weighted reciprocal of temperature weighted thermal flux and their applications in finite time thermodynamics the concepts of weighted reciprocal of temperature and weighted thermal flux are proposed for a heat engine operating between two heat baths and outputting mechanical work with the aid of these two concepts the generalized thermodynamic fluxes and forces can be expressed in a consistent way within the framework of irreversible thermodynamics then the efficiency at maximum power output for a heat engine one of key topics in finite time thermodynamics is investigated on the basis of a generic model under the tight coupling condition the corresponding results have the same forms as those of low dissipation heat engines m esposito r kawai k lindenberg and c van den broeck phys rev lett 105 150603 2010 the mappings from two kinds of typical heat engines such as the low dissipation heat engine and the feynman ratchet into the present generic model are constructed the universal efficiency at maximum power output up to the quadratic order is found to be valid for a heat engine coupled symmetrically and tightly with two baths the concepts of weighted reciprocal of temperature and weighted thermal flux are also transplanted to the optimization of refrigerators

a method of finite element tearing and interconnecting and its parallel solution algorithm a novel domain decomposition approach for the parallel finite element solution of equilibrium equations is presented the spatial domain is partitioned into a set of totally disconnected subdomains each assigned to an individual processor lagrange multipliers are introduced to enforce compatibility at the interface nodes in the static case each floating subdomain induces a local singularity that is resolved in two phases first the rigid body modes are eliminated in parallel from each local problem and a direct scheme is applied concurrently to all subdomains in order to recover each partial local solution next the contributions of these modes are related to the lagrange multipliers through an orthogonality condition a parallel conjugate projected gradient algorithm is developed for the solution of the coupled system of local rigid modes components and lagrange multipliers which completes the solution of the problem when implemented on local memory multiprocessors this proposed method of tearing and interconnecting requires less interprocessor communications than the classical method of substructuring it is also suitable for parallel vector computers with shared memory moreover unlike parallel direct solvers it exhibits a degree of parallelism that is not limited by the bandwidth of the finite element system of equations

a hypothesis testing approach toward identifying active contrasts the problem of identifying the active contrasts in an unreplicated fractional factorial design is approached from a hypothesis testing point of view the null hypothesis that all contrasts are inactive is first tested and if rejected the active contrasts causing rejection are identified and estimated the method is illustrated with examples from box and meyer compared with the confidence interval approach of dong and lenth and found to be a worthy competitor

a preconditioner for substructuring based on constrained energy minimization a preconditioner for substructuring based on constrained energy minimization concepts is presented the preconditioner is applicable to both structured and unstructured meshes and offers a straightforward approach for the iterative solution of second and fourth order structural mechanics problems the approach involves constraints associated with disjoint sets of nodes on substructure boundaries these constraints provide the means for preconditioning at both the substructure and global levels numerical examples are presented that demonstrate the good performance of the method in terms of iterations compute time and condition numbers of the preconditioned equations

coefficient of performance and its bounds for general refrigerators with nonisothermal processes an analysis of the coefficient of performance cop and its bounds at maximum figure of merit for refrigerators is conducted and the heat transfer processes are described using newton s law of cooling with a time dependent heat conductance the upper bound of the cop is independent of the time duration completing either process or the heat conductance the optimal temperature profiles in the heat exchanging processes are analyzed under different dimensionless contact time limits provided the dimensionless contact times satisfy certain relations the endoreversible model is recovered furthermore numerical calculations are conducted to investigate the effect of different heat conductances on temperature profiles under the maximum criterion this work can guide design and operation of actual refrigerators

identifying active contrasts by stepwise testing unreplicated fractional factorial designs are frequently used in industrial experimentation and are characterized by the absence of degrees of freedom for estimation of the error variance this article presents step down and step up testing procedures that efficiently identify the active contrasts significant effects in such experiments and simultaneously provide an accurate estimate of the error variance the methods allow the user to restrict the experimentwise error rate to a prespecified level use of the new methods is illustrated in terms of standard examples from the literature simulation shows that a version of the step up procedure outperforms its competitors

a multilevel hybrid newton krylov schwarz method for the bidomain model of electrocardiology abstract a multilevel hybrid newton krylov schwarz nks method is constructed and studied numerically for implicit time discretizations of the bidomain reaction diffusion system in three dimensions this model describes the bioelectrical activity of the heart by coupling two degenerate parabolic equations with a stiff system of ordinary differential equations the nks bidomain solver employs an outer inexact newton iteration to solve the nonlinear finite element system originating at each time step of the implicit discretization the jacobian update during the newton iteration is solved by a krylov method employing a multilevel hybrid overlapping schwarz preconditioner additive within the levels and multiplicative among the levels several parallel tests on linux clusters are performed showing that the convergence of the method is independent of the number of subdomains scalability the discretization parameters and the number of levels optimality

low dissipation carnot like heat engines at maximum efficient power we study the optimal performance of carnot like heat engines working in the low dissipation regime using the product of the efficiency and the power output also known as the efficient power as our objective function efficient power function represents a trade off between power and efficiency of a heat engine we find lower and upper bounds on the efficiency in the case of extreme asymmetric dissipation when the ratio of dissipation coefficients at the cold and the hot contacts approaches respectively zero or infinity in addition we obtain the form of efficiency for the case of symmetric dissipation we also discuss the universal features of efficiency at maximum efficient power and derive the bounds on the efficiency using a global linear irreversible framework introduced recently by one of the authors

isogeometric bddc preconditioners with deluxe scaling a balancing domain decomposition by constraints bddc preconditioner with a novel scaling introduced by dohrmann for problems with more than one variable coefficient and here denoted as deluxe scaling is extended to isogeometric analysis of scalar elliptic problems this new scaling turns out to be more powerful than the standard rho and stiffness scalings considered in a previous isogeometric bddc study our h analysis shows that the condition number of the resulting deluxe bddc preconditioner is scalable with a quasi optimal polylogarithmic bound which is also independent of coefficient discontinuities across subdomain interfaces extensive numerical experiments support the theory and show that the deluxe scaling yields a remarkable improvement over the older scalings in particular for large isogeometric polynomial degree and high regularity

universality of efficiency at unified trade off optimization we calculate the efficiency at the unified trade off optimization criterion the so called maximum criterion representing a compromise between the useful energy and the lost energy of heat engines operating between two reservoirs at different temperatures and chemical potentials and demonstrate that the linear coefficient 3 4 and quadratic coefficient 1 32 of the efficiency at maximum are universal for heat engines under strong coupling and symmetry conditions it is further proved that the conclusions obtained here also apply to the ecological optimization criterion

a scalable newton krylov schwarz method for the bidomain reaction diffusion system a novel two level newton krylov schwarz nks solver is constructed and analyzed for implicit time discretizations of the bidomain reaction diffusion system in three dimensions this multiscale system describes the bioelectrical activity of the heart by coupling two degenerate parabolic equations with several ordinary differential equations at each point in space together with a finite element discretization in space the proposed nks bidomain solver employs an outer inexact newton iteration to solve the nonlinear finite element system originating at each time step of the decoupled implicit discretization the jacobian update during the newton iteration is solved by a krylov method employing a two level overlapping schwarz preconditioner a convergence rate estimate is proved for the resulting preconditioned operator showing that its condition number is independent of the number of subdomains scalability and bounded by the ratio of the subdomains characteristic size and the overlap size this theoretical result is confirmed by several parallel simulations employing up to more than 2000 processors for scaled and standard speedup tests in three dimensions the results show the scalability of the proposed nks bidomain solver in terms of both nonlinear and linear iterations in both cartesian slabs and ellipsoidal cardiac domains

nonlinear feti dp and bddc methods new nonlinear feti dp dual primal finite element tearing and interconnecting and bddc balancing domain decomposition by constraints domain decomposition methods are introduced in all these methods in each iteration local nonlinear problems are solved on the subdomains the new approaches can significantly reduce communication and show a significantly improved performance especially for problems with localized nonlinearities compared to a standard newton krylov feti dp or bddc approach moreover the coarse space of the nonlinear feti dp methods can be used to accelerate the newton convergence it is also found that the new nonlinear feti dp and nonlinear bddc methods are not as closely related as in the linear context numerical results for the p laplace operator are presented

multilevel additive schwarz preconditioners for the bidomain reaction diffusion system multilevel additive schwarz methods are analyzed and studied numerically for the anisotropic cardiac bidomain model in three dimensions this is the most complete model to date of the bioelectrical activity of the heart tissue consisting of a degenerate parabolic system of nonlinear reaction diffusion equations coupled with a stiff system of several ordinary differential equations describing the ionic currents through the cellular membrane due to the presence of very different scales in both space and time the numerical discretization of this system by finite elements in space and semi implicit methods in time produces very ill conditioned linear systems that must be solved at each time step the proposed multilevel algorithm employs a hierarchy of nested meshes with overlapping schwarz preconditioners on each level and is fully additive hence parallel within and among levels convergence estimates are proved for the resulting multilevel algorithm showing that its convergence rate is independent of the number of subdomains scalability of the mesh sizes of each level and of the number of levels optimality several parallel tests on a linux cluster confirm the scalability and optimality of the method as well as its parallel efficiency on both cartesian and deformed domains in three dimensions

ecological optimization and coefficient of performance bounds of general refrigerators abstract an analysis of cop and its bounds at maximum ecological criterion for general refrigerators is conducted for generality both the non isothermal heat transfer processes and the internal dissipations are considered under different situations the cop under the maximum ecological criterion have been studied systematically and the general upper and lower bounds of the optimal cop have been obtained furthermore under maximum ecological criterion the cop of general endoreversible refrigerators have also been studied and the cop bounds of different kinds of refrigerators have been analyzed as actual refrigerators may not operate under the condition of maximum cop or maximum cooling load but operate under the maximum ecological condition which indicates the best compromise between the refrigeration rate and the loss of refrigeration rate this paper could provide a practical insight for designing and operating actual refrigerators

quantum dot carnot engine at maximum power we evaluate the efficiency at maximum power of a quantum dot carnot heat engine the universal values of the coefficients at the linear and quadratic order in the temperature gradient are reproduced curzon ahlborn efficiency is recovered in the limit of weak dissipation

extending substructure based iterative solvers to multiple load and repeated analyses direct solvers currently dominate commercial finite element structural software but do not scale well in the fine granularity regime targeted by emerging parallel processors substructure based iterative solvers often called also domain decomposition algorithms lend themselves better to parallel processing but must overcome several obstacles before earning their place in general purpose structural analysis programs one such obstacle is the solution of systems with many or repeated right hand sides such systems arise for example in multiple load static analyses and in implicit linear dynamics computations direct solvers are well suited for these problems because after the system matrix has been factored the multiple or repeated solutions can be obtained through relatively inexpensive forward and backward substitutions on the other hand iterative solvers in general are ill suited for these problems because they often must restart from scratch for every different right hand side in this paper we present a methodology for extending the range of applications of domain decomposition methods to problems with multiple or repeated right hand sides basically we formulate the overall problem as a series of minimization problems over k orthogonal and supplementary subspaces and tailor the preconditioned conjugate gradient algorithm to solve them efficiently the resulting solution method is scalable whereas direct factorization schemes and forward and backward substitution algorithms are not we illustrate the proposed methodology with the solution of static and dynamic structural problems and highlight its potential to outperform forward and backward substitutions on parallel computers as an example we show that for a linear structural dynamics problem with 11640 degrees of freedom every time step beyond time step 15 is solved in a single iteration and consumes 1 0 second on a 32 processor ipsc 860 system for the same problem and the same parallel processor a pair of forward backward substitutions at each step consumes 15 0 seconds

feti and neumann neumann iterative substructuring methods connections and new results the feti and neumann neumann families of algorithms are among the best know and most severely tested domain decomposition methods for elliptic partial differential equations they are iterative substructuring methods and have many algorithmic components in common but there are also differences the purpose of this paper is to further unify the theory for these two families of methods and to introduce a new family of feti algorithms bounds on the rate of convergence which are uniform with respect to the coefficients of a family of elliptic problems with heterogeneous coefficients are established for these new algorithms the theory for a variant of the neumann neumann algorithm is also redeveloped stressing similarities to that for the feti methods

dual primal feti methods for linear elasticity dual primal feti methods are nonoverlapping domain decomposition methods where some of the continuity constraints across subdomain boundaries are required to hold throughout the iterations as in primal iterative substructuring methods while most of the constraints are enforced by lagrange multipliers as in one level feti methods these methods are used to solve the large algebraic systems of equations that arise in elliptic finite element problems the purpose of this article is to develop strategies for selecting these constraints which are enforced throughout the iterations such that good convergence bounds are obtained that are independent of even large changes in the stiffness of the subdomains across the interface between them the algorithms are described in terms of a change of basis that has proven to be quite robust in practice a theoretical analysis is provided for the case of linear elasticity and condition number bounds are established that are uniform with respect to arbitrarily large jumps in the young s modulus of the material and otherwise depend only polylogarithmically on the number of unknowns of a single subdomain the strategies have already proven quite successful in large scale implementations of these iterative methods 2006 wiley periodicals inc

a model based block triangular preconditioner for the bidomain system in electrocardiology we introduce a preconditioner for the solution of the bidomain system governing the propagation of action potentials in the myocardial tissue the bidomain model is a degenerate parabolic set of nonlinear reaction diffusion equations the nonlinear term describes the ion flux at the cellular level the degenerate nature of the problem results in a severe ill conditioning of its discretization our preconditioning strategy is based on a suitable adaptation of the monodomain model a simplified version of the bidomain one which is by far simpler to solve nevertheless is unable to capture significant features of the action potential propagation the monodomain preconditioner application to a non symmetric formulation of the bidomain system results at the algebraic level in a lower block triangular preconditioner we prove optimality of the preconditioner with respect to the mesh size and corroborate our theoretical results with 3d numerical simulations both on idealized and real ventricle geometries

robust bddc preconditioners for reissner mindlin plate bending problems and mitc elements a balancing domain decomposition method by constraints bddc is constructed and analyzed for the reissner mindlin plate bending problem discretized with mixed interpolation of tensorial components mitc finite elements this bddc algorithm is based on selecting the plate rotations and deflection degrees of freedom at the subdomain vertices as primal continuity constraints after the implicit elimination of the interior degrees of freedom in each subdomain the resulting plate schur complement is solved by the preconditioned conjugate gradient method the preconditioner is based on the solution of local reissner mindlin plate problems on each subdomain with clamping conditions at the primal degrees of freedom and on the solution of a coarse reissner mindlin plate problem for the primal degrees of freedom the main results of the paper are the proof and numerical verification that the proposed bddc plate algorithm is scalable quasi optimal and most important robust with respect to the plate thickness while this result is due to an underlying mixed formulation of the problem both the interface plate problem and the preconditioner are positive definite the numerical results also show that the proposed algorithm is robust with respect to discontinuities of the material properties

inference for effect saturated fractional factorials industrial scientists and engineers often use experimental designs in which all degrees of freedom are used to estimate effects and consequently no classical estimate of the error is possible robust scale estimates provide an alternative measure of the error in this study several such scale estimators are evaluated based on the power or related significance tests the pseudo standard error method of lenth provides the best overall performance lenth s t approximation for critical values was found to be inaccurate however so new tables are provided additional recommendations are made according to the experimenter s prior belief in the number of likely important factors

the analysis of unreplicated factorial experiments using all possible comparisons this article proposes a new procedure for analyzing small unreplicated factorial experiments this procedure is based on using likelihood ratio tests to compare competing models an easy method of implementing the procedure is presented and then demonstrated on a real set of data results of a simulation study are presented that indicate that the new procedure compares favorably with lenth s method tables of constants are supplied that allow the new procedure to be easily applied to the analysis of 8 run 12 run and 16 run experiments

newton krylov bddc solvers for nonlinear cardiac mechanics abstract the aim of this work is to design and study a balancing domain decomposition by constraints bddc solver for the nonlinear elasticity system modeling the mechanical deformation of cardiac tissue the contraction relaxation process in the myocardium is induced by the generation and spread of the bioelectrical excitation throughout the tissue and it is mathematically described by the coupling of cardiac electro mechanical models consisting of systems of partial and ordinary differential equations in this study the discretization of the electro mechanical models is performed by q1 finite elements in space and semi implicit finite difference schemes in time leading to the solution of a large scale linear system for the bioelectrical potentials and a nonlinear system for the mechanical deformation at each time step of the simulation the parallel mechanical solver proposed in this paper consists in solving the nonlinear system with a newton krylov bddc method based on the parallel solution of local mechanical problems and a coarse problem for the so called primal unknowns three dimensional parallel numerical tests on different machines show that the proposed parallel solver is scalable in the number of subdomains quasi optimal in the ratio of subdomain to mesh sizes and robust with respect to tissue anisotropy

heat engines at optimal power low dissipation versus endoreversible model the low dissipation model and the endoreversible model of heat engines are two of the most commonly studied models of machines in finite time thermodynamics in this paper we compare the performance characteristics of these two models under optimal power output we point out a basic equivalence between them in the linear response regime

finding missing edges in networks based on their community structure many edge prediction methods have been proposed based on various local or global properties of the structure of an incomplete network community structure is another significant feature of networks vertices in a community are more densely connected than average it is often true that vertices in the same community have similar properties which suggests that missing edges are more likely to be found within communities than elsewhere we use this insight to propose a strategy for edge prediction that combines existing edge prediction methods with community detection we show that this method gives better prediction accuracy than existing edge prediction methods alone

feti dp a dual primal unified feti method part i a faster alternative to the two level feti method the feti method and its two level extension feti 2 are two numerically scalable domain decomposition methods with lagrange multipliers for the iterative solution of second order solid mechanics and fourth order beam plate and shell structural problems respectively the feti 2 method distinguishes itself from the basic or one level feti method by a second set of lagrange multipliers that are introduced at the subdomain cross points to enforce at each iteration the exact continuity of a subset of the displacement field at these specific locations in this paper we present a dual primal formulation of the feti 2 concept that eliminates the need for that second set of lagrange multipliers and unifies all previously developed one level and two level feti algorithms into a single dual primal feti dp method we show that this new feti dp method is numerically scalable for both second order and fourth order problems we also show that it is more robust and more computationally efficient than existing feti solvers particularly when the number of subdomains and or processors is very large copyright 2001 john wiley sons ltd

quick and easy analysis of unreplicated factorials box and meyer 1986 introduced a method for assessing the sizes of contrasts in unreplicated factorial and fractional factorial designs this is a useful technique and an associated graphical display popularly known as a bayes plot makes it even more effective this article presents a competing technique that is also effective and is computationally simple an advantage of the new method is that the results are given in terms of the original units of measurement this direct association with the data may make the analysis easier to explain

coefficient of performance at maximum figure of merit and its bounds for low dissipation carnot like refrigerators the figure of merit for refrigerators performing finite time carnot like cycles between two reservoirs at temperature t h and t c t h is optimized it is found that the coefficient of performance at maximum figure of merit is bounded between 0 and sqrt 9 8e c 3 2 for the low dissipation refrigerators where e c t c t h t c is the carnot coefficient of performance for reversible refrigerators these bounds can be reached for extremely asymmetric low dissipation cases when the ratio between the dissipation constants of the processes in contact with the cold and hot reservoirs approaches to zero or infinity respectively the observed coefficients of performance for real refrigerators are located in the region between the lower and upper bounds which is in good agreement with our theoretical estimation

efficiency at and near maximum power of low dissipation heat engines a universality in optimization of trade off between power and efficiency for low dissipation carnot cycles is presented it is shown that any trade off measure expressible in terms of efficiency and the ratio of power to its maximum value can be optimized independently of most details of the dynamics and of the coupling to thermal reservoirs the result is demonstrated on two specific trade off measures the first one is designed for finding optimal efficiency for a given output power and clearly reveals diseconomy of engines working at maximum power as the second example we derive universal lower and upper bounds on the efficiency at maximum trade off given by the product of power and efficiency the results are illustrated on a model of a diffusion based heat engine such engines operate in the low dissipation regime given that the used driving minimizes the work dissipated during the isothermal branches the peculiarities of the corresponding optimization procedure are reviewed and thoroughly discussed

bddc preconditioners for spectral element discretizations of almost incompressible elasticity in three dimensions balancing domain decomposition by constraints bddc algorithms are constructed and analyzed for the system of almost incompressible elasticity discretized with gauss lobatto legendre spectral elements in three dimensions initially mixed spectral elements are employed to discretize the almost incompressible elasticity system but a positive definite reformulation is obtained by eliminating all pressure degrees of freedom interior to each subdomain into which the spectral elements have been grouped appropriate sets of primal constraints can be associated with the subdomain vertices edges and faces so that the resulting bddc methods have a fast convergence rate independent of the almost incompressibility of the material in particular the condition number of the bddc preconditioned operator is shown to depend only weakly on the polynomial degree n the ratio h h of subdomain and element diameters and the inverse of the inf sup constants of the subdomains and the underlying mixed formulation while being scalable i e independent of the number of subdomains and robust i e independent of the poisson ratio and young s modulus of the material considered these results also apply to the related dual primal finite element tearing and interconnect feti dp algorithms defined by the same set of primal constraints numerical experiments carried out on parallel computing systems confirm these results

three level laser heat engine at optimal performance with ecological function although classical and quantum heat engines work on entirely different fundamental principles there is an underlying similarity for instance the form of efficiency at optimal performance may be similar for both types of engines in this work we study a three level laser quantum heat engine operating at maximum ecological function ef which represents a compromise between the power output and the loss of power due to entropy production we present numerical as well as analytic results for the global and local optimization of our laser engine in different operational regimes particularly we observe that in low temperature regimes the three level laser heat engine can be mapped to feynman s ratchet and pawl model a steady state classical heat engine then we derive analytic expressions for efficiency under the assumptions of strong matter field coupling and high bath temperatures upper and lower bounds on the efficiency exist in case of extreme asymmetric dissipation when the ratio of system bath coupling constants at the hot and the cold contacts respectively approaches zero or infinity these bounds have been established previously for various classical models of carnot like engines further for weak or intermediate matter field coupling in the high temperature limit we derive some new bounds on the efficiency of the engine we conclude that while the engine produces at least 75 of the power output as compared with the maximum power conditions the fractional loss of power is appreciably low in case of the engine operating at maximum ef thus making this objective function relevant from an environmental point of view

a fully implicit finite element method for bidomain models of cardiac electromechanics we propose a novel monolithic and unconditionally stable finite element algorithm for the bidomainbased approach to cardiac electromechanics we introduce the transmembrane potential the extracellular potential and the displacement field as independent variables and extend the common two field bidomain formulation of electrophysiology to a three field formulation of electromechanics the intrinsic coupling arises from both excitation induced contraction of cardiac cells and the deformation induced generation of intra cellular currents the coupled reaction diffusion equations of the electrical problem and the momentum balance of the mechanical problem are recast into their weak forms through a conventional isoparametric galerkin approach as a novel aspect we propose a monolithic approach to solve the governing equations of excitation contraction coupling in a fully coupled implicit sense we demonstrate the consistent linearization of the resulting set of non linear residual equations to assess the algorithmic performance we illustrate characteristic features by means of representative three dimensional initial boundary value problems the proposed algorithm may open new avenues to patient specific therapy design by circumventing stability and convergence issues inherent to conventional staggered solution schemes

balancing neumann neumann methods for the cardiac bidomain model balancing neumann neumann preconditioners are constructed analyzed and numerically studied for the cardiac bidomain model in three dimensions this reaction diffusion system is discretized by low order finite elements in space and implicit explicit methods in time yielding very ill conditioned linear systems that must be solved at each time step the proposed algorithm is based on decomposing the domain into nonoverlapping subdomains and on solving iteratively the bidomain schur complement obtained by implicitly eliminating the degrees of freedom interior to each subdomain the iteration is preconditioned by a balancing neumann neumann method employing local neumann solves on each subdomain and a coarse bidomain solve a novel approach for the estimation of the average operator of the nonoverlapping decomposition provides a framework for designing coarse spaces for balancing neumann neumann methods the theoretical estimates obtained show that the proposed method is scalable quasi optimal and robust with respect to possible coefficient discontinuities of the bidomain operator the results of extensive parallel numerical tests in three dimensions confirm the convergence rates predicted by the theory

b and f projection methods for nearly incompressible linear and non linear elasticity and plasticity using higher order nurbs elements abstract this paper presents projection methods to treat the incompressibility constraint in small and large deformation elasticity and plasticity within the framework of isogeometric analysis after reviewing some fundamentals of isogeometric analysis we investigate the use of higher order non uniform rational b splines nurbs within the b projection method the higher continuity property of such functions is explored in nearly incompressible applications and shown to produce accurate and robust results a new non linear f projection method based on a modified minimum potential energy principle and inspired by the b method is proposed for the large deformation case it leads to a symmetric formulation for which the consistent linearized operator for fully non linear elasticity is derived and used in a newton raphson iterative procedure the performance of the methods is assessed on several numerical examples and results obtained are shown to compare favorably with other published techniques

efficiency at maximum power output of an irreversible carnot like cycle with internally dissipative friction we investigate the efficiency at the maximum power output emp of an irreversible carnot engine performing finite time cycles between two reservoirs at constant temperatures t h and t c t h taking into account the internally dissipative friction in two adiabatic processes the emp is retrieved to be situated between c 2 and c 2 c with c 1 t c t h being the carnot efficiency whether the internally dissipative friction is considered or not when dissipations of two isothermal and two adiabatic processes are symmetric respectively and the time allocation between the adiabats and the contact time with the reservoir satisfy a certain relation the curzon ahlborn ca efficiency ca 1 sqrt t c t h is derived

convergence of a substructuring method with lagrange multipliers we analyze the convergence of a substructing iterative method with lagrange multipliers propose recently by farhat and roux the method decomposes finite element discretization of an elliptic boundary value problem into neumann problems on the subdomains plus a coarse problem for the subdomain nullspace components for linear conforming elements and preconditioning by the dirichlet problems on the subdomains we prove the asymptotic bound on the condition number c 1 log h h alpha alpha 2 or 3 where h is the characteristic element size h subdomain size and c is independent of the number of subdomains

feti dp bddc and block cholesky methods the feti dp and bddc algorithms are reformulated using block cholesky factorizations an approach which can provide a useful framework for the design of domain decomposition algorithms for solving symmetric positive definite linear system of equations instead of introducing lagrange multipliers to enforce the coarse level primal continuity constraints in these algorithms a change of variables is used such that each primal constraint corresponds to an explicit degree of freedom with the new formulation of these algorithms a simplified proof is provided that the spectra of a pair of feti dp and bddc algorithms with the same set of primal constraints are essentially the same numerical experiments for a two dimensional laplace s equation also confirm this result copyright 2005 john wiley sons ltd