logic test pattern generation using linear codes logic testing of today s integrated circuits is a task of increasing difficulty as the number of circuits or transistors packed onto a single chip grows higher and higher exhaustive pattern testing with adequate partitioning of logic has been explored regarding its potential in solving the problems in test pattern generation and fault coverage in this paper we propose a new method of simultaneously generating exhaustive test patterns for all possible input subsets each corresponding to an output up tq a specified size the method is based on the structure of linear polynomial codes and can be easily implemented by modifying existing shift registers in an lssd or scan path design to embody additional feedback connections this is particularly attractive since the implementation is compatible with the approach of self testing using pseudorandom patterns thus a very reasonable strategy is to combine limited exhaustive pattern testing with pseudorandom pattern testing ini cases where complete exhaustive testing is not practical

a finite element method for unstructured grid smoothing the finite element method is applied to grid smoothing for two dimensional planar geometry the coordinates of the grid nodes satisfy two quasi linear elliptic equations in the form of laplace equations in a riemann space by forming a dirichlet boundary value problem the proposed method is applicable to both structured and unstructured grids the riemannian metric acting as a driving force in the grid smoothing is computed iteratively beginning with the metric of the unsmoothed grid smoothing is achieved by computing the metric tensor on the dual mesh elements which incorporates the influence of neighbor elements numerical examples of this smoothing methodology demonstrating the efficiency of the proposed approach are presented

the complexity of fault detection problems for combinational logic circuits in this correspondence we analyze the computational complexity of fault detection problems for combinational circuits and propose an approach to design for testability although major fault detection problems have been known to be in general np complete they were proven for rather complex circuits in this correspondence we show that these are still np complete even for monotone circuits and thus for unate circuits we show that for k level k 3 monotone unate circuits these problems are still np complete but that these are solvable in polynomial time for 2 level monotone unate circuits a class of circuits for which these fault detection problems are solvable in polynomial time is presented ripple carry adders decoder circuits linear circuits etc belong to this class a design approach is also presented in which an arbitrary given circuit is changed to such an easily testable circuit by inserting a few additional test points

theoretical analysis and numerical verification of the consistency of viscous smoothed particle hydrodynamics formulations in simulating free surface flows the theoretical formulation of the smoothed particle hydrodynamics sph method deserves great care because of some inconsistencies occurring when considering free surface inviscid flows actually in sph formulations one usually assumes that i surface integral terms on the boundary of the interpolation kernel support are neglected ii free surface conditions are implicitly verified these assumptions are studied in detail in the present work for free surface newtonian viscous flow the consistency of classical viscous weakly compressible sph formulations is investigated in particular the principle of virtual work is used to study the verification of the free surface boundary conditions in a weak sense the latter can be related to the global energy dissipation induced by the viscous term formulations and their consistency numerical verification of this theoretical analysis is provided on three free surface test cases including a standing wave with the three viscous term formulations investigated

a variational form of the winslow grid generator a structured grid generator based on a new approximation of dirichlet s functional is developed an unconstrained minimization process guarantees that all quadrilateral grid cells are convex at each iteration numerical results are presented in comparison with those for the original form of the winslow method a generalization to the case of adaptive grids based on harmonic maps between surfaces is considered

on the connection between hamiltonian many particle systems and the hydrodynamical equations we consider certain hamiltonian systems with many particles interacting through a potential whose range is large in comparison with the typical distance between neighbouring particles it is shown that the empirical processes of the positions and the velocities respectively converge to solutions of the continuity equation and the euler equation in the limit as the particle number tends to infinity

high order unstructured curved mesh generation using the winslow equations we propose a method to generate high order unstructured curved meshes using the classical winslow equations we start with an initial straight sided mesh in a reference domain and fix the position of the nodes on the boundary on the true curved geometry in the interior of the domain we solve the winslow equations using a new continuous galerkin finite element discretization this formulation appears to produce high quality curved elements which are highly resistant to inversion in addition the corresponding nonlinear equations can be solved efficiently using picard iterations even for highly stretched boundary layer meshes compared to several previously proposed techniques such as optimization and approaches based on elasticity analogies this can significantly reduce the computational cost while producing curved elements of similar quality we show a number of examples in both two and three space dimensions including complex geometries and stretched boundary layers and demonstrate the high quality of the generated meshes and the performance of the nonlinear solver

robust untangling of curvilinear meshes this paper presents a technique that allows to untangle high order curvilinear meshes the technique makes use of unconstrained optimization where element jacobians are constrained to lie in a prescribed range through moving log barriers the untangling procedure starts from a possibly invalid curvilinear mesh and moves mesh vertices with the objective of producing elements that all have bounded jacobians bounds on jacobians are computed using the results of johnen et al 2012 2013 1 2 the technique is applicable to any kind of polynomial element for surface volume hybrid or boundary layer meshes a series of examples demonstrate both the robustness and the efficiency of the technique the final example involving a time explicit computation shows that it is possible to control the stable time step of the computation for curvilinear meshes through an alternative element deformation measure

numerical solution of the quasilinear poisson equation in a nonuniform triangle mesh a finite difference method using a nonuniform triangle mesh is described for the numerical solution of the nonlinear two dimensional poisson equation s 0 where is a function of or its derivatives sis a function of position and or its normal derivative is specified on the boundary the finite difference equations are solved by successive overrelaxation the triangle mesh which is constructed numerically by solving laplace s equation is easily adapted to nonrectangular boundaries and interfaces examples of numerical results are given for the magnetostatic problem with iron and other possible applications are mentioned

convergence of the hamiltonian particle mesh method for barotropic fluid flow we prove convergence of the hamiltonian particle mesh hpm method initially proposed by j frank g gottwald and s reich on a pe riodic domain when applied to the irrotational shallow water equations as a prototypical model for barotropic compressible uid ow under appropriate assumptions most notably suciently fast decay in fourier space of the global smoothing operator and a strang fix condition of order 3 for the local par tition of unity kernel the hpm method converges as the number of particles tends to innity and the global interaction scale tends to zero in such a way that the average number of particles per computational mesh cell remains con stant and the number of particles within the global interaction scale tends to innity the classical sph method emerges as a particular limiting case of the hpm algorithm and we nd that the respective rates of convergence are comparable under suitable assumptions since the computational complexity of bare sph is algebraically superlinear and the complexity of hpm is logarithmically su perlinear in the number of particles we can interpret the hpm method as a fast sph algorithm

qualitative measures for initial meshes this paper reviews geometric measures used to assess the shape of finite elements in two and three dimensional meshes measures have been normalized and made scale invariant whenever possible this paper also introduces a universal similarity region that enhances comparisons of triangles and their measures as a byproduct the usr provides a dynamic way to compare improved triangular meshes copyright 2000 john wiley sons ltd

a new insight into the consistency of the sph interpolation formula abstract in this paper the consistency of the smoothed particle hydrodynamics sph interpolation formula is investigated by analytical means a novel error analysis is developed in n dimensional space using the poisson summation formula which enables the simultaneous treatment of both the kernel and particle approximation errors for arbitrary particle distributions new consistency integral relations are derived for the particle approximation which correspond to the cosine fourier transform of the kernel consistency conditions the functional dependence of the error bounds on the sph interpolation parameters namely the smoothing length h and the number of particles within the kernel support n is demonstrated explicitly from which consistency conditions arise as n the particle approximation converges to the kernel approximation independently of h provided that the particle mass scales with h as m h with n where n is the spatial dimension this implies that as h 0 the joint limit m 0 n and n is necessary for complete convergence to the continuum where n is the total number of particles the analysis also reveals a dominant error term of the form ln n n n for finite n as it has long been conjectured based on the similarity between the sph and the quasi monte carlo estimates when n 1 the error of the sph interpolant decays as n 1 independently of the dimension this ensures approximate partition of unity of the kernel volume

mesh generation in curvilinear domains using high order elements the ability to construct suitable computational meshes is currently a significant limiting factor in the development of compact high order algorithms in very complex geometries compact high order algorithms such as spectral element or p type finite element techniques offer the potential of high accuracy if the solution is smooth and a well behaved mapping exists between the local sub domains and a standard region in this paper we address the problem of coupling high order algorithms with unstructured mesh generation and cad representation techniques we present three complementary strategies to alleviate the problem of generation of elemental regions with singular elemental mappings the first strategy investigates the influence of an anisometric parametric surface representation on the quality of high order unstructured meshes we show that a straightforward splitting of a standard linear mesh for use in a high order method can lead to the generation of distorted possibly invalid meshes even for simple computational domains such as cubes the second strategy uses hybrid meshes applying prismatic elements near curvilinear boundaries in the third and final strategy we investigate the use of curvature driven surface discretization to incorporate higher order information about the surface into the mesh generation using the computational reconstruction of the arterial bypass graft as an example computational domain we demonstrate how the combination of all three strategies leads to a valid high order discretization of the computational domain copyright 2001 john wiley sons ltd

the convergence of the sph method abstract in this paper we prove the convergence of a smooth particle flow to the solution of a regularized version of the euler equations describing a generic polytropic fluid this result combined with a stability property of the euler equations with respect to suitable regularizations result of the same authors of the present paper which will be published elsewhere allows to achieve the proof of the convergence of the so called smoothed particle hydrodynamics sph method

elliptic grid generation various types of generating systems for boundary conforming coordinate systems based on the numerical solution of systems of elliptic partial differential equations are discussed particular emphasis is given to the determination of functions in these equations which control the distribution of the curvilinear coordinate lines in the field

elliptic grid generation system control functions revisited i abstract a methodology for the development of control functions associated with the elliptic grid generation system is presented this development is based on the optimal blending of the best characteristics of hyperbolic generation system and algebraic techniques the algorithm is readily applicable to grid adaptation computational examples are presented to demonstrate the success of this methodology

adjoint based airfoil optimization with adaptive isogeometric discontinuous galerkin method abstract in this work an adjoint based airfoil shape optimization algorithm is developed based on the adaptive isogeometric discontinuous galerkin method for compressible euler equations to investigate the significance of each design variable of airfoil b spline parameterization we first parameterize the airfoil by b spline curve approximation with some control points viewed as design variables and build the b spline representation of the flow field with the curve to apply the goal oriented h adaptive isogeometric dg method for flow solution then we compute and employ the discrete adjoint solutions for both multi target error estimation in adaptive mesh refinement with the isogeometric nature not only all the geometrical cells but also the numerical basis functions can be analytically expressed by the design variables indicating that the numerical solutions and objective could be differentiable with respect to those variables consequently the gradient is totally computed in an accurate approach and the sensitivity analysis is thus improved by reducing the spatial discretization error and introducing the analytical expression of derivative to reveal the key parameters for optimization in an intuitive and efficient manner although the sqp optimization algorithm is adopted in the paper the given accurate gradient can be applied to any gradient based optimization algorithm the proposed algorithm is demonstrated on rae2822 airfoil with inviscid transonic flow where the shape is optimized to minimize the drag coefficient at a constrained lift and airfoil area the numerical results show that the drag is much more sensitive to the design variables near the tailing edge at the beginning but sensitivity is reduced when optimal

multilevel first order system least squares for elliptic grid generation a new fully variational approach is studied for elliptic grid generation egg it is based on a general algorithm developed in a companion paper a l codd t a manteuffel and s f mccormick siam j numer anal 41 2003 pp 2197 2209 that involves using newton s method to linearize an appropriate equivalent first order system first order system least squares fosls to formulate and discretize the newton step and algebraic multigrid amg to solve the resulting matrix equation the approach is coupled with nested iteration to provide an accurate initial guess for finer levels using coarse level computation the present paper verifies the assumptions of the companion work and confirms the overall efficiency of the scheme with numerical experiments

efficient vlsi fault simulation let c be an acyclic boolean circuit with n gates and n inputs a circuit manufacture error may result in a stuck at s a fault in a circuit identical to c except a gate v only outputs a fixed boolean value the s a fault simulation problem for c is to determine all possible s a faults which can be detected i e faults circuit and c would give distinct outputs by a given test pattern input we consider the case where c is a tree i e has fan out 1 we give a practical algorithm for fault simulation which simultaneously determines all detectable s a faults for every gate in the circuit tree c our algorithm required only the evaluation of a circuit fs c which has 7n gates and has depth 3 d 1 when d is the depth of c thus the sequential time of our algorithm is 7n and the parallel time is 3 d 1 furthermore fs c requires only a small constant factor more vlsi area than does the original circuit c we also extend our results to get efficient methods for fault simulation of oblivious vlsi circuits with feedback lines

jacobian weighted elliptic grid generation variational grid generation techniques are used to derive and analyze a weighted elliptic grid generator that controls the jacobian of the underlying transformation in a least squares sense the euler lagrange equations for the area and volume generators are weighted forms of the well known laplace generator weights are restricted to the class of p matrices to help achieve global invertibility of the map connecting the weights to the jacobian of the map results in an intuitive means of controlling grid spacing area orthogonality and grid line directions examples are given on the unit square to demonstrate point attraction local refinement directional alignment and adaption to a shock

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

a differential quadrature hierarchical finite element method using fekete points for triangles and tetrahedrons and its applications to structural vibration abstract a differential quadrature hierarchical finite element method dqhfem using fekete points was formulated for triangles and tetrahedrons and applied to structural vibration analyses first orthogonal polynomials on triangles and tetrahedrons that can be used as bases of the hierarchical finite element method hfem were derived and simple formulas of transforming one dimensional non uniform nodes to simplexes were presented then the non uniform nodes were used as initial guesses to solve the fekete points on simplexes through newton raphson s method together with the orthogonal polynomials new differential quadrature dq rules on simplexes were formulated using the hfem bases and the fekete points the numbers of nodes or bases on different edges and faces and inside the body of the new dq elements do not relate with each other like the hfem that can freely assign different numbers of bases on different edges and faces and inside the body so the new dq method was named as a differential quadrature hierarchical dqh method that uses either interpolation functions or orthogonal polynomials as bases inside the element its weak form was named as the dqhfem besides the dqh method and its weak form a simple method of generating high quality linear and high order triangular and tetrahedral meshes from a single nurbs patch was presented numerical tests of the dqhfem through structural vibration analyses showed that high accuracy results can be obtained using only a few nodes even on curvilinear domains using the dqh bases on both physical and geometric fields it was concluded that wide applications of the dqh method and the dqhfem to science and engineering are possible and commercial codes based on them are deserved to be developed