single variable term semi latticized fuzzy relation geometric programming with max product operator considering the practical application background in peer to peer network system we investigate the single variable term semi latticized fuzzy relation geometric programming with max product operator in this paper based on the characteristics of the objective function and feasible domain we develop a matrix approach to deal with the proposed problem a step by step algorithm is proposed to find an optimal solution without solving all the minimal solutions of the constraint two examples are given to illustrate the feasibility and efficiency of the algorithm

affine spaces of strong linearizations for rational matrices and the recovery of eigenvectors and minimal bases abstract the main aim of this paper is two fold first to define and analyze two affine spaces of matrix pencils associated with a realization of an n n rational matrix g and show that almost all of these pencils are strong linearizations of g second to describe the recovery of eigenvectors minimal bases and minimal indices of g from those of the strong linearizations of g the affine spaces of pencils are constructed from the vector spaces of linearizations of matrix polynomials defined and analyzed by mackey et al in siam j matrix anal appl 28 2006 pp 971 1004 we show that eigenvectors minimal bases and minimal indices of g can be easily recovered from those of the strong linearizations of g in particular we construct a symmetric strong linearization of g when g is regular and symmetric we also describe the recovery of pole zero structure of g at infinity from the pole zero structure at infinity of a strong linearization of g

efficient arnoldi type algorithms for rational eigenvalue problems arising in fluid solid systems we develop and analyze efficient methods for computing damped vibration modes of an acoustic fluid confined in a cavity with absorbing walls capable of dissipating acoustic energy the discretization in terms of pressure nodal finite elements gives rise to a rational eigenvalue problem numerical evidence shows that there are no spurious eigenmodes for such discretization and also confirms that the discretization based on nodal pressures is much more efficient than that based on raviart thomas finite elements for the displacement field the trimmed linearization method is used to linearize the associated rational eigenvalue problem into a generalized eigenvalue problem gep of the form ax lbx for solving the gep we apply arnoldi algorithm to two different types of single matrices b 1a and ab 1 numerical accuracy shows that the application of arnoldi on ab 1 is better than that on b 1a

on the minimal solutions of max min fuzzy relational equations in this paper the minimal solutions of max min fuzzy relational equations are investigated a sufficient and necessary condition for discriminating whether a given solution is minimal or not is shown furthermore we propose a new algorithm for computing all minimal solutions less than or equal to a given one

a new indirect anisotropic quadrilateral mesh generation scheme with enhanced local mesh smoothing procedures an enhanced version of indirect advancing front technique is proposed for the construction of full quadrilateral anisotropic meshes on 3d surfaces the final quadrilateral mesh is constructed from a background triangular mesh and the merging procedure is carried out in the parametric space the proposed method employed the systemic merging technique for the formation of quadrilaterals and the metric specifications for controlling the anisotropic characteristics of the elements in order to generate well graded anisotropic quadrilaterals the selection criteria of base segment for merging are carefully defined furthermore in order to improve the shape quality of the final mesh a set of new local smoothing algorithms for anisotropic quadrilateral mesh quality enhancement has been proposed and tested in this study numerical examples obtained indicate that the proposed enhanced local smoothing schemes can effectively improve the quality of the quadrilateral meshes produced and increase the robustness of the mesh generation scheme copyright 2003 john wiley sons ltd

solutions of fuzzy relation equations based on continuous t norms this study is concerned with fuzzy relation equations with continuous t norms in the form atr b where a and b are the fuzzy subsets of x and y respectively email protected xxy is a fuzzy relation and t is a continuous t norm the problem is how to determine a from r and b first an if and only if condition of being solvable is presented novel algorithms are then presented for determining minimal solutions when x and y are finite the proposed algorithms generate all minimal solutions for the equations making them efficient solving procedures

h morph an indirect approach to advancing front hex meshing h morph is a new automatic algorithm for the generation of a hexahedral dominant finite element mesh for arbitrary volumes the h morph method starts with an initial tetrahedral mesh and systematically transforms and combines tetrahedral into hexahedra it uses an advancing front technique where the initial front consists of a set of prescribed quadrilateral surface facets fronts are individually processed by recovering each of the six quadrilateral faces of a hexahedron from the tetrahedral mesh recovery techniques similar to those used in boundary constrained delaunay mesh generation are used tetrahedral internal to the six hexahedral faces are then removed and a hexahedron is formed at any time during the h morph procedure a valid mixed hexahedral tetrahedral mesh is in existence within the volume the procedure continues until no tetrahedral remain within the volume or tetrahedral remain which cannot be transformed or combined into valid hexahedral elements any remaining tetrahedral are typically towards the interior of the volume generally a less critical region for analysis transition from tetrahedral to hexahedra in the final mesh is accomplished through pyramid shaped elements advantages of the proposed method include its ability to conform to an existing quadrilateral surface mesh its ability to mesh without the need to decompose or recognize special classes of geometry and its characteristic well aligned layers of elements parallel to the boundary example test cases are presented on a variety of models

numerical methods for partial differential equations based on power series stable difference schemes that approximate partial differential equations to any desired order are generated by means of power series the method is demonstrated on the one dimensional heat equation and the stability is studied in detail stability analyses are then presented for parabolic linear equations with constant coefficients a nonlinear example is presented which indicates the efficiency of the higher ordered schemes

minimization of linear objective functions under the constraints expressed by a system of fuzzy relation equations this paper considers the following optimization problem minimization of linear objective functions under the constraints expressed by a system of fuzzy relation equations using max product composition we first show some properties of minimal solutions of a system of fuzzy relation equations with max product composition and present some rules for reducing the original problem then we derive an algorithm which enables us to find all the optimal solutions for solving the optimization problem and provide some numerical examples to illustrate

linear optimization problem constrained by fuzzy max min relation equations fang and li introduced the optimization model with a linear objective function and constrained by fuzzy max min relation equations they converted this problem into a 0 1 integer programming problem and solved it using the jump tracking branch and bound method subsequently wu et al improved this method by providing an upper bound on the optimal objective value and presented three rules for simplifying the computation of an optimal solution this work presents new theoretical results concerning this optimization problem they include an improved upper bound on the optimal objective value improved rules for simplifying the problem and a rule for reducing the solution tree accordingly an accelerated approach for finding the optimal objective value is presented and represents an improvement on earlier approaches its potential applications are discussed

automatic generation of anisotropic quadrilateral meshes on three dimensional surfaces using metric specifications a new algorithm for constructing full quadrilateral anisotropic meshes on 3d surfaces is proposed in this paper the proposed method is based on the advancing front and the systemic merging techniques full quadrilateral meshes are constructed by systemically converting triangular elements in the background meshes into quadrilateral elements by using the metric specifications to describe the element characteristics the proposed algorithm is applicable to convert both isotropic and anisotropic triangular meshes into full quadrilateral meshes special techniques for generating anisotropic quadrilaterals such as new selection criteria of base segment for merging new approaches for the modifications of the background mesh and construction of quadrilateral elements are investigated and proposed in this study since the final quadrilateral mesh is constructed from a background triangular mesh and the merging procedure is carried out in the parametric space the mesh generator is robust and no expensive geometrical computation that is commonly associated with direct quadrilateral mesh generation schemes is needed copyright 2002 john wiley sons ltd

a boundary focused quadrilateral mesh generation algorithm for multi material structures this paper describes a new boundary focused mesh generation algorithm the algorithm produces quadrilateral meshes from images of multi material structures the challenge of meshing such images is to create high quality elements which are aligned with complex material boundaries the approach proposed in this paper uses the following steps 1 extract boundaries according to pixel colours 2 smooth the jagged boundaries 3 generate geodesic isolines aligned with smoothed boundaries 4 generate a mesh from the boundaries and isolines 5 optimize the mesh using the pisces pattern which is introduced in this paper application examples are presented to contrast the reliability and effectiveness of the new algorithm with existing approaches

the r function method for the free vibration analysis of thin orthotropic plates of arbitrary shape free flexural vibrations of homogeneous thin orthotropic plates of an arbitrary shape with mixed boundary conditions are studied using the r function method the proposed method is based on the use of the r function theory and variational methods in contrast to the widely used methods of the network type finite differences finite element and boundary element methods in the r function method all the geometric information given in the boundary value problem statement is represented in an analytical form this allows one to seek a solution in a form of some formulas called a solution structure these solution structures contain some indefinite functional components that can be determined by using any variational method a method of constructing the solution structures satisfying the required mixed boundary conditions for eigenvalue plate bending problems is described numerical examples for the vibration analysis of orthotropic plates of complex geometry with mixed boundary conditions for illustrating the aforementioned r function method and comparison against the other methods are made to demonstrate its merits

minimizing a linear function under a fuzzy max min relational equation constraint in this paper we investigate the problem of minimizing a linear objective function subject to a fuzzy relational equation constraint a necessary condition for optimal solution is proposed based on this necessary condition we propose three rules to simplify the work of computing an optimal solution numerical examples are provided to illustrate the procedure experimental results are reported showing that our new procedure systematically outperforms our previous work

an algorithm for aligning a quadrilateral grid with internal boundaries we present a new numerical algorithm that aligns a quadrilateral grid with internal alignment curves iacs these iacs can be used to delineate internal interfaces discontinuities in material properties internal boundaries or major features of a flow field the adaptive iac grid generation algorithm readjusts a predefined reference grid to create a nearby grid where the mesh cell edges are aligned with the iacs on an aligned grid numerical discretizations of partial differential equations can be formulated to satisfy the interfacial relations such as matching fluxes across the discontinuity to reduce the numerical errors introduced by the discontinuity we present examples to demonstrate the effectiveness of the iac grid generation algorithm for multiple embedded interfaces in a quadrilateral grid

structured strong linearizations from fiedler pencils with repetition ii abstract in this paper we give strong linearizations of a matrix polynomial p preserving the skew symmetry or t alternating structure of p the linearizations obtained are of the form s l where l is a block symmetric fiedler pencil with repetition and s is a direct sum of blocks of the form i or i with i the identity matrix this paper is a continuation of 2 where the corresponding problem for p with a symmetric structure was studied and as a consequence the block symmetric fiedler pencils with repetition were characterized

minimizing a linear objective function under a fuzzy max t norm relation equation constraint the work examines the feasibility of minimizing a linear objective function subject to a max t fuzzy relation equation constraint where t is a continuous archimedean t norm conventional methods for solving this problem are significantly improved by first separating the problem into two sub problems according to the availability of positive coefficients this decomposition is thus more easily handled than in previous literature next based on use of the maximum solution of the constraint equation the sub problem with non positive coefficients is solved and the size of the sub problem with positive coefficients reduced as well this step is unique among conventional methods owing to its ability to determine as many optimal variables as possible additionally several rules are developed for simplifying the remaining problem finally those undecided optimal variables are obtained using the covering problem rather than the branch and bound methods three illustrative examples demonstrate that the proposed approach outperforms conventional schemes its potential applications are discussed as well

solving fuzzy relation equations with a linear objective function abstract an optimization model with a linear objective function subject to a system of fuzzy relation equations is presented due to the non convexity of its feasible domain defined by fuzzy relation equations designing an efficient solution procedure for solving such problems is not a trivial job in this paper we first characterize the feasible domain and then convert the problem to an equivalent problem involving 0 1 integer programming with a branch and bound solution technique after presenting our solution procedure a concrete example is included for illustration purpose

min max programming problem subject to addition min fuzzy relation inequalities a bittorrent like peer to peer file sharing system can be reduced into a system of addition min fuzzy relation inequalities addition min is a new composition and the solution set of addition min fuzzy relation inequalities differs much from that of general max t norm fuzzy relation inequalities or equations in order to avoid network congestion and improve the stability of data transmission a min max programming problem is proposed subject to addition min fuzzy relation inequalities in this paper based on some relevant theorems on resolution a novel algorithm is developed step by step to find an optimal solution of the proposed problem moreover an application example is given to illustrate the feasibility and efficiency of the algorithm finally some further discussions are made concerning the optimal solution of the proposed problem

a parallel additive schwarz preconditioned jacobi davidson algorithm for polynomial eigenvalue problems in quantum dot simulation we develop a parallel jacobi davidson approach for finding a partial set of eigenpairs of large sparse polynomial eigenvalue problems with application in quantum dot simulation a jacobi davidson eigenvalue solver is implemented based on the portable extensible toolkit for scientific computation petsc the eigensolver thus inherits petsc s efficient and various parallel operations linear solvers preconditioning schemes and easy usages the parallel eigenvalue solver is then used to solve higher degree polynomial eigenvalue problems arising in numerical simulations of three dimensional quantum dots governed by schrodinger s equations we find that the parallel restricted additive schwarz preconditioner in conjunction with a parallel krylov subspace method e g gmres can solve the correction equations the most costly step in the jacobi davidson algorithm very efficiently in parallel besides the overall performance is quite satisfactory we have observed near perfect superlinear speedup by using up to 320 processors the parallel eigensolver can find all target interior eigenpairs of a quintic polynomial eigenvalue problem with more than 32 million variables within 12 minutes by using 272 intel 3 0ghz processors

an indirect approach for automatic generation of quadrilateral meshes with arbitrary line constraints a new approach to the automatic generation of a quadrilateral mesh with arbitrary line constraints is proposed in this paper it is an indirect all quad mesh generation and presented in the following steps 1 discretizing the constrained lines within the domain 2 converting the above domain to a triangular mesh together with the line constraints 3 transforming the generated triangular mesh with line constraints to an all quad mesh through performing an advancing front algorithm from the line constraints which enables the construction of quadrilaterals layer by layer and roughly keeps the feature of the initial triangular mesh 4 optimizing the topology of the quadrilateral mesh to reduce the number of irregular nodes 5 smoothing the generated mesh toward high quality all quad mesh generation finally a few application examples are given to demonstrate the reliability and usefulness of the proposed algorithm copyright c 2011 john wiley sons ltd

iterative projection methods for computing relevant energy states of a quantum dot a computational technique for computing relevant energy levels and corresponding wave functions of an electron confined by a 3d quantum dot embedded in a semiconductor matrix are studied assuming an energy and position dependent electron effective mass approximation this problem is governed by a rational eigenvalue problem we discuss the application of iterative projection method of arnoldi and jacobi davidson type projected problems of small dimension are solved efficiently by safeguarded iteration

minimizing a linear objective function under a max t norm fuzzy relational equation constraint this paper aims to solve the problem of minimizing a linear objective function subject to a max t fuzzy relational equation constraint with t a continuous t norm this study makes two contributions first two extensions are given based on the results in fang et al where the max min or max product fuzzy relational equation constraint is considered second a procedure for solving optimization problems with the max archimedean t norm fuzzy relational equation constraint is provided a numerical example is provided to illustrate the procedure

optimization of linear problems subjected to the intersection of two fuzzy relational inequalities defined by dubois prade family of t norms abstract in this paper optimization of a linear objective function with fuzzy relational inequality constraints is investigated in doing so the feasible region is formed by the intersection of two inequality fuzzy systems and dubois prade family of t norms which are considered as fuzzy composition the most well known continuous t norms are archimedean such as frank yager hamacher sugeno weber and schweizer sklar family an interesting family of t norms that is not archimedean has been introduced by dubois and prade in this paper the resolution of the feasible region of the problem is initialy investigated when it is defined with max duboise prade composition a necessary and sufficient condition along with three other necessary conditions are derived for determining the feasibility of the problem moreover two procedures have also been presented with the aim of simplifying the current linear problems a method is proposed to generate random feasible max dubois prade fuzzy relational inequalities and an algorithm is accordingly presented to solve the problem finally an example is described to illustrate this algorithm

a simplified approach to fiedler like pencils via block minimal bases pencils abstract the standard way of solving the polynomial eigenvalue problem associated with a matrix polynomial is to embed the matrix coefficients of the polynomial into a matrix pencil transforming the problem into an equivalent generalized eigenvalue problem such pencils are known as linearizations many of the families of linearizations for matrix polynomials available in the literature are extensions of the so called family of fiedler pencils these families are known as generalized fiedler pencils fiedler pencils with repetition and generalized fiedler pencils with repetition or fiedler like pencils for simplicity the goal of this work is to unify the fiedler like pencils approach with the more recent one based on strong block minimal bases pencils introduced in f m dopico et al 2017 17 to this end we introduce a family of pencils that we have named extended block kronecker pencils whose members are under some generic nonsingularity conditions strong block minimal bases pencils and show that with the exception of the non proper generalized fiedler pencils all fiedler like pencils belong to this family modulo permutations as a consequence of this result we obtain a much simpler theory for fiedler like pencils than the one available so far moreover we expect this simplification to allow for further developments in the theory of fiedler like pencils such as global or local backward error analyses and eigenvalue conditioning analyses of polynomial eigenvalue problems solved via fiedler like linearizations

optimization of fuzzy relation equations with max product composition abstract an optimization problem with a linear objective function subject to a system of fuzzy relation equations using max product composition is considered since the feasible domain is non convex traditional linear programming methods cannot be applied we study this problem and capture some special characteristics of its feasible domain and the optimal solutions some procedures for reducing the original problem are presented the problem is transformed into a 0 1 integer program which is then solved by the branch and bound method for illustration purpose an example of the procedures is provided

robust geometrically based automatic two dimensional mesh generation a technical description of the algorithms employed in the modified quadtree mesh generator is given although the basis of the mesh generator is the same as the original version developed by yerry and shephard 1 2 the actual algorithms on which it is built have been entirely changed for the purpose of ensuring the robustness of the technique as demonstrated in the paper the algorithmic changes made do ensure the robustness of the approach but introduce additional algorithmic difficulties the solutions of which are also presented in addition to examples showing the capability of the mesh generator the linear computational growth rate of the mesh generator is demonstrated

an accelerated approach for solving fuzzy relation equations with a linear objective function in literature the optimization model with a linear objective function subject to fuzzy relation equations has been converted into a 0 1 integer programming problem by fang and li 1999 they proposed a jump tracking branch and bound method to solve this 0 1 integer programming problem in this paper we propose an upper bound for the optimal objective value based on this upper bound and rearranging the structure of the problem we present a backward jump tracking branch and bound scheme for solving this optimization problem a numerical example is provided to illustrate our scheme furthermore testing examples show that the performance of our scheme is superior to the procedure in the paper by fang and li several testing examples show that our initial upper bound is sharp

solution to the covering problem this work is motivated by recent investigations that reveal the intractability of the covering problem current methods for solving this problem lack an explicit procedure therefore they are of limited value this work presents the steps for solving such problems using a novel algorithm the search performance is better than that achieved in other works some numerical examples are presented to demonstrate the performance and to compare it with the performance of other methods the proposed algorithm can be utilized to solve fuzzy relation equations that exhibit the zero or greatest property

automatic adaptive grid refinement for the euler equations a method of adaptive grid refinement for the solution of the steady euler equations for transonic flow is presented the algorithm automatically decides where the coarse grid accuracy is insufficient and creates locally uniform refined grids in these regions this typically occurs at the leading and trailing edges the solution is then integrated to steady state using the same integrator flo52 in the interior of each grid the boundary conditions needed on the fine grids are examined and the importance of treating the fine coarse grid interface conservatively is discussed numerical results indicate substantial computational savings for the same solution accuracy can be achieved

palindromic companion forms for matrix polynomials of odd degree the standard way to solve polynomial eigenvalue problems p x 0 is to convert the matrix polynomial p into a matrix pencil that preserves its spectral information a process known as linearization when p is palindromic the eigenvalues elementary divisors and minimal indices of p have certain symmetries that can be lost when using the classical first and second frobenius companion linearizations for numerical computations since these linearizations do not preserve the palindromic structure recently new families of pencils have been introduced with the goal of finding linearizations that retain whatever structure the original p might possess with particular attention to the preservation of palindromic structure however no general construction of palindromic linearizations valid for all palindromic polynomials has as yet been achieved in this paper we present a family of linearizations for odd degree polynomials p which are palindromic whenever p is and which are valid for all palindromic polynomials of odd degree we illustrate our construction with several examples in addition we establish a simple way to recover the minimal indices of the polynomial from those of the linearizations in the new family

algebraic grid generation on trimmed parametric surface using non self overlapping planar coons patch using a coons patch mapping to generate a structured grid in the parametric region of a trimmed surface can avoid the singularity of elliptic pde methods when only c1 continuous boundary is given the error of converting generic parametric c1 boundary curves into a specified representation form is also avoided however overlap may happen on some portions of the algebraically generated grid when a linear or naive cubic blending function is used in the mapping this severely limits its usage in most of engineering and scientific applications where a grid system of non self overlapping is strictly required to solve the problem non trivial blending functions in a coons patch mapping should be determined adaptively by the given boundary so that self overlapping can be averted we address the adaptive determination problem by a functional optimization method the governing equation of the optimization is derived by adding a virtual dimension in the parametric space of the given trimmed surface both one and two parameter blending functions are studied to resolve the difficulty of guessing good initial blending functions for the conjugate gradient method used a progressive optimization algorithm is then proposed which has been shown to be very effective in a variety of practical examples also an extension is added to the objective function to control the element shape finally experiment results are shown to illustrate the usefulness and effectiveness of the presented method copyright 2004 john wiley sons ltd

addition min fuzzy relation inequalities with application in bittorrent like peer to peer file sharing system abstract the data transmission mechanism in bittorrent like peer to peer p2p file sharing systems may be reduced to some addition min fuzzy relation inequalities the solution set of addition min fuzzy relation inequalities plays an important role in the corresponding optimization problem in this paper we study some properties of the solutions to such system convexity of the solution set and number of minimal solutions are discussed with comparison to those of the classical max t fuzzy relation equations or inequalities besides vertex solution and variable ordering minimal solution are also investigated with application in bittorrent like p2p file sharing system two numerical examples are given to illustrate the feasibility and efficiency of the algorithm for solving the variable ordering solution

large vector spaces of block symmetric strong linearizations of matrix polynomials abstract given a matrix polynomial p i 0 k i a i of degree k where a i are n n matrices with entries in a field f the development of linearizations of p that preserve whatever structure p might posses has been a very active area of research in the last decade most of the structure preserving linearizations of p discovered so far are based on certain modifications of block symmetric linearizations the block symmetric linearizations of p available in the literature fall essentially into two classes linearizations based on the so called fiedler pencils with repetition which form a finite family and a vector space of dimension k of block symmetric pencils called dl p such that most of its pencils are linearizations one drawback of the pencils in dl p is that none of them is a linearization when p is singular in this paper we introduce new vector spaces of block symmetric pencils most of which are strong linearizations of p the dimensions of these spaces are o n 2 which for n k are much larger than the dimension of dl p when k is odd many of these vector spaces contain linearizations also when p is singular the coefficients of the block symmetric pencils in these new spaces can be easily constructed as k k block matrices whose n n blocks are of the form 0 i n a i or arbitrary n n matrices where is an arbitrary nonzero scalar

block kronecker linearizations of matrix polynomials and their backward errors we introduce a new family of strong linearizations of matrix polynomials which we call block kronecker pencils and perform a backward stability analysis of complete polynomial eigenproblems these problems are solved by applying any backward stable algorithm to a block kronecker pencil such as the staircase algorithm for singular pencils or the qz algorithm for regular pencils this analysis allows us to identify those block kronecker pencils that yield a computed complete eigenstructure which is exactly that of a slightly perturbed matrix polynomial these favorable pencils include the famous fiedler linearizations which are just a very particular case of block kronecker pencils thus our analysis offers the first proof available in the literature of global backward stability for fiedler pencils in addition the theory developed for block kronecker pencils is much simpler than the theory available for fiedler pencils especially in the case of rectangular matrix polynomials the global backward error analysis in this work presents for the first time the following key properties it is a rigorous analysis valid for finite perturbations i e it is not a first order analysis it provides precise bounds it is valid simultaneously for a large class of linearizations and it establishes a framework that may be generalized to other classes of linearizations these features are related to the fact that block kronecker pencils are a particular case of the new family of strong block minimal bases pencils which include certain perturbations of block kronecker pencils this allows us to extend the results in this paper to other contexts

development of an automatic two dimensional finite element mesh generator using quadrilateral elements and bezier curve boundary definition this paper describes the development of an automatic two dimensional quadrilateral element mesh generator the methodology is based on the looping algorithm developed in part by dr m l c sluiter bezier curves are used to define the boundaries of the parts to be meshed the required interaction by the user is reduced to specifying the boundary geometry the preferred element size and the refinement coefficient transition elements are automatically generated between regions of varying element sizes the ability to offset specified boundary curves insures well conditioned elements along the boundary meshes for several sample geometries are presented to illustrate the versatility of the mesh generator

a new approach to the development of automatic quadrilateral mesh generation a methodology for the automatic mesh generation of quadrilateral elements is proposed the methodology is based on the facts that i a region can always be subdivided entirely into quadrilaterals if the polygon which forms the boundary of the region has an even number of sides ii a quadrilateral can be formed by two triangles which share a common side by taking advantage of the techniques developed in an existing automatic triangular mesh generator quadrilateral meshes can be generated according to the distribution of user specified element size over the domain of interest in particular an automatic quadrilateral mesh generator based on the advancing front technique for triangular mesh generation1 is described techniques to improve the quality of the generated quadrilateral meshes are introduced the robustness and versatility of the mesh generator are demonstrated by a variety of examples

recovery of minimal bases and minimal indices of rational matrices from fiedler like pencils abstract let g be an n n rational matrix by considering a minimal realization of g fiedler like pencils such as fiedler pencils generalized fiedler pencils and fiedler pencils with repetition of g have been proposed recently which are shown to be linearizations of g we show that the fiedler like pencils allow operation free recovery of eigenvectors and minimal bases of g that is eigenvectors and minimal bases of g can be recovered from those of the fiedler like pencils of g without performing any arithmetic operations further we show that the minimal indices of g can be easily recovered from those of the fiedler like pencils of g we also show that a fiedler pencil with repetition of g can be constructed directly from that of a matrix polynomial

automatic recovery of eigenvectors and minimal bases of matrix polynomials from generalized fiedler pencils with repetition abstract linearization is a widely used method for solving polynomial eigenproblems in which a matrix polynomial is transformed to a matrix pencil of larger size fiedler pencils generalized fiedler pencils fiedler pencils with repetition fprs and generalized fiedler pencils with repetition gfprs are well known classes of strong linearizations of matrix polynomials the class gfprs is also a rich source of structure preserving strong linearizations of structured matrix polynomials the recovery of eigenvectors minimal bases and minimal indices of matrix polynomials from those of the linearizations is an important task it is well known that eigenvectors and minimal bases of matrix polynomials can be easily recovered from those of the fiedler and generalized fiedler pencils by contrast barring a small subclass of fprs the recovery of eigenvectors and minimal bases of matrix polynomials from those of the fprs and gfprs is still an open problem the purpose of this paper is to fill this gap we consider the class of gfprs which subsumes the class of fprs and describe the recovery of eigenvectors minimal bases and minimal indices of matrix polynomials from those of the gfprs and show that the recovery is operation free

adaptive mesh generation for viscous flows using delaunay triangulation abstract a method for generating an unstructured triangular mesh in two dimensions suitable for computing high reynolds number flows over arbitrary configurations is presented the method is based on a delaunay triangulation which is perfored in a locally stretched space in order to obtain very high aspect ratio tiangles in the boundary layer and wake regions it is shown how the method can be coupled with an unstructured navier stokes solver to produce a solution adaptive mesh generation procedure for viscous flows

lexicographic optimal solution of the multi objective programming problem subject to max product fuzzy relation inequalities abstract it is shown in this paper that the emission base stations in wireless communication can be reduced into a system of fuzzy relation inequalities with max product composition for optimal management in such system we introduce the fuzzy relation multi objective programming concept of feasible index set fis is defined based on which a novel algorithm named fis algorithm is developed to find the unique lexicographic optimal solution of the proposed problem with polynomial computational complexity applying this method we needn t to find out all the minimal solutions of the constraint a numerical application example is provided to illustrate the feasibility and efficiency of the fis algorithm

adaptive triangular quadrilateral mesh generation in this paper we begin by recalling an adaptive mesh generation method governed by isotropic and anisotropic discrete metric maps by means of the generation of a unit mesh with respect to a riemannian structure we propose then an automatic triangular to quadrilateral mesh conversion scheme which generalizes the standard case to the anisotropic context in addition we introduce an optimal vertex smoothing procedure application test examples in particular a cfd test are given to demonstrate the eciency of the proposed method 1998 john wiley sons ltd int j numer meth engng 41 915 934 1998

linear optimization of bipolar fuzzy relational equations with max łukasiewicz composition according to the literature a linear optimization problem subjected to a system of bipolar fuzzy relational equations with max ukasiewicz composition can be translated into a 0 1 integer linear programming problem and solved using integer optimization techniques however the technique of integer optimization may involve hight computation complexity to improve computational efficiency for solving such an optimization problem this paper proves that each component of an optimal solution obtained from such an optimization problem can either be the corresponding component s lower bound or upper bound value because of this characteristic a simple value matrix with some simplified rules can be proposed to reduce the problem size first a simple solution procedure is then presented for determining optimal solutions without translating such an optimization problem into a 0 1 integer linear programming problem two examples are provided to illustrate the simplicity and efficiency of the proposed algorithm

recovery of eigenvectors of rational matrix functions from fiedler like linearizations abstract linearization is a standard method often used when dealing with matrix polynomials recently the concept of linearization has been extended to rational matrix functions and fiedler like matrix pencils for rational matrix functions have been constructed a linearization l of a rational matrix function g does not necessarily guarantee a simple way of recovering eigenvectors of g from those of l we show that fiedler like pencils of g allow an easy operation free recovery of eigenvectors of g that is eigenvectors of g are recovered from eigenvectors of fiedler like pencils of g without performing any arithmetic operations we also consider fiedler like pencils of the rosenbrock system polynomial s associated with an lti system in state space form ssf and show that the fiedler like pencils allow operation free recovery of eigenvectors of s the eigenvectors of s are the invariant zero directions of the lti system

local linearizations of rational matrices with application to rational approximations of nonlinear eigenvalue problems abstract this paper presents a definition for local linearizations of rational matrices and studies their properties this definition allows to introduce matrix pencils associated to a rational matrix that preserve its structure of zeros and poles in subsets of any algebraically closed field and also at infinity this new theory of local linearizations captures and explains rigorously the properties of all the different pencils that have been used from the 1970 s until 2020 for computing zeros poles and eigenvalues of rational matrices particular attention is paid to those pencils that have appeared recently in the numerical solution of nonlinear eigenvalue problems through rational approximation

a linear programming approach for minimizing a linear function subject to fuzzy relational inequalities with addition min composition in this paper we study an optimization problem of minimizing a linear function subject to fuzzy relational inequalities with the addition min composition this optimization setting has recently been proposed to model the network cogestion issue when a bittorrent like peer to peer file sharing system is used for data transmission in a 2014 paper a pseudominimal index pmi based approach was proposed to search for an optimal solution it turns out that the pmi based approach may require to solve several to many linear programming problems in order to get an optimal solution in this paper we point out that the feasible domain is indeed convex and we only need to solve a single linear programming problem to generate an optimal solution for the original optimization problem furthermore our approach could be extended to the case with a nonlinear continuous objective function

numerical methods for semiconductor heterostructures with band nonparabolicity this article presents numerical methods for computing bound state energies and associated wave functions of three dimensional semiconductor heterostructures with special interest in the numerical treatment of the effect of band nonparabolicity a nonuniform finite difference method is presented to approximate a model of a cylindrical shaped semiconductor quantum dot embedded in another semiconductor matrix a matrix reduction method is then proposed to dramatically reduce huge eigenvalue systems to relatively very small subsystems moreover the nonparabolic band structure results in a cubic type of nonlinear eigenvalue problems for which a cubic jacobi davidson method with an explicit nonequivalence deflation method are proposed to compute all the desired eigenpairs numerical results are given to illustrate the spectrum of energy levels and the corresponding wave functions in rather detail

structured strong linearizations from fiedler pencils with repetition i abstract in many applications the polynomial eigenvalue problem p x 0 arises with p being a structured matrix polynomial for example palindromic symmetric skew symmetric in order to solve a structured polynomial eigenvalue problem it is convenient to use strong linearizations with the same structure as p to ensure that the symmetries in the eigenvalues due to that structure are preserved in numerical computations in this paper we characterize all the pencils in the family of the fiedler pencils with repetition introduced by vologiannidis and antoniou 25 associated with a square matrix polynomial p that are block symmetric for every matrix polynomial p we show that this family of pencils is precisely the set of all fiedler pencils with repetition that are symmetric when p is when some generic nonsingularity conditions are satisfied these pencils are strong linearizations of p in particular our family strictly contains the standard basis for dl p a k dimensional vector space of symmetric pencils introduced by mackey mackey mehl and mehrmann 20

a modified pso algorithm for linear optimization problem subject to the generalized fuzzy relational inequalities with fuzzy constraints fri fc in this paper optimization of a linear objective function subject to a generalized fuzzy relational inequalities is investigated in which an arbitrary continuous t norm is considered as fuzzy composition and fuzzy inequality replaces ordinary inequality in the constraints unlike most optimization algorithms in fuzzy relational inequalities with fuzzy constraints fri fc we find a near feasible solution having a better objective value than those resulting from the resolution of the similar problems with crisp ordinary inequality constraints such solutions are called super optima in this paper subsequently an algorithm is proposed to find a super optimum with pre specified desirable infeasibility for this purpose we firstly study some structural properties of the fri fc problem and present a new formulization that is independent of t norms used in the constraints of the problem this new formulation converts the primary problem into an equivalent problem with simple constraints without considering any penalty parameters however it is proved that the transformed equivalent problem enables our algorithm to distinguish unfavorable points and generate a sequence of solutions converging to a super optimum under a certain sufficient condition finally a modified pso is presented in which the ability of pso to solve unconstrained problems with continuous domain the structure of the transformed problem and some fuzzy structural modifications are combined and form an efficient algorithm to solve the generalized fri fc problems the modified pso algorithm has been applied to the generalized fri fc problem defined with ten well known continuous t norms additionally an idea of the fri fc problems as outer approximators for fri problems with ordinary inequalities is also investigated

a study of boundary layers in plates using mindlin reissner and 3 d elements finite elements based on mindlin reissner theory and three dimensional theory are used to study the distribution of shear forces and twisting moments in plates with various simple support conditions differences between the results obtained using these two theories are highlighted a crude adaptive mesh refinement procedure is applied to improve the accuracy of the finite element analysis

unconstrained plastering hexahedral mesh generation via advancing front geometry decomposition the generation of all hexahedral finite element meshes has been an area of ongoing research for the past two decades and remains an open problem unconstrained plastering is a new method for generating all hexahedral finite element meshes on arbitrary volumetric geometries starting from an unmeshed volume boundary unconstrained plastering generates the interior mesh topology without the constraints of a pre defined boundary mesh using advancing fronts unconstrained plastering forms partially defined hexahedral dual sheets by decomposing the geometry into simple shapes each of which can be meshed with simple meshing primitives by breaking from the tradition of previous advancing front algorithms which start from pre meshed boundary surfaces unconstrained plastering demonstrates that for the tested geometries high quality boundary aligned orientation insensitive all hexahedral meshes can be generated automatically without pre meshing the boundary examples are given for meshes from both solid mechanics and geotechnical applications copyright 2009 john wiley sons ltd

numerical simulation of three dimensional pyramid quantum dot we present a simple and efficient numerical method for the simulation of the three dimensional pyramid quantum dot heterostructure the pyramid shaped quantum dot is placed in a computational box with uniform mesh in cartesian coordinates the corresponding schrodinger equation is discretized using the finite volume method and the interface conditions are incorporated into the discretization scheme without explicitly enforcing them the resulting matrix eigenvalue problem is then solved using a jacobi davidson based method both linear and non linear eigenvalue problems are simulated the scheme is 2nd order accurate and converges extremely fast the superior performance is a combined effect of the uniform spacing of the grids and the nice structure of the resulting matrices we have successfully simulated a variety of test problems including a quintic polynomial eigenvalue problem with more than 32 million variables

optimal vector based algorithm for solving min max programming subject to addition min fuzzy relation inequality optimal management model in bittorrent like peer to peer p2p file sharing system can be reduced into a min max programming problem subject to addition min fuzzy relation inequality to deal with such problem we introduce the concept of optimal vector besides a novel optimal vector based ovb algorithm is developed to find a minimal optimal solution based on practical application consideration solution obtained by the ovb algorithm is theoretically demonstrated to be better than or equal to that obtained by the existing method advantage of our proposed ovb algorithm is illustrated by detailed numerical examples

adaptive remeshing for compressible flow computations an adaptive mesh procedure for improving the quality of steady state solutions of the euler equations in two dimensions is described the procedure is implemented in conjunction with a finite element solution algorithm using linear triangular elements and an explicit time stepping scheme the mesh adaptation is accomplished by regeneration using information provided by the computed solution on the current mesh the meshes produced are characterised by the appearance of stretched elements in the vicinity of one dimensional flow features and can exhibit a large variation in element size this allows solutions of enhanced quality to be produced in a computationally efficient manner

posynomial geometric programming problem subject to max min fuzzy relation equations we discuss a class of posynomial geometric programming problem pgpf aimed at minimizing a posynomial subject to fuzzy relational equations with max min composition by introducing auxiliary variables we convert the pgpf into an equivalent programming problem whose objective function is a non decreasing function with an auxiliary variable we show that an optimal solution consists of a maximum feasible solution and one of the minimal feasible solutions by an equivalent programming problem in addition we introduce some rules for simplifying the problem then by using a branch and bound method and fuzzy relational equations fre path we present an algorithm to obtain an optimal solution to the pgpf finally numerical examples are provided to illustrate the steps of the procedure