on the spectral expansion of hyperbolic eisenstein series in this article we determine the spectral expansion meromorphic continuation and location of poles with identifiable singularities for the scalar valued hyperbolic eisenstein series similar to the form valued hyperbolic eisenstein series studied in kudla and millson invent math 54 193 211 1979 the scalar valued hyperbolic eisenstein series is defined for each primitive hyperbolic conjugacy class within the uniformizing group associated to any finite volume hyperbolic riemann surface going beyond the results in kudla and millson invent math 54 193 211 1979 and risager int math res not 41 2125 2146 2004 we establish a precise spectral expansion for the hyperbolic eisenstein series for any finite volume hyperbolic riemann surface by first proving that the hyperbolic eisenstein series is in l2 our other results such as meromorphic continuation and determination of singularities are derived from the spectral expansion

on the wave representation of hyperbolic elliptic and parabolic eisenstein series abstract we develop a unified approach to the construction of the hyperbolic and elliptic eisenstein series on a finite volume hyperbolic riemann surface specifically we derive expressions for the hyperbolic and elliptic eisenstein series as integral transforms of the kernel of a wave operator established results in the literature relate the wave kernel to the heat kernel which admits explicit construction from various points of view therefore we obtain a sequence of integral transforms which begins with the heat kernel obtains a poisson and wave kernel and then yields the hyperbolic and elliptic eisenstein series in the case of a non compact finite volume hyperbolic riemann surface we finally show how to express the parabolic eisenstein series in terms of the integral transform of a wave kernel

accelerated gcro dr method for solving sequences of systems of linear equations by recycling some error approximations generated during a previous cycle of iterations we present a technique for improving the convergence of gcro dr the scheme is able to mitigate the occurrence of small skip angles occurring in gcro dr and thus considerably accelerates the convergence the alternative phenomenon of the residual vectors is examined numerically and the effectiveness of the new method is illustrated by several examples from practical applications

the effect of local distortions on time domain electromagnetic measurements based on the time domain integral equation we derive expressions for the effect of an anomalous body close to the receiver or close to the transmitter on transient electromagnetic measurements similar to magnetotellurics the distortion of electric fields at late times can be described by a constant distortion tensor relating the secondary electric field to the primary field components that would be obtained in the absence of the body the distortion of a single electric field transient is a static shift only for particular configurations over a layered half space in the general case the perturbation is time dependent because the direction of the total electric field vector varies with time the theory nicely explains spatial variations in electric field transients measured during a high redundancy long offset transient electromagnetics lotem survey over an underground gas storage site an inversion example with synthetic data illustrates how distortion can be corrected the elements of the distortion tensor are determined simultaneously with the model parameters ambiguity is reduced by a regularization of the distortion parameters in the example the background model is recovered well even for the difficult case where only one transmitter is used the distortion of the magnetic field time derivatives caused by bodies close to the receiver is proportional to the time derivative of the primary electric step response the distortion is generally not limited to early times and cannot be neglected in general transmitter overprint effects resulting in static shifts of vertical magnetic field time derivatives may also be understood from the theory

recycling subspace information for diffuse optical tomography we discuss the efficient solution of a long sequence of slowly varying linear systems arising in computations for diffuse optical tomographic imaging the reconstruction of three dimensional absorption and scattering information by matching computed solutions from a parameterized model to measured data leads to a nonlinear least squares problem that we solve using the gauss newton method with a line search this algorithm requires the solution of a long sequence of linear systems each choice of parameters in the nonlinear least squares algorithm results in a different matrix describing the optical properties of the medium these matrices change slowly from one step to the next but may change significantly over many steps for each matrix we must solve a set of linear systems with multiple shifts and multiple right hand sides for this problem we derive strategies for recycling krylov subspace information that exploit properties of the application and the nonlinear optimization algorithm to significantly reduce the total number of iterations over all linear systems furthermore we introduce variants of gcro that exploit symmetry and that allow simultaneous solution of multiple shifted systems using a single krylov subspace in combination with recycling although we focus on a particular application and optimization algorithm our approach is applicable generally to problems where sequences of linear systems must be solved this may guide other researchers to exploit the opportunities of tunable solvers we provide results for two sets of numerical experiments to demonstrate the effectiveness of the resulting method

a simplified and flexible variant of gcrot for solving nonsymmetric linear systems there is a need for flexible iterative solvers that can solve large scale 10 6 unknowns nonsymmetric sparse linear systems to a small tolerance among flexible solvers flexible gmres fgmres is attractive because it minimizes the residual norm over a particular subspace in practice fgmres is often restarted periodically to keep memory and work requirements reasonable however like restarted gmres restarted fgmres can suffer from stagnation this has led us to develop a flexible variant of the krylov linear solver gcrot generalized conjugate residual with inner orthogonalization and outer truncation unlike the original gcrot algorithm the proposed gcrot variant uses a simplified truncation strategy similar to loose gmres lgmres this modification is motivated by numerical experiments that suggest the specific subspace retained in the outer iteration of gcrot is less important than its size the flexible gcrot variant appears to be well suited for advection dominated problems in particular when applied to an adjoint problem from computational aerodynamics the proposed gcrot variant is robust and efficient compared with several popular truncated krylov subspace methods finally a flexible version of lgmres is easily constructed by recognizing algorithmic similarities to gcrot

solving shifted linear systems with restarted gmres augmented with error approximations abstract in this paper we investigate a variant of the restarted gmres method for solving a series of large sparse linear systems restarting is carried out by augmenting krylov subspaces with some recently generated error approximations from the seed system the method can preserve a nice property that allows solving the seed and the added linear systems at the cost of only one matrix vector multiplication per iteration compared with solving each added linear system separately the advantage of the new scheme is to lower down the overall cost of solving all added linear systems numerical experiments illustrate the efficiency of the acceleration strategy

qmr a quasi minimal residual method for non hermitian linear systems the biconjugate gradient bcg method is the natural generalization of the classical conjugate gradient algorithm for hermitian positive definite matrices to general non hermitian linear systems unfortunately the original bcg algorithm is susceptible to possible breakdowns and numerical instabilities in this paper we present a novel bcg like approach the quasi minimal residual qmr method which overcomes the problems of bcg an implementation of qmr based on a look ahead version of the nonsymmetric lanczos algorithm is proposed it is shown how bcg iterates can be recovered stably from the qmr process some further properties of the qmr approach are given and an error bound is presented finally numerical experiments are reported

transient electromagnetic inversion a remedy for magnetotelluric static shifts surficial bodies can severely distort magnetotelluric mt apparent resistivity data to arbitrarily low frequencies this distortion known as the mt static shift is due to an electric field generated from boundary charges on surficial inhomogeneities and persists throughout the entire mt recording range static shifts are manifested in the data as vertical parallel shifts of log log apparent resistivity sounding curves the impedance phase being unaffected using a three dimensional 3 d numerical modeling algorithm simulated mt data with finite length electrode arrays are generated significant static shifts are produced in this simulation however for some geometries they are impossible to identify techniques such as spatial averaging and electromagnetic array profiling emap are effective in removing static shifts but they are expensive especially for correcting a previously collected mt data set parametric representation and use of a single invariant quantity such as the impedance tensor

a multiscale preconditioner for stochastic mortar mixed finite elements the aim of this paper is to introduce a new approach to efficiently solve sequences of problems that typically arise when modeling flow in stochastic porous media the governing equations are based on darcy s law with a stochastic permeability field starting from a specified covariance relationship the log permeability is decomposed using a truncated karhunen loeve expansion multiscale mortar mixed finite element approximations are used in the spatial domain and a nonintrusive sampling method is used in the stochastic dimensions a multiscale mortar flux basis is computed for a single permeability called a training permeability that captures the main characteristics of the porous media and is used as a preconditioner for each stochastic realization we prove that the condition number of the preconditioned interface operator is independent of the subdomain mesh size and the mortar mesh size computational results confirm that our approach provides an efficient means to quantify the uncertainty for stochastic flow in porous media

three dimensional induction logging problems part i an integral equation solution and model comparisons a 3 d frequency domain solution based on a volume integral equation approach has been implemented to simulate induction log responses in our treatment of the problem we assume that the electrical properties of the bedding as well as the borehole and invasion zones can exhibit transverse anisotropy the solution process uses a krylov subspace iteration to solve the scattering equation which is based on the modified iterative dissipative method internal consistency checks and comparisons with mode matching and finite difference solutions for vertical borehole models demonstrate the accuracy of the solution there are no known analytical solutions for induction log responses arising from deviated boreholes intersecting horizontal bed boundaries to simulate such responses requires the numerical solution of maxwell s equations in three dimensions along with independent tests to validate the solution approach and its accuracy in this paper we compare two independent 3 d frequency domain solutions for the

large scale topology optimization using preconditioned krylov subspace methods with recycling summary the computational bottleneck of topology optimization is the solution of a large number of linear systems arising in the finite element analysis we propose fast iterative solvers for large threedimensional topology optimization problems to address this problem since the linear systems in the sequence of optimization steps change slowly from one step to the next we can significantly reduce the number of iterations and the runtime of the linear solver by recycling selected search spaces from previous linear systems in addition we introduce a minres minimum residual method version with recycling and a short term recurrence to make recycling more efficient for symmetric problems furthermore we discuss preconditioning to ensure fast convergence we show that a proper rescaling of the linear systems reduces the huge condition numbers that typically occur in topology optimization to roughly those arising for a problem with constant density we demonstrate the effectiveness of our solvers by solving a topology optimization problem with more than a million unknowns on a fast pc

implicit space time domain decomposition methods for stochastic parabolic partial differential equations we introduce and study parallel space time domain decomposition methods for solving deterministic and stochastic parabolic equations traditional parallel algorithms solve parabolic problems time step by time step the parallelism is restricted to each time step and the algorithms are purely sequential in time in this paper we develop some overlapping schwarz methods whose subdomains cover both space and time variables and we show that the methods work well for stochastic parabolic equations discretized with an implicit stochastic galerkin method one and two level schwarz preconditioned recycling gmres methods are carefully investigated such that many components of the methods are reused when a large number of linear systems are solved the key elements of this approach include an ordering algorithm and two grouping algorithms we present some experimental results obtained on a parallel computer with more than one thousand processors

multipreconditioned gmres for shifted systems an implementation of gmres with multiple preconditioners is proposed for solving shifted linear systems with shift and invert preconditioners with this type of preconditioner the krylov subspace can be built without requiring the matrix vector product with the shifted matrix furthermore the multipreconditioned search space is shown to grow only linearly with the number of preconditioners this allows for a more efficient implementation of the algorithm the proposed implementation is tested on shifted systems that arise in computational hydrology and the evaluation of different matrix functions the numerical results indicate the effectiveness of the proposed approach

the asymptotic behavior of green s functions for degenerating hyperbolic surfaces given a degenerating family of riemann surfaces of genus g 2 it is a natural and important question to study their spectral behaviors in particular green s functions during degeneration see 9 10 17 11 13 and 5 by the uniformization theorem any riemann surface of genus g 2 has a canonical metric of constant curvature 1 from now on we call a riemann surface with this canonical metric a hyperbolic surface and a degenerating family of hyperbolic surfaces is denoted by st l 0 the degeneration of st is caused by the pinching of several simple closed geodesics 71 l 7 1 on st that is the lengths of these geodesics go to zero as l 0 let at be the laplacian of st then the kernel of at consists of functions which are constant on each connected component of st and at is invertible on the orthogonal complement of the kernel the schwartz kernel of this inverse is called the green function of st and denoted by g z w t for z w sl we would like to study the asymptotic behavior of g z w i as l o in order to compare functions on s o and st we use the harmonic map of infinite energy so s 71 l 7 l constructed by wolf el4 intuitively speaking this map z opens up each node a pair of cusps of so into a simple closed pinching geodesic of sf at first we assume that there is only one pinching geodesic l 7 of length l on s if 7 separates st then so has two components se and so z of genus g gz respectively

truncation strategies for optimal krylov subspace methods optimal krylov subspace methods like gmres and gcr have to compute an orthogonal basis for the entire krylov subspace to compute the minimal residual approximation to the solution therefore when the number of iterations becomes large the amount of work and the storage requirements become excessive in practice one has to limit the resources the most obvious ways to do this are to restart gmres after some number of iterations and to keep only some number of the most recent vectors in gcr this may lead to very poor convergence and even stagnation therefore we will describe a method that reveals which subspaces of the krylov space were important for convergence thus far and exactly how important they are this information is then used to select which subspace to keep for orthogonalizing future search directions numerical results indicate this to be a very effective strategy

dual consistency and functional accuracy consider the discretization of a partial differential equation pde and an integral functional that depends on the pde solution the discretization is dual consistent if it leads to a discrete dual problem that is a consistent approximation of the corresponding continuous dual problem consequently a dual consistent discretization is a synthesis of the so called discrete adjoint and continuous adjoint approaches we highlight the impact of dual consistency on summation by parts sbp finite difference discretizations of steady state pdes specifically superconvergent functionals and accurate functional error estimates in the case of functional superconvergence the discrete adjoint variables do not need to be computed since dual consistency on its own is sufficient numerical examples demonstrate that dual consistent schemes significantly outperform dual inconsistent schemes in terms of functional accuracy and error estimate effectiveness the dual consistent and dual inconsistent discretizations have similar computational costs so dual consistency leads to improved efficiency to illustrate the dual consistency analysis of sbp schemes we thoroughly examine a discretization of the euler equations of gas dynamics including the treatment of the boundary conditions numerical dissipation interface penalties and quadrature by sbp norms

a flexible inner outer preconditioned gmres algorithm a variant of the gmres algorithm is presented that allows changes in the preconditioning at every step there are many possible applications of the new algorithm some of which are briefly discussed in particular a result of the flexibility of the new variant is that any iterative method can be used as a preconditioner for example the standard gmres algorithm itself can be used as a preconditioner as can cgnr or cgne the conjugate gradient method applied to the normal equations however the more appealing utilization of the method is in conjunction with relaxation techniques possibly multilevel techniques the possibility of changing preconditioners may be exploited to develop efficient iterative methods and to enhance robustness a few numerical experiments are reported to illustrate this fact

a block gcrot m k method for linear systems with multiple right hand sides this study is mainly focused on iterative solution to multiple linear systems with several right hand sides for solving such systems efficiently we explore a new block gcrot m k bgcrot m k method which is derived by extending gcrot m k method jason e hicken david w zingg a simplified and flexible variant of gcrot for solving nonsymmetric linear systems siam j sci comput 32 2010 1672 1694 we analyze its main properties it is shown that under the condition of full rank of block residual the frobenius norm of the block residual generated by the proposed method is always nonincreasing moreover we also present its block flexible version bfgcrot m k finally numerical examples demonstrate that the bgcrot m k method and its flexible variant can achieve a smoothed residual and can be more competitive than some other block solvers

harmonic differentials and infinite geodesic joining two punctures on a riemann surface let m be a hyperbolic riemann surface of finite volume the harmonic dual form to an infinite geodesic joining two punctures on m is obtained in two different ways first of all using the degeneration of hyperbolic eisenstein series it is made explicit in terms of these secondly generalizing the construction of kudla and millson to the case of an infinite geodesic joining two punctures we give an automorphic realization of this harmonic form

drag minimization based on the navier stokes equations using a newton krylov approach a methodology is presented for performing numerical aerodynamic shape optimization based on the three dimensional reynolds averaged navier stokes rans equations an initial multiblock structured mesh is first fit with b spline volumes that form the basis for a hybrid mesh movement scheme that is tightly integrated with the geometry parameterization based on b spline surfaces the rans equations and the one equation spalart allmaras turbulence model are solved in a fully coupled manner using an efficient parallel newton krylov algorithm with approximate schur preconditioning gradient evaluations are performed using the discrete adjoint approach with analytical differentiation of the discrete flow and mesh movement equations the overall methodology remains robust even in the presence of large shape changes several examples of lift constrained drag minimization are provided including a study of the common research model wing geometry a wing body tail geometry with a prescribed spanwise load distributi

magnetotelluric strike rules the distortion of the magnetotelluric impedance tensor by complex near surface structure leads to leakage between the elements of the tensor the magnetotelluric impedance tensor for our principal model which has both a local and a regional strike can be written in the long period limit as a sum of the regional undistorted impedance and a perturbed impedance the latter can be written as a product of a local distortion which can be regarded as thin sheet distortion in the long period range tensor and the regional impedance local and regional strikes are found by rotating the impedance tensor into directions in which diagonal elements are proportional and column elements are proportional respectively the regional impedance tensor is calculated assuming that the strikes are uniquely defined an example from a crystalline area with well conducting fracture zones illustrates the model concepts a weighted least squares procedure is used for the estimation of distortion parameters

degenerescence de series d eisenstein hyperboliques in this work we deal with hyperbolic eisenstein series and more particularly given a degenerating family sl l 0 of riemann surfaces with their canonical hyperbolic metrics we work out the degeneration of hyperbolic eisenstein series associated to the pinching geodesics in sl our principal results are theorems 2 2 4 1 et 4 2

asymptotics of the spectrum and the selberg zeta function on the space of riemann surfaces letz s r be the selberg zeta function of a compact riemann surfacer we study the behavior ofz s r asr tends to infinity in the moduli space of stable curves the main result is an estimate forz s r valid fors in a neighborhood depending only on the genus ofs 1 our analysis gives an alternate proof of the belavin knizhnik double pole result 5

flexible inner outer krylov subspace methods flexible krylov methods refers to a class of methods which accept preconditioning that can change from one step to the next given a krylov subspace method such as cg gmres qmr etc for the solution of a linear system ax b instead of having a fixed preconditioner m and the right preconditioned equation am 1 y b mx y one may have a different matrix say mk at each step in this paper the case where the preconditioner itself is a krylov subspace method is studied there are several papers in the literature where such a situation is presented and numerical examples given a general theory is provided encompassing many of these cases including truncated methods the overall space where the solution is approximated is no longer a krylov subspace but a subspace of a larger krylov space we show how this subspace keeps growing as the outer iteration progresses thus providing a convergence theory for these inner outer methods numerical tests illustrate some important implementation aspects that make the discussed inner outer methods very appealing in practical circumstances

block conjugate gradient algorithms for least squares problems abstract in this paper extensions for the conjugate gradient least squares cgls algorithm in block forms so called block conjugate gradient least squares bcgls are described block parameter matrices are designed to explore the block krylov subspace so that multiple right hand sides can be treated simultaneously while maintaining orthogonality and minimization properties along iterations search subspace is reduced adaptively in case of near rank deficiency to prevent breakdown a deflated form of bcgls is developed to accelerate convergence numerical examples demonstrate effectiveness in handling rank deficiency and efficiency in convergence accelerations in these bcgls forms

nested krylov methods based on gcr abstract recently the gmresr method for the solution of linear systems of equations has been introduced by vuik and van der vorst 1991 similar methods have been proposed by axelsson and vassilevski 1991 and saad 1993 fgmres 1 gmresr involves an outer and an inner method the outer method is gcr which is used to compute the optimal approximation over a given set of search vectors in the sense that the residual is minimized the inner method is gmres which computes a new search vector by approximately solving the residual equation this search vector is then used by the outer algorithm to compute a new approximation however the optimality of the approximation over the space of search vectors is ignored in the inner gmres algorithm this leads to suboptimal corrections to the solution in the outer algorithm therefore we propose to preserve the orthogonality relations of gcr in the inner gmres algorithm this gives optimal corrections to the solution and also leads to solving the residual equation in a smaller subspace and with an improved operator which should also lead to faster convergence however this involves using krylov methods with a singular nonsymmetric operator we will discuss some important properties of this we will show by experiments that in terms of matrix vector products this modification almost always leads to better convergence because we do more orthogonalizations it does not always give an improved performance in time this depends on the costs of the matrix vector products relative to the costs of the orthogonalizations of course we can also use methods other than gmres as the inner method methods with short recurrences like bicgstab seem especially interesting the experimental results indicate that especially for such methods it is advantageous to preserve the orthogonality in the inner method

comparison of b spline surface and free form deformation geometry control for aerodynamic optimization two aerodynamic shape optimization geometry control methods b spline surface control and free form deformation are applied to three optimization problems and compared on the bases of optimal shap

recycling krylov subspaces for cfd applications and a new hybrid recycling solver we focus on robust and efficient iterative solvers for the pressure poisson equation in incompressible navier stokes problems preconditioned krylov subspace methods are popular for these problems with bicgstab and gmres m most frequently used for nonsymmetric systems bicgstab is popular because it has cheap iterations but it may fail for stiff problems especially early on as the initial guess is far from the solution restarted gmres is better more robust in this phase but restarting may lead to very slow convergence therefore we evaluate the rgcrot method for these systems this method recycles a selected subspace of the search space called recycle space after a restart this generally improves the convergence drastically compared with gmres m recycling subspaces is also advantageous for subsequent linear systems if the matrix changes slowly or is constant however rgcrot iterations are still expensive in memory and computation time compared with those of bicgstab hence we propose a new hybrid approach that combines the cheap iterations of bicgstab with the robustness of rgcrot for the first few time steps the algorithm uses rgcrot and builds an effective recycle space and then it recycles that space in the rbicgstab solver we evaluate rgcrot on a turbulent channel flow problem and we evaluate both rgcrot and the new hybrid combination of rgcrot and rbicgstab on a porous medium flow problem we see substantial performance gains for both the problems

routine 2d inversion of magnetotelluric data using the determinant of the impedance tensor recent developments in the speed and quality of data acquisition using the radiomagnetotelluric rmt method whereby large amounts of broadband rmt data can be collected along profiles have prompted us to develop a strategy for routine inverse modeling using 2d models we build a rather complicated numerical model containing both 2d and 3d elements believed to be representative for shallow conductors in crystalline basement overlain by a thin sedimentary cover we then invert the corresponding synthetic data on selected profiles using both traditional mt approaches as well as the proposed approach which is based on the determinant of the mt impedance tensor we compare the estimated resistivity models with the true models along the selected profiles and find that the traditional approaches often lead to strongly biased models and bad data fit in contrast to those using the determinant in this case much of the bias is removed and the data fit is improved the determinant of the impedance tensor is independent of the chosen strike direction and once the a priori model is set the best fitting model is found to be practically independent of the starting model used we conclude that the determinant of the impedance tensor is a useful tool for routine inverse modeling

gmres with deflated restarting a modification is given of the gmres iterative method for nonsymmetric systems of linear equations the new method deflates eigenvalues using wu and simon s thick restarting approach siam j matrix anal appl 22 2000 pp 602 616 it has the efficiency of implicit restarting but is simpler and does not have the same numerical concerns the deflation of small eigenvalues can greatly improve the convergence of restarted gmres also it is demonstrated that using harmonic ritz vectors is important because then the whole subspace is a krylov subspace that contains certain important smaller subspaces

recycling krylov subspaces for sequences of linear systems many problems in science and engineering require the solution of a long sequence of slowly changing linear systems we propose and analyze two methods that significantly reduce the total number of matrix vector products required to solve all systems we consider the general case where both the matrix and right hand side change and we make no assumptions regarding the change in the right hand sides furthermore we consider general nonsingular matrices and we do not assume that all matrices are pairwise close or that the sequence of matrices converges to a particular matrix our methods work well under these general assumptions and hence form a significant advancement with respect to related work in this area we can reduce the cost of solving subsequent systems in the sequence by recycling selected subspaces generated for previous systems we consider two approaches that allow for the continuous improvement of the recycled subspace at low cost we consider both hermitian and non hermitian problems and we analyze our algorithms both theoretically and numerically to illustrate the effects of subspace recycling we also demonstrate the effectiveness of our algorithms for a range of applications from computational mechanics materials science and computational physics

necessary and sufficient conditions for the existence of a conjugate gradient method we characterize the class cg s of matrices a for which the linear system a bf x bf b can be solved by an s term conjugate gradient method we show that except for a few anomalies the class cg s consists of matrices a for which conjugate gradient methods are already known these matrices are the hermitian matrices a a and the matrices of the form ae i theta di b with b b

output error estimation for summation by parts finite difference schemes the paper develops a posteriori error estimates of integral output functionals for summation by parts finite difference methods the error estimates are based on the adjoint weighted residual method and take advantage of a variational interpretation of summation by parts discretizations the estimates are computed on a fixed grid and do not require an embedded grid or explicit interpolation operators for smooth boundary value problems containing first and second derivatives the error estimates converge to the exact error as the mesh is refined the theory is verified using linear boundary value problems and the euler equations

decomposition spectrale de 1 formes differentielles sur une surface de riemann et series d eisenstein on etablit la formule de decomposition spectrale des 1 formes differentielles sur une surface de riemann non compacte m en introduisant le fibre en spheres de m on explicite egalement les series d eisenstein qui entrent en jeu on en donne quelques proprietes notamment dans le cas de la surface gamma 2 backslash h ou gamma 2 est le sous groupe de congruence principal d ordre 2

analysis of acceleration strategies for restarted minimal residual methods we provide an overview of existing strategies which compensate for the deterioration of convergence of minimum residual mr krylov subspace methods due to restarting we evaluate the popular practice of using nearly invariant subspaces to either augment krylov subspaces or to construct preconditioners which invert on these subspaces in the case where these spaces are exactly invariant the augmentation approach is shown to be superior we further show how a strategy recently introduced by de sturler for truncating the approximation space of an mr method can be interpreted as a controlled loosening of the condition for global mr approximation based on the canonical angles between subspaces for the special case of krylov subspace methods we give a concise derivation of the role of ritz and harmonic ritz values and vectors in the polynomial description of krylov spaces as well as of the use of the implicitly updated arnoldi method for manipulating krylov spaces

a new deflated block gcrot m k method for the solution of linear systems with multiple right hand sides linear systems with multiple right hand sides arise in many applications to solve such systems efficiently a new deflated block gcrot m k method is explored in this paper by exploiting a modified block arnoldi deflation incorporating this modified block arnoldi deflation the new algorithm can address the possible linear dependence at each iteration during the block arnoldi procedure and reduces expensive computational operations moreover as a block version of gcrot m k the new method inherits the property of easy operability finally some numerical examples also illustrate the effectiveness of the proposed method

occam s inversion a practical algorithm for generating smooth models from electromagnetic sounding data the inversion of electromagnetic sounding data does not yield a unique solution but inevitably a single model to interpret the observations is sought we recommend that this model be as simple or smooth as possible in order to reduce the temptation to overinterpret the data and to eliminate arbitrary discontinuities in simple layered models to obtain smooth models the nonlinear forward problem is linearized about a starting model in the usual way but it is then solved explicitly for the desired model rather than for a model correction by parameterizing the model in terms of its first or second derivative with depth the minimum norm solution yields the smoothest possible model rather than fitting the experimental data as well as possible which maximizes the roughness of the model the smoothest model which fits the data to within an expected tolerance is sought a practical scheme is developed which optimizes the step size at each iteration and retains the computational efficiency of layered models resulting in a stable and rapidly convergent algorithm the inversion of both magnetotelluric and schlumberger sounding field data and a joint magnetotelluric resistivity inversion demonstrate the method and show it to have practical application

controlled source tensor magnetotellurics impedance tensor and tipper vectors known to connect the electromagnetic surface components for plane wave excitation are shown to be uniquely defined for horizontal electric or horizontal magnetic dipole sources two independent source polarizations are needed for their estimation in practice analysis of impedance tensors and tipper vectors for a layered half space shows that the impedance tensor can be antidiagonalized by rotating the measurement system so that one of the measurement directions coincides with the direction to the transmitter dipole the tipper vector points towards the transmitter dipole in the static limit all transfer functions are real and simple analytic results for a homogeneous half space show that impedance elements are proportional to the inverse of the product of conductivity and distance between source and receiver while the tipper vector is a unit vector pointing towards the transmitter dipole

augmented lagrangian preconditioner for large scale hydrodynamic stability analysis abstract hydrodynamic linear stability analysis of large scale three dimensional configurations is usually performed with a time stepping approach based on the adaptation of existing solvers for the unsteady incompressible navier stokes equations we propose instead to solve the nonlinear steady equations with the newton method and to determine the largest growth rate eigenmodes of the linearized equations using a shift and invert spectral transformation and a krylov schur algorithm the solution of the shifted linearized navier stokes problem which is the bottleneck of this approach is computed via an iterative krylov subspace solver preconditioned by the modified augmented lagrangian mal preconditioner benzi et al 2011 the well known efficiency of this preconditioned iterative strategy for solving the real linearized steady state equations is assessed here for the complex shifted linearized equations the effect of various numerical and physical parameters is investigated numerically on a two dimensional flow configuration confirming the reduced number of iterations over state of the art steady state and time stepping based preconditioners a parallel implementation of the steady navier stokes and eigenvalue solvers developed in the freefem language suitably interfaced with the petsc slepc libraries is described and made openly available to tackle three dimensional flow configurations its application on a small scale three dimensional problem shows the good performance of this iterative approach over a direct l u factorization strategy in regards of memory and computational time on a large scale three dimensional problem with 75 million unknowns a 80 parallel efficiency on 256 up to 2048 processes is obtained

energy distribution of harmonic 1 forms and jacobians of riemann surfaces with a short closed geodesic we study the energy distribution of harmonic 1 forms on a compact hyperbolic riemann surface s where a short closed geodesic is pinched if the geodesic separates the surface into two parts then the jacobian variety of s develops into a variety that splits if the geodesic is nonseparating then the jacobian degenerates the aim of this work is to get insight into this process and give estimates in terms of geometric data of both the initial surface s and the final surface such as its injectivity radius and the lengths of geodesics that form a homology basis the jacobians in this paper are represented by gram period matrices as an invariant we introduce new families of symplectic matrices that compensate for the lack of full dimensional gram period matrices in the noncompact case

a hybrid regularization scheme for the inversion of magnetotelluric data from natural and controlled sources to layer and distortion parameters magnetotelluric mt radiomagnetotelluric rmt and in particular controlled source audiomagnetotelluric csamt data are often heavily distorted by near surface inhomogeneities we developed a

analytic investigations of the effects of near surface three dimensional galvanic scatterers on mt tensor decompositions an outcropping hemispherical inhomogeneity embedded in a two dimensional 2 d earth is used to model the effects of three dimensional 3 d near surface electromagnetic em static distortion analytical solutions are first derived for the galvanic electric and magnetic scattering operators of the heterogeneity to represent the local distortion by 3 d structures of fields which were produced by a large scale 2 d structure these 3 d scattering operators are applied to 2 d electric and magnetic fields derived by numerical modeling to synthesize an mt data set synthetic noise is also included in the data these synthetic data are used to study the parameters recovered by several published methods for decomposing or parameterizing the measured mt impedance tensor the stability of these parameters in the presence of noise is also examined the parameterizations studied include the conventional 2 d parameterization swift 1967 eggers s 1982 and spitz s 1985 eigenstate formulations latorraca et al