diagonal implicit multigrid algorithm for the euler equations a multigrid implementation of the alternating direction implicit algorithm has been developed to solve the euler equations of inviscid compressible flow the equations are approximated using a finite volume spatial approximation with added dissipation provided by an adaptive blend of second and fourth differences for computational efficiency the equations are diagonalized by a local similariity transformation so that only a decoupled system of scalar pentadiagonal systems need be solved along each line results are computed for transonic flows past airfoils and include pressure distributions to verify the accuracy of the basic scheme and convergence histories to demonstrate the efficiency of the method

fully dynamic algorithms for 2 edge connectivity this paper studies the problem of maintaining the 2 edge connected components of a graph undergoing repeated dynamic modifications such as edge insertions and edge deletions it is shown how to test at any time whether two vertices belong to the same 2 edge connected component and how to insert and delete an edge in o m 2 3 time in the worst case where m is the current number of edges in the graph this answers a question posed by westbrook and tarjan tech report cs tr 229 89 dept of computer science princeton university princeton nj august 1989 algorithmica to appear for planar graphs the paper presents algorithms that support all these operations in o sqrt n log log n worst case time each where n is the total number of vertices in the graph

algorithms and data structures for an expanded family of matroid intersection problems consider a matroid of rank n in which each element has a real valued cost and one of d 1 colors a class of matroid intersection problems is studied in which one of the matroids is a partition matroid that specifies that a base has q j elements of color j for j 1 2 cdots d relationships are characterized among the solutions to the family of problems generated when the vector q 1 q 2 cdots q d is allowed to range over all values that sum to n a fast algorithm is given for solving such matroid intersection problems when d is small a characterization is presented for how the solution changes when one element changes in cost data structures are given for updating the solution on line each time the cost of an arbitrary matroid element is modified efficient update algorithms are given for maintaining a color constrained minimum spanning tree in either a general or a planar graph an application of the techniques to the problem of finding a minimum spanning tree with several degree

black box multigrid one major problem with the multigrid method has been that each new grid configuration has required a major programming effort to develop a code that specifically handles that grid configuration such a penalty is not required for methods like sor iccg etc in these methods one need only specify the matrix problem no matter what the grid configuration in this paper we investigate such a situation for the multigrid method the end result is code boxmg in which one need only specify the logically rectangular positive definite matrix problem boxmg does everything else necessary to set up the auxilliary coarser problems to achieve a multigrid solution

lower upper implicit schemes with multiple grids for the euler equations on montre qu une methode de surrelaxation successive pour la resolution du schema implicite non factorise est equivalente a une forme modifiee du schema implicite inferieur superieur

an inclusion principle for dynamic systems the purpose of this paper is to present a detailed study of the inclusion concept in dynamic systems which is a suitable mathematical framework for comparing systems with different dimensions the framework offers immediate results in reduced order modeling and the overlapping decentralized control of complex systems the presentation which is limited to linear constant systems relies on both the matrix algebra computations and the geometric elements structure to provide a balanced view of the issues involved in the concept of inclusion the framework is quite broad and has been used to consider nonlinear and time varying systems as well as systems with hereditary and stochastic effects

interconnection based performance analysis for a class of decentralized controllers this paper is concerned with decentralized controller design for large scale interconnected systems of pseudo hierarchical structure given such a system one can use existing techniques to design a decentralized controller for the reference hierarchical model obtained by eliminating certain weak interconnections of the original system although this indirect controller design is appealing as far as the computational complexity is concerned it does not necessarily result in satisfactory performance for the original pseudo hierarchical system an lq cost function is defined in order to evaluate the performance discrepancy between the pseudo hierarchical system and its reference hierarchical model under the designed decentralized controller a discrete lyapunov equation is then solved to compute this performance index however due to the large scale nature of the system this equation cannot be handled efficiently in many real world systems thus attaining an upper bound on this cost function can be more desirable than finding its exact value in practice for this purpose a novel technique is proposed which only requires solving a simple lmi optimization problem with three variables the problem is then reduced to a scalar optimization problem for which an explicit solution is provided it is also shown that when the original model is exactly hierarchical then the upper bounds obtained from the lmi and scalar optimization problems will both be equal to zero

acceleration of multigrid flow computations through dynamic adaptation of the smoothing procedure abstract the paper presents the development and investigation of an adaptive smoothing as procedure in conjunction with the full multigrid full approximation storage method the latter has been previously implemented by the authors 1 for the incompressible navier stokes equations in conjunction with the artificial compressibility method and forms the basis for investigating the current as approach the principle of adaptive smoothing is to exploit the nonuniform convergence behavior of the numerical solution during the iterations to reduce the size of the computational domain and subsequently to reduce the total computing time the implementation of the as approach is investigated in conjunction with three different adaptivity criteria for two and three dimensional incompressible flows furthermore a dynamic procedure henceforth labeled dynamic adaptivity for defining variably the as parameters during the computation is also proposed and its performance is investigated in contrast to as with constant parameters henceforth labeled static adaptivity both static and dynamic adaptivity can provide similar acceleration but the latter additionally provides more stable numerical solutions and also requires less experimentation for optimizing the performance of the method numerical experiments are presented for attached and separated flows around airfoils as well as for three dimensional flow in a curved channel for external flows the as performs better when it is applied in all grid levels of the multigrid method while for internal flows the best performance is achieved when as is applied in the finest grid only overall the results show that substantial acceleration of multigrid computations can be achieved by using adaptive smoothing

local solution acceleration method for the euler and navier stokes equations the solution of the compressible euler and navier stokes equations via an upwind finite volume scheme is obtained for the inviscid fluxes the monotone upstream centered scheme for conservation laws muscl has been incorporated into a riemann solver the muscl scheme is used for the unfactored implicit equations that are solved by a newton form and relaxation is performed via gauss seidel relaxation technique the solution on the fine grid is obtained by iterating first on a sequence of coarser grids and then interpolating the solution up to the next refined grid since the distribution of the numerical error is nonuniform the local solution of the equations can be obtained in regions where the numerical errors are large the construction of the partial meshes in which the iterations will be continued is determined by an adaptive procedure taking into account some convergence criteria reduction of the computational work units for two dimensional problems is obtained via the local adaptive mesh solution which is expected to be more effective in three dimensional complex flow computations

multi exchange neighborhood structures for the capacitated minimum spanning tree problem the capacitated minimum spanning tree cmst problem is to find a minimum cost spanning tree with an additional cardinality constraint on the sizes of the subtrees incident to a given root node the cmst problem is an np complete problem and existing exact algorithms can solve only small size problems currently the best available heuristic procedures for the cmst problem are tabu search algorithms due to amberg et al and sharaiha et al these algorithms use two exchange neighborhood structures that are based on exchanging a single node or a set of nodes between two subtrees in this paper we generalize their neighborhood structures to allow exchanges of nodes among multiple subtrees simultaneously we refer to such neighborhood structures as multi exchange neighborhood structures our first multi exchange neighborhood structure allows exchanges of single nodes among several subtrees our second multi exchange neighborhood structure allows exchanges that involve multiple subtrees the size of each of these neighborhood structures grows exponentially with the problem size without any substantial increase in the computational times needed to find improved neighbors our approach which is based on the cyclic transfer neighborhood structure due to thompson and psaraftis and thompson and orlin transforms a profitable exchange into a negative cost subset disjoint cycle in a graph called an improvement graph and identifies these cycles using variants of shortest path label correcting algorithms our computational results with grasp and tabu search algorithms based on these neighborhood structures reveal that i for the unit demand case our algorithms obtained the best available solutions for all benchmark instances and improved some and ii for the heterogeneous demand case our algorithms improved the best available solutions for most of the benchmark instances with improvements by as much as 18 the running times our multi exchange neighborhood search algorithms are comparable to those taken by two exchange neighborhood search algorithms

pair wise decomposition and coordinated control of complex systems pair wise decomposition and coordinated control for complex interconnected systems with any information structure constraints are proposed in this paper based on the inclusion principle a permuted inclusion principle is presented to expand the system into an expanded space from which a recurrent reverse order of pair wise subsystems is extracted by a standard lq control pair wise controllers can be designed to stabilize and coordinate the pair wise subsystems according to these controllers a coordinated compensator of subsystem interconnections is introduced in order to obtain a coordination based controller for the expanded system therefore a coordinated controller of the system can be contracted from the expanded space under the conditions of the inclusion principle moreover a sufficient condition of connective stability for the system is also proved by the lyapunov function and m matrix a main advantage of the proposed decomposition and control is that it allows any variation of information structure constraints of the system especially the increase and decrease of subsystem numbers finally the effectiveness of the proposed methodology is demonstrated by an application of automatic generation control to a four area electric power system

the spatially non uniform convergence of the numerical solutions of flows abstract the spatial distribution of the numerical disturbances that are generated during a numerical solution of a flow is examined it is shown that the distribution of the disturbances is not uniform in regions where the structure of a flow is simple the magnitude of the generated disturbances is small and their decay is fast however in complex flow regions as in separation and vortical areas large magnitude disturbances appear and their decay may be very slow the observed nonuniformity of the numerical disturbances makes possible the reduction of the calculation time by application of what may be called the partial grid calculation technique in which a major part of the calculation procedure is applied in selective subregions where the velocity disturbances are large and not within the whole grid this technique is expected to prove beneficial in large scale calculations such as the flow about complete aircraft configurations at high angle of attack also it has been shown that if the navier stokes equations are written in a generalized coordinate system then in regions in which the grid is fine such as near solid boundaries the norms become infinitesimally small because in these regions the jacobian has very large values thus the norms unless they are unscaled by the jacobian reflect only the changes that happen at the outer boundaries of the computation domain where the value of the jacobian approaches unity and not in the whole flow field inc

contractible controller design and optimal control with state and input inclusion abstract a new inclusion concept which involves both state and input expansion is introduced it is shown that with the approach undertaken here any control law designed in the expanded spaces is always contractible to the original spaces the inclusion of the cost functions is also discussed and necessary and sufficient conditions are derived it is shown that unlike the case when the two input spaces are identical the inclusion conditions must in general depend on the control laws however certain sufficient conditions which do not involve final control laws can be found if the inclusion is taken with respect to the optimal control finally controller design with overlapping decompositions is discussed within the framework of the new inclusion concept and optimal control

ambivalent data structures for dynamic 2 edge connectivity and k smallest spanning trees ambivalent data structures are presented for several problems on undirected graphs these data structures are used in finding the k smallest spanning trees of a weighted undirected graph in o m log beta m n min k 3 2 km 1 2 time where m is the number of edges and n the number of vertices in the graph the techniques are extended to find the k smallest spanning trees in an embedded planar graph in o n k log n 3 time ambivalent data structures are also used to dynamically maintain 2 edge connectivity information edges and vertices can be inserted or deleted in o m 1 2 time and a query as to whether two vertices are in the same 2 edge connected component can be answered in o log n time where m and n are understood to be the current number of edges and vertices respectively

maintaining the 3 edge connected components of a graph on line the problem of maintaining the 3 edge connected components of a graph undergoing repeated dynamic modifications such as edge and vertex insertions is studied this paper shows how to answer the question of whether or not two vertices belong to the same 3 edge connected component of a connected graph that is undergoing only edge insertions any sequence of q query and updates on an n vertex graph can be performed in o n q alpha q n time

sparsification a technique for speeding up dynamic graph algorithms we provide data strutures that maintain a graph as edges are inserted and deleted and keep track of the following properties with the following times minimum spanning forests graph connectivity graph 2 edge connectivity and bipartiteness in time o n 1 2 per change 3 edge connectivity in time o n 2 3 per change 4 edge connectivity in time o n n per change k edge connectivity for constant k in time o n log n per change 2 vertex connectivity and 3 vertex connectivity in the o n per change and 4 vertex connectivity in time o n n per change further results speed up the insertion times to match the bounds of known partially dynamic algorithms all our algorithms are based on a new technique that transforms an algorithm for sparse graphs into one that will work on any graph which we call sparsification

overlapping decompositions and expansions of petri nets overlapping decompositions and expansions are considered to design decentralized controllers for discrete event systems dess modeled by petri nets the inclusion principle for petri nets is first defined it is shown that properties like boundedness reversibility and liveness with a mild additional condition carry over from the including net to the included net moreover a new property called obstruction is introduced for the including net and it is shown that if obstruction does not occur in the including net then deadlock does not occur in the included net an expansion procedure which guarantees inclusion for an overlappingly decomposed petri net is then introduced

scan first search and sparse certificates an improved parallel algorithm for k vertex connectivity given a graph g v e a certificate of k vertex connectivity is an edge subset e subset e such that the subgraph v e is k vertex connected if and only if g is k vertex connected let n and m denote the number of vertices and edges a certificate is called sparse if it contains o kn edges for undirected graphs this paper introduces a graph search called the scan first search and shows that a certificate with at most k n 1 edges can be computed by executing scan first search k times in sequence on subgraphs of g for each of the parallel distributed and sequential models of computation the complexity of scan first search matches the best complexity of any graph search on that model in particular the parallel scan first search runs in o log n time using c n m processors on a crcw pram where c n m is the number of processors needed to find a spanning tree in each connected component in o log n time and the parallel certificate algorithm runs in o k log n time us

computing minimal spanning subgraphs in linear time let p be a property of undirected graphs we consider the following problem given a graph g that has property p find a minimal spanning subgraph of g with property p we describe general algorithms for this problem and prove their correctness under fairly weak assumptions about p we establish that the worst case running time of these algorithms is theta m n log n for 2 edge connectivity and biconnectivity where n and m denote the number of vertices and edges respectively in the input graph by refining the basic algorithms we obtain the first linear time algorithms for computing a minimal 2 edge connected spanning subgraph and for computing a minimal biconnected spanning subgraph we also devise general algorithms for computing a minimal spanning subgraph in directed graphs these algorithms allow us to simplify an earlier algorithm of gibbons karp ramachandran soroker and tarjan for computing a minimal strongly connected spanning subgraph we also provide the first tight analysis of the latter algorithm showing that its worst case time complexity is theta m n log n

data structures for on line updating of minimum spanning trees with applications data structures are presented for the problem of maintaining a minimum spanning tree on line under the operation of updating the cost of some edge in the graph for the case of a general graph mai

zonal local solution method for the turbulent navier stokes equations azonal local solution method is developed for the solution of the compressible navier stokes equations the main feature of the method is coupling of the navierstokes equations with the euler equations and the local mesh solution procedure mesh sequencing multilevel technique is also used for the improvement of the efficiency of the algorithm the methodology is applied to turbulent flowfields past an airfoil a flux vector splitting method with an upwind scheme up to fourth order accuracy is used for the discretization of the inviscid fluxes the system of the equations is solved by an unfactored implicit method using gauss seidel relaxation contents techological improvements in supercomputer speed and memory size provided the means to solve the full compressible navier stokes equations for turbulent flowfields and complex geometries however large amounts of computer time are required for the solution of the equations especially for problems in design practice to reduce the computational time a zonal local solution method is presented for the solution of the two dimensional navier stokes equations in high reynolds number flows the equations are solved in time dependent form and for a curvilinear body fitted coordinate system jut gvis r 1 where is the jacobian of the transformation of the cartesian coordinates x z to curvilinear coordinates f the subscripts inv vis indicate the inviscid and viscous fluxes respectively and u is the conservative variables matrix the equations are solved by a finite volume navier stokes code1 which uses a modified 1 steger warming flux vector splitting fvs method for the discretization of the inviscid fluxes the fvs method split the fluxes into two parts positive and negative in accordance with the sign of the eigenvalues 2

sequential design of multi overlapping controllers for longitudinal multi overlapping systems in this paper a strategy to design multi overlapping controllers for systems with longitudinal multi overlapping structure is presented the design process uses the inclusion principle to carry out a multi step expansion that allows the decentralized design of a sequence of expanded local controllers these expanded local controllers are subsequently contracted to produce a multi overlapping controller that can be implemented in the original system to illustrate the proposed methodology the response of a four story building under a seismic excitation is considered

function segment artificial moment method for sensor based path planning of single robot in complex environments abstract a function segment artificial moment method is proposed for sensor based path planning of a single robot in complex environments similar to the existing artificial moment method an attractive point is obtained first at each step for guiding the robot to move along a shorter path then the robot moves one step to the next position under the guidance of the attractive point and the control of an artificial moment motion controller different from the existing one attractive function segment s are used for attractive point s and the artificial moment motion controller is improved as each attractive function segment can be used for several steps the computational burden for attractive point s is reduced considerably furthermore positive and negative key obstacle function segment sets are proposed to determine whether the target is reachable when a new attractive function segment is required if the target is reachable then a motion direction for the robot is determined by using the key obstacle function segment sets simulation results indicate that the proposed method is effective and can yield better solutions in complex environments

verification and sensitivity analysis of minimum spanning trees in linear time komlos has devised a way to use a linear number of binary comparisons to test whether a given spanning tree of a graph with edge costs is a minimum spanning tree the total computational work required by his method is much larger than linear however this paper describes a linear time algorithm for verifying a minimum spanning tree this algorithm combines the result of komlos with a preprocessing and table look up method for small subproblems and with a previously known almost linear time algorithm additionally an optimal deterministic algorithm and a linear time randomized algorithm for sensitivity analysis of minimum spanning trees are presented