in the solvent we applied a stable regularization scheme to remove the singular component of the electrostatic potential induced by the permanent charges inside biomolecules and formulated regular well posed pnp equations an inexact newton method was used to solve the coupled nonlinear elliptic equations for the steady problems while an adams bashforth crank nicolson method was devised for time integration for the unsteady electrodiffusion we numerically investigated the conditioning of the stiffness matrices for the finite element approximations of the two formulations of the nernst planck equation and theoretically proved that the transformed formulation is always associated with an ill conditioned stiffness matrix we also studied the electroneutrality of the solution and its relation with the boundary conditions on the molecular surface and concluded that a large net charge concentration is always present near the molecular surface due to the presence of multiple species of charged particles in the solution the numerical methods are shown to be accurate and stable by various test problems and are applicable to real large scale biophysical electrodiffusion problems

mesh refinement processes based on the generalized bisection of simplices mesh refinement processes based on the generalized bisection of simplices are discussed and characterized in the context of the general theory of rheinboldt siam j numer anal 17 1980 pp 766 778 then it is proved that such processes allow the construction of sequences of naturally smooth conforming and nested nonuniform meshes in fact it is shown that there exists a generalized mesh refinement operator that for any conforming triangulation delta and for any v subset delta produces a nested smooth conforming triangulation delta containing successors of all elements of v and such that the minimum cell size of delta is bounded from below by half the minimum cell size of delta two conforming mesh refinement algorithms that allow the selective refinement of computational triangulations are explicitly given

affine parameter dependent lyapunov functions and real parametric uncertainty this paper presents new tests to analyze the robust stability and or performance of linear systems with uncertain real parameters these tests are extensions of the notions of quadratic stability and performance where the fixed quadratic lyapunov function is replaced by a lyapunov function with affine dependence on the uncertain parameters admittedly with some conservatism the construction of such parameter dependent lyapunov functions can be reduced to a linear matrix inequality lmi problem and hence is numerically tractable these lmi based tests are applicable to constant or time varying uncertain parameters and are less conservative than quadratic stability in the case of slow parametric variations they also avoid the frequency sweep needed in real spl mu analysis and numerical experiments indicate that they often compare favorably with spl mu analysis for time invariant parameter uncertainty

modeling electrokinetic flows by the smoothed profile method we propose an efficient modeling method for electrokinetic flows based on the smoothed profile method spm 1 4 and spectral element discretizations the new method allows for arbitrary differences in the electrical conductivities between the charged surfaces and the surrounding electrolyte solution the electrokinetic forces are included into the flow equations so that the poisson boltzmann and electric charge continuity equations are cast into forms suitable for spm the method is validated by benchmark problems of electroosmotic flow in straight channels and electrophoresis of charged cylinders we also present simulation results of electrophoresis of charged microtubules and show that the simulated electrophoretic mobility and anisotropy agree with the experimental values

convergent adaptive finite elements for the nonlinear laplacian the numerical solution of the homogeneous dirichlet problem for the p laplacian p in 1 infty is considered we propose an adaptive algorithm with continuous piecewise affine finite elements and prove that the approximate solutions converge to the exact one while the algorithm is a rather straight forward generalization of those for the linear case p 2 the proof of its convergence is different in particular it does not rely on a strict error reduction

a finite element recovery approach to green s function approximations with applications to electrostatic potential computation in this paper a finite element recovery approach is proposed to improve the accuracy of finite element approximations for green s functions in three dimensions this recovery approach is based on some simple postprocessing it is proved by both theory and numerics that the recovery approach is very efficient in particular the approach is successfully applied to some electrostatic potential computations

finite element approximations of nonlinear eigenvalue problems in quantum physics in this paper we study finite element approximations of a class of nonlinear eigenvalue problems arising from quantum physics we derive both a priori and a posteriori finite element error estimates and obtain optimal convergence rates for both linear and quadratic finite element approximations in particular we analyze the convergence and complexity of an adaptive finite element method in our analysis we utilize certain relationship between the finite element eigenvalue problem and the associated finite element boundary value approximations we also present several numerical examples in quantum physics that support our theory

robust h 2 and h control of discrete time systems with polytopic uncertainties via dynamic output feedback this paper addresses the problem of robust h 2 and h control of discrete linear time invariant lti systems with polytopic uncertainties via dynamic output feedback the problem has been known to be difficult when a parameter dependent lyapunov function is to be applied for a less conservative design due to non convexity our approach is based on a novel bounding technique that converts the non convex optimization into a convex one together with a line search which is simple but may be conservative to further reduce the design conservatism an algorithm based on the sequentially linear programming method slpmm is proposed a numerical example is given which demonstrates the feasibility of the proposed design methods

a linear programming oriented procedure for quadratic stabilization of uncertain systems abstract this paper gives a new necessary and sufficient condition for linear quadratic stabilization of linear uncertain systems when both the dynamic as well as the control matrix are subject to uncertainty a constructive numerical procedure is defined to check the condition and it furthermore provides a stabilizing linear feedback gain some experiments are presented

stability robustness of interval matrices via lyapunov quadratic forms a sufficient condition for the robust stability of a class of interval matrices is derived using the lyapunov approach the matrices considered have elements which are nonlinear functions of a vector of independent and bounded parameters the robust stability condition requires that a quadratic form be positive definite in a finite number of conspicuous points of an enlarged parameter space

a descriptor system approach to robust stability analysis and controller synthesis this note revisits the problem of robust stability analysis and synthesis via parameter dependent lyapunov functions a descriptor system approach is taken to deriving linear matrix inequality conditions for robust stability and robust stabilizability of the polytopic systems and the affine parameter systems under these robust stabilizability conditions state feedback laws that achieve robust stabilization are also constructed the developed results can be viewed as a continuous time counterpart of the discrete time results by oliveira et al the effectiveness of the proposed analysis and synthesis approach is demonstrated by numerical examples

convergence of adaptive finite element methods for general second order linear elliptic pdes we prove convergence of adaptive finite element methods afems for general nonsymmetric second order linear elliptic pdes thereby extending the result of morin nochetto and siebert it siam j numer anal 38 2000 pp 466 488 it siam rev 44 2002 pp 631 658 the proof relies on quasi orthogonality which accounts for the bilinear form not being a scalar product together with novel error and oscillation reduction estimates which now do not decouple we show that afems are a contraction for the sum of energy error plus oscillation numerical experiments including oscillatory coefficients and both coercive and noncoercive convection diffusion pde illustrate the theory and yield optimal meshes

sufficient lmi conditions for output feedback control problems the authors present linear matrix inequality lmi conditions for output feedback control problems the results are based on sufficient conditions because they are dependent on the particular state space representation used for describing the system nevertheless the conditions are not sensitive to a certain class of state space transformations and if the control problem is feasible then there exists some state space transformation leading the conditions to be necessary and sufficient for the problem the authors approach can be used for designing decentralized controllers and is easily extended to h sub 2 h sub spl infin and mixed h sub 2 h sub spl infin problems via standard lmi techniques the continuous and discrete time cases are considered and numerical examples are given to illustrate the results

a monotone finite element scheme for convection diffusion equations a simple technique is given in this paper for the construction and analysis of a class of finite element discretizations for convection diffusion problems in any spatial dimension by properly averaging the pde coefficients on element edges the resulting finite element stiffness matrix is an m matrix under some mild assumption for the underlying generally unstructured finite element grids as a consequence the proposed edge averaged finite element scheme is particularly interesting for the discretization of convection dominated problems this scheme admits a simple variational formulation it is easy to analyze and it is also suitable for problems with a relatively smooth flux variable some simple numerical examples are given to demonstrate its effectiveness for convection dominated problems

new solution decomposition and minimization schemes for poisson boltzmann equation in calculation of biomolecular electrostatics the poisson boltzmann equation pbe is one widely used implicit solvent continuum model in the calculation of electrostatic potential energy for biomolecules in ionic solvent but its numerical solution remains a challenge due to its strong singularity and nonlinearity caused by its singular distribution source terms and exponential nonlinear terms to effectively deal with such a challenge in this paper new solution decomposition and minimization schemes are proposed together with a new pbe analysis on solution existence and uniqueness moreover a pbe finite element program package is developed in python based on the fenics program library and gamer a molecular surface and volumetric mesh generation program package numerical tests on proteins and a nonlinear born ball model with an analytical solution validate the new solution decomposition and minimization schemes and demonstrate the effectiveness and efficiency of the new pbe finite element program package

robust filtering of discrete time linear systems with parameter dependent lyapunov functions robust filtering of linear time invariant discrete time uncertain systems is investigated through a new parameter dependent lyapunov matrix procedure its main interest relies on the fact that the lyapunov matrix used in stability checking does not appear in any multiplicative term with the uncertain matrices of the dynamic model we show how to use such an approach to determine high performance h2 robust filters by solving a linear problem constrained by linear matrix inequalities lmis the results encompass the previous works in the quadratic lyapunov setting numerical examples illustrate the theoretical results

on the computation and reduction of the peak to average power ratio in multicarrier communications for any code c defined over an equal energy constellation it is first shown that at any time instance the problem of determining codewords of c with high peak to average power ratios papr in a multicarrier communication system is intimately related to the problem of minimum distance decoding of c subsequently a method is proposed for computing the papr by minimum distance decoding of c at many points of time moreover an upper bound on the error between this computed value and the true one is derived analogous results are established for codes defined over arbitrary signal constellations as an application of this computational method an approach for reducing the papr of c proposed by jones and wilkinson 1996 is revisited this approach is based on introducing a specific phase shift to each coordinate of all the codewords where phase shifts are independent of the codewords and known both to the transmitter and the receiver we optimize the phase shifts offline by applying our method for computing the papr for the coding scenario proposed by the etsi bran standardization committee reductions of order 4 5 db can be freely obtained using the computed phase shifts examples are provided showing that most of the gain is preserved when the computed optimal phase shifts are rounded to quantenary phase shift keying psk 8 psk and 16 psk type phase shifts

a two component matched interface and boundary mib regularization for charge singularity in implicit solvation abstract we present a new matched interface and boundary mib regularization method for treating charge singularity in solvated biomolecules whose electrostatics are described by the poisson boltzmann pb equation in a regularization method by decomposing the potential function into two or three components the singular component can be analytically represented by the green s function while other components possess a higher regularity our new regularization combines the efficiency of two component schemes with the accuracy of the three component schemes based on this regularization a new mib finite difference algorithm is developed for solving both linear and nonlinear pb equations where the nonlinearity is handled by using the inexact newton s method compared with the existing mib pb solver based on a three component regularization the present algorithm is simpler to implement by circumventing the work to solve a boundary value poisson equation inside the molecular interface and to compute related interface jump conditions numerically moreover the new mib algorithm becomes computationally less expensive while maintains the same second order accuracy this is numerically verified by calculating the electrostatic potential and solvation energy on the kirkwood sphere on which the analytical solutions are available and on a series of proteins with various sizes

l stability of finite element approximations to elliptic gradient equations we examine thel stability of piecewise linear finite element approximationsu to the solutionu to elliptic gradient equations of the form a x u f x u g x wheref is monotonically increasing inu we identify a prioril bounds for the finite element solutionu which we call reduced bounds and which are marginally weaker than those for the original differential equations for the general n dimensionai case we identify new conditions on the mesh such that under the assumption thatf is lipschitz continuous on a finite interval u satisfies the reduced l bounds mentioned above the new n dimensional regularity conditions preclude quasi rectangular meshes moreover we show thatu is stable inl in two dimensions for a discretization mesh on which a x u gives rise to anm matrix whileu is stable for any mesh in one dimension the condition that the discretization of a x u has to be anm matrix still allows the inclusion of the important case of triangulating in a quasi rectangular fashion the results are valid for either the pure neumann problem or the general mixed dirichlet neumann boundary value problem while interfaces may be present the boundary conditions foru are obtained by use of nonexpansive pointwise projection operators

constant modulus and reduced papr block differential encoding for frequency selective channels frequency selective channels can be converted to a set of flat fading subchannels by employing orthogonal frequency division multiplexing ofdm conventional differential encoding on each subchannel however suffers from loss of multipath diversity and a very high peak to average power ratio papr which causes undesirable nonlinear effects to mitigate these effects we design a block differential encoding scheme over the subchannels that preserves multipath diversity and in addition results in constant modulus transmitted symbols this property is shown to ensure that the papr of the continuous time transmitted waveform is reduced by a large factor the maximum likelihood decoder for the proposed scheme conditioned on the current and previous received block is shown to have linear complexity in the number of subcarriers the constant modulus scheme will yield good bit error rate performance with full rate only if short blocks are used however one may mitigate this problem by relaxing the constant modulus requirement we show that in a practical ofdm system we can group the subcarriers into shorter subblocks in a certain manner and apply the constant modulus technique to each subblock thus we improve diversity at a very low decoder complexity and at the same time we introduce an upper bound on the discrete time papr which in turn may lead to appreciable reduction in continuous time papr depending on the system parameters finally in situations where we can sacrifice rate additional complex field coding may be used to exploit the multipath diversity provided by channels longer than those the simple scheme can handle

an adaptive uzawa fem for the stokes problem convergence without the inf sup condition we introduce and study an adaptive finite element method fem for the stokes system based on an uzawa outer iteration to update the pressure and an elliptic adaptive inner iteration for velocity we show linear convergence in terms of the outer iteration counter for the pairs of spaces consisting of continuous finite elements of degree k for velocity whereas for pressure the elements can be either discontinuous of degree k 1 or continuous of degree k 1 and k the popular taylor hood family is the sole example of stable elements included in the theory which in turn relies on the stability of the continuous problem and thus makes no use of the discrete inf sup condition we discuss the realization and complexity of the elliptic adaptive inner solver and provide consistent computational evidence that the resulting meshes are quasi optimal

convergence analysis of an adaptive nonconforming finite element method an adaptive nonconforming finite element method is developed and analyzed that provides an error reduction due to the refinement process and thus guarantees convergence of the nonconforming finite element approximations the analysis is carried out for the lowest order crouzeix raviart elements and leads to the linear convergence of an appropriate adaptive nonconforming finite element algorithm with respect to the number of refinement levels important tools in the convergence proof are a discrete local efficiency and a quasi orthogonality property the proof does neither require regularity of the solution nor uses duality arguments as a consequence on the data control no particular mesh design has to be monitored

an improved lmi condition for robust d stability of uncertain polytopic systems a sufficient condition for robust d stability of linear systems with polytope type uncertainties is proposed the result is based on a linear parameter dependent lyapunov function obtained from the feasibility test of a set of linear matrix inequalities lmis defined at the vertices of the polytope this improved lmi condition encompasses previous results based on additional inequalities as well as results based on extra variables

adaptive finite element methods with convergence rates adaptive finite element methods for numerically solving elliptic equations are used often in practice only recently 12 17 have these methods been shown to converge however this convergence analysis says nothing about the rates of convergence of these methods and therefore does in principle not guarantee yet any numerical advantages of adaptive strategies versus non adaptive strategies the present paper modifies the adaptive method of morin nochetto and siebert 17 for solving the laplace equation with piecewise linear elements on domains in 2 by adding a coarsening step and proves that this new method has certain optimal convergence rates in the energy norm which is equivalent to the h1 norm namely it is shown that whenever s 0 and the solution u is such that for each n 1 it can be approximated to accuracy o n s in the energy norm by a continuous piecewise linear function on a triangulation with n cells using complete knowledge of u then the adaptive algorithm constructs an approximation of the same type with the same asymptotic accuracy while using only information gained during the computational process moreover the number of arithmetic computations in the proposed method is also of order o n for each n 1 the construction and analysis of this adaptive method relies on the theory of nonlinear approximation

continuous time analysis eigenstructure assignment and h sub 2 synthesis with enhanced linear matrix inequalities lmi characterizations this note describes a new framework for the analysis and synthesis of control systems which constitutes a genuine continuous time extension of results that are only available in discrete time in contrast to earlier results the proposed methods involve a specific transformation on the lyapunov variables and a reciprocal variant of the projection lemma in addition to the classical linearizing transformations on the controller data for a wide range of problems including robust analysis and synthesis multichannel h sub 2 stateand output feedback syntheses the approach leads to potentially less conservative linear matrix inequality lmi characterizations this comes from the fact that the technical restriction of using a single lyapunov function is to some extent ruled out in this new approach moreover the approach offers new potentials for problems that cannot be handled using earlier techniques an important instance is the eigenstructure assignment problem blended with lyapunov type constraints which is given a simple and tractable formulation

an efficient higher order fast multipole boundary element solution for poisson boltzmann based molecular electrostatics in order to compute polarization energy of biomolecules we describe a boundary element approach to solving the linearized poisson boltzmann equation our approach combines several important features including the derivative boundary formulation of the problem and a smooth approximation of the molecular surface based on the algebraic spline molecular surface state of the art software for numerical linear algebra and the kernel independent fast multipole method is used for both simplicity and efficiency of our implementation we perform a variety of computational experiments testing our method on a number of actual proteins involved in molecular docking and demonstrating the effectiveness of our solver for computing molecular polarization energy

near shannon limit and low peak to average power ratio turbo block coded ofdm in this paper we present an advanced solution for the long standing problem of large peak to average power ratio papr in orthogonal frequency division multiplexing ofdm systems although the design of low papr codewords has been extensively studied and the existence of asymptotically good codes with low papr is also proven still no code has been constructed to satisfy all requirements the main goal of the paper is to develop a coding scheme that not only generates low papr codewords but it also performs relatively close to the shannon limit we achieve this goal by implementing a time frequency turbo block coded ofdm in this scheme we design the frequency domain component to have a tightly bounded papr the time domain component code is designed to obtain good performance while the decoding algorithm has reasonable complexity through comparative performance evaluation we show that utilizing the proposed method we achieve considerable improvement in terms of papr while we slightly loose the performance compared to capacity achieving codes with similar overall block length

pointwise a posteriori error estimates for monotone semi linear equations we derive upper and lower a posteriori estimates for the maximum norm error in finite element solutions of monotone semi linear equations the estimates hold for lagrange elements of any fixed order non smooth nonlinearities and take numerical integration into account the proof hinges on constructing continuous barrier functions by correcting the discrete solution appropriately and then applying the continuous maximum principle no geometric mesh constraints are thus required numerical experiments illustrate reliability and efficiency properties of the corresponding estimators and investigate the performance of the resulting adaptive algorithms in terms of the polynomial order and quadrature

a mortar finite element approximation for the linear poisson boltzmann equation in this paper a new numerical method is presented for solving the linear poisson boltzmann equation a mortar finite element method with fundamental solution and artificial boundary condition are used to deal with the difficulties in numerical simulation and optimal error estimates are obtained

convergence of adaptive finite element methods adaptive finite element methods fems have been widely used in applications for over 20 years now in practice they converge starting from coarse grids although no mathematical theory has been able to prove this assertion ensuring an error reduction rate based on a posteriori error estimators together with a reduction rate of data oscillation information missed by the underlying averaging process we construct a simple and efficient adaptive fem for elliptic partial differential equations we prove that this algorithm converges with linear rate without any preliminary mesh adaptation nor explicit knowledge of constants any prescribed error tolerance is thus achieved in a finite number of steps a number of numerical experiments in two and three dimensions yield quasi optimal meshes along with a competitive performance extensions to higher order elements and applications to saddle point problems are discussed as well

the finite element approximation of the nonlinear poisson boltzmann equation a widely used electrostatics model in the biomolecular modeling community the nonlinear poisson boltzmann equation along with its finite element approximation are analyzed in this paper a regularized poisson boltzmann equation is introduced as an auxiliary problem making it possible to study the original nonlinear equation with delta distribution sources a priori error estimates for the finite element approximation are obtained for the regularized poisson boltzmann equation based on certain quasi uniform grids in two and three dimensions adaptive finite element approximation through local refinement driven by an a posteriori error estimate is shown to converge the poisson boltzmann equation does not appear to have been previously studied in detail theoretically and it is hoped that this paper will help provide molecular modelers with a better foundation for their analytical and computational work with the poisson boltzmann equation note that this article apparently gives the first rigorous convergence result for a numerical discretization technique for the nonlinear poisson boltzmann equation with delta distribution sources and it also introduces the first provably convergent adaptive method for the equation this last result is currently one of only a handful of existing convergence results of this type for nonlinear problems

regularity results for elliptic equations in lipschitz domains abstract we develop a simple variational argument based on the usual nirenberg difference quotient technique to deal with the regularity of the solutions of dirichlet and neumann problems for some linear and quasilinear elliptic equation in lipschitz domains we obtain optimal regularity results in the natural family of sobolev spaces associated with the variational structure of the equations in the linear case we obtain in a completely different way some of the results of d jerison and c e kenig about the laplace equation

a poisson boltzmann solver on irregular domains with neumann or robin boundary conditions on non graded adaptive grid we introduce a second order solver for the poisson boltzmann equation in arbitrary geometry in two and three spatial dimensions the method differs from existing methods solving the poisson boltzmann equation in the two following ways first non graded quadtree in two spatial dimensions and octree in three spatial dimensions grid structures are used second neumann or robin boundary conditions are enforced at the irregular domain s boundary the irregular domain is described implicitly and the grid needs not to conform to the domain s boundary which makes grid generation straightforward and robust the linear system is symmetric positive definite in the case where the grid is uniform nonsymmetric otherwise in this case the resulting matrix is an m matrix thus the linear system is invertible convergence examples are given in both two and three spatial dimensions and demonstrate that the solution is second order accurate and that quadtree octree grid structures save a significant amount of computational power at no sacrifice in accuracy

a class of robust stability conditions where linear parameter dependence of the lyapunov function is a necessary condition for arbitrary parameter dependence abstract in previous works we have proposed a robust stability condition for linear time invariant discrete time systems which makes use of a lyapunov function with linear dependence on the uncertain parameters this condition is expressed as a set of linear matrix inequalities lmi where an additional variable is kept common to all lmi these features have enabled the development of successful robust filtering and control algorithms in this short note we investigate possible extensions of this stability condition to handle lyapunov functions with arbitrary parameter dependence while keeping a variable common to all lmi by showing that feasibility of the original condition is indeed necessary for the existence of a family of robust stability conditions where the lyapunov function can have arbitrary dependence on the uncertain parameters we conclude that no such extensions are possible

improved lmi representations for the analysis and the design of continuous time systems with polytopic type uncertainty simple modifications to the representation of the bounded real lemma brl in the linear continuous time invariant case are introduced these modifications reduce the overdesign that occurs in the analysis and the design of systems with polytopic type uncertainties a different lyapunov function accompanies each of the vertices of the uncertainty polytope thus eliminating the need for quadratic stability or stabilizability the advantages of these new representations are demonstrated by way of two examples

synthesis of power efficient multitone signals with flat amplitude spectrum it is shown that generally any binary or polyphase sequence belonging to a pair of complementary sequences can be used to construct the initial phases of tones forming a multitone signal with the crest factor less than or equal to 6 db the previously proposed shapiro rudin sequences are representatives of a much larger family of binary golay complementary sequences numerical investigations show that the values of the crest factors obtained by applying complementary sequences binary or polyphase are between 5 and 6 db regardless of the number of tones

an optimal adaptive finite element method although existing adaptive finite element methods for solving second order elliptic equations often perform better in practical computations than nonadaptive ones usually they are not even proven to converge only recently in the work of dorfler siam j numer anal 33 1996 pp 1106 1124 and that of morin nochetto and siebert siam j numer anal 38 2000 pp 466 488 adaptive methods were constructed for which convergence could be demonstrated however convergence alone does not imply that the method is more efficient than its nonadaptive counterpart in numer math 97 2004 pp 219 268 binev dahmen and devore added a coarsening step to the routine of morin nochetto and siebert and proved that the resulting method is quasi optimal in the following sense if the solution is such that for some s 0 the error in energy norm of the best continuous piecewise linear approximations subordinate to any partition with n triangles is mathcal o n s then given an eps 0 the adaptive method produces an approximation with an error less than eps subordinate to a partition with mathcal o eps 1 s triangles in only mathcal o eps 1 s operations in this paper employing a different type of adaptive partition we develop an adaptive method with properties similar to those of binev dahmen and devore s method but unlike their method our coarsening routine will be based on a transformation to a wavelet basis and we expect it to have better quantitative properties furthermore all our results are valid uniformly in the size of possible jumps of the diffusion coefficients since the algorithm uses solely approximations of the right hand side we can even allow right hand sides in h 1 omega that lie outside l 2 omega at least when they can be sufficiently well approximated by piecewise constants in our final adaptive algorithm all tolerances depend on an a posteriori estimate of the current error instead of an a priori one this can be expected to provide quantitative advantages

adaptive multivlevel methods in three space dimensions we consider the approximate solution of self adjoint elliptic problems in three space dimensions by piecewise linear finite elements with respect to a highly non uniform tetrahedral mesh which is generated adaptively the arising linear systems are solved iteratively by the conjugate gradient method provided with a multilevel preconditioner here the accuracy of the iterative solution is coupled with the discretization error as the performance of hierarchical bases preconditioners deteriorates in three space dimensions the bpx preconditioner is used taking special care of an efficient implementation reliable a posteriori estimates for the discretization error are derived from a local comparison with the approximation resulting from piecewise quadratic elements to illustrate the theoretical results we consider a familiar model problem involving reentrant corners and a real life problem arising from hyperthermia a recent clinical method for cancer therapy

robust static output feedback control for linear discrete time systems with time varying uncertainties this paper is concerned with the problem of designing robust static output feedback controllers for linear discrete time systems with timevarying polytopic uncertainties sufficient conditions for robust static output feedback stabilizing controller designs are given in terms of solutions to a set of linear matrix inequalities and the results are extended to h2 and h static output feedback controller designs numerical examples are given to illustrate the effectiveness of the proposed design methods 2007 elsevier b v all rights reserved

on cosets of the generalized first order reed muller code with low pmepr golay sequences are well suited for use as codewords in orthogonal frequency division multiplexing ofdm since their peak to mean envelope power ratio pmepr in q ary phase shift keying psk modulation is at most 2 it is known that a family of polyphase golay sequences of length 2m organizes in m 2 cosets of a q ary generalization of the first order reed muller code rmq 1 m in this paper a more general construction technique for cosets of rm q 1 m with low pmepr is established these cosets contain so called near complementary sequences the application of this theory is then illustrated by providing some construction examples first it is shown that the m 2 cosets of rmq 1 m comprised of golay sequences just arise as a special case second further families of cosets of rmq 1 m with maximum pmepr between 2 and 4 are presented showing that some previously unexplained phenomena can now be understood within a unified framework a lower bound on the pmepr of cosets of rmq 1 m is proved as well and it is demonstrated that the upper bound on the pmepr is tight in many cases finally it is shown that all upper bounds on the pmepr of cosets of rmq 1 m also hold for the peak to average power ratio papr under the walsh hadamard transform wht

iterative decoding of binary block and convolutional codes iterative decoding of two dimensional systematic convolutional codes has been termed turbo de coding using log likelihood algebra we show that any decoder can be used which accepts soft inputs including a priori values and delivers soft outputs that can be split into three terms the soft channel and a priori inputs and the extrinsic value the extrinsic value is used as an a priori value for the next iteration decoding algorithms in the log likelihood domain are given not only for convolutional codes but also for any linear binary systematic block code the iteration is controlled by a stop criterion derived from cross entropy which results in a minimal number of iterations optimal and suboptimal decoders with reduced complexity are presented simulation results show that very simple component codes are sufficient block codes are appropriate for high rates and convolutional codes for lower rates less than 2 3 any combination of block and convolutional component codes is possible several interleaving techniques are described at a bit error rate ber of 10 sup 4 the performance is slightly above or around the bounds given by the cutoff rate for reasonably simple block convolutional component codes interleaver sizes less than 1000 and for three to six iterations

simplified approach to optimized iterative clipping and filtering for papr reduction of ofdm signals iterative clipping and filtering icf is a well known technique to reduce the peak to average power ratio papr of orthogonal frequency division multiplexing ofdm signals recently wang and luo investigated the clipped signal and proposed a modified algorithm called optimized icf oicf this is an optimal algorithm since it can achieve the required papr reduction with minimum in band distortion and far fewer iterations however oicf needs to solve a convex optimization problem with o n3 complexity where n represents the number of subcarriers in this paper instead of analyzing the clipped signal we study the clipping noise and propose a simplified oicf algorithm in the new algorithm solving the convex optimization problem is approximated by some simple algebraic operations and the computational complexity reduces to o n simulation results show that after three iterations the original oicf algorithm can achieve the desired papr while the simplified one exhibits almost the same performance for a 128 subcarrier and quadrature phase shift keying qpsk modulated ofdm system the papr reduction performance difference between the two algorithms are 5 10 3db at a 10 4 clipping probability and the bit error rate performance difference is 6 10 3 db at a 10 7 error probability

a weighted adaptive least squares finite element method for the poisson boltzmann equation abstract the finite element methodology has become a standard framework for approximating the solution to the poisson boltzmann equation in many biological applications in this article we examine the numerical efficacy of least squares finite element methods for the linearized form of the equations in particular we highlight the utility of a first order form noting optimality control of the flux variables and flexibility in the formulation including the choice of elements we explore the impact of weighting and the choice of elements on conditioning and adaptive refinement in a series of numerical experiments we compare the finite element methods when applied to the problem of computing the solvation free energy for realistic molecules of varying size

extended h 2 and h norm characterizations and controller parametrizations for discrete time systems this paper presents new synthesis procedures for discrete time linear systems it is based on a recently developed stability condition which contains as particular cases both the celebrated lyapunov theorem for precisely known systems and the quadratic stability condition for systems with uncertain parameters these new synthesis conditions have some nice properties a they can be expressed in terms of lmi linear matrix inequalities and b the optimization variables associated with the controller parameters are independent of the symmetric matrix that defines a quadratic lyapunov function used to test stability this second feature is important for several reasons first structural constraints as those appearing in the decentralized and static output feedback control design can be addressed less conservatively second parameter dependent lyapunov function can be considered with a very positive impact on the design of robust h 2 and h x control problems third the design of controller with mixed

consistency of semiconductor modeling an existence stability analysis for the stationary van roosbroeck system this paper examines the solution map of the stationary version of the van roosbroeck model for the flow of electrons and holes in a crystalline semiconductor thermodynamic equilibrium and the einstein relations linking mobility and diffusion are assumed to hold for this model incorporated into the model is the quantum statistical assumption that the carrier densities satisfy fermi dirac statistical laws with localization in the boltzmann tail this latter approximation which is seen to be inessential characterizes the conduction and valence bands as nondegenerate the boundary conditions are of two types and correspond to applied potential differences and doping on the contact portions of the device and insulation on the remainder the complete system then involves a coupled set of three nonlinear partial differential equations with their boundary conditions for the electrostatic potential and for the quasi fermi levels corresponding to the electron and hole concentrations in the absence of the classical nondegeneracy approximation the model remains valid but without a natural physical interpretation for two ofthe three dependent variables we demonstrate the existence ofsolutions for this system by associating a solution mapping t such that the fixed points of t define solutions of the system a priori estimates or weak maximum principles permit t to act invariantly on a naturally chosen subset of a hilbert product space the definition of t roughly follows the gummel procedure for uncoupling systems the schauder fixed point theorem is used to prove the existence of a fixed point for t uniqueness is not demonstrated and very possibly does not hold for these systems without special restrictions on the boundary conditions we also introduce a discrete version of the mapping t which is defined in terms of a family of finite difference approximations this mapping enjoys the stability property that it acts invariantly on a rectangular region in euclidean space the dimensions are the same as those specified in the pointwise bounds which define the domain of t a second existence theory framework with quasi constructive aspects is also studied this is based upon pseudomonotone operators the presentation is technology independent except for a section on mos fet devices these typically induce a breakdown ofuniform ellipticity and may be handled by modifications of the major arguments they also exemplify a class of devices for which the electrostatic field is defined on a strictly larger domain than the carriers themselves 1 introduction and model description this paper provides a mathematical analysis of a stationary system solution map which forms the basis for the highly successful computational algorithms used for the numerical solution of the semiconductor system cf bank rose and fichtner 3 our methods involve pointwise stability estimates on solution components organized in such a way that the solution map and a family of discrete approximations may be studied in parallel if desired moreover the weak solution methods do not require regularity theory hence are applicable to physical domains commonly encountered in practice such domains may include re entrant corner points etc and typically induce degenerate elliptic systems we shall also develop the model from physical principles the reason for this is not primarily to compile source material from several different references but rather to indicate clearly to the reader what the level of generality is and to facilitate the discussion of important variations in the device models the models studied herein are reaction diffusion con vection models for which the einstein relations linking carrier mobility and diffusion are assumed to hold the dependent variables of the system include one potential variable inducing an ambient field and two concentration variables for carriers whose convective movement is field dependent this suggests a fairly rich set ofpossible

a nonlinear elasticity model of macromolecular conformational change induced by electrostatic forces in this paper we propose a nonlinear elasticity model of macromolecular conformational change deformation induced by electrostatic forces generated by an implicit solvation model the poisson boltzmann equation for the electrostatic potential is analyzed in a domain varying with the elastic deformation of molecules and a new continuous model of the electrostatic forces is developed to ensure solvability of the nonlinear elasticity equations we derive the estimates of electrostatic forces corresponding to four types of perturbations to an electrostatic potential field and establish the existance of an equilibrium configuration using a fixed point argument under the assumption that the change in the ionic strength and charges due to the additional molecules causing the deformation are sufficiently small the results are valid for elastic models with arbitrarily complex dielectric interfaces and cavities and can be generalized to large elastic deformation caused by high ionic strength large charges and strong external fields by using continuation methods

convergence and optimality of adaptive mixed finite element methods the convergence and optimality of adaptive mixed finite element methods for the poisson equation are established in this paper the main difficulty for mixed finite element methods is the lack of minimization principle and thus the failure of orthogonality a quasi orthogonality property is proved using the fact that the error is orthogonal to the divergence free subspace while the part of the error that is not divergence free can be bounded by the data oscillation using a discrete stability result this discrete stability result is also used to get a localized discrete upper bound which is crucial for the proof of the optimality of the adaptive approximation

a new robust d stability condition for real convex polytopic uncertainty abstract the problem of robust d stability analysis with respect to real convex polytopic uncertainties is tackled a new lmi based sufficient condition for the existence of parameter dependent lyapunov functions is proposed this condition generalises previously published conditions numerical comparisons with quadratic stability results as well as previous results based on parameter dependent lyapunov functions illustrate the relevance of this new condition finally this result appears to be promising for robust multi objective performance analysis and control synthesis purposes

finite element methods and their convergence for elliptic and parabolic interface problems in this paper we consider the finite element methods for solving second order elliptic and parabolic interface problems in two dimensional convex polygonal domains nearly the same optimal l 2 norm and energy norm error estimates as for regular problems are obtained when the interfaces are of arbitrary shape but are smooth though the regularities of the solutions are low on the whole domain the assumptions on the finite element triangulation are reasonable and practical

data oscillation and convergence of adaptive fem data oscillation is intrinsic information missed by the averaging process associated with finite element methods fem regardless of quadrature ensuring a reduction rate of data oscillation together with an error reduction based on a posteriori error estimators we construct a simple and efficient adaptive fem for elliptic partial differential equations pdes with linear rate of convergence without any preliminary mesh adaptation nor explicit knowledge of constants any prescribed error tolerance is thus achieved in a finite number of steps a number of numerical experiments in two and three dimensions yield quasi optimal meshes along with a competitive performance

simple map decoding of first order reed muller and hamming codes a maximum a posteriori map probability decoder of a block code minimizes the probability of error for each transmitted symbol separately the standard way of implementing map decoding of a linear code is the bahl cocke jelinek raviv bcjr algorithm which is based on a trellis representation of the code the complexity of the bcjr algorithm for the first order reed muller rm 1 codes and hamming codes is proportional to n sup 2 where n is the code s length in this correspondence we present new map decoding algorithms for binary and nonbinary rm 1 and hamming codes the proposed algorithms have complexities proportional to q sup 2 n log sub q n where q is the alphabet size in particular for the binary codes this yields complexity of order n log n

a new discrete time robust stability condition a new robust stability condition for uncertain discrete time systems with convex polytopic uncertainty is given it enables to check stability using parameter dependent lyapunov functions which are derived from lmi conditions it is shown that this new condition provides better results than the classical quadratic stability besides the use of a parameter dependent lyapunov function this condition exhibits a kind of decoupling between the lyapunov and the system matrices which may be explored for control synthesis purposes a numerical example illustrates the results

a posteriori error estimates for nonlinear problems finite element discretizations of elliptic equations we give a general framework for deriving a posteriori error estimates for approximate solutions of nonlinear problems in a first step it is proven that the error of the approximate solution can be bounded from above and from below by an appropriate norm of its residual in a second step this norm of the residual is bounded from above and from below by a similar norm of a suitable finite dimensional approximation of the residual this quantity can easily be evaluated and for many practical applications sharp explicit upper and lower bounds are readily obtained the general results are then applied to finite element discretizations of scalar quasi linear elliptic partial differential equations of 2nd order the eigenvalue problem for scalar linear elliptic operators of 2nd order and the stationary incompressible navier stokes equations they immediately yield a posteriori error estimates which can easily be computed from the given data of the problem and the computed numerical solution and which give global upper and local lower bounds on the error of the numerical solution

optimality of multilevel preconditioners for local mesh refinement in three dimensions in this article we establish optimality of the bramble pasciak xu bpx norm equivalence and optimality of the wavelet modified or stabilized hierarchical basis whb preconditioner in the setting of local 3d mesh refinement in the analysis of whb methods a critical first step is to establish the optimality of bpx norm equivalence for the refinement procedures under consideration while the available optimality results for the bpx norm have been constructed primarily in the setting of uniformly refined meshes a notable exception is the local 2d red green result due to dahmen and kunoth the purpose of this article is to extend this original 2d optimality result to the local 3d red green refinement procedure introduced by bornemann erdmann and kornhuber and then to use this result to extend the whb optimality results from the quasi uniform setting to local 2d and 3d red green refinement scenarios the bpx extension is reduced to establishing that locally enriched finite element subspaces allow for the construction of a scaled basis which is formally riesz stable this construction turns out to rest not only on the shape regularity of the refined elements but also critically on a number of geometrical properties we establish between neighboring simplices produced by the bornemann erdmann kornhuber bek refinement procedure it is possible to show that the number of degrees of freedom used for smoothing is bounded by a constant times the number of degrees of freedom introduced at that level of refinement indicating that a practical implementable version of the resulting bpx preconditioner for the bek refinement setting has provably optimal linear computational complexity per iteration an interesting implication of the optimality of the whb preconditioner is the a priori h1 stability of the l2 projection the existing a posteriori approaches in the literature dictate a reconstruction of the mesh if such conditions cannot be satisfied the theoretical framework employed supports arbitrary spatial dimension d geq 1 and requires no coefficient smoothness assumptions beyond those required for well posedness in h1

an lpd approach to robust h sub 2 and h sub spl infin static output feedback design a linear parameter dependent approach for designing a constant output feedback controller for a linear time invariant system with uncertain parameters that achieves a minimum bound on either the h sub 2 or h sub spl infin performance level is introduced assuming that the uncertain parameters reside in a given polytope a parameter dependent lyapunov function is described which enables the derivation of the required constant gain via a solution of a set of linear matrix inequalities that correspond to the vertices of the uncertainty polytope

a convergent adaptive algorithm for poisson s equation we construct a converging adaptive algorithm for linear elements applied to poisson s equation in two space dimensions starting from a macro triangulation we describe how to construct an initial triangulation from a priori information then we use a posteriors error estimators to get a sequence of refined triangulation and approximate solutions it is proved that the error measured in the energy norm decreases at a constant rate in each step until a prescribed error bound is reached extension to higher order elements in two space dimension and numerical results are included

on developing stable finite element methods for pseudo time simulation of biomolecular electrostatics abstract the poisson boltzmann equation pbe is a widely used implicit solvent model for the electrostatic analysis of solvated biomolecules to address the exponential nonlinearity of the pbe a pseudo time approach has been developed in the literature which completely suppresses the nonlinear instability through an analytic integration in a time splitting framework this work aims to develop novel finite element methods fems in this pseudo time framework for solving the pbe two treatments to the singular charge sources are investigated one directly applies the definition of the delta function in the variational formulation and the other avoids numerical approximation of the delta function by using a regularization formulation to apply the proposed fems for both pbe and regularized pbe in real protein systems a new tetrahedral mesh generator based on the minimal molecular surface definition is developed with a body fitted mesh the proposed pseudo time fem solvers are more accurate than the existing pseudo time finite difference solvers moreover based on the implicit euler time integration the proposed fems are unconditionally stable for solvated proteins with source singularities and non smooth potentials so that they could be more efficient than the existing pseudo time discontinuous galerkin method based on the explicit euler time stepping due to the unconditional stability the proposed pseudo time algorithms are free of blow up or overflow issues without resorting to any thresholding technique numerical experiments of several benchmark examples and free energy calculations of protein systems are conducted to validate the stability accuracy and robustness of the proposed pbe solvers

static h2 and h output feedback of discrete time lti systems with state multiplicative noise abstract a parameter dependent approach for designing static output feedback controller for linear time invariant systems with state multiplicative noise is introduced which achieves a minimum bound on either the stochastic h 2 or the h performance levels a solution is obtained also for the case where in addition to the stochastic parameters the system matrices reside in a given polytope in this case a parameter dependent lyapunov function is described which enables the derivation of the required constant feedback gain via a solution of a set of linear matrix inequalities that correspond to the vertices of the uncertainty polytope the stochastic parameters appear in both the dynamics and the input matrices of the state space model of the system the problems are solved using the expected value of the standard performance indices over the stochastic parameters the theory developed is demonstrated by a simple example

robust stability of time varying polytopic systems abstract this paper provides global asymptotic stability conditions for time varying continuous time polytopic systems using a parameter dependent lyapunov function the time varying parameter uncertainty as well as its time derivative are modelled as belonging to polytopic convex sets and their dependence is made explicit to get less conservative results a particular case characterized by the parameter uncertainty satisfying a linear differential equation is analyzed and a simpler version of the aforementioned stability conditions is presented the results are expressed in terms of linear matrix inequalities being thus numerically solvable with no big difficulty the theory is illustrated by the determination of the asymptotic stability region of a mathieu s type equation with an uncertain time varying parameter

parameter dependent lyapunov functions for discrete time systems with time varying parametric uncertainties abstract in this paper we consider discrete time systems with polytopic time varying uncertainty we look for a class of parameter dependent lyapunov functions which are quadratic on the system state and depend in a polytopic way on the uncertain parameter we show that extending the new discrete time stability condition proposed by de oliveira et al systems control lett 36 1999 135 to the case of time varying uncertainty leads to a necessary and sufficient condition for the computation of such a lyapunov function this allows to check asymptotic stability of the system under study the obtained linear matrix inequalities condition can also be used to cope with the control synthesis problem

a triangulation approach to asymptotically exact conditions for fuzzy summations many takagi sugeno t s fuzzy control synthesis problems in the literature are expressed as the problem of finding decision variables in a double convex sum fuzzy summation of positive definite matrices matricespsila coefficients in the summation take values in the standard simplex this paper presents a triangulation approach to the problem of generating simplicial partitions of the standard simplex in order to set up a family of sufficient conditions and in parallel another family of necessary ones for fuzzy summations the conditions proposed in this paper are asymptotically exact as the size of the involved simplices decreases its conservativeness vanishes for a sufficiently fine partition sufficiently dense mesh of vertex points the set of conditions is in the form of linear matrix inequalities lmis for which efficient software is available