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

identifying spatial clustering phenomena in forest fire sequences abstract spatial clustering in fire data recorded from 1997 to 2003 in an area of central italy has been deeply investigated using indices of different type i a topological index the voronoi polygon area ii a statistical index the morishita index iii a dimensional index the fractal dimension our findings reveal the presence of clustering in the spatial distribution of the fire set analysed the knowledge of such property can be very useful to estimate overdensity of fires in those areas where particular prevention and allocation of resources should be assessed

multigrid newton krylov method for radiation in diffusive semitransparent media we present a fast multigrid solver for simplified p n sp n approximations to the diffusive radiation in non grey semitransparent media the method consists on reformulating the equations as a nonlinear fixed point problem in the temperature only given a mesh hierarchy time and space discretizations are performed using second order implicit and finite differencing methods respectively at each mesh level a newton krylov algorithm is applied to the discrete equations as a smoother on the coarse meshes we propose the atkinson brakhage operator numerical results are shown for glass cooling process using different geometry enclosures the sp n approximations capture the correct asymptotic behavior of the numerical solution with a computational cost lower than using the full radiative transfer equations

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 partition of unity enriched dual boundary element method for accurate computations in fracture mechanics we introduce a novel enriched boundary element method bem and dual boundary element method dbem approach for accurate evaluation of stress intensity factors sifs in crack problems the formulation makes use of the partition of unity method pum such that functions obtained from a priori knowledge of the solution space can be incorporated in the element formulation an enrichment strategy is described in which boundary integral equations formed at additional collocation points are used to provide auxiliary equations in order to accommodate the extra introduced unknowns in addition an efficient numerical quadrature method is outlined for the evaluation of strongly singular and hypersingular enriched boundary integrals finally results are shown for mixed mode crack problems these illustrate that the introduction of pum enrichment provides for an improvement in accuracy of approximately one order of magnitude in comparison to the conventional unenriched dbem

a systematic method for constructing sparse gaussian integer sequences with ideal periodic autocorrelation functions a gaussian integer is a complex number whose real and imaginary parts are both integers meanwhile a sequence is defined as perfect if and only if it has an ideal periodic auto correlation function this paper proposes a method for constructing sparse perfect gaussian integer sequences spgiss in which most of the sequence elements are zero the proposed spgiss are obtained by linearly combining four base sequences or their cyclic shift equivalents using nonzero gaussian integer coefficients of equal magnitudes each base sequence contains four nonzero elements belonging to the set pm 1 pm j the number of nonzero elements of the constructed spgiss depends on the choice of complex coefficients and cyclic shifts however each spgis has at most 16 nonzero elements irrespective of the sequence length a systematic investigation is performed into the properties of the spgiss and their fourier dual equivalents finally a general expression is derived for a perfect gaussian integer sequence pgis of length 4n where n is any positive integer and most of the sequence elements are nonzero

multifractal analysis of managed and independent float exchange rates abstract we investigate multifractal properties of daily price changes in currency rates using the multifractal detrended fluctuation analysis mf dfa we analyze managed and independent floating currency rates in eight countries and determine the changes in multifractal spectrum when transitioning between the two regimes we find that after the transition from managed to independent float regime the changes in multifractal spectrum position of maximum and width indicate an increase in market efficiency the observed changes are more pronounced for developed countries that have a well established trading market after shuffling the series we find that the multifractality is due to both probability density function and long term correlations for managed float regime while for independent float regime multifractality is in most cases caused by broad probability density function

multifractal characterization of brazilian market sectors abstract we study auto correlations and cross correlations of daily price returns for seven brazilian market bovespa sectors using multifractal detrended fluctuation analysis mf dfa and multifractal detrended cross correlation analysis mf dxa we discover rather distinct multifractal behavior for different market sectors which indicates that individual sectors follow different dynamics from the entire market our analysis reveals that most sectors are market efficient due to the lack of long term correlations shuffling the series suggests that multifractality in the auto correlations arises both from a broad probability density function and from different long term correlations comparisons of multifractal cross correlations between bovespa and market sectors reveals that some sectors are more affected by multifractality of the entire market while others are more affected by multifractality of the sectors themselves a multifractal analysis of cross correlations between different market sectors provides a multifractal description of the brazilian sectors

complex hadamard matrices related to bent sequences hadamard matrices are often used for some applications such as error correcting codes and spread sequences this article gives the construction of complex hadamard matrices of order p sup n where p is prime and n is even the complex hadamard matrices include bi phase hadamard matrices whose elements take 1 1 and four phase hadamard matrices whose elements take spl plusmn 1 spl plusmn j with j spl radic 1

self organized criticality in a forest fire model a forest fire model is introduced which contains a lightning probability f this leads to a self organized critical state in the limit f 0 provided that the time scales of free growth and burning down of forest clusters are separated we derive scaling laws and calculate all critical exponents the values of the critical exponents are confirmed by computer simulations for a two dimensional system there is evidence that the forest density in the critical state assumes its minimum possible value i e that energy dissipation is maximum

the ultra weak variational formulation for elastic wave problems the ultra weak variational formulation has been used effectively to solve time harmonic acoustic and electromagnetic wave propagation in inhomogeneous media we develop the ultra weak variational formulation for elastic wave propagation in two space dimensions in order to improve the accuracy and stability of the method we find it necessary to approximate the s and p wave components of the solution in a balanced way some preliminary analysis is provided and numerical evidence is presented for the efficiency of the scheme in comparison to piecewise linear finite elements

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

multifractal detrended fluctuation analysis of nonstationary time series abstract we develop a method for the multifractal characterization of nonstationary time series which is based on a generalization of the detrended fluctuation analysis dfa we relate our multifractal dfa method to the standard partition function based multifractal formalism and prove that both approaches are equivalent for stationary signals with compact support by analyzing several examples we show that the new method can reliably determine the multifractal scaling behavior of time series by comparing the multifractal dfa results for original series with those for shuffled series we can distinguish multifractality due to long range correlations from multifractality due to a broad probability density function we also compare our results with the wavelet transform modulus maxima method and show that the results are equivalent

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

local adaptive q enrichments and generalized finite elements for transient heat diffusion problems abstract a residual a posteriori error estimate is used in conjunction with a q adaptive procedure for selecting enrichment functions in the modelling of transient heat diffusion problems with the generalized finite element method gfem the error estimate allows to assess local as well as global errors of the gfem solutions and provides a tool to adaptively enrich the approximation space with the proposed adaptive algorithm the total number of degrees of freedom dofs is significantly reduced in comparison to uniform enrichment for a comparable accuracy a reduction of up to 80 in dofs is achieved moreover the error estimate captures the deterioration of the conditioning of the system matrix typically encountered in enrichment based methods and enables the possibility of keeping the condition number within an acceptable limit

an a posteriori error estimate for the generalized finite element method for transient heat diffusion problems summary we propose the study of a posteriori error estimates for time dependent generalized finite element simulations of heat transfer problems a residual estimate is shown to provide reliable and practically useful upper bounds for the numerical errors independent of the heuristically chosen enrichment functions two sets of numerical experiments are presented first the error estimate is shown to capture the decrease in the error as the number of enrichment functions is increased or the time discretization refined second the estimate is used to predict the behaviour of the error where no exact solution is available it also reflects the errors incurred in the poorly conditioned systems typically encountered in generalised finite element methods finally we study local error indicators in individual time steps and elements of the mesh this creates a basis towards the adaptive selection and refinement of the enrichment functions this article is protected by copyright all rights reserved

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

stock market return distributions from past to present abstract we show that recent stock market fluctuations are characterized by the cumulative distributions whose tails on short minute time scales exhibit power scaling with the scaling index 3 and this index tends to increase quickly with decreasing sampling frequency our study is based on high frequency recordings of the s p500 dax and wig20 indices over the interval may 2004 may 2006 our findings suggest that dynamics of the contemporary market may differ from the one observed in the past this effect indicates a constantly increasing efficiency of world markets

analysis of the efficiency and multifractality of gold markets based on multifractal detrended fluctuation analysis abstract in this paper we investigate the efficiency and multifractality of a gold market based on multifractal detrended fluctuation analysis our evidence shows that the gold return series are multifractal both for time scales smaller than a month and for time scales larger than a month for time scales smaller than a month the main contribution of multifractality is fat tail distribution for time scales larger than a month both long range correlations and fat tail distribution play important roles in the contribution of multifractality using the method of rolling windows we find that the gold market became more and more efficient over time especially after 2001 the abnormal points of scaling exponents can also be related to some occasional events by defining a new inefficiency measure related to the multifractality we find that the gold market is more efficient during the upward periods than during the downward periods

gaussian integer sequences with ideal periodic autocorrelation functions a gaussian integer is a complex number whose real and imaginary parts are both integers meanwhile a sequence is defined as perfect if and only if the out of phase value of the periodic autocorrelation function is equal to zero this paper presents two novel classes of perfect sequences constructed using two groups of base sequences the nonzero elements of these base sequences belong to the set 1 j a perfect sequence can be obtained by linearly combining these base sequences or their cyclic shift equivalents with arbitrary nonzero complex coefficients of equal magnitudes in general the elements of the constructed sequences are not gaussian integers however if the complex coefficients are gaussian integers then the resulting perfect sequences will be gaussian integer perfect sequences gipss in addition a periodic cross correlation function is derived which has the same mathematical expression as the investigated sequences finally the maximal energy efficiency of the proposed gipss is investigated

multifractality in the stock market price increments versus waiting times abstract by applying the multifractal detrended fluctuation analysis to the high frequency tick by tick data from deutsche borse both in the price and in the time domains we investigate multifractal properties of the time series of logarithmic price increments and inter trade intervals of time we show that both quantities reveal multiscaling and that this result holds across different stocks the origin of the multifractal character of the corresponding dynamics is among others the long range correlations in price increments and in inter trade time intervals as well as the non gaussian distributions of the fluctuations since the transaction to transaction price increments do not strongly depend on or are almost independent of the inter trade waiting times both can be sources of the observed multifractal behaviour of the fixed delay returns and volatility the results presented also allow one to evaluate the applicability of the multifractal model of asset returns in the case of tick by tick data

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

multifractal behavior of wild land and forest fire time series in brazil abstract we examine statistical properties of a daily hot pixel time series recorded in brazil during the period 1998 2006 using multifractal detrended fluctuation analysis mf dfa we find that generalized scaling exponent h q is a decreasing function of q indicating multifractal behavior of hot pixel dynamics we also calculate multifractal spectra f and use fourth degree polynomial regression to estimate complexity parameters that describe the degree of multifractality of the underlying process after july 2002 when a significant increase of the number of hot pixel observations is recorded the complexity of the series is reduced manifested by the reduction of width of the f spectrum while small fluctuations increase their dominance over large scale fluctuations manifested by the increase of skew parameter r these results should be taken into account when devising ecological and climatic models for brazil that contemplate the phenomena of wild land and forest fires

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

finite size effect and the components of multifractality in transport economics volatility based on multifractal detrending moving average method abstract analysis of freight rate volatility characteristics attracts more attention after year 2008 due to the effect of credit crunch and slowdown in marine transportation the multifractal detrended fluctuation analysis technique is employed to analyze the time series of baltic dry bulk freight rate index and the market trend of two bulk ship sizes namely capesize and panamax for the period march 1st 1999 february 26th 2015 in this paper the degree of the multifractality with different fluctuation sizes is calculated besides multifractal detrending moving average mf dma counting technique has been developed to quantify the components of multifractal spectrum with the finite size effect taken into consideration numerical results show that both capesize and panamax freight rate index time series are of multifractal nature the origin of multifractality for the bulk freight rate market series is found mostly due to nonlinear correlation

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

the in efficiency of nymex energy futures a multifractal analysis abstract we performed a systematic analysis to investigate the multifractal properties and efficient market hypothesis emh in time series of volatility for nymex new york mercantile exchange energy futures using the multifractal detrended fluctuations analysis mf dfa we studied the generalized hurst exponent h q and the renyi exponent q for each record and quantify their statistical properties which allowed us to observe separately the contributing small scale primarily via the negative moments q and the large scale via the positive moments q we also calculated the multifractal spectrum f and used a fourth degree polynomial regression fit to estimate the complexity parameters that describe the degree of multifractality of the underlying process the results obtained from our fitting procedure show that the volatility time series of nymex energy futures display overall persistent behavior 0 0 5 a higher degree of multifractality and the dominance of large fluctuations in this sense our empirical results related to 0 0 5 categorically reject the emh furthermore our results presented that crude oil light sweet cushing oklahoma the no 2 heating oil new york harbor and propane mont belvieu texas energy futures are highly concentrated with behavior more closely associated to oligopolistic market

parametric enrichment adaptivity by the extended finite element method an adaptive method within the extended finite element method xfem framework which adapts the enrichment function locally to the physics of a problem as opposed to polynomial or mesh refinement is presented the method minimizes a local residual and determines the parameters of the enrichment function we consider an energy form and a strong form of the residual as error measures to drive the algorithm numerical examples for boundary layers and solid mechanics problems illustrate that the procedure converges moreover when only the character of the solution is known a good approximation is obtained in the area of interest it is also shown that the method can be used to determine the order of singularities in solutions copyright 2007 john wiley sons ltd

on solving boundary value problems of modified helmholtz equations by plane wave functions plane wave functions e x w in r2 where 0 x x y w cos sin and x w x cos y sin are used as basis functions to solve boundary value problems of modified helmholtz equations u x 2u x 0 x u x h x x where is the laplace operator and a bounded and simply connected domain in r2 approximations of the exact solution of the above problem by plane wave functions are explicitly constructed for the case that is a disc and the order of approximations is derived a computational algorithm by collocation methods based on a simple singular decomposition of circular matrices is proposed and numerical examples are shown to demonstrate the efficiency of the methods

multifractal detrended fluctuation analysis of the chinese stock index futures market abstract based on the multifractal detrended fluctuation analysis mf dfa and multifractal spectrum analysis this paper empirically studies the multifractal properties of the chinese stock index futures market using a total of 2942 ten minute closing prices we find that the chinese stock index futures returns exhibit long range correlations and multifractality making the single scale index insufficient to describe the futures price fluctuations further by comparing the original time series with the transformed time series through shuffling procedure and phase randomization procedure we show the existence of two different sources of the multifractality for the chinese stock index futures market our results suggest that the multifractality is mainly due to long range correlations although the fat tailed probability distributions also contribute to such multifractal behaviour

numerical modelling of elastic wave scattering in frequency domain by the partition of unity finite element method in this paper we investigate a numerical approach based on the partition of unity finite element method for the time harmonic elastic wave equations the aim of the proposed work is to accurately model two dimensional elastic wave problems with fewer elements capable of containing many wavelengths per nodal spacing and without refining the mesh at each frequency the approximation of the displacement field is performed via the standard finite element shape functions enriched by superimposing pressure and shear plane wave basis which incorporate knowledge of the wave propagation a variational framework able to handle mixed boundary conditions is described numerical examples dealing with the radiation and the scattering of elastic waves by a circular body are presented the results show the performance of the proposed method in both accuracy and efficiency copyright 2008 john wiley sons ltd

three dimensional discontinuous galerkin elements with plane waves and lagrange multipliers for the solution of mid frequency helmholtz problems recently a discontinuous galerkin finite element method with plane wave basis functions and lagrange multiplier degrees of freedom was proposed for the efficient solution in two dimensions of helmholtz problems in the mid frequency regime in this paper this method is extended to three dimensions and several new elements are proposed computational results obtained for several wave guide and acoustic scattering model problems demonstrate one to two orders of magnitude solution time improvement over the higher order galerkin method

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

balanced quadriphase sequences with optimal periodic correlation properties constructed by real valued bent functions the real valued bent function was previously introduced by the authors 1991 as a generalization of the usual p ary bent function p a prime in such a way that the range of the function is the set of real numbers i e not restricted to gf p the real valued bent function was used to construct a family of 2 sup n 2 balanced quadriphase sequences of period 2 sup n 1 with optimal periodic correlation properties where n is a multiple of four a class of real valued bent functions that map the set of all the m tuples over gf 2 into the set 0 1 2 1 3 2 for an arbitrary m is given this is applied to generalize a previous construction to the case where n is even i e not restricted to a multiple of four it is also shown that the quadriphase sequences given by t novosad can be considered as one kind of sequence constructed by real valued bent functions conditions are given for some families of the quadriphase sequences constructed by some real valued bent functions to be balanced the exact distributions of the periodic correlation values are derived for the families of the balanced quadriphase sequences

multifractal characterization of gold market a multifractal detrended fluctuation analysis abstract the multifractal detrended fluctuation analysis technique is employed to analyze the time series of gold consumer price index cpi and the market trend of three world s highest gold consuming countries namely china india and turkey for the period 1993 july 2013 various multifractal variables such as the generalized hurst exponent the multifractal exponent and the singularity spectrum are calculated and the results are fitted to the generalized binomial multifractal gbm series that consists of only two parameters special emphasis is given to identify the possible source s of multifractality in these series our analysis shows that the cpi series and all three market series are of multifractal nature the origin of multifractality for the cpi time series and indian market series is found due to a long range time correlation whereas it is mostly due to the fat tailed probability distributions of the values for the chinese and turkey markets the gbm model series more or less describes all the time series analyzed here

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

scaling and correlations in the dynamics of forest fire occurrence forest fire waiting times defined as the time between successive fires above a certain size in a given region are obtained for italy the probability densities of the waiting times are found to verify a scaling law despite that fact that the distribution of fire sizes is not a power law the meaning of such behavior in terms of the possible self similarity of the process in a nonstationary system is discussed we find that the scaling law arises as a consequence of the stationarity of fire sizes and the existence of a nontrivial instantaneous scaling law sustained by the correlations of the process as a consequence the nonstationary poisson process model does not account for all the complexity of the structure of fire occurrence

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

light transport in biological tissue based on the simplified spherical harmonics equations in this work we demonstrate the validity of the simplified spherical harmonics equations to approximate the more complicated equation of radiative transfer for modeling light propagation in biological tissue we derive the simplified spherical harmonics equations up to order n 7 for anisotropic scattering and partially reflective boundary conditions we compare numerical results with diffusion and discrete ordinates transport solutions we find that the simplified spherical harmonics methods significantly improve the diffusion solution in transport like domains with high absorption and small geometries and are computationally less expensive than the discrete ordinates transport method for example the simplified p 3 method is approximately two orders of magnitude faster than the discrete ordinates transport method but only 2 5 times computationally more demanding than the diffusion method we conclude that the simplified spherical harmonics methods can accurately model light propagation in small tissue geometries at visible and near infrared wavelengths yielding transport like solutions with only a fraction of the computational cost of the transport calculation

self organized critical forest fire model a forest fire model is introduced which contains a lightning probability f this leads to a self organized critical state in the limit f ensuremath rightarrow 0 provided that the time scales of tree growth and burning down of forest clusters are separated we derive scaling laws and calculate all critical exponents the values of the critical exponents are confirmed by computer simulations for a two dimensional system we show that the forest density in the critical state assumes its minimum possible value i e that energy dissipation is maximum

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

scaling of the distribution of fluctuations of financial market indices up to more than one month we find that the distributions for dt 4d 1560 min are consistent with a power law asymptotic behavior characterized by an exponent a 3 well outside the stable levy regime 0 a 2 to test the robustness of the s p result we perform a parallel analysis on two other financial market indices database iv contains 3560 daily records of the nikkei index for the 14 year period 1984 1997 and database v contains 4649 daily records of the hang seng index for the 18 year period 1980 1997 we find estimates ofa consistent with those describing the distribution of s p 500 daily returns one possible reason for the scaling of these distributions is the long persistence of the autocorrelation function of the volatility for time scales longer than dt 3 4 d our results are consistent with a slow convergence to gaussian behavior s1063 651x 99 11211 x pacs number s 05 40 fb 05 45 tp 89 90 1n

wavelet versus detrended fluctuation analysis of multifractal structures we perform a comparative study of applicability of the multifractal detrended fluctuation analysis mfdfa and the wavelet transform modulus maxima wtmm method in proper detecting of monofractal and multifractal character of data we quantify the performance of both methods by using different sorts of artificial signals generated according to a few well known exactly soluble mathematical models monofractal fractional brownian motion bifractal levy flights and different sorts of multifractal binomial cascades our results show that in the majority of situations in which one does not know a priori the fractal properties of a process choosing mfdfa should be recommended in particular wtmm gives biased outcomes for the fractional brownian motion with different values of hurst exponent indicating spurious multifractality in some cases wtmm can also give different results if one applies different wavelets we do not exclude using wtmm in real data analysis but it occurs that while one may apply mfdfa in a more automatic fashion wtmm must be applied with care in the second part of our work we perform an analogous analysis on empirical data coming from the american and from the german stock market for this data both methods detect rich multifractality in terms of broad f alpha but mfdfa suggests that this multifractality is poorer than in the case of wtmm

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 complexity and fractal structures of csi300 before and after the introduction of csi300if abstract this paper employs multifractal detrended fluctuation analysis mf dfa approach to analyze the complexity and fractal structures of china securities index 300 csi300 which covers the period from april 5 2006 to may 9 2014 through comparing the statistic properties before and after the introduction of csi300 index futures csi300if we find that 1 the price return series exhibits multifractal properties for the two periods 2 by comparing the efficient measure based on the general hurst exponent we find the market becomes more efficient after the introduction of csi300if 3 the width of multifractal spectrum becomes narrower which means the complexity of the market is decreased therefore the introduction of csi300if is beneficial to reduce the risk and increase the efficiency of chinese securities market furthermore the main sources of multifractality of these time series are examined through the shuffle method and the results show that before csi300if the multifractality is mainly due to the long range correlation properties between small and large fluctuations while after csi300if it is more due to fat tailed probability distributions

testing for nonlinearity in time series the method of surrogate data we describe a statistical approach for identifying nonlinearity in time series the method first specifies some linear process as a null hypothesis then generates surrogate data sets which are consistent with this null hypothesis and finally computes a discriminating statistic for the original and for each of the surrogate data sets if the value computed for the original data is significantly different than the ensemble of values computed for the surrogate data then the null hypothesis is rejected and nonlinearity is detected we discuss various null hypotheses and discriminating statistics the method is demonstrated for numerical data generated by known chaotic systems and applied to a number of experimental time series which arise in the measurement of superfluids brain waves and sunspots we evaluate the statistical significance of the evidence for nonlinear structure in each case and illustrate aspects of the data which this approach identifies

multifractal random walk we introduce a class of multifractal processes referred to as multifractal random walks mrws to our knowledge it is the first multifractal process with continuous dilation invariance properties and stationary increments mrws are very attractive alternative processes to classical cascadelike multifractal models since they do not involve any particular scale ratio the mrws are indexed by four parameters that are shown to control in a very direct way the multifractal spectrum and the correlation structure of the increments we briefly explain how in the same way one can build stationary multifractal processes or positive random measures

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

time dependent simplified pn approximation to the equations of radiative transfer the steady state simplified pn approximation to the radiative transport equation has been successfully applied to many problems involving radiation this paper presents the derivation of time dependent simplified pn spn equations up to n 3 via two different approaches first we use an asymptotic analysis similar to the asymptotic derivation of the steady state spn equations second we use an approach similar to the original derivation of the steady state spn equations and we show that both approaches lead to similar results special focus is put on the well posedness of the equations and the question whether it can be guaranteed that the solution satisfies the correct physical bounds several numerical test cases are shown including an analytical benchmark due to su and olson b su g l olson an analytical benchmark for non equilibrium radiative transfer in an isotropically scattering medium ann nucl energy 24 1997 1035 1055

analysis and applications of a generalized finite element method with global local enrichment functions abstract this paper presents a procedure to build enrichment functions for partition of unity methods like the generalized finite element method and the hp cloud method the procedure combines classical global local finite element method concepts with the partition of unity approach it involves the solution of local boundary value problems using boundary conditions from a global problem defined on a coarse discretization the local solutions are in turn used to enrich the global space using the partition of unity framework the computations at local problems can be parallelized without difficulty allowing the solution of large problems very efficiently the effectiveness of the approach in terms of convergence rates and computational cost is investigated in this paper we also analyze the effect of inexact boundary conditions applied to local problems and the size of the local domains on the accuracy of the enriched global solution key aspects of the computational implementation in particular the numerical integration of generalized fem approximations built with global local enrichment functions are presented the method is applied to fracture mechanics problems with multiple cracks in the domain our numerical experiments show that even on a serial computer the method is very effective and allows the solution of complex problems our analysis also demonstrates that the accuracy of a global problem defined on a coarse mesh can be controlled using a fixed number of global degrees of freedom and the proposed global local enrichment functions