an algebraic multigrid method for a class of elliptic differential systems the development numerical investigation and analysis of an algebraic multigrid amg method for the numerical solution of a representative class of elliptic differential systems are presented our amg scheme is based on the amg strategy of brandt ruge and stuben however the present approach may be implemented within other amg schemes by means of numerical experiments with model problems arising from some application areas it is demonstrated that the computational performance of the proposed amg scheme is comparable to that of amg applied to a single scalar equation an amg convergence theory is presented that extends convergence results for amg methods for scalar problems to the case of amg applied to elliptic systems some details of our amg implementation are given

nonparametric estimation and testing of fixed effects panel data models in this paper we consider the problem of estimating nonparametric panel data models with fixed effects we introduce an iterative nonparametric kernel estimator we also extend the estimation method to the case of a semiparametric partially linear fixed effects model to determine whether a parametric semiparametric or nonparametric model is appropriate we propose test statistics to test between the three alternatives in practice we further propose a test statistic for testing the null hypothesis of random effects against fixed effects in a nonparametric panel data regression model simulations are used to examine the finite sample performance of the proposed estimators and the test statistics

a preconditioned gmres method for nonsymmetric or indefinite problems a preconditioning technique is proposed for nonsymmetric or indefinite linear systems of equations the main idea in our theory roughly speaking is first to use some coarser mesh space to correct the nonpositive portion of the eigenvalues of the underlying operator and then switch to use a symmetric positive definite preconditioner the generality of our theory allows us to apply any known preconditioners that were orginally designed for symmetric positive definite problems to nonsymmetric or indefinite problems without losing the optimality that the original one has some numerical experiments based on gmres are reported

a consistent nonparametric test of parametric regression functional form in fixed effects panel data models abstract we propose a consistent test for a linear functional form against a nonparametric alternative in a fixed effects panel data model we show that the test has a limiting standard normal distribution under the null hypothesis and show that the test is a consistent test we also establish the asymptotic validity of a bootstrap procedure which is used to better approximate the finite sample null distribution of the test statistic simulation results show that the proposed test performs well for panel data with a large number of cross sectional units and a finite number of observations across time

a p cycle analysis of multigrid method we suggest a new strategy for multigrid iterations based on our analysis for p cycle multigrid method first we improve a recent result on multigrid v cycle analysis given by bramble and pasciak to p cycle multigrid method we show that the convergence rate improves slowly with p eventually bounded by a constant which is in agreement with many previous experiments based on the this observation we use p cycle only in the first few multigrid iterations which is more effective than the standard p cycle

multigrid methods for two dimensional maxwell s equations on graded meshes in this paper we investigate the numerical solution for two dimensional maxwell s equations on graded meshes the approach is based on the hodge decomposition the solution u of maxwell s equations is approximated by solving standard second order elliptic problems quasi optimal error estimates for both u and i u in the l 2 norm are obtained on graded meshes we prove the uniform convergence of the w cycle and full multigrid algorithms for the resulting discrete problem the performance of these methods is illustrated by numerical results

multigrid methods for saddle point problems stokes and lame systems we develop new multigrid methods for a class of saddle point problems that include the stokes system in fluid flow and the lame system in linear elasticity as special cases the new smoothers in the multigrid methods involve optimal preconditioners for the discrete laplace operator we prove uniform convergence of the w w cycle algorithm in the energy norm and present numerical results for w w cycle and v v cycle algorithms

on the consistency of bayes estimates on etudie les proprietes de frequence des regles de bayes avec une attention particuliere a la consistence

convergence estimates for multigrid algorithms without regularity assumptions a new technique for proving rate of convergence estimates of multi grid algorithms for symmetric positive definite problems will be given in this paper the standard multigrid theory requires a regularity and approxima tion assumption in contrast the new theory requires only an easily verified approximation assumption this leads to convergence results for multigrid re finement applications problems with irregular coefficients and problems whose coefficients have large jumps in addition the new theory shows why it suffices to smooth only in the regions where new nodes are being added in multigrid refinement applications

specification test for panel data models with interactive fixed effects abstract in this paper we propose a consistent nonparametric test for linearity in a large dimensional panel data model with interactive fixed effects both lagged dependent variables and conditional heteroskedasticity of unknown form are allowed in the model we estimate the model under the null hypothesis of linearity to obtain the restricted residuals which are then used to construct the test statistic we show that after being appropriately centered and standardized the test statistic is asymptotically normally distributed under both the null hypothesis and a sequence of pitman local alternatives by using the concept of conditional strong mixing that was recently introduced by prakasa rao 2009 to improve the finite sample performance we propose a bootstrap procedure to obtain the bootstrap p value a small set of monte carlo simulations illustrates that our test performs well in finite samples an application to an economic growth panel dataset indicates significant nonlinear relationships between economic growth initial income level and capital accumulation

consistent bootstrap tests of parametric regression functions abstract this paper introduces specification tests of parametric mean regression models the null hypothesis of interest is that the parametric regression function is correctly specified the proposed tests are generalizations of the kolmogorov smirnov and cramer von mises tests to the regression framework they are consistent against all alternatives to the null hypothesis powerful against 1 n local alternatives not dependent on any smoothing parameters and simple to compute a wild bootstrap procedure is suggested to obtain critical values for the tests and is justified asymptotically a small scale monte carlo experiment shows that our tests especially cramer von mises test have outstanding small sample performance compared to some of the existing tests

phase behavior under the averaging over disorder realizations abstract effects of the averaging over disorder realizations samples on the phase behavior are analyzed in terms of the mean field approximation for the random field ising model with infinite range interactions it is found that the averaging is equivalent to a drastic modification in the statistics of the quenched variables in its turn this lowers the critical temperature of a second order phase transition or depending on the sampling even suppresses the ordered phase possible first order transitions are shown to be softened by the sample averaging common issues and differences in the interpretation of these effects in the context of the simulation and experimental studies are discussed

a central limit theorem for generalized quadratic forms random variables of the form w n mathop sum limits 1 leqq i leqq n mathop sum limits text 1 leqq j leqq n w ijn x i x j are considered with x i independent not necessarily identically distributed and w ijn borel functions such that w ijn x i x j is square integrable and has vanishing conditional expectations e w ijn x i x j x i e w ijn x i x j x j 0 text a text s text a central limit theorem is proved under the condition that the normed fourth moment tends to 3 under some restrictions the condition is also necessary finally conditions on the individual tails of w ijn x i x j and an eigenvalue condition are given that ensure asymptotic normality of w n

panel nonparametric regression with fixed effects nonparametric regression is developed for data with both a temporal and a cross sectional dimension the model includes additive unknown individual specific components and allows also for cross sectional and temporal dependence and conditional heteroscedasticity a simple nonparametric estimate is shown to be dominated by a gls type one asymptotically optimal bandwidth choices are justified for both estimates feasible optimal bandwidths and feasible optimal regression estimates are also asymptotically justified finite sample performance is examined in a monte carlo study

lack of self averaging of the specific heat in the three dimensional random field ising model we apply the recently developed critical minimum energy subspace scheme for the investigation of the random field ising model we point out that this method is well suited for the study of this model the density of states is obtained via the wang landau and broad histogram methods in a unified implementation by employing the n fold version of the wang landau scheme the random fields are obtained from a bimodal distribution h i ifmmode pm else textpm fi 2 and the scaling of the specific heat maxima is studied on cubic lattices with sizes ranging from l 4 to l 32 observing the finite size scaling behavior of the maxima of the specific heats we examine the question of saturation of the specific heat the lack of self averaging of this quantity is fully illustrated and it is shown that this property may be related to the question mentioned above

towards adaptive smoothed aggregation alpha sa for nonsymmetric problems applying smoothed aggregation sa multigrid to solve a nonsymmetric linear system a mathbf x mathbf b is often impeded by the lack of a minimization principle that can be used as a basis for the coarse grid correction process this paper proposes a petrov galerkin pg approach based on applying sa to either of two symmetric positive definite spd matrices sqrt a t a or sqrt aa t these matrices however are typically full and difficult to compute so it is not computationally efficient to use them directly to form a coarse grid correction the proposed approach approximates these coarse grid corrections by using sa to accurately approximate the right and left singular vectors of a that correspond to the lowest singular value these left and right singular vectors are used to construct the restriction and interpolation operators respectively a preliminary two level convergence theory is presented suggesting that more relaxation should be applied than for an spd problem additionally a nonsymmetric version of adaptive sa alpha sa is given that automatically constructs sa multigrid hierarchies using a stationary relaxation process on all levels numerical results are reported for convection diffusion problems in two dimensions with varying amounts of convection for constant variable and recirculating convection fields the results suggest that the proposed approach is algorithmically scalable for problems coming from these nonsymmetric scalar pdes with the exception of recirculating flow this paper serves as a first step for nonsymmetric alpha sa the long term goal of this effort is to develop nonsymmetric alpha sa for systems of pdes where the sa framework has proven to be well suited for adaptivity in spd problems

consistent model specification tests for time series econometric models in this paper we consider general hypothesis testing problems for nonparametric and semiparametric time series econometric models we apply the general methodology to construct a consistent test for omitted variables and a consistent test for a partially linear model the proposed tests are shown to have asymptotic normal distributions under their respective null hypotheses we also discuss the problems of testing portfolio conditional mean variance efficiency and testing a semiparametric single index model monte carlo simulations are conducted to examine the finite sample performances of the nonparametric omitted variable test and the test for a partially linear specification

multilevel solution of the time harmonic maxwell s equations based on edge elements a widely used approach for the computation of time harmonic electromagnetic fields is based on the well known double curl equation for either e or h where edge elements are an appealing choice for finite element discretizations yet the nullspace of the curl operator comprises a considerable part of all spectral modes on the finite element grid thus standard multilevel solvers are rendered inefficient as they essentially hinge on smoothing procedures like gauss seidel relaxation which cannot provide a satisfactory error reduction for modes with small or even negative eigenvalues we propose to remedy this situation by an extended multilevel algorithm which relies on corrections in the space of discrete scalar potentials after every standard v cycle with respect to the canonical basis of edge elements error components in the nullspace are removed by an additional projection step furthermore a simple criterion for the coarsest mesh is derived to guarantee both stability and efficiency of the iterative multilevel solver for the whole scheme we observe convergence rates independent of the refinement level of the mesh the sequence of nested meshes required for our multilevel techniques is constructed by adaptive refinement to this end we have devised an a posteriori error indicator based on stress recovery copyright 1999 john wiley sons ltd

softening of first order transition in three dimensions by quenched disorder we study by extensive monte carlo simulations the effect of random bond dilution on the phase transition of the three dimensional four state potts model that is known to exhibit a strong first order transition in the pure case the phase diagram in the dilution temperature plane is determined from the peaks of the susceptibility for sufficiently large system sizes in the strongly disordered regime numerical evidence for softening to a second order transition induced by randomness is given here a large scale finite size scaling analysis made difficult due to strong crossover effects presumably caused by the percolation fixed point is performed

multigrid convergence for nonsymmetric indefinite variational problems and one smoothing step we prove that the multigrid method for linear systems arising from nonsymmetric and indefinite elliptic variational problems converges for all sufficiently small h with one smoothing step only previous proofs required that the number of smoothing steps be within certain bounds which were quite difficult to compute our theory is based on sharp energy norm convergence estimates for the symmetric definite case and lower order terms are treated as perturbations the resulting estimates are so sharp that we obtain even the convergence of the v cycle

nonparametric semiparametric estimation and testing of econometric models with data dependent smoothing parameters we consider nonparametric semiparametric estimation and testing of econometric models with data dependent smoothing parameters most of the existing works on asymptotic distributions of a nonparametric semiparametric estimator or a test statistic are based on some deterministic smoothing parameters while in practice it is important to use data driven methods to select the smoothing parameters in this paper we give a simple sufficient condition that can be used to establish the first order asymptotic equivalence of a nonparametric estimator or a test statistic with stochastic smoothing parameters to those using deterministic smoothing parameters we also allow for general weakly dependent data

a simple framework for nonparametric specification testing this paper presents a simple framework for testing the specification of parametric conditional means the test statistics are based on quadratic forms in the residuals of the null model under general assumptions the test statistics are asymptotically normal under the null with an appropriate choice of the weight matrix the tests are shown to be consistent and to have good local power specific implementations involving matrices of bin and kernel weights are discussed finite sample properties are explored in simulations

comparing nonparametric versus parametric regression fits in general there will be visible differences between a parametric and a nonparametric curve estimate it is therefore quite natural to compare these in order to decide whether the parametric model could be justified an asymptotic quantification is the distribution of the integrated squared difference between these curves we show that the standard way of bootstrapping this statistic fails we use and analyse a different form of bootstrapping for this task we call this method the wild bootstrap and apply it to fitting engel curves in expenditure data analysis

consistent model specification tests omitted variables and semiparametric functional forms in this paper we develop several consistent tests in the context of a nonparametric regression model these include tests for the significance of a subset of regressors and tests for the specification of the semiparametric functional form of the regression function where the latter covers tests for a partially linear and a single index specification against a general nonparametric alternative one common feature to the construction of all these tests is the use of the central limit theorem for degenerate u statistics of order higher than two as a result they share the same advantages over most of the corresponding existing tests in the literature a they do not depend on any ad hoc modifications such as sample splitting random weighting etc b under the alternative hypotheses the test statistics in this paper diverge to positive infinity at a faster rate than those based on ad hoc modifications

the analysis of smoothers for multigrid algorithms the purpose of this paper is to provide a general technique for defining and analyzing smoothing operators for use in multigrid algorithms the smoothing operators considered are based on subspace decomposition and include point line and block versions of jacobi and gauss seidel iteration as well as generalizations we shall show that these smoothers will be effective in multigrid algorithms provided that the subspace decomposition satisfies two simple conditions in many applications these conditions are trivial to verify

constistent specification testing via nonparametric series regression this paper proposes two consistent one sided specification tests for parametric regression models one based on the sample covariance between the residual from the parametric model and the discrepancy between the parametric and nonparametric fitted values the other based on the difference in sums of squared residuals between the parametric and nonparametric models we estimate the nonparametric model by series regression the new test statistics converge in distribution to a unit normal under correct specification and grow to infinity faster than the parametric rate n 1 2 under misspecification while avoiding weighting sample splitting and non nested testing procedures used elsewhere in the literature asymptotically our tests can be viewed as a test of the joint hypothesis that the true parameters of a series regression model are zero where the dependent variable is the residual from the parametric model and the series terms are functions of the explanatory variables chosen so as to support nonparametric estimation of a conditional expectation we specifically consider fourier series and regression splines and present a monte carlo study of the finite sample performance of the new tests in comparison to consistent tests of bierens 1990 eubank and spiegelman 1990 jayasuriya 1990 wooldridge 1992 and yatchew 1992 the results show the new tests have good power performing quite well in some situations we suggest a joint bonferroni procedure that combines a new test with those of bierens and wooldridge to capture the best features of the three approaches

a simple consistent bootstrap test for a parametric regression function abstract a simple consistent test is considered and a bootstrap method is proposed for testing a parametric regression functional form it is shown that the bootstrap method gives a more accurate approximation to the null distribution of the test than the asymptotic normal theory result we also propose a consistent test for testing a parametric partially linear model versus a semiparametric partially linear alternative monte carlo simulations suggest that the bootstrap test performs well based on wild bootstrap critical values

consistent hypothesis testing in semiparametric and nonparametric models for econometric time series abstract in this paper we modify the general hypothesis studied by robinson 1989 for semi nonparametric time series models and present a consistent testing procedure for the modified hypothesis as examples we provide consistent tests for the portfolio conditional mean variance efficiency hypothesis for theomitted variables in a multivariate nonparametric time series regression model and for the two original examples in robinson the asymptotic distributions under the null and pitman local alternatives are established by invoking central limit theorems for hilbert valued dependent random arrays to approximate the critical values of the general test we modify the conditional monte carlo approach of hansen 1996 and the stationary bootstrap of politis and romano 1994a b and show that both work asymptotically

wang landau study of the critical behavior of the bimodal 3d random field ising model we apply the wang landau method to the study of the critical behavior of the three dimensional random field ising model with a bimodal probability distribution for high values of the random field intensity we find that the energy probability distribution at the transition temperature is double peaked suggesting that the phase transition is first order on the other hand the transition looks continuous for low values of the field intensity in spite of the large sample to sample fluctuations observed the double peak in the probability distribution is always present for high fields

analysis and comparison of geometric and algebraic multigrid for convection diffusion equations the discrete convection diffusion equations obtained from streamline diffusion finite element discretization are solved on both uniform meshes and adaptive meshes estimates of error reduction rates for both geometric multigrid gmg and algebraic multigrid amg are established on uniform rectangular meshes for a model problem our analysis shows that gmg with line gauss seidel smoothing and bilinear interpolation converges if h gg epsilon 2 3 and amg with the same smoother converges more rapidly than gmg if the interpolation constant beta in the approximation assumption of amg satisfies beta ll frac h sqrt epsilon alpha hs 1mm mbox where alpha big begin smallmatrix 1 h sqrt varepsilon 2 h ge sqrt varepsilon end smallmatrix on unstructured triangular meshes the performance of gmg and amg both as solvers and as preconditioners for gmres are evaluated numerical results show that gmres with amg preconditioning is a robust and reliable solver on both type of meshes

multigrid algorithms for nonconforming and mixed methods for nonsymmetric and indefinite problems in this paper we consider multigrid algorithms for nonconforming and mixed finite element methods for nonsymmetric and or indefinite elliptic problems we show that a simple cal v cycle multigrid iteration using conforming coarse grid corrections converges at a uniform rate provided that the coarsest level in the multilevel iteration is sufficiently fine but independent of the number of multigrid levels various types of smoothers for the nonsymmetric and indefinite problems are discussed extensive numerical results are presented

nonparametric dynamic panel data models kernel estimation and specification testing abstract motivated by the first differencing method for linear panel data models we propose a class of iterative local polynomial estimators for nonparametric dynamic panel data models with or without exogenous regressors the estimators utilize the additive structure of the first differenced model the fact that the two additive components have the same functional form and the unknown function of interest is implicitly defined as a solution of a fredholm integral equation of the second kind we establish the uniform consistency and asymptotic normality of the estimators we also propose a consistent test for the correct specification of linearity in typical dynamic panel data models based on the l 2 distance of our nonparametric estimates and the parametric estimates under the linear restriction we derive the asymptotic distributions of the test statistic under the null hypothesis and a sequence of pitman local alternatives and prove its consistency against global alternatives simulations suggest that the proposed estimators and tests perform well for finite samples we apply our new method to study the relationships among economic growth the initial economic condition and capital accumulation and find a significant nonlinear relation between economic growth and the initial economic condition

multigrid convergence for second order elliptic problems with smooth complex coefficients the finite element method when applied to a second order partial differential equation in divergence form can generate operators that are neither hermitian nor definite when the coefficient function is complex valued for such problems under a uniqueness assumption we prove the continuous dependence of the exact solution and its finite element approximations on data provided that the coefficients are smooth and uniformly bounded away from zero then we show that a multigrid algorithm converges once the coarse mesh size is smaller than some fixed number providing an efficient solver for computing discrete approximations numerical experiments while confirming the theory also reveal pronounced sensitivity of gauss seidel iterations on the ordering of the unknowns for certain problems

uniform convergence and schwarz method for the mortar element method for non selfadjoint and indefinite problems in this paper the mortar element method for non selfadjoint and indefinite second order elliptic problems is studied only under minimal regularity assumption the existence uniqueness and uniform convergence of the solution for the mortar element method are proven furthermore an additive schwarz preconditioning method is proposed and nearly optimal convergence rate for the preconditioned gmres method is shown under minimal regularity assumption

uniform convergence of multigrid v cycle iterations for indefinite and nonsymmetric problems in this paper an analysis of a multigrid method for nonsymmetric and or indefinite elliptic problems is presented in this multigrid method various types of smoothers may be used one type of smoother considered is defined in terms of an associated symmetric problem and includes point and line jacobi and gauss seidel iterations smoothers based entirely on the original operator are also considered one smoother is based on the normal form that is the product of the operator and its transpose other smoothers studied include point and line jacobi and gauss seidel it is shown that the uniform estimates of j h bramble and j e pasciak math comp 60 1993 pp 447 471 for symmetric positive definite problems carry over to these algorithms more precisely the multigrid iteration for the nonsymmetric and or indefinite problem is shown to converge at a uniform rate provided that the coarsest grid in the multilevel iteration is sufficiently fine but not dependent on the number of multigrid levels

a consistent test of functional form via nonparametric estimation techniques abstract this paper presents a consistent test of functional form of nonlinear regression models the test combines the methodology of the conditional moment test and nonparametric estimation techniques using degenerate and nondegenerate u statistic theories the test statistic is shown to be asymptotically distributed standard normal under the null hypothesis that the parametric model is correct while diverging to infinity at a rate arbitrarily close to n the sample size if the parametric model is misspecified therefore the test is consistent against all deviations from the parametric model the test is robust to heteroskedasticity a version of the test can be constructed which will have asymptotic power equal to 1 against any local alternatives approaching the null at rates slower than the parametric rate 1 n a simulation study reveals that the test has good finite sample properties

maximum entropy approach to power law distributions in coupled dynamic stochastic systems statistical properties of coupled dynamic stochastic systems are studied within a combination of the maximum information principle and the superstatistical approach the conditions at which the shannon entropy functional leads to power law statistics are investigated it is demonstrated that from a quite general point of view the power law dependencies may appear as a consequence of global constraints restricting both the dynamic phase space and the stochastic fluctuations as a result at sufficiently long observation times the dynamic counterpart is driven into a nonequilibrium steady state whose deviation from the usual exponential statistics is given by the distance from the conventional equilibrium

model checking for parametric single index models a dimension reduction model adaptive approach summary local smoothing testing based on multivariate non parametric regression estimation is one of the main model checking methodologies in the literature however the relevant tests suffer from the typical curse of dimensionality resulting in slow rates of convergence to their limits under the null hypothesis and less deviation from the null hypothesis under alternative hypotheses this problem prevents tests from maintaining the level of significance well and makes tests less sensitive to alternative hypotheses in the paper a model adaptation concept in lack of fit testing is introduced and a dimension reduction model adaptive test procedure is proposed for parametric single index models the test behaves like a local smoothing test as if the model were univariate it is consistent against any global alternative hypothesis and can detect local alternative hypotheses distinct from the null hypothesis at a fast rate that existing local smoothing tests can achieve only when the model is univariate simulations are conducted to examine the performance of our methodology an analysis of real data is shown for illustration the method can be readily extended to global smoothing methodology and other testing problems

a new convergence proof for the multigrid method including the v cycle for a positive definite finite element equation we describe a multigrid iteration and prove convergence under natural assumptions on the discretization and the elliptic problem hitherto existing convergence proofs require a sufficiently large number of smoothing iterations and exclude the v cycle the presented proof applies to procedures with any number of smoothing iterations and to the v cycle

how large a shift is needed in the shifted helmholtz preconditioner for its effective inversion by multigrid the shifted helmholtz operator has received a lot of attention over the past decade as a preconditioner for the iterative solution of the helmholtz equation the idea is that if one uses a small complex shift the shifted helmholtz operator is still close to the original helmholtz operator and could thus be an effective preconditioner it was shown in m j gander i g graham and e a spence numer math 53 2015 pp 573 579 that the shift can be at most o k to prove rigorously wave number independent convergence of the preconditioned system solved with gmres provided the preconditioner is inverted exactly in practice however the preconditioner is inverted only approximately and if one shifts enough this can be done effectively by standard multigrid methods we show in this paper that for a finite element discretization the shift has to be at least o k 2 to be able to invert the shifted helmholtz preconditioner using multigrid there is therefore a gap between being a good precondi

testing capital asset pricing models using functional coefficient panel data models with cross sectional dependence abstract this paper proposes a functional coefficient panel data model with cross sectional dependence motivated by re examining the empirical performance of conditional capital asset pricing model in order to characterize the time varying property of assets betas and alpha our proposed model allows the betas to be unknown functions of some macroeconomic and financial instruments moreover a common factor structure is introduced to characterize cross sectional dependence which is an attractive feature under a panel data regression setting as different assets or portfolios may be affected by same unobserved shocks compared to the existing studies such as the classic fama macbeth two step procedure our model can achieve substantial efficiency gains for inference by adopting a one step procedure using the entire sample rather than a single cross sectional regression at each time point we propose a local linear common correlated effects estimator for estimating time varying betas by pooling the data the consistency and asymptotic normality of the proposed estimators are established another methodological and empirical challenge in asset pricing is how to test the constancy of conditional betas and the significance of pricing errors we echo this challenge by constructing an l 2 norm statistic for functional coefficient panel data models allowing for cross sectional dependence we show that the new test statistic has a limiting standard normal distribution under the null hypothesis finally the method is applied to test the model in fama and french 1993 using fama french 25 and 100 portfolios sorted by size and book to market ratio respectively dated from july 1963 to july 2018

local multilevel methods for adaptive finite element methods for nonsymmetric and indefinite elliptic boundary value problems in this paper we propose some local multilevel algorithms for solving linear systems arising from adaptive finite element approximations of nonsymmetric and indefinite elliptic boundary value problems two types of local smoothers are constructed one is based on the original nonsymmetric problems and the other is defined in terms of the associated symmetric problems it is shown that the local multilevel methods for the nonsymmetric and indefinite elliptic boundary value problems are optimal which means that the convergence rates of the local multilevel methods are independent of mesh sizes and mesh levels provided that the coarsest grid is sufficiently fine numerical experiments are reported to confirm our theory

solution of lambda omega systems theta schemes and multigrid methods the numerical solution of a time dependent reaction diffusion lambda omega system discretized by theta schemes and finite differences is considered stability and accuracy of finite difference theta schemes for this system are established to solve the time implicit evolution equations a nonlinear multigrid method is applied the convergence properties of this solver are investigated considering a linearized lambda omega model

the analysis of multigrid algorithms for nonsymmetric and indefinite elliptic problems we prove some new estimates for the convergence of multigrid algorithms applied to nonsymmetric and indefinite elliptic boundary value problems we provide results for the so called symmetric multigrid schemes we show that for the variable v script cycle and the w script cycle schemes multigrid algorithms with any amount of smoothing on the finest grid converge at a rate that is independent of the number of levels or unknowns provided that the initial grid is sufficiently fine we show that the v script cycle algorithm also converges under appropriate assumptions on the coarsest grid but at a rate which may deteriorate as the number of levels increases this deterioration for the v script cycle may occur even in the case of full elliptic regularity finally the results of numerical experiments are given which illustrate the convergence behavior suggested by the theory

iterative schemes for nonsymmetric and indefinite elliptic boundary value problems the purpose of this paper is twofold the first is to describe some simple and robust iterative schemes for nonsymmetric and indefinite elliptic boundary value problems the schemes are based in the sobolev space h omega and require minimal hypotheses the second is to develop algorithms utilizing a coarse grid approximation this leads to iteration matrices whose eigenvalues lie in the right half of the complex plane in fact for symmetric indefinite problems the iteration is reduced to a well conditioned symmetric positive definite system which can be solved by conjugate gradient interation applications of the general theory as well as numerical examples are given 20 refs 8 tabs

the analysis of pmhss multigrid methods for elliptic problems with smooth complex coefficients in this paper we investigate a class of multigrid methods with hss smoothers applied to second order elliptic problems whose dominant coefficient is complex valued these smoothers are based on hermitian skew hermitian splitting hss modified hss mhss and preconditioned mhss pmhss iterations it is shown that the abstract theory for multigrid method can be extended and applied to elliptic problems with complex coefficient under some assumption conditions we prove that multigrid method with pmhss smoother is convergent and optimal numerical results are reported to confirm the theoretical analysis