block edit models for approximate string matching in this paper we examine string block edit distance in which two strings a and b are compared by extracting collections of substrings and placing them into correspondence this model accounts for certain phenomena encountered in important real world applications including pen computing and molecular biology the basic problem admits a family of variations depending on whether the strings must be matched in their entireties and whether overlap is permitted we show that several variants are npcomplete and give polynomial time algorithms for solving the remainder

an isogeometric collocation approach for bernoulli euler beams and kirchhoff plates abstract in this paper iga collocation methods are for the first time introduced for the solution of thin structural problems described by the bernoulli euler beam and kirchhoff plate models in particular a precise description of the proposed methods of the relevant implementation details and of the strategy to efficiently deal with different combinations of boundary conditions is given finally several numerical experiments confirm that the proposed formulations represent an efficient and geometrically flexible tool for the simulation of thin structures

continuous time quantum algorithms for unstructured problems we consider a family of unstructured optimization problems for which we propose a method for constructing analogue continuous time not necessarily adiabatic quantum algorithms that are faster than their classical counterparts in this family of problems which we refer to as scrambled input problems one has to find a minimum cost configuration of a given integer valued n bit black box function whose input values have been scrambled in some unknown way special cases within this set of problems are grover s search problem of finding a marked item in an unstructured database certain random energy models and the functions of the deutsch josza problem we consider a couple of examples in detail in the first we provide an o 1 deterministic analogue quantum algorithm to solve the seminal problem of deutsch and josza in which one has to determine whether an n bit boolean function is constant gives 0 on all inputs or 1 on all inputs or balanced returns 0 on half the input states and 1 on the other half we also study one variant of the random energy model and show that as one might expect its minimum energy configuration can be found quadratically faster with a quantum adiabatic algorithm than with classical algorithms

quantum monte carlo with directed loops we introduce the concept of directed loops in stochastic series expansion and path integral quantum monte carlo methods using the detailed balance rules for directed loops we show that it is possible to smoothly connect generally applicable simulation schemes in which it is necessary to include backtracking processes in the loop construction to more restricted loop algorithms that can be constructed only for a limited range of hamiltonians where backtracking can be avoided the algorithmic discontinuities between general and special points or regions in parameter space can hence be eliminated as a specific example we consider the anisotropic s 1 2 heisenberg antiferromagnet in an external magnetic field we show that directed loop simulations are very efficient for the full range of magnetic fields zero to the saturation point and anisotropies in particular for weak fields and anisotropies the autocorrelations are significantly reduced relative to those of previous approaches the back tracking probability vanishes continuously as the isotropic heisenberg point is approached for the mathrm xy model we show that back tracking can be avoided for all fields extending up to the saturation field the method is hence particularly efficient in this case we use directed loop simulations to study the magnetization process in the two dimensional heisenberg model at very low temperatures for l ifmmode times else texttimes fi l lattices with l up to 64 we utilize the step structure in the magnetization curve to extract gaps between different spin sectors finite size scaling of the gaps gives an accurate estimate of the transverse susceptibility in the thermodynamic limit ensuremath chi ensuremath perp 0 0659 ifmmode pm else textpm fi 0 0002

a nurbs based hybrid collocation galerkin method for the analysis of boundary represented solids abstract the paper is concerned with a new numerical method nurbs based hybrid collocation galerkin method nurbs hcgm to solve the in plane motion problem of elastic solids it combines the merits of the so called scaled boundary finite element method sb fem and the isogeometric collocation method for the analysis the boundary scaling technique of sb fem is adopted it leads to a formulation where only the boundary of a structure is discretized here the nurbs basis functions are employed for the description of the geometry of the boundary as well as for the approximation of the displacements at the boundary this is in accordance with the boundary representation modeling technique which is commonly employed in computer aided design software the inner domain is described by a radial scaling parameter applying the weak form only in circumferential direction the governing partial differential equations of elasticity are transformed to an ordinary differential equation ode of euler type where the unknown displacements are a function of the radial scaling parameter in the present work a nurbs based collocation scheme is introduced to solve this equation nurbs basis functions are suggested for the approximation of the displacements in scaling direction the higher continuity provided by nurbs allows to use collocation to solve the ode directly instead of using the weak form in scaling direction the proposed approach is validated by comparison with the eigenvalue solution of the ode it is remarked that the eigenvalue solution is restricted to linear problems whereas the proposed method could be extended to nonlinear problems in general the presented formulation will allow to model patches bounded by an arbitrary number of contour boundaries the accuracy of the proposed approach is analyzed and estimated with respect to analytical solutions the computational cost is investigated with the help of numerical examples and is compared to isogeometric galerkin approach

a generalization of handscomb s quantum monte carlo scheme application to the 1d hubbard model a recently introduced generalization of handscomb s quantum monte carlo scheme 1962 is further developed expressions for expectation values of various observables are studied in detail a more efficient algorithm for importance sampling in a space of state vectors and operator strings is constructed using the 1d hubbard model as an illustrative example as a test of the method 32 site rings at band fillings 1 4 3 8 and 1 2 are studied at a low temperature results for spin and charge density structure factors and static susceptibilities are presented

complexity of several constraint satisfaction problems using the heuristic classical algorithm walksat we determine the complexity of several constraint satisfaction problems using the heuristic algorithm walksat at large sizes n the complexity increases exponentially with n in all cases perhaps surprisingly out of all the models studied the hardest for walksat is the one for which there is a polynomial time algorithm

isogeometric collocation for elastostatics and explicit dynamics we extend the development of collocation methods within the framework of isogeometric analysis iga to multi patch nurbs configurations various boundary and patch interface conditions and explicit dynamic analysis the methods developed are higher order accurate stable with no hourglass modes and efficient in that they require a minimum number of quadrature evaluations the combination of these attributes has not been obtained previously within standard finite element analysis

isogeometric collocation neumann boundary conditions and contact abstract isogeometric collocation methods have been proposed recently and their accuracy and efficiency demonstrated for elastostatics and explicit dynamics this paper addresses two important aspects in the development of the isogeometric collocation technology namely the imposition of neumann boundary conditions and the enforcement of contact constraints which are both treated within the same framework it is shown that the strong imposition of neumann boundary conditions may lead to a significant loss of accuracy in some situations in particular when non uniform meshes are used two possible remedies are proposed to restore the desired level of accuracy while keeping the computational cost virtually unchanged i e a hybrid collocation galerkin approach and an enhanced collocation ec approach a frictionless contact formulation suitable for the collocation framework is further proposed and shown to pass the contact patch test to machine precision when combined with the ec approach the formulation is shown to deliver accurate results and to perform robustly also for highly non uniform meshes for all the collocation formulations contact pressures are greater than or equal to zero pointwise in contrast with standard lagrange finite elements

a finite element formulation in boundary representation for the analysis of nonlinear problems in solid mechanics abstract the contribution is concerned with a numerical element formulation in boundary representation it results in a polynomial element description with an arbitrary number of nodes on the boundary scaling the boundary description determines the interior domain the scaling approach is adopted from the so called scaled boundary finite element method sbfem which is a semi analytical formulation to analyze problems in linear elasticity within this method the basic idea is to scale the boundary with respect to a scaling center the boundary which is denoted as circumferential direction and the scaling direction span the parameter space in the present approach interpolations in scaling direction and circumferential direction are introduced the interpolation in circumferential direction is independent of the scaling direction the formulation is suitable to analyze problems in nonlinear solid mechanics the displacement degrees of freedom are located at the nodes on the boundary and in the interior element domain the degrees of freedom located at the interior domain are eliminated by static condensation which leads to a polygonal finite element formulation with an arbitrary number of nodes on the boundary the element formulation allows per definition for voronoi meshes and quadtree mesh generation numerical examples give rise to the performance of the present approach in comparison to other polygonal element formulations like the virtual element method vem some benchmark tests show the capability of the element formulation a comparison to standard and mixed element formulations is presented the present approach is perfectly suitable to model heterogeneous structures with inclusions and voids it avoids also staircase approximation of curved boundaries

density matrix formulation for quantum renormalization groups a generalization of the numerical renormalization group procedure used first by wilson for the kondo problem is presented it is shown that this formulation is optimal in a certain sense as a demonstration of the effectiveness of this approach results from numerical real space renormalization group calculations for heisenberg chains are presented

exponential complexity of the quantum adiabatic algorithm for certain satisfiability problems we determine the complexity of several constraint satisfaction problems using the quantum adiabatic algorithm in its simplest implementation we do so by studying the size dependence of the gap to the first excited state of typical instances we find that at large sizes n the complexity increases exponentially for all models that we study we also compare our results against the complexity of the analogous classical algorithm walksat and show that the harder the problem is for the classical algorithm the harder it is also for the quantum adiabatic algorithm

isogeometric collocation methods for the reissner mindlin plate problem abstract within the general framework of isogeometric methods collocation schemes have been recently proposed as a viable and promising low cost alternative to standard isogeometric galerkin approaches in this paper isogeometric collocation methods for the numerical approximation of reissner mindlin plate problems are proposed for the first time locking free primal and mixed formulations are herein considered and the potential of isogeometric collocation as a geometrically flexible and computationally efficient simulation tool for shear deformable plates is shown through the solution of several numerical tests

the role of bezier extraction in adaptive isogeometric analysis local refinement and hierarchical refinement summary we present two adaptive refinement techniques namely adaptive local refinement and adaptive hierarchical refinement for isogeometric analysis an element wise point of view is adopted exploiting bezier extraction which facilitates the implementation of adaptive refinement in isogeometric analysis locally refined t splines lr t splines and hierarchical t splines are employed for the description of the geometry as well as for the approximation of the solution space in the analysis the refinement is carried out with the aid of a subdivision operator which is computed by again exploiting the bezier extraction operator the concept and algorithm of an element based adaptive isogeometric analysis are illustrated numerical examples are given to examine the accuracy the convergence and the condition number this article is protected by copyright all rights reserved

the finite cell method for three dimensional problems of solid mechanics this article presents a generalization of the recently proposed finite cell method to three dimensional problems of linear elasticity the finite cell method combines ideas from embedding or fictitious domain methods with the p version of the finite element method besides supporting a fast simple generation of meshes it also provides high convergence rates mesh generation for a boundary representation of solids and for voxel based data obtained from ct scans is addressed in detail in addition the implementation of non homogeneous neumann boundary conditions and the computation of cell matrices based on a composed integration is presented the performance of the proposed method is demonstrated by three numerical examples including the elastostatic computation of a human bone biopsy

convergence estimates for a plane elasticity problem solved by the galerkin boundary integral formulation with nurbs abstract a classical mixed boundary value problem of linear elasticity in two dimensions in the galerkin boundary integral formulation is considered we prove a priori error estimates of the solution to this problem by the isogeometric adaptive method using nurbs the estimates include approximation of the boundary of the domain

isogeometric analysis of lagrangian hydrodynamics axisymmetric formulation in the rz cylindrical coordinates a recent isogeometric analysis iga formulation of lagrangian shock hydrodynamics 4 is extended to the 3d axisymmetric case the euler equations of compressible hydrodynamics are formulated using the rz cylindrical coordinates and are discretized in the weak form using nurbs based iga artificial shock viscosity and internal energy projection are added to stabilize the formulation the resulting discretization exhibits good accuracy and robustness properties it also gives exact symmetry preservation on the appropriately constructed meshes several benchmark examples are computed to examine the performance of the proposed formulation

spectral gap amplification many problems can be solved by preparing a specific eigenstate of some hamiltonian h the generic cost of quantum algorithms for these problems is determined by the inverse spectral gap of h for that eigenstate and the cost of evolving with h for some fixed time the goal of spectral gap amplification is to construct a hamiltonian h with the same eigenstate as h but a bigger spectral gap requiring that constant time evolutions with h and h are implemented with nearly the same cost we show that a quadratic spectral gap amplification is possible when h satisfies a frustration free property and give h for these cases this results in quantum speedups for optimization problems it also yields improved constructions for adiabatic simulations of quantum circuits and for the preparation of projected entangled pair states which play an important role in quantum many body physics defining a suitable black box model we establish that the quadratic amplification is optimal for frustration f

how fast can quantum annealers count we outline an algorithm for the quantum counting problem using adiabatic quantum computation aqc we show that the mechanism of quantum adiabatic evolution may be utilized toward estimating the number of solutions to a problem and not only to find them using local adiabatic evolution a process in which the adiabatic procedure is performed at a variable rate the problem of counting the number of marked items in an unstructured database is solved quadratically faster than the corresponding classical algorithm the above algorithm provides further evidence for the potentially powerful capabilities of aqc as a paradigm for more efficient problem solving on a quantum computer and may be used as the basis for solving more sophisticated problems

stochastic series expansion method for quantum ising models with arbitrary interactions a quantum monte carlo algorithm for the transverse ising model with arbitrary short or long range interactions is presented the algorithm is based on sampling the diagonal matrix elements of the power series expansion of the density matrix stochastic series expansion and avoids the interaction summations necessary in conventional methods in the case of long range interactions the scaling of the computation time with the system size n is therefore reduced from n 2 to n mathrm ln n the method is tested on a one dimensional ferromagnet in a transverse field with interactions decaying as 1 r 2

weak coupling for isogeometric analysis of non matching and trimmed multi patch geometries nitsche s method can be used as a coupling tool for non matching discretizations by weakly enforcing interface constraints we explore the use of weak coupling based on nitsche s method in the context of higher order and higher continuity b splines and nurbs we demonstrate that weakly coupled spline discretizations do not compromise the accuracy of isogeometric analysis we show that the combination of weak coupling with the finite cell method opens the door for a truly isogeometric treatment of trimmed b spline and nurbs geometries that eliminates the need for costly reparameterization procedures we test our methodology for several relevant technical problems in two and three dimensions such as gluing together trimmed multi patches and connecting non matching meshes that contain b spline basis functions and standard triangular finite elements the results demonstrate that the concept of nitsche based weak coupling in conjunction with the finite cell method has the potential to considerably increase the flexibility of the design through analysis process in isogeometric analysis

a nitsche type formulation and comparison of the most common domain decomposition methods in isogeometric analysis this paper provides a detailed elaboration and assessment of the most common domain decomposition methods for their application in isogeometric analysis the methods comprise a penalty approach lagrange multiplier methods and a nitsche type method for the nitsche method a new stabilized formulation is developed in the context of isogeometric analysis to guarantee coercivity all these methods are investigated on problems of linear elasticity and eigenfrequency analysis in 2d in particular focus is put on non uniform rational b spline patches which join nonconformingly along their common interface thus the application of isogeometric analysis is extended to multi patches which can have an arbitrary parametrization on the adjacent edges moreover it has been shown that the unique properties provided by isogeometric analysis that is high order functions and smoothness across the element boundaries carry over for the analysis of multiple domains copyright 2013 john wiley sons ltd

the scaled boundary finite element method analytical solution in frequency domain the scaled boundary finite element equation a system of ordinary differential equations in the radial coordinate is solved analytically applying a series expansion an eigenvalue problem of a hamiltonian matrix is solved when the difference of two eigenvalues is an even number besides the power series logarithmic functions occur two sets of independent solutions are obtained the scaled boundary finite element method is thus a semi analytical procedure to solve partial differential equations with the polynomial approximation of finite elements in the two circumferential directions and a closed form solution in the radial direction applications to bounded and unbounded domains demonstrate excellent accuracy

hybrid collocation galerkin approach for the analysis of surface represented 3d solids employing sb fem abstract this paper presents a numerical method to solve the three dimensional elasticity problem of surface represented solids a surface oriented formulation is derived in which the three dimensional solid is described by its boundary surfaces and a radial scaling center scaling the boundary surfaces with respect to the scaling center yields a parameterization of the complete solid the definition of the boundary surfaces is sufficient for the description of the solid thus the formulation conforms ideally to the boundary representation modeling technique used in cad in the present approach no tensor product structure of three dimensional objects is exploited to parameterize the physical domain the weak form of the equation of motion and the weak form of the neumann boundary conditions are enforced only at the boundary surfaces it leads to a transformation of the governing partial differential equations of elasticity to an ordinary differential equation ode of euler type solving the ode leads to the displacement in the radial scaling direction in the present approach the isogeometric galerkin finite element method is employed to describe the geometry of the boundary surfaces and also to approximate the displacement response of the boundary surfaces it exploits two dimensional nurbs objects to parameterize the boundary surfaces the final euler type ode is solved by the nurbs based collocation method the displacement response in the radial scaling direction is approximated by the nurbs basis functions hence the method can be extended to nonlinear problems the accuracy of the method is validated against analytical solutions in general the proposed formulation is able to model solids bounded by an arbitrary number of surfaces

isogeometric analysis enhanced by the scaled boundary finite element method abstract by leveraging the information of a typical cad model in the analysis the intensive process of discretization can be circumvented this unification has led to the isogeometric analysis iga hughes et al 2005 however as the cad model provides information only of the boundary a 2d 3d stress analysis is still one major step away in this work the concepts of isogeometric analysis and the scaled boundary finite element method sbfem are combined the sbfem requires only the boundary information and hence provides a seamless integration with the cad modeling within the proposed framework the nurbs basis functions are used to discretize the unknown fields in the circumferential direction whilst analytical solution is sought in the radial direction we further extend the framework to problems with singularities and to dynamic analysis the accuracy and the convergence properties of the proposed method are demonstrated with benchmark problems in the context of linear elasticity and linear elastic fracture mechanics

a scaled boundary isogeometric formulation for the elasto plastic analysis of solids in boundary representation abstract this contribution deals with the nonlinear analysis of boundary represented solids with elasto plastic material behavior based on the so called scaled boundary isogeometric formulation sb iga the proposed approach combines the features of the scaled boundary finite element method and isogeometric analysis based on the original boundary representation of the cad model a formulation is provided where the geometrical description of the boundary is sufficient to define the entire surface the domain is parameterized by a radial scaling parameter emanating from a scaling center and a parameter in circumferential direction along the boundary non star shaped domains are tackled by standard sub structuring here conforming discretizations are considered for the two dimensional case according to the isogeometric paradigm nurbs basis functions are employed for the approximation of the solution the displacement response is derived based on a multiplicative decomposition of the approximation in circumferential and radial scaling direction the boundary value problem is solved with the galerkin method the newton raphson iterative scheme is employed to obtain the nonlinear response several benchmark tests demonstrate the accuracy and computational efficiency of the formulation

three dimensional mortar based frictional contact treatment in isogeometric analysis with nurbs a three dimensional mortar based frictional contact treatment in isogeometric analysis with nurbs is presented in the finite deformation regime within a setting where the nurbs discretization of the contact surface is inherited directly from the nurbs discretization of the volume the contact integrals are evaluated through a mortar approach where the geometrical and frictional contact constraints are treated through a projection to control point quantities the formulation delivers a non negative pressure distribution and minimally oscillatory local contact interactions with respect to alternative lagrange discretizations independent of the discretization order these enable the achievement of improved smoothness in global contact forces and moments through higher order geometrical descriptions it is concluded that the presented mortar based approach serves as a common basis for treating isogeometric contact problems with varying orders of discretization throughout the contact surface and the volume

fast algorithms for finding nearest common ancestors we consider the following problem given a collection of rooted trees answer on line queries of the form what is the nearest common ancester of vertices x and y we show that any pointer machine that solves this problem requires omega log log n time per query in the worst case where n is the total number of vertices in the trees on the other hand we present an algorithm for a random access machine with uniform cost measure and a bound of omega log n on the number of bits per word that requires o 1 time per query and o n preprocessing time assuming that the collection of trees is static for a version of the problem in which the trees can change between queries we obtain an almost linear time and linear space algorithm

a scaled boundary polygon formulation for elasto plastic analyses this study presents a novel scaled boundary polygon formulation to model elasto plastic material responses in structures the polygons have flexible mesh generation capabilities and are more accurate than standard finite elements especially for problems with cracks and notches shape functions of arbitrary n sided polygons are constructed using the scaled boundary finite element method these shape functions are conforming and linearly complete when modeling a crack strain singularities are analytically modeled without enrichment standard finite element procedures are used to formulate the stiffness matrix and residual load vector the nonlinear material constitutive matrix and the internal stresses are approximated locally in each polygon by a polynomial function the stiffness matrix and the residual load vector are matrix power integrals that can be evaluated analytically even when a strain singularity is present standard nonlinear equation solvers e g the modified newton raphson algorithm are used to obtain the nonlinear response of the structure the proposed formulation is validated using several numerical benchmarks

isogeometric reissner mindlin shell analysis with exactly calculated director vectors abstract an isogeometric reissner mindlin shell derived from the continuum theory is presented the geometry is described by nurbs surfaces the kinematic description of the employed shell theory requires the interpolation of the director vector and of a local basis system hence the definition of nodal basis systems at the control points is necessary for the proposed formulation the control points are in general not located on the shell reference surface and thus several choices for the nodal values are possible the proposed new method uses the higher continuity of the geometrical description to calculate nodal basis system and director vectors which lead to geometrical exact interpolated values thereof thus the initial director vector coincides with the normal vector even for the coarsest mesh in addition to that a more accurate interpolation of the current director and its variation is proposed instead of the interpolation of nodal director vectors the new approach interpolates nodal rotations account is taken for the discrepancy between interpolated basis systems and the individual nodal basis systems with an additional transformation the exact evaluation of the initial director vector along with the interpolation of the nodal rotations lead to a shell formulation which yields precise results even for coarse meshes the convergence behavior is shown to be correct for k refinement allowing the use of coarse meshes with high orders of nurbs basis functions this is potentially advantageous for applications with high numerical effort per integration point the geometrically nonlinear formulation accounts for large rotations the consistent tangent matrix is derived various standard benchmark examples show the superior accuracy of the presented shell formulation a new benchmark designed to test the convergence behavior for free form surfaces is presented despite the higher numerical effort per integration point the improved accuracy yields considerable savings in computation cost for a predefined error bound

geometric modeling isogeometric analysis and the finite cell method the advent of isogeometric analysis iga using the same basis functions for design and analysis constitutes a milestone in the unification of geometric modeling and numerical simulation however an important class of geometric models based on the csg constructive solid geometry concept such as trimmed nurbs surfaces do not fully support the isogeometric paradigm since basis functions do not explicitly represent the boundary the finite cell method fcm is a high order fictitious domain method which offers simple meshing of potentially complex domains into a structured grid of cuboid cells while still achieving exponential rates of convergence for smooth problems in the present paper we first discuss the possibility to directly couple the finite cell method to csg without any necessity for meshing the three dimensional domain and then explore a combination of the best of the two approaches iga and fcm closely following ideas of the recently introduced shell fcm the resulting finite cell extension to isogeometric analysis achieves a truly straightforward transfer of a trimmed nurbs surface into an analysis suitable nurbs basis while benefiting from the favorable properties of the high order and high continuity basis functions accuracy and efficiency of the new approach are demonstrated by a numerical benchmark and its versatility is outlined by the analysis of different trimmed design variants of a brake disk

efficient quadrature for nurbs based isogeometric analysis abstract we initiate the study of efficient quadrature rules for nurbs based isogeometric analysis a rule of thumb emerges the half point rule indicating that optimal rules involve a number of points roughly equal to half the number of degrees of freedom or equivalently half the number of basis functions of the space under consideration the half point rule is independent of the polynomial order of the basis efficient rules require taking into account the precise smoothness of basis functions across element boundaries several rules of practical interest are obtained and a numerical procedure for determining efficient rules is presented we compare the cost of quadrature for typical situations arising in structural mechanics and fluid dynamics the new rules represent improvements over those used previously in isogeometric analysis

rapid solution of problems by quantum computation a class of problems is described which can be solved more efficiently by quantum computation than by any classical or stochastic method the quantum computation solves the problem with certainty in exponentially less time than any classical deterministic computation

scaled boundary parametrizations in isogeometric analysis abstract this paper deals with a special class of parametrizations for isogeometric analysis iga the so called scaled boundary parametrizations are easy to construct and particularly attractive if only a boundary description of the computational domain is available the idea goes back to the scaled boundary finite element method sb fem which has recently been extended to iga we take here a different viewpoint and study these parametrizations as bivariate or trivariate b spline functions that are directly suitable for standard galerkin based iga our main results are first a general framework for this class of parametrizations including aspects such as smoothness and regularity as well as a generalization to domains that are not star shaped second using the poisson equation as an example we explain the relation between standard galerkin based iga and the scaled boundary iga by means of the laplace beltrami operator and derive an equivalence theorem further results concern the separation of integrals in both approaches and an analysis of the singularity in the scaling center among the computational examples we present a rotor geometry that stems from a screw compressor machine and compare different parametrization strategies

excitation gap from optimized correlation functions in quantum monte carlo simulations we give a prescription for finding optimized correlation functions for the extraction of the gap to the first excited state within quantum monte carlo simulations we demonstrate that optimized correlation functions provide a more accurate reading of the gap when compared to other nonoptimized correlation functions and are generally characterized by considerably larger signal to noise ratios we also analyze the cost of the procedure and show that it is not computationally demanding we illustrate the effectiveness of the proposed procedure by analyzing several exemplary many body systems of interacting spin 1 2 particles

a nurbs based galerkin approach for the analysis of solids in boundary representation abstract the paper is concerned with a new numerical method to solve the elasticity problem of solids in boundary representation a formulation is derived where the geometrical description of the boundary is sufficient for defining the equations of elasticity of the complete solid while the interior of the domain is described by a radial scaling parameter the scaling of the boundary with respect to the specified scaling center leads to the complete solid this idea fits perfectly to the boundary representation modeling technique commonly employed in cad in the present approach the tensor product structure of the solid will be reduced by one dimension to parametrize the physical domain i e the three dimensional solid exploits only two dimensional nurbs objects which parametrize the boundary surfaces for the analysis the weak form of the equilibrium equations is enforced for the entire solid in particular the weak form is employed in the scaling direction and the circumferential direction applying the isogeometric paradigm the nurbs functions that describe the boundary of the geometry form also the basis for the approximation of the displacement at the boundary the displacement response in the radial scaling direction on the other hand is approximated by a one dimensional nurbs overall the galerkin projection of the weak form yields a linear system of equilibrium equations whose solution gives rise to the displacement response the accuracy of the method is validated by means of analytical reference data in conclusion the proposed method allows the analysis of solids which are bounded by an arbitrary number of contour boundaries

isogeometric collocation cost comparison with galerkin methods and extension to adaptive hierarchical nurbs discretizations abstract we compare isogeometric collocation with isogeometric galerkin and standard c 0 finite element methods with respect to the cost of forming the matrix and residual vector the cost of direct and iterative solvers the accuracy versus degrees of freedom and the accuracy versus computing time on this basis we show that isogeometric collocation has the potential to increase the computational efficiency of isogeometric analysis and to outperform both isogeometric galerkin and standard c 0 finite element methods when a specified level of accuracy is to be achieved with minimum computational cost we then explore an adaptive isogeometric collocation method that is based on local hierarchical refinement of nurbs basis functions and collocation points derived from the corresponding multi level greville abscissae we introduce the concept of weighted collocation that can be consistently developed from the weighted residual form and the two scale relation of b splines using weighted collocation in the transition regions between hierarchical levels we are able to reliably handle coincident collocation points that naturally occur for multi level greville abscissae the resulting method combines the favorable properties of isogeometric collocation and hierarchical refinement in terms of computational efficiency local adaptivity robustness and straightforward implementation which we illustrate by numerical examples in one two and three dimensions

an efficient algorithm for sequence comparison with block reversals given two sequences x and y that are strings over some alphabet set we consider the distance d x y between them defined to be minimum number of character replacements and block substring reversals needed to transform x to y or vice versa the operations are required to be disjoint this is the simplest sequence comparison problem we know of that allows natural block edit operations block reversals arise naturally in genomic sequence comparison they are also of interest in matching music data we present an algorithm for exactly computing the distance d x y it takes time o x log2 x and hence is near linear trivial approach takes quadratic time

the scaled boundary finite element method alias consistent infinitesimal finite element cell method for elastodynamics the scaled boundary finite element method alias the consistent infinitesimal finite element cell method is developed starting from the governing equations of linear elastodynamics only the boundary of the medium is discretized with surface finite elements yielding a reduction of the spatial dimension by one no fundamental solution is necessary and thus no singular integrals must be evaluated general anisotropic material is analysed without any increase in computational effort boundary conditions on free and fixed surfaces and on interfaces between different materials are enforced exactly without any discretization this method is exact in the radial direction and converges to the exact solution in the finite element sense in the circumferential directions for a bounded medium symmetric static stiffness and mass matrices with respect to the degrees of freedom on the boundary result without any additional assumption a stress singularity is represented very accurately as the condition on the boundary in the vicinity of the point of singularity is satisfied without spatial discretization

the weak substitution method an application of the mortar method for patch coupling in nurbs based isogeometric analysis in this contribution a mortar type method for the coupling of non conforming nurbs surface patches is proposed the connection of non conforming patches with shared degrees of freedom requires mutual refinement which propagates throughout the whole patch due to the tensor product structure of nurbs surfaces thus methods to handle non conforming meshes are essential in nurbs based isogeometric analysis the main objective of this work is to provide a simple and efficient way to couple the individual patches of complex geometrical models without altering the variational formulation the deformations of the interface control points of adjacent patches are interrelated with a master slave relation this relation is established numerically using the weak form of the equality of mutual deformations along the interface with the help of this relation the interface degrees of freedom of the slave patch can be condensated out of the system a natural connection of the patches is attained without additional terms in the weak form the proposed method is also applicable for nonlinear computations without further measures linear and geometrical nonlinear examples show the high accuracy and robustness of the new method a comparison to reference results and to computations with the lagrange multiplier method is given

adiabatic quantum computation is equivalent to standard quantum computation adiabatic quantum computation has recently attracted attention in the physics and computer science communities but its computational power was unknown we describe an efficient adiabatic simulation of any given quantum algorithm which implies that the adiabatic computation model and the conventional quantum computation model are polynomially equivalent our result can be extended to the physically realistic setting of particles arranged on a two dimensional grid with nearest neighbor interactions the equivalence between the models allows stating the main open problems in quantum computation using well studied mathematical objects such as eigenvectors and spectral gaps of sparse matrices