the discontinuous enrichment method for medium frequency helmholtz problems with a spatially variable wavenumber numerical dispersion or what is often referred to as the pollution effect presents a challenge to an efficient finite element discretization of the helmholtz equation in the medium frequency regime to alleviate this effect and improve the unsatisfactory pre asymptotic convergence of the classical galerkin finite element method based on piecewise polynomial basis functions several discretization methods based on plane wave bases have been proposed among them is the discontinuous enrichment method that has been shown to offer superior performance to the classical galerkin finite element method for a number of constant wavenumber helmholtz problems and has also outperformed two representative methods that use plane waves the partition of unity and the ultra weak variation formulation methods in this paper the discontinuous enrichment method is extended to the variable wavenumber helmholtz equation to this effect the concept of enrichment functions based on free space solutions of the homogeneous form of the governing differential equation is enlarged to include free space solutions of approximations of this equation obtained in this case by successive taylor series expansions of the wavenumber around a reference point this leads to plane wave enrichment functions based on the piece wise constant approximation of the wavenumber and to airy wave enrichment functions several elements based on these enrichment functions are constructed and evaluated on benchmark problems modeling sound hard scattering by a disk submerged in an acoustic fluid where the speed of sound varies in space all these elements are shown to outperform by a substantial margin their continuous polynomial counterparts

a partition of unity finite element method for three dimensional transient diffusion problems with sharp gradients abstract an efficient partition of unity finite element method for three dimensional transient diffusion problems is presented a class of multiple exponential functions independent of time variable is proposed to enrich the finite element approximations as a consequence of this procedure the associated matrix for the linear system is evaluated once at the first time step and the solution is obtained at subsequent time step by only updating the right hand side of the linear system this results in an efficient numerical solver for transient diffusion equations in three space dimensions compared to the conventional finite element methods with h refinement the proposed approach is simple more efficient and more accurate the performance of the proposed method is assessed using several test examples for transient diffusion in three space dimensions we present numerical results for a transient diffusion equation with known analytical solution to quantify errors for the new method we also solve time dependent diffusion problems in complex geometries we compare the results obtained using the partition of unity finite element method to those obtained using the standard finite element method it is shown that the proposed method strongly reduces the necessary number of degrees of freedom to achieve a prescribed accuracy

signaling over arbitrarily permuted parallel channels the problem of transmission of information over arbitrarily permuted parallel channels is studied here the transmitter does not know over which channel a certain code sequence will actually be transmitted however the receiver knows how the sequences are permuted the permutation is arbitrary but constant during the simultaneous transmission of the code sequences via the parallel channels it is shown first that the sum of the capacities of each channel is achievable for such a communication system in the special case where the capacity achieving input distributions of all channels are identical more important is that this sum capacity can also be achieved using a single channel code for all channels combined with a sequential decoding method the construction of a rate matching code based on maximum distance separable mds codes turns out to be crucial finally the case where the parallel channels have different capacity achieving input distributions is investigated also for this case the capacity is determined again this capacity is achievable with a sequential decoding procedure

multi dimensional fuzzy reasoning this paper suggests a method of multi dimensional fuzzy reasoning concerned with both modus ponens and modus tollens it also discusses an example to show how the method works

on stability of fuzzy systems expressed by fuzzy rules with singleton consequents addresses the issue of stability of a fuzzy system described by fuzzy rules with singleton consequents it first presents two canonical forms of a fuzzy system a parametric expression and a state space expression a fuzzy system with singleton consequents is found to be a piecewise polytopic affine system then the paper gives stability theorems for a discrete time system as well as for a continuous time system it also gives a brief survey on the stability issues of fuzzy control systems

the generalized finite element method for helmholtz equation theory computation and open problems in this paper we address the generalized finite element method for the helmholtz equation we obtain our method by employing the finite element method on cartesian meshes which may overlap the boundaries of the problem domain and by enriching the approximation by plane waves pasted into the finite element basis at each mesh vertex by the partition of unity method here we address the q convergence of the method where q is the number of plane waves added at each vertex for the class of smooth analytic solutions for which we get better than exponential convergence for sufficiently small h depending on p an important observation is that we can monitor the accuracy in any computed solution quantity of interest at negligible cost by using q extrapolation our results assume exact integration of all the employed integrals further studies are needed to analyze the effects of the numerical integrations and also the effect of the roundoff errors

a computational approach to approximate and plausible reasoning with applications to expert systems the intended purpose of this paper is twofold proposing a common basis for the modeling of uncertainty and imprecision and discussing various kinds of approximate and plausible reasoning schemes in this framework together with probability different kinds of uncertainty measures credibility and plausibility functions in the sense of shafer possibility measures in the sense of zadeh and the dual measures of necessity sugeno s g fuzzy measures are introduced in a unified way the modeling of imprecision in terms of possibility distribution is then presented and related questions such as the measure of the uncertainty of fuzzy events the probability and possibility qualification of statements the concept of a degree of truth and the truth qualification of propositions are discussed at length deductive inference from premises weighted by different kinds of measures by uncertainty or by truth values in the framework of various multivalued logics is fully investigated then deductive inferences from imprecise or fuzzy premises are dealt with patterns of reasoning where both uncertainty and imprecision are present are also addressed the last section is devoted to the combination of uncertain or imprecise pieces of information given by different sources on the whole this paper is a tentative survey of quantitative approaches in the modeling of uncertainty and imprecision including recent theoretical proposals as well as more empirical techniques such as the ones developed in expert systems such as mycin or prospector the management of uncertainty and imprecision in reasoning patterns being a key issue in artificial intelligence

performances of the partition of unity finite element method for the analysis of two dimensional interior sound fields with absorbing materials the paper deals with the numerical simulation of the acoustic field in two dimensional cavities in which absorbing materials are present though finite element method fem could be employed for this purpose the discretization level required for achieving reasonable accuracy renders the method impractical in the mid frequency range to alleviate this limitation the partition of unity finite element method pufem using plane wave functions has been shown to be very effective for solving short wave helmholtz problems in the present work the method is extended to the computation of the pressure wave field within the absorbing media which is modeled as a bulk reacting material characterized by a complex valued and frequency dependent mean density and dynamic compressibility lagrange multipliers are used to enforce the transmission conditions at the air material interface performances of the pufem are compared with a standard fem in several examples of practical interests it is shown that the technique is a good candidate for solving noise control problems at high frequency

fuzzy modeling of high dimensional systems complexity reduction and interpretability improvement fuzzy modeling of high dimensional systems is a challenging topic this paper proposes an effective approach to data based fuzzy modeling of high dimensional systems an initial fuzzy rule system is generated based on the conclusion that optimal fuzzy rules cover extrema redundant rules are removed based on a fuzzy similarity measure then the structure and parameters of the fuzzy system are optimized using a genetic algorithm and the gradient method during optimization rules that have a very low firing strength are deleted finally interpretability of the fuzzy system is improved by fine training the fuzzy rules with regularization the resulting fuzzy system generated by this method has the following distinct features 1 the fuzzy system is quite simplified 2 the fuzzy system is interpretable and 3 the dependencies between the inputs and the output are clearly shown this method has successfully been applied to a system that has 11 inputs and one output with 20 000 training data and 80 000 test data

practical inference with systems of gradual implicative rules a general approach to practical inference with gradual implicative rules and fuzzy inputs is presented gradual rules represent constraints restricting outputs of a fuzzy system for each input they are tailored for interpolative reasoning our approach to inference relies on the use of inferential independence it is based on fuzzy output computation under an interval valued input a double decomposition of fuzzy inputs is done in terms of alpha cuts and in terms of a partitioning of these cuts according to areas where only a few rules apply the case of 1 d and 2 d inputs is considered as well as higher dimensional cases an application to a cheese making process illustrates the approach

neuro fuzzy reasoning for occluded object recognition abstract to tackle the problem of occluded object recognition first we give a new interpretation to the multidimensional fuzzy reasoning and then realize that new interpretation through backpropagation type neural network at the learning stage of the neural network fuzzy linguistic statements are used once learned the nonfuzzy features of an occluded object can be classified at the time of classification of the nonfuzzy features of an occluded object we use the concept of fuzzy singleton an effective approach to recognize an unknown scene which consists of a set of occluded objects is to detect a number of significant local features on the boundary of the unknown scene thus the major problems fall into the selection of the appropriate set of features local for representing the object in the training stage as well as in the detection of these features in the recognition process the features should be invariant to scale orientation and minor distortions in boundary shape the performance of the proposed scheme is tested through several examples

the influence of some fuzzy implication operators on the accuracy of a fuzzy model part ii abstract the influence of fuzzy implication operators and the connective also on the accuracy of a fuzzy model of a d c series motor is considered some typical fuzzy implication operators are applied to the construction of a fuzzy model of a d c series motor a root mean square error is used as the criterion of the fuzzy model s adequacy to the real system a number of mathematical operations necessary for the implementation of the fuzzy model are used as the criterion by which the fuzzy model s applicability if estimated from the point of view of computing techniques the best types of fuzzy relations representing fuzzy models of a real system are chosen in order to secure the least root mean square error with minimal number of mathematical operations necessary for computer implementation

convergence analysis of the batch gradient based neuro fuzzy learning algorithm with smoothing l 1 2 regularization for the first order takagi sugeno system abstract it has been proven that takagi sugeno systems are universal approximators and they are applied widely to classification and regression problems the main challenges of these models are convergence analysis and their computational complexity due to the large number of connections and the pruning of unnecessary parameters the neuro fuzzy learning algorithm involves two tasks generating comparable sparse networks and training the parameters in addition regularization methods have attracted increasing attention for network pruning particularly the l q 0 q 1 regularizer after l 1 regularization which can obtain better solutions to sparsity problems the l 1 2 regularizer has a specific sparsity capacity and it is representative of l q 0 q 1 regularizations however the nonsmoothness of the l 1 2 regularizer may lead to oscillations in the learning process in this study we propose a gradient based neuro fuzzy learning algorithm with a smoothing l 1 2 regularization for the first order takagi sugeno fuzzy inference system the proposed approach has the following three advantages i it enhances the original l 1 2 regularizer by eliminating the oscillation of the gradient in the cost function during the training ii it performs better by pruning inactive connections where the number of the redundant connections for removal is higher than that generated by the original l 1 2 regularizer while it is also implemented by simultaneous structure and parameter learning processes and iii it is possible to demonstrate the theoretical convergence analysis of this learning method which we focus on explicitly we also provide a series of simulations to demonstrate that the smoothing l 1 2 regularization can often obtain more compressive representations than the current l 1 2 regularization

transient analysis of sharp thermal gradients using coarse finite element meshes abstract this paper investigates the application of the generalized finite element method with global local enrichments gfemgl to problems of transient heat transfer involving localized features the gfemgl is utilized in order to numerically construct general specially tailored shape functions yielding high levels of accuracy on coarse fem meshes the use of time dependent shape functions requires that the system of equations be discretized temporally first and then spatially in order to properly account for the time dependency the standard method is used for the time integration scheme the transient three dimensional gfemgl is then applied to a laser heating example in order to demonstrate its ability to resolve localized transient features on a fixed coarse mesh convergence analysis of the proposed method as well as applications to heterogeneous materials and moving heat sources are also provided

the generalized finite element method for helmholtz equation part ii effect of choice of handbook functions error due to absorbing boundary conditions and its assessment abstract in part i t strouboulis i babuska r hidajat the generalized finite element method for helmholtz equation theory computation and open problems comput methods appl mech engrg 195 2006 4711 4731 we introduced the q version of the generalized finite element method gfem for the helmholtz equation and we addressed its a pollution error due to the wave number b exponential q convergence c robustness to perturbations of the mesh the roundoff and numerical quadrature errors and d a posteriori error estimation here we continue the development of the gfem for helmholtz and we address the effects of a alternative handbook functions and mesh types b the error due to the artificial truncation boundary conditions and its assessment the conclusions are 1 the employment of plane wave wave band and vekua handbook functions lead to equivalent results and 2 for high q the most significant component of error may be the one due to the artificial truncation boundary conditions a rather straightforward approach for assessing this error is proposed

fuzzy identification using fuzzy neural networks with stable learning algorithms in general fuzzy neural networks cannot match nonlinear systems exactly unmodeled dynamic leads parameters drift and even instability problem according to system identification theory robust modification terms must be included in order to guarantee lyapunov stability this paper suggests new learning laws for mamdani and takagi sugeno kang type fuzzy neural networks based on input to state stability approach the new learning schemes employ a time varying learning rate that is determined from input output data and model structure stable learning algorithms for the premise and the consequence parts of fuzzy rules are proposed the calculation of the learning rate does not need any prior information such as estimation of the modeling error bounds this offer an advantage compared to other techniques using robust modification

multistage fuzzy inference formulated as linguistic truth value propagation and its learning algorithm based on back propagating error information multistage fuzzy inference where in the consequence in an inference stage is passed to the next stage as a fact is studied and formulated as a type of linguistic truth value propagation based on a concept of linguistic similarities between conditional propositions in successive stages the formulation is useful in studying the characteristics of multistage fuzzy inference and reveals its structural relationship to multilayer perceptrons the learning algorithm for multistage fuzzy inference is then derived using backpropagating error information the algorithm provides a means of automatically training the multistage fuzzy inference network using input output exemplar patterns intermediate membership functions based on simulation results which are generated automatically in the intermediate stage are proposed the intermediate stage fuzzy classifies the input space using intermediate membership functions in this way intermediate membership functions provide information regarding regional characteristics in exemplar patterns

time independent hybrid enrichment for finite element solution of transient conduction radiation in diffusive grey media we investigate the effectiveness of the partition of unity finite element method for transient conduction radiation problems in diffusive grey media the governing equations consist of a semi linear transient heat equation for the temperature field and a stationary diffusion approximation to the radiation in grey media the coupled equations are integrated in time using a semi implicit method in the finite element framework we show that for the considered problems a combination of hyperbolic and exponential enrichment functions based on an approximation of the boundary layer leads to improved accuracy compared to the conventional finite element method it is illustrated that this approach can be more efficient than using h adaptivity to increase the accuracy of the finite element method near the boundary walls the performance of the proposed partition of unity method is analyzed on several test examples for transient conduction radiation problems in two space dimensions

joint unitary triangularization for gaussian multi user mimo networks the problem of transmitting a common message to multiple users over the gaussian multiple input multiple output broadcast channel is considered where each user is equipped with an arbitrary number of antennas a closed loop scenario is assumed for which a practical capacity approaching scheme is developed by applying judiciously chosen unitary operations at the transmit and receive nodes the channel matrices are triangularized so that the resulting matrices have equal diagonals up to a possible multiplicative scalar factor this along with the utilization of successive interference cancellation reduces the coding and decoding tasks to those of coding and decoding over the single antenna additive white gaussian noise channel over the resulting effective channel any off the shelf code may be used for the two user case it was recently shown that such joint unitary triangularization is always possible in this paper it is shown that for more than two users it is necessary to carry out the unitary linear processing jointly over multiple channel uses i e space time processing is employed it is further shown that exact triangularization where all resulting diagonals are equal is still not always possible and appropriate conditions for the existence of such are established for certain cases when exact triangularization is not possible an asymptotic construction is proposed that achieves the desired property of equal diagonals up to edge effects that can be made arbitrarily small at the price of processing a sufficiently large number of channel uses together

perturbation of fuzzy reasoning we propose the concepts of maximum and average perturbations of fuzzy sets and estimate maximum and average perturbation parameters for various methods of fuzzy reasoning

mixed enrichment for the finite element method in heterogeneous media summary problems of multiple scales of interest or of locally nonsmooth solutions may often involve heterogeneous media these problems are usually very demanding in terms of computations with the conventional finite element method on the other hand different enriched finite element methods such as the partition of unity which proved to be very successful in treating similar problems are developed and studied for homogeneous media in this work we present a new idea to extend the partition of unity finite element method to treat heterogeneous materials the idea is studied in applications to wave scattering and heat transfer problems where significant advantages are noted over the standard finite element method although presented within the partition of unity context the same enrichment idea can also be extended to other enriched methods to deal with heterogeneous materials copyright 2014 john wiley sons ltd

wave interpolation finite elements for helmholtz problems with jumps in the wave speed finite elements for short wave scattering problems have recently been developed by various authors these have almost exclusively dealt with the helmholtz equation the elements have been very successful in terms of drastic reductions of the number of degrees of freedom in the numerical model however most of them are not directly applicable to problems in which the wave speed is not constant but varies with position many important wave problems fall into this latter category this is because short waves are often present in materials whose properties vary in space the present paper demonstrates how the method may be extended so as to deal with problems in which the wave speed is piecewise constant in various regions of the problem domain lagrange multipliers are used to enforce the necessary conditions of compatibility between the different regions the paper gives numerical results for problems for which the analytical solution is known this shows how these methods may be extended in a relatively simple fashion to solve a much larger class of wave problems of great practical interest

the logic of tied implications part 1 properties applications and representation a conjunction t ties an implication operator a if the identity a a a b z a t a b z holds a a abdel hamid n n morsi associatively tied implications fuzzy sets and systems 136 2003 291 311 we study the class of tied adjointness algebras which are five connective algebras on two partially ordered sets in which the implications are tied by triangular norms this class contains besides residuated implications several other implications employed in fuzzy logic nevertheless we show that the algebraic inequalities of residuated algebras remain true for our tied implications but in forms that distribute roles over the five connectives of the algebra we apply the properties of tied implications to a generalized modus ponens inference scheme with two successive rules we prove its equivalence to a scheme with one compound rule when both schemata are interpreted by the compositional rule of inference and all connectives are taken from one tied adjointness algebra then we quote another application of this rich theory a notion of many valued rough sets which exhibit the basic mathematical behaviour of the rough sets of pawlak a comparator h is said to be prelinear if it satisfies h y z h z y 1 for all y z hajek we introduce prelinear tied adjointness algebras in which two comparators are prelinear we provide a representation of those algebras as subdirect products of tied adjointness chains on the lines of hajek s representation of bl algebras but our representations are more economical because we employ minimal prime filters on residuated lattices only rather than all prime filters

fuzzy wavelet neural network with an accelerated hybrid learning algorithm an accelerated hybrid learning algorithm is proposed for the training of fuzzy wavelet neural networks fwnns the algorithm gives the initial parameters by the clustering algorithm and then updates them with a combination of backpropagation and recursive least squares methods the parameters are updated in the direction of steepest descent but with a local adaptive learning rate that is different for each epoch and only depends on the sign of the gradient error function this adaptive learning rate is chosen such as to accelerate convergence the learning algorithm is inspired from the halving method to find polynomials roots even though the results are quite satisfactory the algorithm is much simpler than others that have been reported in addition it does includes no excessive terms in adapting formulation unlike much of the research in this area furthermore this algorithm somewhat increases accuracy while using far fewer parameters simulation results indicate a superior convergence speed in comparison with other training methods in fwnn

an online gradient based parameter identification algorithm for the neuro fuzzy systems abstract online gradient descent method has been widely applied for parameter learning in neuro fuzzy systems the success of the application relies on the convergence of the learning procedure however there barely have been convergence analyses on the online learning procedure for neuro fuzzy systems in this paper an online gradient learning algorithm with adaptive learning rate is proposed to identify the parameters of the neuro fuzzy systems representing the mamdani fuzzy model with gaussian fuzzy sets we take the reciprocals of the variances of the gaussian membership functions rather than the variances themselves as independent variables when computing the gradient with respect to the variance parameters subsequently oscillation of the gradient value in the learning process can be avoided furthermore some convergence results for this online learning scheme are studied finally three numerical examples are provided to illustrate the performance of the proposed algorithm

application of an ultra weak variational formulation of elliptic pdes to the two dimensional helmholtz problem a new technique to solve elliptic linear pdes called ultra weak variational formulation uwvf in this paper is introduced in b despres c r acad sci paris 318 1994 pp 939 944 this paper is devoted to an evaluation of the potentialities of this technique it is applied to a model wave problem the two dimensional helmholtz problem the new method is presented in three parts following the same style of presentation as the classical one of the finite elements method even though they are definitely conceptually different methods the first part is committed to the variational formulation and to the continuous problem the second part defines the discretization process using a galerkin procedure the third part actually studies the efficiency of the technique from the order of convergence point of view this is achieved using theoretical proofs and a series of numerical experiments in particular it is proven and shown the order of convergence is lower bounded by a linear function of the number of degrees of freedom an application to scattering problems is presented in a fourth part

modelling of short wave diffraction problems using approximating systems of plane waves this paper describes a finite element model for the solution of helmholtz problems at higher frequencies that offers the possibility of computing many wavelengths in a single finite element the approach is based on partition of unity isoparametric elements at each finite element node the potential is expanded in a discrete series of planar waves each propagating at a specified angle these angles can be uniformly distributed or may be carefully chosen they can also be the same for all nodes of the studied mesh or may vary from one node to another the implemented approach is used to solve a few practical problems such as the diffraction of plane waves by cylinders and spheres the wave number is increased and the mesh remains unchanged until a single finite element contains many wavelengths in each spatial direction and therefore the dimension of the whole problem is greatly reduced issues related to the integration and the conditioning are also discussed

pollution studies for high order isogeometric analysis and finite element for acoustic problems abstract it is well known that galerkin finite element methods suffer from pollution error when solving wave problems to reduce the pollution impact on the solution different approaches were proposed to enrich the finite element method with wave like functions so that the exact wavenumber is incorporated into the finite element approximation space solving wave problems with isogeometric analysis was also investigated in the literature where the superior behaviour of isogeometric analysis due to higher continuity in the underlying basis has been studied recently a plane wave enriched isogeometric analysis was introduced for acoustic problems however it remains unquantified the impact of these different approaches on the pollution or how they perform compared to each other in this work we show that isogeometric analysis outperforms finite element method in dealing with pollution we observe similar behaviour when both the methods are enriched with plane waves using higher order polynomials with fewer enrichment functions seems to improve the pollution compared to lower order polynomials with more functions however the latter still leads to smaller errors using similar number of degrees of freedom in conclusion we propose that partition of unity isogeometric analysis can be an efficient tool for wave problems as enrichment eliminates the need for domain re meshing at higher frequencies and also due to its ability to capture the exact geometry even on coarse meshes as well as its improved pollution behaviour

parallel fuzzy inference based on a level sets and generalized means abstract in this paper a parallel fuzzy inference method is proposed in which inference consequences are unified on the basis of level sets and generalized means it has the following advantages over conventional methods 1 it can control the degree to which the fuzziness and specificity of given facts are reflected to those of unified inference consequences 2 it can deduce unified inference consequences in the form of normal and convex fuzzy sets which can thus be treated as fuzzy numbers and 3 it effectively matches systems that include fuzzy set operations based on the extension principle this paper first reviews the generalized mean and describes the computational steps of the proposed inference method then the properties of this method are investigated and the control mechanism of the fuzziness and specificity in unified inference consequences reflecting those in given facts are presented the efficient inference computations are also provided taking advantage of the level set based scheme of the proposed inference method next a learning algorithm is derived for the proposed inference method based on the error back propagation by feeding fuzzy exemplar patterns it can automatically adjust the above mentioned degree of fuzziness and specificity as well as the fuzzy sets in conditional propositions the simulation studies show the feasibility of the proposed inference method

implication operators in fuzzy logic the choice of fuzzy implication as well as other connectives is an important problem in the theoretical development of fuzzy logic and at the same time it is significant for the performance of the systems in which fuzzy logic technique is employed there are mainly two ways in fuzzy logic to define implication operators 1 an implication operator is considered as the residuation of conjunction operator and 2 it is directly defined in terms of negation conjunction and disjunction operators the purpose of this paper is to determine the number of implication operators defined in the second way for some usual negation conjunction and disjunction operators in fuzzy logic

fuzzy logic and meteorological variables a case study of solar irradiance solar irradiance is an extreme case of an uncertain variable when measured on an hourly or shorter time interval in this paper solar irradiance has been considered as a case study for physical fuzzy modelling of a climate variable the uncertainty of the solar irradiance is treated as a fuzzy uncertainty whilst other variables are considered crisp the approach is robust as it does not rely on statistical assumptions and it is a possible alternative to modelling complex systems to our knowledge this is the first time that a physical model of a meteorological variable based on fuzzy numbers has been proposed previous rule based fuzzy meteorological models are only descriptive and cannot be extrapolated to non measured cases when compared with previous non fuzzy models of solar irradiance the fuzzy model shows an improved performance and when compared with experimental data the performance can be evaluated by fuzzy indices that take into account the uncertainty of the data and the model output

generalized finite element analysis of three dimensional heat transfer problems exhibiting sharp thermal gradients abstract in this paper heat transfer problems exhibiting sharp thermal gradients are analyzed using the classical and generalized finite element methods the effect of solution roughness on the ability of the methods to obtain accurate approximations is investigated convergence studies show that low order linear and quadratic elements require strongly refined meshes for acceptable accuracy we propose a generalized fem with global local enrichments for the class of problems investigated in the paper in this procedure a global solution space defined on a coarse mesh is enriched through the partition of unity framework of the generalized fem with solutions of local boundary value problems the local problems are defined using the same procedure as in the global local fem where boundary conditions are provided by a coarse scale global solution coarse uniform global meshes are acceptable even at regions with thermal spikes that are orders of magnitude smaller than the element size convergence on these discretizations was achieved even when no or limited convergence was observed in the local problems two approaches are proposed to improve the boundary conditions prescribed on local problems and their convergence the use of the corresponding improved local solutions as enrichments for the global problem extends the range of target error level for the enriched global problem the two way information transfer provided by the proposed generalized fem is appealing to several classes of problems especially those involving multiple spatial scales the proposed methodology brings the benefits of generalized fem to problems where limited or no information about the solution is known a priori

a partition of unity fem for time dependent diffusion problems using multiple enrichment functions an enriched partition of unity fem is developed to solve time dependent diffusion problems in the present formulation multiple exponential functions describing the spatial and temporal diffusion decay are embedded in the finite element approximation space the resulting enrichment is in the form of a local asymptotic expansion unlike previous works in this area where the enrichment must be updated at each time step here the temporal decay in the solution is embedded in the asymptotic expansion thus the system matrix that is evaluated at the first time step may be decomposed and retained for every next time step by just updating the right hand side of the linear system of equations the advantage is a significant saving in the computational effort where previously the linear system must be reevaluated and resolved at every time step in comparison with the traditional finite element analysis with p version refinements the present approach is much simpler more efficient and yields more accurate solutions for a prescribed number of dofs numerical results are presented for a transient diffusion equation with known analytical solution the performance of the method is analyzed on two applications the transient heat equation with a single source and the transient heat equation with multiple sources the aim of such a method compared with the classical fem is to solve time dependent diffusion applications efficiently and with an appropriate level of accuracy

a unified real time approximate reasoning approach for use in intelligent control part 1 theoretical development taking account of the fuzzy nature of human decision making processes and real time properties this paper establishes a unified approximate reasoning model based on possibility theory rather than on relational matrix computation both fuzzy and random uncertainties can be coped with in the model in the case of sensor based situations a simpler reasoning scheme is derived by introducing the concepts of matching measures the proposed models may provide another possibility for on line reasoning in real time expert system applications in part 1 the theoretical foundations are provided while in part 2 their application to multivariate blood pressure control is described

a discontinuous galerkin method with lagrange multipliers for the solution of helmholtz problems in the mid frequency regime we present a discontinuous galerkin method dgm for the solution of the helmholtz equation in the mid frequency regime our approach is based on the discontinuous enrichment method in which the standard polynomial field is enriched within each finite element by a non conforming field that contains free space solutions of the homogeneous partial differential equation to be solved hence for the helmholtz equation the enrichment field is chosen here as the superposition of plane waves we enforce a weak continuity of these plane waves across the element interfaces by suitable lagrange multipliers preliminary results obtained for two dimensional model problems discretized by uniform meshes reveal that the proposed dgm enables the development of elements that are far more competitive than both the standard linear and the standard quadratic galerkin elements for the discretization of helmholtz problems

a discontinuous enrichment method for capturing evanescent waves in multiscale fluid and fluid solid problems abstract an evanescent wave is produced when a propagating incident wave impinges on an interface between two media or materials at a sub critical angle the sub scale nature of such a wave makes it difficult to be captured computationally in this paper the discontinuous enrichment method dem developed in c farhat i harari l p franca the discontinuous enrichment method comput methods appl mech engrg 190 2001 6455 6479 c farhat i harari u hetmaniuk a discontinuous galerkin method with lagrange multipliers for the solution of helmholtz problems in the mid frequency regime comput methods appl mech engrg 192 2003 1389 1419 c farhat i harari u hetmaniuk the discontinuous enrichment method for multiscale analysis comput methods appl mech engrg 192 2003 3195 3210 c farhat r tezaur p weidemann goiran higher order extensions of a discontinuous galerkin method for mid frequency helmholtz problems int j numer methods engrg 61 2004 1938 1956 c farhat p wiedemann goiran r tezaur a discontinuous galerkin method with plane waves and lagrange multipliers for the solution of short wave exterior helmholtz problems on unstructured meshes new computational methods for wave propagation wave motion 39 4 2004 307 317 l zhang r tezaur c farhat the discontinuous enrichment method for elastic wave propagation in the medium frequency regime int j numer methods engrg 66 2006 2086 2114 r tezaur c farhat three dimensional discontinuous galerkin elements with plane waves and lagrange multipliers for the solution of mid frequency helmholtz problems int j numer methods engrg 66 2006 796 815 is extended to a class of evanescent wave problems new dem elements are constructed by enriching polynomial approximations with free space evanescent solutions in order to achieve high accuracy for problems with fluid fluid or fluid solid interfaces on which evanescent waves may occur the new dem elements are applied to the solution of various two dimensional model problems with evanescent waves their performance is observed to be better than that of the basic helmholtz type dem elements and superior to that of the classical higher order polynomial finite element method

time dependent shape functions for modeling highly transient geothermal systems this paper presents new time dependent finite element shape functions suitable for modeling high gradient transient conductive heat flow in geothermal systems the shape functions are made adaptive by enhancing the approximation functions with time dependent variables which may vary according to the transient process without adding extra degrees of freedom or applying mesh adaptation two different approaches are presented first an iterative method is proposed in which an exponential approximation function which is optimized continually during the transient process is incorporated in the shape function second an analytical method is suggested in which an analytical solution of a simplified process is incorporated in the shape function enabling an explicit update of the shape functions in each time step a methodology for modeling the variation of temperature in one and two dimensions is introduced the ability of the method to capture high gradient temperature profiles using relatively large elements is illustrated with numerical examples of cases in which equally large standard finite elements fail copyright 2008 john wiley sons ltd

an enriched finite element model with q refinement for radiative boundary layers in glass cooling radiative cooling in glass manufacturing is simulated using the partition of unity finite element method the governing equations consist of a semi linear transient heat equation for the temperature field and a stationary simplified p 1 approximation for the radiation in non grey semitransparent media to integrate the coupled equations in time we consider a linearly implicit scheme in the finite element framework a class of hyperbolic enrichment functions is proposed to resolve boundary layers near the enclosure walls using an industrial electromagnetic spectrum the proposed method shows an immense reduction in the number of degrees of freedom required to achieve a certain accuracy compared to the conventional h version finite element method furthermore the method shows a stable behaviour in treating the boundary layers which is shown by studying the solution close to the domain boundaries the time integration choice is essential to implement a q refinement procedure introduced in the current study the enrichment is refined with respect to the steepness of the solution gradient near the domain boundary in the first few time steps and is shown to lead to a further significant reduction on top of what is already achieved with the enrichment the performance of the proposed method is analysed for glass annealing in two enclosures where the simplified p 1 approximation solution with the partition of unity method the conventional finite element method and the finite difference method are compared to each other and to the full radiative heat transfer as well as the canonical rosseland model

an interface enriched generalized fem for problems with discontinuous gradient fields summary a new generalized fem is introduced for solving problems with discontinuous gradient fields the method relies on enrichment functions associated with generalized degrees of freedom at the nodes generated from the intersection of the phase interface with element edges the proposed approach has several advantages over conventional generalized fem formulations such as a lower computational cost easier implementation and straightforward handling of dirichlet boundary conditions a detailed convergence study of the proposed method and a comparison with the standard fem are presented for heat transfer problems the method achieves the optimal rate of convergence using meshes that do not conform to the interfaces present in the domain while achieving a level of accuracy comparable to that of the standard fem with conforming meshes various application problems are presented including the conjugate heat transfer problem encountered in microvascular materials copyright 2011 john wiley sons ltd

representation and use of imprecise temporal knowledge in dynamic systems abstract in this paper the importance of representation and use of imprecise temporal knowledge for problem solving in industrial dynamic systems is emphasized first a representation of imprecise temporal knowledge is then given for describing the dynamic behavior of systems a novel problem on on line temporal matching and numeric matching is presented and a method for solving this problem is proposed a method for fuzzy proposition reasoning and temporal reasoning is put forward finally as two application examples the fault diagnosis of a fluidized catalytic cracking unit is taken up to illustrate the usefulness of the proposed knowledge representation and methods

an identification algorithm in fuzzy relational systems abstract the paper presents an effective identification method in fuzzy relational systems we propose an algorithm for constructing models on the basis of fuzzy and nonfuzzy data with the aid of fuzzy discretization and clustering techniques the usefulness of the method provided is demonstrated by means of two numerical examples also a possible way of generating a linguistic decision making algorithm is discussed

a modified gradient based neuro fuzzy learning algorithm and its convergence neuro fuzzy approach is known to provide an adaptive method to generate or tune fuzzy rules for fuzzy systems in this paper a modified gradient based neuro fuzzy learning algorithm is proposed for zero order takagi sugeno inference systems this modified algorithm compared with conventional gradient based neuro fuzzy learning algorithm reduces the cost of calculating the gradient of the error function and improves the learning efficiency some weak and strong convergence results for this algorithm are proved indicating that the gradient of the error function goes to zero and the fuzzy parameter sequence goes to a fixed value respectively a constant learning rate is used some conditions for the constant learning rate to guarantee the convergence are specified numerical examples are provided to support the theoretical findings

a wavenumber independent boundary element method for an acoustic scattering problem in this paper we consider the impedance boundary value problem for the helmholtz equation in a half plane with piecewise constant boundary data a problem which models for example outdoor sound propagation over inhomogeneous flat terrain to achieve good approximation at high frequencies with a relatively low number of degrees of freedom we propose a novel galerkin boundary element method using a graded mesh with smaller elements adjacent to discontinuities in impedance and a special set of basis functions so that on each element the approximation space contains polynomials of degree nu multiplied by traces of plane waves on the boundary we prove stability and convergence and show that the error in computing the total acoustic field is cal o n nu 1 log 1 2 n where the number of degrees of freedom is proportional to n log n this error estimate is independent of the wavenumber and thus the number of degrees of freedom required to achieve a prescribed level of accuracy does not increase as the wavenumber tends to infinity

the discontinuous enrichment method we propose a finite element based discretization method in which the standard polynomial field is enriched within each element by a nonconforming field that is added to it the enrichment contains free space solutions of the homogeneous differential equation that are not represented by the underlying polynomial field continuity of the enrichment across element interfaces is enforced weakly by lagrange multipliers in this manner we expect to attain high coarse mesh accuracy without significant degradation of conditioning assuring good performance of the computation at any mesh resolution examples of application to acoustics and advection diffusion are presented

a robust weakly compressible sph method and its comparison with an incompressible sph summary this paper presents a comparative study for the weakly compressible wcsph and incompressible isph smoothed particle hydrodynamics methods by providing numerical solutions for fluid flows over an airfoil and a square obstacle improved wcsph and isph techniques are used to solve these two bluff body flow problems it is shown that both approaches can handle complex geometries using the multiple boundary tangents mbt method and eliminate particle clustering induced instabilities with the implementation of a particle fracture repair procedure as well as the corrected sph discretization scheme wcsph and isph simulation results are compared and validated with those of a finite element method fem the quantitative comparisons of wcsph isph and fem results in terms of strouhal number for the square obstacle test case and the pressure envelope surface traction forces and velocity gradients on the airfoil boundaries as well as the lift and drag values for the airfoil geometry indicate that the wcsph method with the suggested implementation produces numerical results as accurate and reliable as those of the isph and fem methods copyright 2011 john wiley sons ltd

identifying the wavenumber for the inverse helmholtz problem using an enriched finite element formulation abstract we investigate the inverse problem of identifying the wavenumber for the helmholtz equation the problem solution is based on measurements taken at few points from inside the computational domain or on its boundary a novel iterative approach is proposed based on coupling the secant and the descent methods with the partition of unity method starting from an initial guess for the unknown wavenumber the forward problem is solved using the partition of unity method then the secant descent methods are used to improve the initial guess by minimizing a predefined objective function based on the difference between the solution and a set of data points in the next round of iterations the improved wavenumber estimate is used for the forward problem solution and the partition of unity approximation is improved by adding more enrichment functions the iterative process is terminated when the objective function has converged and a set of two predefined tolerances are met to evaluate the estimate accuracy we propose to utilize extra data points to validate the approach and test its efficiency two wave applications with known analytical solutions are studied the results show that the proposed approach can achieve high accuracy for the studied applications even when the considered data is contaminated with noise despite the clear advantages that were previously shown in the literature for solving the forward helmholtz problem this work presents a first attempt to solve the inverse helmholtz problem with an enriched finite element approach

neuro genetic approach to multidimensional fuzzy reasoning for pattern classification to tackle the pattern classification problems first we give a new interpretation to the multidimensional fuzzy implication mfi this new interpretation of mfi is used for multidimensional fuzzy reasoning mfr for pattern classification we realize the new interpretation through multilayer perceptron the learning scheme of the network is based on genetic algorithm ga a weight smoothing scheme is also proposed to improve neural network s generalization capability the smoothing constraint is incorporated into the objective function of the network to reflect the neighborhood correlation and to seek those solutions which have smooth connection weights at the learning stage of the neural network fuzzy linguistic statements have been used once learned the nonfuzzy features of a pattern can be classified using a fuzzy masking the performance of the proposed scheme is tested through synthetic data finally we apply the proposed scheme to the vowel recognition problem of one indian language

capacity achieving polar codes for arbitrarily permuted parallel channels channel coding over arbitrarily permuted parallel channels was first studied by willems and coworkers this paper introduces capacity achieving polar coding schemes for arbitrarily permuted parallel channels where the component channels are memoryless binary input and output symmetric