automatic energy conserving space time refinement for linear dynamic structural problems in this paper a local space time automatic refinement method star method is developed to efficiently solve time dependent problems using fem techniques the automatic process is driven by an energy or a displacement error indicator which controls the precision of the result the star method solves the numerical problem on grids with different mesh size for the newmark schemes a general demonstration using the energy method gives the interface conditions between two successive grids which is compatible with the stability of the scheme finally using a linear one dimensional example the convergence of the method and the precision of the results are discussed copyright 2005 john wiley sons ltd

binary spatial partitioning of the central difference time integration scheme for explicit fast transient dynamics this paper proposes a generalization of the explicit central difference time integration scheme using a time step variable not only in time but also in space the solution at each element node is advanced in time following local rather than global stability limitations this allows substantial saving of computer time in realistic applications with non uniform meshes especially in multi field problems like fluid structure interactions a binary scheme in space is used time steps are not completely arbitrary but stay in a constant ratio of two when passing from one partition level to the next one this choice greatly facilitates implementation via an integer based logic ensures inherent synchronization and avoids any interpolations necessary in other partitioning schemes in the literature but which may reduce numerical stability the mesh partition is automatically built up and continuously updated by simple spatial adjacency considerations the resulting algorithm deals automatically with large variations in time of stability limits the paper introduces the core spatial partitioning technique in the lagrangian formulation some academic numerical examples allow a detailed comparison with the standard spatially uniform algorithm a final more realistic example shows the application of partitioning in simulations with arbitrary lagrangian eulerian formulation and fully coupled boundary conditions fluid structure interaction copyright 2008 john wiley sons ltd

stability of a mach configuration we prove the stability of a mach configuration which occurs in shock reflection off an obstacle or shock interaction in compressible flow the compressible flow is described by a full steady euler system of gas dynamics the unperturbed mach configuration is composed of three straight shock lines and a slip line carrying contact discontinuity among four regions divided by these four lines in the neighborhood of the intersection two are supersonic regions and other two are subsonic regions we prove that if the constant states in the supersonic regions are slightly perturbed then the structure of the whole configuration holds while the other two shock fronts and the slip line as well as the flow field in the subsonic regions are also slightly perturbed such a conclusion asserts the existence and stability of the general mach configuration in shock theory in order to prove the result we reduce the problem to a free boundary value problem where two unknown shock fronts are free boundaries while the slip line is transformed to a fixed line by a lagrange transformation in the region where the solution is to be determined we have to deal with an elliptic hyperbolic composed system by decoupling this system and combining the technique for both hyperbolic equations and elliptic equations we establish the required estimates which are crucial in the proof of the existence of a solution to the free boundary value problem 2005 wiley periodicals inc

a projection method for generalized eigenvalue problems using numerical integration in this paper we propose a method for finding certain eigenvalues of a generalized eigenvalue problem that lie in a given domain of the complex plane the proposed method projects the matrix pencil onto a subspace associated with the eigenvalues that are located in the domain via numerical integration

a numerical scheme to couple subdomains with different time steps for predominantly linear transient analysis abstract this paper generalizes the explicit implicit time integration algorithms pioneered by belytschko hughes and their respective co workers and the feti domain decomposition methods introduced by farhat and his co workers to the case where the same newmark scheme but different and coefficients and different time steps are specified in each subdomain building upon the work of farhat crivelli and geradin it considers various interface boundary constraints and performs a stability analysis of the proposed time integration algorithms

local modal reduction in explicit dynamics with domain decomposition part 1 extension to subdomains undergoing finite rigid rotations we present an extension of the dual schur multidomain method with local linear modal reduction previously introduced by gravouil combescure herry and faucher to the case of modal reduction on geometrically non linear vibrating subdomains this first part of a two part paper describes a new formalism based on an original set of parameters to represent a subdomain s finite rigid body motion special attention is paid to the stability issues with time integration using the central difference scheme the method is validated on an academic example and its efficiency is demonstrated on a large scale example copyright 2004 john wiley sons ltd

coupled fe be method for eigenvalue analysis of elastic structures submerged in an infinite fluid domain summary for thin elastic structures submerged in heavy fluid e g water a strong interaction between the structural domain and the fluid domain occurs and significantly alters the eigenfrequencies therefore the eigenanalysis of the fluid structure interaction system is necessary in this paper a coupled finite element and boundary element fe be method is developed for the numerical eigenanalysis of the fluid structure interaction problems the structure is modeled by the finite element method the compressibility of the fluid is taken into consideration and hence the helmholtz equation is employed as the governing equation and solved by the boundary element method bem the resulting nonlinear eigenvalue problem is converted into a small linear one by applying a contour integral method adequate modifications are suggested to improve the efficiency of the contour integral method and avoid missing the eigenvalues of interest the burton miller formulation is applied to tackle the fictitious eigenfrequency problem of the bem and the optimal choice of its coupling parameter is investigated for the coupled fe be method numerical examples are given and discussed to demonstrate the effectiveness and accuracy of the developed fe be method copyright 2016 john wiley sons ltd

nonlinear eigenvalue problems and contour integrals in this paper beyn s algorithm for solving nonlinear eigenvalue problems is given a new interpretation and a variant is designed in which the required information is extracted via the canonical polyadic decomposition of a hankel tensor a numerical example shows that the choice of the filter function is very important particularly with respect to where it is positioned in the complex plane

potential theory for regular and mach reflection of a shock at a wedge if a plane shock hits a wedge a self similar pattern of reflected shocks travels outward as the shock moves forward in time the nature of the pattern is explored for weak incident shocks strength b and small wedge angles 2 w through potential theory a number of different scalings some study of mixed equations and matching asymptotics for the different scalings the self similar equations are of mixed type a linearization gives a linear mixed flow valid away from a sonic curve near the sonic curve a shock solution is constructed in another scaling except near the zone of interaction between the incident shock and the wall where a special scaling is used the parameter c1 2w 1 b ranges from 0 to here is the polytropic constant and c1 is the sound speed behind the incident shock for 2 regular reflection weak or strong can occur and the whole pattern is reconstructed to lowest order in shock strength for 1 2 mach reflection occurs and the flow behind the reflection is subsonic and can be constructed in principle with an open elliptic problem and matched the case 0 can be solved for 1 2 2 or even larger the flow behind a mach reflection may be transonic and further investigation must be made to determine what happens the basic pattern of reflection is an almost semi circular shock issuing for regular reflection from the reflection point on the wedge and for mach reflection matched with a local interaction flow assuming their nature choosing the least entropy generation the weak regular reflection will occur for sufficiently large von neumann paradox an accumulation point of vorticity occurs on the wedge above the leading point 1994 john wiley sons inc

e h type mach configuration and its stability this paper is devoted to the study of the classification and stability of mach configurations in the mach reflection of a shock wave by a rigid wall the flow behind the reflected shock front can be supersonic or subsonic correspondingly the mach configuration can be classified as e e type and e h type in this paper we proved the stability of e h type mach configurations provided the reflected shock is weak the result is the complement of the stability of e e type mach configurations in our earlier work

analysis and implementation of a new constant acceleration subcycling algorithm an algorithm for explicit integration of structural dynamics problems with multiple time steps is proposed that averages accelerations to obtain subcycle states at a nodal interface between regions integrated with different time steps with integer time step ratios the resulting subcycle updates at the interface sum to give the same effect as a central difference update over a major cycle the algorithm is shown to have good accuracy and stability properties in linear elastic analysis similar to those of constant velocity subcycling algorithms the implementation of a generalised form of the algorithm with non integer time step ratios is presented c 1997 by john wiley sons ltd

a feti based multi time step coupling method for newmark schemes in structural dynamics we present an efficient and accurate multi time step coupling method using feti domain decomposition for structural dynamics using this method one can divide a large structural mesh into a number of smaller subdomains solve the individual subdomains separately and couple the solutions together to obtain the solution to the original problem the various subdomains can be integrated in time using different time steps and or different newmark schemes this approach will be most effective for very large scale simulations on complex geometries our coupling method builds upon a method previously proposed by gravouil and combescure gc method we show that for the simplest case when the same time step is used in all subdomains of the mesh our method reduces to the gc method and is unconditionally stable and energy preserving in addition we show that our method possesses these desirable properties for general multi time step cases too unlike the gc method which is dissipative greater computational efficiency is also achieved through our method by limiting the computation of interface forces to the largest time step as opposed to the smallest time step in the gc method copyright 2004 john wiley sons ltd

a novel numerical method to determine the algebraic multiplicity of nonlinear eigenvalues we generalize the algebraic multiplicity of the eigenvalues of nonlinear eigenvalue problems neps to the rational form and give the extension of the argument principle in addition we propose a novel numerical method to determine the algebraic multiplicity of the eigenvalues of the neps in a given region by the contour integral method finally some numerical experiments are reported to illustrate the effectiveness of our method

a block arnoldi chebyshev method for computing the leading eigenpairs of large sparse unsymmetric matrices in this paper we describe a block version of arnoldi s method for computing a few eigenvalues with largest or smallest real parts the method is accelerated via chebyshev iteration and a procedure is developed to identify the optimal ellipse which encloses the spectrum a parallel implementation of this method is investigated on the eight processor alliant fx 80 numerical results and comparisons with simultaneous iteration on some harwell boeing matrices are reported

a proof of existence of perturbed steady transonic shocks via a free boundary problem we prove the existence of a solution of a free boundary problem for the transonic small disturbance equation the free boundary is the position of a transonic shock dividing two regions of smooth flow assuming inviscid irrotational flow as modeled by the transonic small disturbance equation the equation is hyperbolic upstream where the flow is supersonic and elliptic in the downstream subsonic region to study the stability of a uniform planar transonic shock we consider perturbation by a steady c1 upstream disturbance if the upstream disturbance is small in a c1 sense then there is a steady solution in which the downstream flow and the transonic shock are holder continuous perturbations of the uniform configuration this result provides a new use of inviscid perturbation techniques to demonstrate in two dimensions the stability of transonic shock waves of the type that appear for example over the wing of an airplane along an airfoil or as bow shocks in a flow with a supersonic free stream velocity 2000 john wiley sons inc

stability of the e h type regular shock refraction abstract in this paper the refraction of shocks on the interface for 2 d steady compressible flow is discussed particularly the e h type regular refraction is defined and its global stability of the wave structure is proved the 2 d steady potential flow equation is employed to describe the motion of the fluid the stability of the e h type regular refraction can be reduced to a free boundary problem of a nonlinear mixed type equation in an unbounded domain the corresponding linearized problem is a generalized tricomi problem of the lavrentiev bitsadze mixed type equation and it can be reduced to a nonlocal boundary value problem of an elliptic system the later is finally solved by establishing the bijection of a corresponding nonlocal operator in a weighted holder space the result obtained in this paper develops the theory of nonlinear mixed type equations and gives an application to a significant physical problem

a feti based domain decomposition technique for time dependent first order systems based on a dae approach we present a novel partitioned coupling algorithm to solve first order time dependent non linear problems e g transient heat conduction the spatial domain is partitioned into a set of totally disconnected subdomains the continuity conditions at the interface are modeled using a dual schur formulation where the lagrange multipliers represent the interface fluxes or the reaction forces that are required to maintain the continuity conditions the interface equations along with the subdomain equations lead to a system of differential algebraic equations daes for the resulting equations a numerical algorithm is developed which includes choosing appropriate constraint stabilization techniques the algorithm first solves for the interface lagrange multipliers which are subsequently used to advance the solution in the subdomains the proposed coupling algorithm enables arbitrary numeric schemes to be coupled with different time steps i e it allows subcycling in each subdomain this implies that existing software and numerical techniques can be used to solve each subdomain separately the coupling algorithm can also be applied to multiple subdomains and is suitable for parallel computers we present examples showing the feasibility of the proposed coupling algorithm copyright 2008 john wiley sons ltd

an approach to the connection between subdomains with non matching meshes for transient mechanical analysis this paper describes a general method for coupling non matching linear finite element meshes in transient dynamic analysis we propose a method based on schur s dual formulation whose main advantage is to provide equilibrium as well as kinematic continuity throughout the interface the essence of our work lies in the particular discretization of the space of lagrange multipliers and in the validation of the method through two and three dimensional static calculations as well as two dimensional dynamic calculations an example is also presented and the results are compared to those of the mortar method copyright 2002 john wiley sons ltd

a monolithic energy conserving method to couple heterogeneous time integrators with incompatible time steps in structural dynamics a new hybrid multi time method for multi time scales structural dynamics simulations is described a monolithic method in a schur dual domain decomposition framework is proposed and allows to consider heterogeneous time integrators with their own time discretization and possible large ratio between the time steps for each subdomain in the proposed method zero numerical dissipation is ensured at the interface this implies that the global stability of the coupling method is governed by the stability of each time integrator without influence of the interface for that purpose velocity continuity is ensured in a weak sense at the interfaces and time integrators newmark hht simo krenk verlet are introduced in a unified framework incremental velocity formulation furthermore dynamics governing equations are introduced from a weak formulation in time in other words equilibrium equation is no more ensured in a strong sense at a given time step but rather on average on a time interval some numerical examples illustrate the efficiency and the robustness of the proposed method for ratio of time scales close to 1000 without any numerical dissipation at the interfaces

stability of multi time step partitioned integrators for first order finite element systems abstract mixed time integration procedures are those in which different time steps and different integrators are used in different parts of the mesh a rigorous stability analysis is provided for the first time for this type of time integration for first order semidiscretizations such as arise in diffusion problems the stability analysis is verified by some numerical examples

a free boundary problem for a quasi linear degenerate elliptic equation regular reflection of weak shocks we prove the existence of a solution to the weak regular reflection problem for the unsteady transonic small disturbance utsd model for shock reflection by a wedge in weak regular reflection the state immediately behind the reflected shock is supersonic and constant the flow becomes subsonic further downstream the equation in self similar coordinates is degenerate at the sonic line the reflected shock becomes transonic and begins to curve there its position is the solution to a free boundary problem for the degenerate equation using the rankine hugoniot conditions along the reflected shock we derive an evolution equation for the transonic shock and an oblique derivative boundary condition at the unknown shock position by regularizing the degenerate problem we construct uniform bounds we apply local compactness arguments to extract a limit that solves the problem the solution is smooth in the interior and continuous up to the degenerate boundary this work completes a stage in our program to construct self similar solutions of two dimensional riemann problems in a series of papers we developed techniques for solving the degenerate elliptic equations that arise in self similar reductions of hyperbolic conservation laws in other papers especially in joint work with gary lieberman we developed techniques for solving free boundary problems of the type that arise from rankine hugoniot relations for the first time in this paper we combine these approaches and show that they are compatible although our construction is limited to a finite part of the unbounded subsonic region it suggests that this approach has the potential to solve a variety of problems in weak shock reflection including mach and von neumann reflection in the utsd equation and the analogous problems for the unsteady full potential equation 2002 john wiley sons inc

numerical algorithms based on analytic function values at roots of unity let f z be an analytic or meromorphic function in the closed unit disk sampled at the n th roots of unity based on these data how can we approximately evaluate f z or f m z at a point z in the disk how can we calculate the zeros or poles of f in the disk these questions exhibit in the purest form certain algorithmic issues that arise across computational science in areas including integral equations partial differential equations and large scale linear algebra we analyze some of the possibilities and emphasize the distinction between algorithms based on polynomial or rational interpolation and those based on trapezoidal rule approximations of cauchy integrals we then show how these developments apply to the problem of computing the eigenvalues in the disk of a matrix of large dimension finally we highlight the power of rational in comparison with polynomial approximations for some of these problems

verified partial eigenvalue computations using contour integrals for hermitian generalized eigenproblems abstract we propose a verified computation method for partial eigenvalues of a hermitian generalized eigenproblem the block sakurai sugiura hankel method a contour integral type eigensolver can reduce a given eigenproblem into a generalized eigenproblem of block hankel matrices whose entries consist of complex moments in this study we evaluate all errors in computing the complex moments we derive a truncation error bound of the quadrature then we take numerical errors of the quadrature into account and rigorously enclose the entries of the block hankel matrices each quadrature point gives rise to a linear system and its structure enables us to develop an efficient technique to verify the approximate solution numerical experiments show that the proposed method outperforms a standard method and infer that the proposed method is potentially efficient in parallel

multidimensional transonic shocks and free boundary problems for nonlinear equations of mixed type we are concerned with the existence and stability of multidimensional transonic shocks for the euler equations for steady potential compressible fluids the euler equations consisting of the conservation law of mass and the bernoulli law for the velocity can be written as the following second order nonlinear equation of mixed elliptic hyperbolic type for the velocity potential r r 1 1 div d d 0 where the density function q is

a study of the stability of subcycling algorithms in structural dynamics algorithms for explicit integration of structural dynamics problems with multiple time steps subcycling are investigated only one such algorithm due to smolinski and sleith has proved to be stable in a classical sense a simplified version of this algorithm that retains its stability is presented however as with the original version it can be shown to sacrifice accuracy to achieve stability another algorithm in use is shown to be only statistically stable in that a probability of stability can be assigned if appropriate time step limits are observed this probability improves rapidly with the number of degrees of freedom in a finite element model the stability problems are shown to be a property of the central difference method itself which is modified to give the subcycling algorithm a related problem is shown to arise when a constraint equation in time is introduced into a time continuous space time finite element model

mach configuration in pseudo stationary compressible flow when a shock front in unsteady compressible flow is moving along an inclined ramp the incident shock will be reflected by the ramp as it moves forward in the process of reflection various reflected wave pattern may occur depending on the slope of the ramp and the strength of the incident shock 14 23 this problem is one of the most important multidimensional prototype problems in gas dynamics generally if the angle of inclination is larger than a critical value then the reflected shock starting from the intersection of the incident shock with the ramp forms a smooth bubble which expands when time goes on such a reflection is called regular reflection on the other hand if the angle of inclination is small then the intersection of the incident shock and the reflected shock will not touch the ramp and an additional shock front called mach stem appears which connects the ramp with the intersection of the incident shock and the reflected shock in this case three shock fronts meet at one point and form a triple shock configuration an important fact is that the structure solely containing three shock fronts separating the neighborhood of the triple intersection into three zones with different continuous states does not exist 14 27 many physical experiments indicate that there is a slip line issuing from the triple intersection such a local wave pattern is called mach configuration or mach structure correspondingly the whole process of reflection is called mach reflection because of the complexity of the whole picture of mach reflection it is natural and necessary to start work on getting a clear understanding of the local mach configuration mach reflection also occurs in various other cases for compressible flow for instance in the study on oblique shock reflection in stationary compressible flow von neumann indicated that see 14 25 if the incident shock hit a wall with an angle larger than a critical value then the reflection must be mach reflection many physical experiments approximate analysis and numerical computations verified the appearance of mach configuration and a tremendous amount of literature is devoted to study such problems see 3 4 11 19 20 24 and the references therein however for the rigorous proof on the stability of mach configuration we can only mention a related result on stationary flow in 13

multigrid solver with automatic mesh refinement for transient elastoplastic dynamic problems this paper presents an adaptive refinement strategy based on a hierarchical element subdivision dedicated to modelling elastoplastic materials in transient dynamics at each time step the refinement is automatic and starts with the calculation of the solution on a coarse mesh then an error indicator is used to control the accuracy of the solution and a finer localized mesh is created where the user prescribed accuracy is not reached a new calculation is performed on this new mesh using the non linear full approximation scheme multigrid strategy applying the error indicator and the refinement strategy recursively the optimal mesh is obtained this mesh verifies the error indicator on the whole structure the multigrid strategy is used for two purposes first it optimizes the computational cost of the solution on the finest localized mesh second it ensures information transfer among the different hierarchical meshes a standard time integration scheme is used and the mesh is reassessed at each time step copyright 2010 john wiley sons ltd

an algorithm for permanent fluid structure interaction in explicit transient dynamics abstract this paper presents the strategies and models adopted in the plexis 3c computer code for the description of interactions of the permanent type between fluids and structures in fast transient dynamic problems a careful analysis of geometrical issues and the use of a method based on lagrange multipliers for the treatment of essential boundary conditions lead to a scheme which appears to be both general and robust while remaining reasonably simple the method is implemented via an algorithm able to deal automatically with situations of large geometrical complexity such as those encountered with box like structures multiple interactions structural bifurcations or even arbitrary structural intersections submerged structural edges etc in the presence of large structural displacements rotations and deformations the algorithm turns out to be efficient and dramatically reduces the amount of information that has to be supplied in order to describe a given interaction compared with the algorithms used in previous plexis 3c implementations as a consequence the time and effort needed for input preparation in large and complex realistic simulations is substantially reduced and the possibility for human errors in this phase is almost eliminated several examples show the application of the method to problems of practical interest

multi time step explicit implicit method for non linear structural dynamics we present a method with domain decomposition to solve time dependent non linear problems this method enables arbitrary numeric schemes of the newmark family to be coupled with different time steps in each subdomain this coupling is achieved by prescribing continuity of velocities at the interface we are more specifically interested in the coupling of implicit explicit numeric schemes taking into account material and geometric non linearities the interfaces are modelled using a dual schur formulation where the lagrange multipliers represent the interfacial forces unlike the continuous formulation the discretized formulation of the dynamic problem is unable to verify simultaneously the continuity of displacements velocities and accelerations at the interfaces we show that within the framework of the newmark family of numeric schemes continuity of velocities at the interfaces enables the definition of an algorithm which is stable for all cases envisaged to prove this stability we use an energy method i e a global method over the whole time interval in order to verify the algorithms properties then we propose to extend this to non linear situations in the following cases implicit linear explicit non linear explicit non linear explicit non linear and implicit non linear explicit non linear finally we present some examples showing the feasibility of the method copyright 2001 john wiley sons ltd

two feti based heterogeneous time step coupling methods for newmark and α schemes derived from the energy method abstract the purpose of this paper is to describe a general methodology to obtain multi time step coupling methods for different time integration schemes newmark hht wbz ch on the basis of energetic considerations the general framework of the feti method is considered for building the heterogeneous time step coupling methods by ensuring the gluing of subdomains with lagrange multipliers the proposed methods for coupling subdomains with different time integration schemes and time steps fine and large time steps are based on the pseudo energy measure as introduced by hughes in the so called energy method employed for proving the stability of implicit explicit algorithms assuming a given variation of the lagrange multipliers over the large time step kinematic conditions are derived by ensuring the zero pseudo energy at the interface two methods will be derived in this paper the first new method for which the interface problem involving the lagrange multipliers is solved at the large time scale can handle the popular dissipative schemes hht wbz ch in the particular case of the newmark schemes the new method matches with the ph method proposed by prakash and hjelmstad the second new method is based at the micro time scale it can be viewed as an extension of the method proposed by gravouil and combescure gc method for the coupling of the schemes nonetheless like the gc method the new micro time based method turns out to be dissipative when non dissipative second order accurate schemes are involved and looses one order of accuracy

on the non hermitian feast algorithms with oblique projection for eigenvalue problems abstract the feast algorithm due to polizzi is a typical contour integral based eigensolver for computing the eigenvalues along with their eigenvectors inside a given region in the complex plane it was formulated under the circumstance that the considered eigenproblem is hermitian the feast algorithm is stable and accurate and has attracted much attention in recent years however yin et al 2017 observed that the feast algorithm may fail to find the target eigenpairs when applied to non hermitian problems this observation motivated them to formulate a non hermitian version for the feast algorithm the key to the success of their method is that they use the oblique projection rather than the orthogonal projection used in the feast algorithm to extract desired eigenpairs the objective of the present work is two folded firstly we would like to present a new non hermitian scheme for the feast algorithm which also uses the oblique projection technique to extract the desired eigenpairs secondly we would like to study the convergence properties of the non hermitian feast algorithms based on oblique projection to illustrate the effectiveness numerical experiments are reported to demonstrate the numerical performance of the non hermitian feast algorithms based on oblique projection and to validate the convergence properties studied

local modal reduction in explicit dynamics with domain decomposition part 2 specific interface treatment when modal subdomains are involved during the last 2 years a multidomain formalism for structural dynamics based on a multi time step algorithm and local linear modal reduction was proposed by gravouil combescure herry faucher in the first part of this paper we extended modal reduction to subdomains undergoing finite rigid body rotations here we focus on the consequences of local modal projection either linear or geometrically non linear on the treatment of interface problems between subdomains in particular we address the issues of the invertibility and efficiency of the solution process we illustrate our propositions with specific interpretations of the examples presented in part 1 and present an additional example to demonstrate the properties of special sets of modes copyright 2004 john wiley sons ltd

a filter diagonalization for generalized eigenvalue problems based on the sakurai sugiura projection method the sakurai sugiura projection method which solves generalized eigenvalue problems to find certain eigenvalues in a given domain was reformulated by using the resolvent theory a new interpretation based on filter diagonalization was given and the corresponding filter function was derived explicitly a block version of the method was also proposed which enabled not only resolution of degenerated eigenvalues but also an improvement in numerical accuracy three numerical examples were provided to illustrate the method

bicr type methods for families of shifted linear systems the shifted linear systems with non hermitian matrices often arise from the numerical solutions for time dependent pdes computing the large scale eigenvalue problems control theory and so on in the present paper we develop two shifted variants of bicr type methods for solving such linear systems these variants of bicr type methods take advantage of the shifted structure so that the number of matrix vector multiplications and the number of inner products are the same as a single linear system finally extensive numerical examples are reported to illustrate the performance and effectiveness of the proposed methods

stability analysis of time delay systems using a contour integral method in this paper we propose a contour integral method for computing the rightmost characteristic roots of systems of linear time delay differential equations ddes these roots are very important in the context of stability analysis of the time delay systems the effectiveness of the proposed method is illustrated by some numerical experiments

zolotarev quadrature rules and load balancing for the feast eigensolver the feast method for solving large sparse eigenproblems is equivalent to subspace iteration with an approximate spectral projector and implicit orthogonalization this relation allows to characterize the convergence of this method in terms of the error of a certain rational approximant to an indicator function we propose improved rational approximants leading to feast variants with faster convergence in particular when using rational approximants based on the work of zolotarev numerical experiments demonstrate the possible computational savings especially for pencils whose eigenvalues are not well separated and when the dimension of the search space is only slightly larger than the number of wanted eigenvalues the new approach improves both convergence robustness and load balancing when feast runs on multiple search intervals in parallel

designing rational filter functions for solving eigenvalue problems by contour integration abstract solving nonlinear eigenvalue problems by contour integration requires an effective discretization for the corresponding contour integrals in this paper it is shown that good rational filter functions can be computed using nonlinear least squares optimization techniques as opposed to designing those functions based on a thorough understanding of complex analysis the conditions that such an effective filter function should satisfy are derived and translated in a nonlinear least squares optimization problem solved by optimization algorithms from tensorlab numerical experiments illustrate the validity of this approach