a critical evaluation of the resolution properties of b spline and compact finite difference methods resolution properties of b spline and compact finite difference schemes are compared using fourier analysis in periodic domains and tests based on solution of the wave and heat equations in finite domains with uniform and nonuniform grids results show that compact finite difference schemes have a higher convergence rate and in some cases better resolution however b spline schemes have a more straightforward and robust formulation particularly near boundaries on nonuniform meshes

locking free isogeometric collocation methods for spatial timoshenko rods in this work we present the application of isogeometric collocation techniques to the solution of spatial timoshenko rods the strong form equations of the problem are presented in both displacement based and mixed formulations and are discretized via nurbs based isogeometric collocation several numerical experiments are reported to test the accuracy and efficiency of the considered methods as well as their applicability to problems of practical interest in particular it is shown that mixed collocation schemes are locking free independently of the choice of the polynomial degrees for the unknown fields such an important property is also analytically proven

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

isogeometric analysis using polynomial splines over hierarchical t meshes for two dimensional elastic solids isogeometric analysis has become a powerful alternative to standard finite elements due to its flexibility in handling complex geometries one of the major drawbacks of nurbs based isogeometric finite elements is the inefficiency of local refinement in this study we present an alternative to nurbs based isogeometric analysis that allows for local refinement the idea is based on polynomial splines and exploits the flexibility of t meshes for local refinement the shape functions satisfy important properties such as non negativity local support and partition of unity several numerical examples are used to demonstrate the reliability of the present method

some estimates for h p k refinement in isogeometric analysis in this paper we propose a theoretical study of the approximation properties of nurbs spaces which are used in isogeometric analysis we obtain error estimates that are explicit in terms of the mesh size h the degree p and the global regularity measured by the parameter k our approach covers the approximation with global regularity from c 0 up to c k 1 with 2k 1 p notice that the interesting case of higher regularity up to k p is still open however our results give an indication of the role of the smoothness k in the approximation properties and offer a first mathematical justification of the potential of isogeometric analysis based on globally smooth nurbs

explicit isogeometric collocation for the dynamics of three dimensional beams undergoing finite motions abstract we initiate the study of three dimensional shear deformable geometrically exact beam dynamics through explicit isogeometric collocation methods the formulation we propose is based on a natural combination of the chosen finite rotations representation with an explicit geometrically consistent lie group time integrator we focus on extending the integration scheme originally proposed for rigid body dynamics to our nonlinear initial boundary value problem where special attention is required by neumann boundary conditions the overall formulation is simple and only relies on a geometrically consistent procedure to compute the internal forces once control angular and linear accelerations of the beam cross sections are obtained from the previous time step the capabilities of the method are shown through numerical applications involving very large displacements and rotations and different boundary conditions

optimal and reduced quadrature rules for tensor product and hierarchically refined splines in isogeometric analysis abstract we continue the study initiated in hughes et al 2010 in search of optimal quadrature rules for tensor product and hierarchically refined splines in isogeometric analysis these rules are optimal in the sense that there exists no other quadrature rule that can exactly integrate the elements of the given spline space with fewer quadrature points we extend the algorithm presented in hughes et al 2010 with an improved starting guess which combined with arbitrary precision arithmetic results in the practical computation of quadrature rules for univariate non uniform splines up to any precision explicit constructions are provided in sixteen digits of accuracy for some of the most commonly used uniform spline spaces defined by open knot vectors we study the efficacy of the proposed rules in the context of full and reduced quadrature applied to two and three dimensional diffusion reaction problems using tensor product and hierarchically refined splines and prove a theorem rigorously establishing the stability and accuracy of the reduced rules

propositional default logics made easier computational complexity of model checking liberatore and schaerf proceedings of the ecai 98 1998 give a proof that model checking for propositional normal default theories is in 2p and 2p o log n hard however the precise complexity is left as an open problem we solve this problem by proving that model checking for normal default theories is complete for 2p o log n this is the class of decision problems solvable in polynomial time with a logarithmic number of calls to an oracle in np additionally we analyse the computational cost of model checking w r t weak extensions stable expansions and n expansions and take a look at the complexity of model checking for disjunction free default theories furthermore we show that not only for disjunction free default theories but also for a larger class of default theories which we call default theories in extended horn normal form the complexity of model checking is in the case of normal default theories tractable additionally the complexity results are used to draw some interesting conclusions on translatability issues in particular there exists no function from default logic into logic programming which is polynomial faithful and modular unless conp 2p finally we give an overview of our results concerning model checking in case of disjunctive default logic and stationary default logic

interior two dimensional acoustic modelling and modal analysis using isogeometric approach abstract in this paper the interior two dimensional acoustic modelling and modal analysis are presented in the framework of isogeometric analysis iga the acoustic domain governed by the helmholtz equation is parameterized and analysed by non uniform rational lagrange nurl basis which can construct exact geometry model inherently like non uniform rational b spines nurbs and can provide a more straightforward way than nurbs to impose dirichlet boundary conditions the verification and versatility of iga using nurl are assessed in the investigation of a unit square domain and a unit circular domain by comparison with analytical solutions furthermore a quadrilateral domain with concave or convex conics is studied and some innovative results are presented which can be the benchmark data for other algorithm researches the effects of geometric weight and aspect ratio on acoustic eigenvalue and eigenmode of the quadrilateral domain are investigated in detail

translating default logic into standard autoepistemic logic since konolige s translation of default logic into strongly grounded autoepistemic logic several other variants of moore s original autoepistemic logic that embody default logic have been studied all these logics differ significantly from moore s autoepistemic logic standard ael in that expansions are subject to additional groundedness conditions hence the question naturally arises whether default logic can be translated into standard ael at all we show that a modular translation is not possible however we are able to construct a faithful polynomial time translation from default logic into standard ael which is nonmodular our translation exploits the self referentiality of ael it uses as an important intermediate step an embedding of marek s and truszczyn ski s nonmonotonic logic n into standard ael it follows from our results that the expressive power of standard ael is strictly greater than that of default logic

on the variational formulation of stress constraints in isogeometric design the isogeometric paradigm is aimed at unifying the geometric and analysis descriptions of engineering problems this unification is brought about by employing the same basis functions to describe exact geometry and to approximate the physical response the isogeometric framework has recently been extended to include design optimisation a novel variational stress constraint formulation is proposed in this paper that further extends recent efforts in isogeometric design the weak form of the constraint is obtained by utilising the same basis functions not only to represent geometry response and design variables but also lagrange multipliers in this form the proposed variational formulation fits seamlessly with the underlying analysis and design environment the variational constraint formulation is compared to the widely utilised stress averaging and collocation approaches to this end volume minimisation of elastic arches subjected to stress constraints is considered results indicate that the proposed variational approach has the best convergence rates and utilises a much smaller number of discrete constraints than competing methods

fast formation and assembly of finite element matrices with application to isogeometric linear elasticity abstract recently a new formation and assembly strategy was proposed in 1 which resulted in significant speedups in the formation and assembly time of the galerkin mass matrix in isogeometric analysis the strategy relies on three key ingredients 1 assembly row by row instead of element by element and an efficient formation strategy based on 2 sum factorization and 3 weighted quadrature that is applied to each specific row of the matrix compared to traditional element procedures applied to three dimensional problems the computational complexity is lowered from o p 9 per degree of freedom to o p 4 where p is the order of polynomials this is close to the theoretical minimum of o p 3 attained by for example collocation consequently this type of formation and assembly scales favorably with polynomial degree which opens the way for high order isogeometric analysis employing k refinement that is use of maximally smooth higher order splines in this work we discuss various important details for the practical implementation of the weighted quadrature formation strategy proposed in 1 specifically we extend the weighted quadrature scheme to accurately integrate the elements of the stiffness matrix in linear elasticity and propose a means of distributing quadrature points for non uniform mixed continuity spline spaces furthermore we discuss efficient access and assignment into the prevalent sparse matrix data structures namely compressed sparse row csr and compressed sparse column csc in particular row by row or column by column assembly allows matrix rows or columns respectively to be formed contiguously in the storage order of the sparse matrix thereby minimizing the memory overhead and eliminating the addition assignment operation on sparse matrices several three dimensional benchmark problems illustrate the efficiency and efficacy of the proposed formation and assembly technique applied to isogeometric linear elasticity we show that the accuracy of full gauss quadrature is maintained while the computational burden of forming the matrix equations is significantly reduced

duality and unified analysis of discrete approximations in structural dynamics and wave propagation comparison of p method finite elements with k method nurbs we study the discretization behavior of classical finite element and nurbs approximations on problems of structural vibrations and wave propagation we find that on the basis of equal numbers of degrees of freedom and bandwidth nurbs have superior approximation properties in fact we observe that the high mode behavior of classical finite elements is divergent with the order of approximation a surprisingly negative result on the other hand nurbs offer almost spectral approximation properties and all modes converge with increasing order of approximation

three dimensional simulation of unstable gravity driven infiltration of water into a porous medium infiltration of water in dry porous media is subject to a powerful gravity driven instability although the phenomenon of unstable infiltration is well known its description using continuum mathematical models has posed a significant challenge for several decades the classical model of water flow in the unsaturated flow the richards equation is unable to reproduce the instability here we present a computational study of a model of unsaturated flow in porous media that extends the richards equation and is capable of predicting the instability and captures the key features of gravity fingering quantitatively the extended model is based on a phase field formulation and is fourth order in space the new model poses a set of challenges for numerical discretizations such as resolution of evolving interfaces stiffness in space and time treatment of singularly perturbed equations and discretization of higher order spatial partial differential operators we develop a numerical algorithm based on isogeometric analysis a generalization of the finite element method that permits the use of globally smooth basis functions leading to a simple and efficient discretization of higher order spatial operators in variational form we illustrate the accuracy efficiency and robustness of our method with several examples in two and three dimensions in both homogeneous and strongly heterogeneous media we simulate for the first time unstable gravity driven infiltration in three dimensions and confirm that the new theory reproduces the fundamental features of water infiltration into a porous medium our results are consistent with classical experimental observations that demonstrate a transition from stable to unstable fronts depending on the infiltration flux

reduced bezier element quadrature rules for quadratic and cubic splines in isogeometric analysis abstract we explore the use of various element based reduced quadrature strategies for bivariate and trivariate quadratic and cubic spline elements used in isogeometric analysis the rules studied encompass tensor product gauss and gauss lobatto rules and certain so called monomial rules that do no possess a tensor product structure the objective of the study is to determine quadrature strategies which enjoy the same accuracy and stability behavior as full gauss quadrature but with significantly fewer quadrature points several cases emerge that satisfy this objective and also demonstrate superior efficiency compared with standard c 0 continuous finite elements of the same order

evaluating the effect of semi normality on the expressiveness of defaults normal default logic ndl and semi normal default logic sndl are syntactically restricted variants of reiter s default logic dl although semi normal defaults have only a slightly more general form than normal defaults sndl does not share the nice properties of ndl e g semi monotonicity in this note we address the effect of semi normality on the expressive power of defaults using a classification method based on polynomial faithful and modular pfm translation functions the resulting classification indicates that sndl and dl are of equal expressive power which strictly exceeds that of ndl this strengthens an earlier result achieved by marek and truszczynski who establish the equivalence of weak semi normal defaults with general defaults furthermore it is established that prerequisite free fragments of dl and sndl pdl and psndl are of equal expressive power consequently psndl is less expressive than dl and sndl incomparable with ndl and more expressive than preferential entailment a generalized form of circumscription the latter result is in sharp contrast with imielinski s result which states that prerequisite free and semi normal default theories can be modularly translated into preferential entailment

isogeometric analysis of geometric partial differential equations abstract we consider the numerical approximation of geometric partial differential equations pdes defined on surfaces in the 3d space in particular we focus on the geometric pdes deriving from the minimization of an energy functional by l 2 gradient flow we analyze two energy functionals the area which leads to the mean curvature flow a nonlinear second order pde and the willmore energy leading to the willmore flow a nonlinear fourth order pde we consider surfaces represented by single patch tensor product nurbs and discretize the pdes by means of nurbs based isogeometric analysis in the framework of the galerkin method to approximate the high order geometric pdes we use high order continuous nurbs basis functions for the time discretization of the nonlinear geometric pdes we use backward differentiation formulas bdf with extrapolation of the geometric quantities involved in the weak formulation of the problem in this manner we solve a linear problem at each time step we report numerical results concerning the mean curvature and willmore flows on different geometries of interest and we show the accuracy and efficiency of the proposed approximation scheme

results on translating defaults to circumscription abstract in this paper we define different concepts of translating a set of defaults into circumscription the most important of these modular translation requires that additive changes of specific facts not defaults of default theory translate to additive changes of the simple abnormality theory corresponding to circumscription we show that surprisingly enough an important class of defaults normal defaults with prerequisites does not have such a modular translation into circumscription abnormality theory we also establish the classes of defaults which are translatable into circumscription

an unfitted hp adaptive finite element method based on hierarchical b splines for interface problems of complex geometry generating finite element discretizations with direct interface parameterizations constitutes a considerable computational expense in case of complex interface geometries the paper at hand introduces a b spline finite element method which circumvents parameterization of interfaces and offers fast and easy meshing irrespective of the geometric complexity involved its core idea is the adaptive approximation of discontinuities by hierarchical grid refinement which adds several levels of local basis functions in the close vicinity of interfaces but unfitted to their exact location so that a simple regular grid of knot span elements can be maintained numerical experiments show that an hp refinement strategy which simultaneously increases the polynomial degree of the b spline basis and the levels of refinement around interfaces achieves exponential rates of convergence despite the presence of discontinuities it is also demonstrated that the hierarchical b spline fem can be used to transfer the recently introduced finite cell concept to geometrically nonlinear problems its computational performance imposition of unfitted boundary conditions and fast hierarchical grid generation are illustrated for a set of benchmark problems in one two and three dimensions and the advantages of the regular grid approach for complex geometries are demonstrated by the geometrically nonlinear simulation of a voxel based foam composite

semantical considerations on nonmonotonic logic abstract commonsense reasoning is nonmonotonic in the sense that we often draw on the basis of partial information conclusions that we later retract when we are given more complete information some of the most interesting products of recent attempts to formalize nonmonotonic reasoning are the nonmonotonic logics of mcdermott and doyle 1 2 these logics however all have peculiarities that suggest they do not quite succeed in capturing the intuitions that prompted their development in this paper we reconstruct nonmonotonic logic as a model of an ideally rational agent s reasoning about his own beliefs for the resulting system called autoepistemic logic we define an intuitively based semantics for which we can show autoepistemic logic to be both sound and complete we then compare autoepistemic logic with the approach of mcdermott and doyle showing how it avoids the peculiarities of their nonmonotonic logic

dispersion analysis and error estimation of galerkin finite element methods for the helmholtz equation when applying numerical methods for the computation of stationary waves from the helmholtz equation one obtains numerical waves that are dispersive also in non dispersive media the numerical wave displays a phase velocity that depends on the parameter k of the helmholtz equation in dispersion analysis the phase difference between the exact and the numerical solutions is investigated in this paper the authors recent result on the phase difference for one dimensional problems is numerically evaluated and discussed in the context of other work directed to this topic it is then shown that previous error estimates in h1 norm are of nondispersive character but hold for medium or high wavenumber on extremely refined mesh only on the other hand recently proven error estimates for constant resolution contain a pollution term with certain assumptions on the exact solution this term is of the order of the phase difference thus a link is established between the results of dispersion analysis and the results of numerical analysis throughout the paper the presentation and discussion of theoretical results is accompanied by numerical evaluation of several model problems special attention is given to the performance of the galerkin method with a higher order of polynomial approximation p h p version

on the relation between default and autoepistemic logic abstract default logic is a formal means of reasoning about defaults what normally is the case in the absence of contradicting information autoepistemic logic on the other hand is meant to describe the consequences of reasoning about ignorance what must be true if a certain fact is not known although the motivation and formal character of these two systems are different a closer analysis shows that they share a common trait which is the indexical nature of certain elements in the theory in this paper we compare the expressive power of the two systems first we give an effective translation of default logic into autoepistemic logic default theories can thus be embedded into autoepistemic logic we also present a more surprising result the reverse translation is also possible so that every set of sentences in autoepistemic logic can be effectively rewritten as a default theory the formal equivalence of these two differing systems is thus established this analysis gives an interpretive semantics to default logic and yields insight into the nature of defaults in autoepistemic reasoning

experiments based parameter identification on the gpu for cooperative systems abstract in this paper we describe how to enhance experimental parameter identification for cooperative systems using the gpu this kind of identification is necessary for example in the area of developing robust controllers and observers based on available measurement data first we point out which parts of the general global optimization based parameter identification procedure can be parallelized and compare it to the experiments based technique after that we illustrate the principle and its implementation with the help of a close to life textbook example finally we demonstrate how the gpu based experimental parameter identification works for identifying experimentally the parameters of the reduced order temperature model for the distributed heating system this is an important step towards working with uncertain models in the context of solid oxide fuel cells

isogeometric schwarz preconditioners for linear elasticity systems isogeometric schwarz preconditioners are constructed and analyzed for both compressible elasticity in primal formulation and almost incompressible elasticity in mixed formulation these preconditioners require the solution of local elasticity problems on overlapping subdomains forming a decomposition of the problem domain and the solution of a coarse elasticity problem associated with the subdomain coarse mesh an h analysis of the preconditioner for the primal formulation of compressible elasticity yields an optimal convergence rate bound that is scalable in the number of subdomains and is linear in the ratio between subdomain and overlap sizes extensive numerical experiments in 2d and 3d confirm this theoretical bound and show that an analogous bound holds for the mixed formulation of almost incompressible elasticity the numerical tests also show the good preconditioner performance with respect to the polynomial degree p and regularity k of the isogeometric basis functions as well as with respect to the presence of discontinuous elastic coefficients in composite materials and to domain deformation

dispersion minimizing quadrature rules for c1 quadratic isogeometric analysis abstract we develop quadrature rules for the isogeometric analysis of wave propagation and structural vibrations that minimize the discrete dispersion error of the approximation the rules are optimal in the sense that they only require two quadrature points per element to minimize the dispersion error barto et al 2017 1 and they are equivalent to the optimized blending rules we recently described our approach further simplifies the numerical integration instead of blending two three point standard quadrature rules we construct directly a single two point quadrature rule that reduces the dispersion error to the same order for uniform meshes with periodic boundary conditions also we present a 2 5 point rule for both uniform and non uniform meshes with arbitrary boundary conditions consequently we reduce the computational cost by using the proposed quadrature rules various numerical examples demonstrate the performance of these quadrature rules

isogeometric analysis of the cahn hilliard phase field model abstract the cahn hilliard equation involves fourth order spatial derivatives finite element solutions are not common because primal variational formulations of fourth order operators are only well defined and integrable if the finite element basis functions are piecewise smooth and globally c 1 continuous there are a very limited number of two dimensional finite elements possessing c 1 continuity applicable to complex geometries but none in three dimensions we propose isogeometric analysis as a technology that possesses a unique combination of attributes for complex problems involving higher order differential operators namely higher order accuracy robustness two and three dimensional geometric flexibility compact support and most importantly the possibility of c 1 and higher order continuity a nurbs based variational formulation for the cahn hilliard equation was tested on two and three dimensional problems we present steady state solutions in two dimensions and for the first time in three dimensions to achieve these results an adaptive time stepping method is introduced we also present a technique for desensitizing calculations to dependence on mesh refinement this enables the calculation of topologically correct solutions on coarse meshes opening the way to practical engineering applications of phase field methodology

discrete dispersion relation for hp version finite element approximation at high wave number the dispersive properties of high order finite element schemes are analyzed in the setting of the helmholtz equation and an explicit form of the discrete dispersion relation is obtained for elements of arbitrary order it is shown that the numerical dispersion displays three different types of behavior depending on the size of the order of the method relative to the mesh size and the wave number quantitative estimates are obtained for the behavior and rates of decay of the dispersion error in the differing regimes all estimates are fully explicit and are shown to be sharp limits are obtained where transitions between the different regimes occur and used to provide guidelines for the selection of the mesh size and the polynomial order in terms of the wave number so that the dispersion error is controlled

provably unconditionally stable second order time accurate mixed variational methods for phase field models we introduce provably unconditionally stable mixed variational methods for phase field models our formulation is based on a mixed finite element method for space discretization and a new second order accurate time integration algorithm the fully discrete formulation inherits the main characteristics of conserved phase dynamics namely mass conservation and nonlinear stability with respect to the free energy we illustrate the theory with the cahn hilliard equation but our method may be applied to other phase field models we also propose an adaptive time stepping version of the new time integration method we present some numerical examples that show the accuracy stability and robustness of the new method

nonmonotonic logic ii nonmonotonic modal theories tradmonal logics suffer from the monotomclty problem new axioms never mvahdate old theorems one way to get nd of this problem ts to extend traditional modal logic in the following way the operator m usually read possible is extended so that mp is true whenever p is consistent with the theory then any theorem of this form may be mvahdated if p s added as an axiom this extension results m nonmonotomc versions of the systems t 4 and 5 these systems are complete in that a theorem is provable in a theory based on one of them just if it is true m all noncommittal models of that theory where a noncommittal model ts one m which as many thmgs are possible as possible nonmonotomc 4 is probably the most interesting of the three since it is stronger than ordinary 4 but has all the usual inferential machinery of 4 there is a straightforward proof procedure for the sententlal subset of nonmonotomc 4 this approach to nonmonotonlc logic may be applied to several problems in knowledge representation for aruficml mtelhgence its main advantages over competmg approaches are that tt factors out problems of resource hmltattons and allows the symbol m to appear m any context since m is a meaningful part of the language

studies of refinement and continuity in isogeometric structural analysis we investigate the effects of smoothness of basis functions on solution accuracy within the isogeometric analysis framework we consider two simple one dimensional structural eigenvalue problems and two static shell boundary value problems modeled with trivariate nurbs solids we also develop a local refinement strategy that we utilize in one of the shell analyses we find that increased smoothness that is the k method leads to a significant increase in accuracy for the problems of structural vibrations over the classical c0c0 continuous p method whereas a judicious insertion of c0c0 continuous surfaces about singularities in a mesh otherwise generated by the k method usually outperforms a mesh in which all basis functions attain their maximum level of smoothness we conclude that the potential for the k method is high but smoothness is an issue that is not well understood due to the historical dominance of c0c0 continuous finite elements and therefore further studies are warranted

overlapping schwarz methods for isogeometric analysis we construct and analyze an overlapping schwarz preconditioner for elliptic problems discretized with isogeometric analysis the preconditioner is based on partitioning the domain of the problem into overlapping subdomains solving local isogeometric problems on these subdomains and solving an additional coarse isogeometric problem associated with the subdomain mesh we develop an h analysis of the preconditioner showing in particular that the resulting algorithm is scalable and its convergence rate depends linearly on the ratio between subdomain and overlap sizes for fixed polynomial degree p and regularity k of the basis functions numerical results in two and three dimensional tests show the good convergence properties of the preconditioner with respect to the isogeometric discretization parameters h p k number of subdomains n overlap size and also jumps in the coefficients of the elliptic operator

spline based meshfree method summary in the present work the spline based meshfree method sbmfm is presented the sbmfm uses spline basis functions for field variables and boundary representation because of the inherent properties of splines that is nurbs nonuniform rational b splines the analysis domain used in the sbmfm has its own parametric domain unlike the classical concepts in the computer aided design cad community in which the nurbs patches are used to model the body the nurbs patch is treated as a background mesh in the present work the real analysis domain is created by trimming operation so that the domain boundaries are described by spline curves only on a single nurbs patch building the geometry in this way enables a convenient boundary representation of the domains because direct manipulation of spline curves becomes possible from a deformation point of view the mesh distortion problem is effectively avoided even if the analysis domain undergoes a large deformation in the sbmfm boundary spline curves freely move with complete independence from the quadrilateral background nurbs patch the so called element connectivity is unnecessary for geometry description in this paper geometrically nonlinear problems are considered implementation strategy is presented and the effectiveness of the present sbmfm is shown through various numerical examples copyright 2012 john wiley sons ltd

robust controlled invariance for monotone systems the robust controlled invariance describes the ability to maintain using suitable control actions the state of a system in a set for any value of the disturbances by considering a class of monotone systems and a multidimensional interval as target set we obtain a simple characterization of the robust controlled invariance we then give a method to stabilize the state into a robust controlled invariant interval when it is initialized outside of the target set these results are applied to a model for the temperature control in an intelligent building equipped with automated underfloor air distribution ufad and implemented in a small scale experimental ufad flat

dispersion minimized mass for isogeometric analysis abstract we introduce the dispersion minimized mass for isogeometric analysis to approximate the structural vibration which we model as a second order differential eigenvalue problem the dispersion minimized mass reduces the eigenvalue error significantly from the optimum order of 2 p to the superconvergence order of 2 p 2 for the p th order isogeometric elements with maximum continuity which in return leads to a more accurate method we first establish the dispersion error where the leading error term is explicitly written in terms of the stiffness and mass entries for arbitrary polynomial order isogeometric elements we derive the dispersion minimized mass in one dimension by solving a p dimensional local matrix problem for the p th order approximation and then extend it to multiple dimensions on tensor product grids we show that the dispersion minimized mass can also be obtained by approximating the mass matrix using optimally blended quadratures we generalize the lower order quadrature blending results to arbitrary polynomial order isogeometric approximations as well as to arbitrary quadrature rules various numerical examples validate the eigenvalue and eigenfunction error estimates

redundancy in logic iii non monotonic reasoning results about the redundancy of certain versions of circumscription and default logic are presented in particular propositional circumscription where all variables are minimized and skeptical default logics are considered this restricted version of circumscription is shown to have the unitary redundancy property a cnf formula is redundant it is equivalent to one of its proper subsets if and only if it contains a redundant clause it is equivalent to itself minus one clause default logic does not have this property in general we also give the complexity of checking redundancy in the considered formalisms

grounded fixpoints and their applications in knowledge representation in various domains of logic researchers have made use of a similar intuition that facts or models can be derived from the ground up they typically phrase this intuition by saying e g that the facts should be grounded or that they should not be unfounded or that they should be supported by cycle free arguments et cetera in this paper we formalise this intuition in the context of algebraical fixpoint theory we define when a lattice element x l is grounded for lattice operator o l l on the algebraical level we investigate the relationship between grounded fixpoints and the various classes of fixpoints of approximation fixpoint theory including supported minimal kripke kleene stable and well founded fixpoints on the logical level we investigate groundedness in the context of logic programming autoepistemic logic default logic and argumentation frameworks we explain what grounded points and fixpoints mean in these logics and show that this concept indeed formalises intuitions that existed in these fields we investigate which existing semantics are grounded we study the novel semantics for these logics that is induced by grounded fixpoints which has some very appealing properties not in the least its mathematical simplicity and generality our results unveil a remarkable uniformity in intuitions and mathematics in these fields

a phase field description of dynamic brittle fracture abstract in contrast to discrete descriptions of fracture phase field descriptions do not require numerical tracking of discontinuities in the displacement field this greatly reduces implementation complexity in this work we extend a phase field model for quasi static brittle fracture to the dynamic case we introduce a phase field approximation to the lagrangian for discrete fracture problems and derive the coupled system of equations that govern the motion of the body and evolution of the phase field we study the behavior of the model in one dimension and show how it influences material properties for the temporal discretization of the equations of motion we present both a monolithic and staggered time integration scheme we study the behavior of the dynamic model by performing a number of two and three dimensional numerical experiments we also introduce a local adaptive refinement strategy and study its performance in the context of locally refined t splines we show that the combination of the phase field model and local adaptive refinement provides an effective method for simulating fracture in three dimensions

a logic for default reasoning the need to make default assumptions is frequently encountered in reasoning about incompletely specified worlds inferences sanctioned by default are best viewed as beliefs which may well be modified or rejected by subsequent observations it is this property which leads to the non monotonicity of any logic of defaults in this paper we propose a logic for default reasoning we then specialize our treatment to a very large class of commonly occuring defaults for this class we develop a complete proof theory and show how to interface it with a top down resolution theorem prover finally we provide criteria under which the revision of derived beliefs must be effected

on embedding default logic into moore s autoepistemic logic abstract recently gottlob proved 2 that there does not exist a faithful modular translation of default logic into autoepistemic logic and presented a non modular translation gottlob s translation however is indirect it uses nonmonotonic logic n as an intermediate point quite complex and exploits sophisticated encoding of proof theory in autoepistemic formulas we provide a simpler and more intuitive non modular direct translation in addition our argument is purely model theoretic

a hybrid bounding method for computing an over approximation for the reachable set of uncertain nonlinear systems in this paper we show how to compute an over approximation for the reachable set of uncertain nonlinear continuous dynamical systems by using guaranteed set integration we introduce two ways to do so the first one is a full interval method which handles whole domains for set computation and relies on state of the art validated numerical integration methods the second one relies on comparison theorems for differential inequalities in order to bracket the uncertain dynamics between two dynamical systems where there is no uncertainty since the derived bracketing systems are piecewise ck differentiable functions validated numerical integration methods cannot be used directly hence our contribution resides in the use of hybrid automata to model the bounding systems we give a rule for building these automata and we show how to run them and address mode switching in a guaranteed way in order to compute the over approximation for the reachable set the computational cost of our method is also analyzed and shown to be smaller that the one of classical interval techniques sufficient conditions are given which ensure the epsiv practical stability of the enclosures given by our hybrid bounding method two examples are also given which show that the performance of our method is very promising

on the quadratic finite element approximation of one dimensional waves propagation observation and control we study the propagation observation and control properties of the quadratic p 2 classical finite element semidiscretization of the one dimensional wave equation on a bounded interval a careful fourier analysis of the discrete wave dynamics reveals two different branches in the spectrum the acoustic one of physical nature and the optic one related to the perturbations that this second order finite element approximation introduces with respect to the p 1 one on both modes there are high frequencies with vanishing group velocity as the mesh size tends to zero this shows that the classical property of continuous waves of being observable from the boundary fails to be uniform for this discretization scheme as a consequence of this the controls of the discrete waves may blow up as the mesh size tends to zero to remedy these high frequency pathologies we design filtering mechanisms based on the fourier truncation method or on a bi grid algorithm for which one can recover the uniformity of the

effects of parameterization and knot placement techniques on primal and mixed isogeometric collocation formulations of spatial shear deformable beams with varying curvature and torsion abstract we present a displacement based and a mixed isogeometric collocation iga c formulation for free form three dimensional shear deformable beams with high and rapidly varying curvature and torsion when such complex shapes are concerned the approach used to build the iga geometric model becomes relevant although iga c has been so far successfully applied to a wide range of problems the effects that different parameterization and knot placement techniques may have on the accuracy of collocation based formulations is still an unexplored field to fill this gap primal and mixed formulations are used combining two parameterization methods chord length and equally spaced with two knot placement techniques uniformly spaced and de boor with respect to the space varying frenet local frame we derive the strong form of the governing equations in a compact form through the definition of two matrix operators conveniently used to perform first and second order derivatives of the vector fields involved in the formulations this approach is very efficient and easy to implement within a collocation based scheme several challenging numerical experiments allow to test the different considered parameterizations and knot placement techniques revealing in particular that with the primal formulation an equally spaced parameterization is definitively the most recommended choice and it should always be used with an approximation degree of at least p 6 although some caution must be adopted when very high jacobians and small curvatures occur the same holds for the mixed formulation with the difference that p 4 is enough to yield accurate results

autoepistemic logic autoepistemic logic is one of the principal modes of nonmonotonic reasoning it unifies several other modes of nonmonotonic reasoning and has important application in logic programming in the paper a theory of autoepistemic logic is developed this paper starts with a brief survey of some of the previously known results then the nature of nonmonotonicity is studied by investigating how membership of autoepistemic statements in autoepistemic theories depends on the underlying objective theory a notion similar to set theoretic forcing is introduced expansions of autoepistemic theories are also investigated expansions serve as sets of consequences of an autoepistemic theory and they can also be used to define semantics for logic programs with negation theories that have expansions are characterized and a normal form that allows the description of all expansions of a theory is introduced our results imply algorithms to determine whether a theory has a unique expansion sufficient conditions stratification that imply existence of a unique expansion are discussed the definition of stratified theories is extended and under some additional assumptions efficient algorithms for testing whether a theory is stratified are proposed the theorem characterizing expansions is applied to two classes of theories k1 theories and ae programs in each case simple hypergraph characterization of expansions of theories from each of these classes is given finally connections with stable model semantics for logic programs with negation is discussed in particular it is proven that the problem of existence of stable models is np complete authors abstract

approximating operators and semantics for abstract dialectical frameworks we provide a systematic in depth study of the semantics of abstract dialectical frameworks adfs a recent generalisation of dung s abstract argumentation frameworks this is done by associating with an adf its characteristic one step consequence operator and defining various semantics for adfs as different fixpoints of this operator we first show that several existing semantical notions are faithfully captured by our definition then proceed to define new adf semantics and show that they are proper generalisations of existing argumentation semantics from the literature most remarkably this operator based approach allows us to compare adfs to related nonmonotonic formalisms like dung argumentation frameworks and propositional logic programs we use polynomial faithful and modular translations to relate the formalisms and our results show that both abstract argumentation frameworks and abstract dialectical frameworks are at most as expressive as propositional normal logic programs

modal nonmonotonic logics ranges characterization computation many nonmonotonic formalism including default logic logic programming with stable models and autoepistemic logic can be represented faithfully by means of modal nonmonotonic logics in the family proposed by mcdermott and doyle in this paper properties of logics in this family are thoroughly investigated we present several results on characterization of expansions these results are applicable to a wide class of nonmonotonic modal logics using these characterization results algorithms for computing expansions for finite theories are developed perhaps the most important finding of this paper is that the structure of the family of modal nonmonotonic logics is much simpler than that of the family of underlying modal monotonic logics namely it is often the case that different monotonic modal logics collapse to the same nonmonotonic system we exhibit four families of logics whose nonmonotonic variants coincide 5 kd45 tw5 sw5 n wk and w5 d4wb these nonmonotonic logics naturally represent logics related to commonsense reasoning and knowledge representation such as autoepistemic logic reflexive autoepistemic logic default logic and truth maintenance with negation

a hybrid variational collocation immersed method for fluid structure interaction using unstructured t splines summary we present a hybrid variational collocation immersed and fully implicit formulation for fluid structure interaction fsi using unstructured t splines in our immersed methodology we define an eulerian mesh on the whole computational domain and a lagrangian mesh on the solid domain which moves arbitrarily on top of the eulerian mesh mathematically the problem reduces to solving three equations namely the linear momentum balance mass conservation and a condition of kinematic compatibility between the lagrangian displacement and the eulerian velocity we use a weighted residual approach for the linear momentum and mass conservation equations but we discretize directly the strong form of the kinematic relation deriving a hybrid variational collocation method we use t splines for both the spatial discretization and the information transfer between the eulerian mesh and the lagrangian mesh t splines offer us two main advantages against non uniform rational b splines they can be locally refined and they are unstructured the generalized method is used for the time discretization we validate our formulation with a common fsi benchmark problem achieving excellent agreement with the theoretical solution an example involving a partially immersed solid is also solved the numerical examples show how the use of t junctions and extraordinary nodes results in an accurate efficient and flexible method copyright 2015 john wiley sons ltd

variationally consistent domain integration for isogeometric analysis abstract spline type approximations for solving partial differential equations are the basis of isogeometric analysis while the common approach of using integration cells defined by single knot spans using standard e g gaussian quadrature rules is sufficient for accuracy more efficient domain integration is still in high demand the recently introduced concept of variational consistency provides a guideline for constructing accurate and convergent methods requiring fewer quadrature points than standard integration techniques in this work variationally consistent domain integration is proposed for isogeometric analysis test function gradients are constructed to meet the consistency conditions which only requires solving small linear systems of equations the proposed approach allows for significant reduction in the number of quadrature points employed while maintaining the stability accuracy and optimal convergence properties of higher order quadrature rules several numerical examples are provided to illustrate the performance of the proposed domain integration technique

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

dispersion and pollution of the fem solution for the helmholtz equation in one two and three dimensions for high wave numbers the helmholtz equation suffers the so called pollution effect this effect is directly related to the dispersion a method to measure the dispersion on any numerical method related to the classical galerkin fem is presented this method does not require to compute the numerical solution of the problem and is extremely fast numerical results on the classical galerkin fem p method is compared to modified methods presented in the literature a study of the influence of the topology triangles is also carried out the efficiency of the different methods is compared the numerical results in two of the mesh and for square elements show that the high order elements control the dispersion well the most effective modified method is the qsfem 1 2 but it is also very complicated in the general setting the residual free bubble 3 4 is effective in one dimension but not in higher dimensions the least square method 1 5 approach lowers the dispersion but relatively little the results for triangular meshes show that the best topology is the criss cross pattern copyright 1999 john wiley sons ltd

b and f projection methods for nearly incompressible linear and non linear elasticity and plasticity using higher order nurbs elements abstract this paper presents projection methods to treat the incompressibility constraint in small and large deformation elasticity and plasticity within the framework of isogeometric analysis after reviewing some fundamentals of isogeometric analysis we investigate the use of higher order non uniform rational b splines nurbs within the b projection method the higher continuity property of such functions is explored in nearly incompressible applications and shown to produce accurate and robust results a new non linear f projection method based on a modified minimum potential energy principle and inspired by the b method is proposed for the large deformation case it leads to a symmetric formulation for which the consistent linearized operator for fully non linear elasticity is derived and used in a newton raphson iterative procedure the performance of the methods is assessed on several numerical examples and results obtained are shown to compare favorably with other published techniques

non monotonic logic i abstract non monotonic logical systems are logics in which the introduction of new axioms can invalidate old theorems such logics are very important in modeling the beliefs of active processes which acting in the presence of incomplete information must make and subsequently revise assumptions in light of new observations we present the motivation and history of such logics we develop model and proof theories a proof procedure and applications for one non monotonic logic in particular we prove the completeness of the non monotonic predicate calculus and the decidability of the non monotonic sentential calculus we also discuss characteristic properties of this logic and its relationship to stronger logics logics of incomplete information and truth maintenance systems

uniform semantic treatment of default and autoepistemic logics we revisit the issue of epistemological and semantic foundations for autoepistemic and default logics two leading formalisms in nonmonotonic reasoning we develop a general semantic approach to autoepistemic and default logics that is based on the notion of a belief pair and that exploits the lattice structure of the collection of all belief pairs for each logic we introduce a monotone operator on the lattice of belief pairs we then show that a whole family of semantics can be defined in a systematic and principled way in terms of fixpoints of this operator or as fixpoints of certain closely related operators our approach elucidates fundamental constructive principles in which agents form their belief sets and leads to approximation semantics for autoepistemic and default logics it also allows us to establish a precise one to one correspondence between the family of semantics for default logic and the family of semantics for autoepistemic logic the correspondence exploits the modal interpretation of a default proposed by konolige our results establish conclusively that default logic can be viewed as a fragment of autoepistemic logic a result that has been long anticipated at the same time they explain the source of the difficulty to formally relate the semantics of default extensions by reiter and autoepistemic expansions by moore these two semantics occupy different locations in the corresponding families of semantics for default and autoepistemic logics

a high order numerical approach with cartesian meshes for modeling of wave propagation and heat transfer on irregular domains with inhomogeneous materials abstract recently we have developed a new numerical approach for pdes with constant coefficients on irregular domains and cartesian meshes in this paper we extend it to a much more general case of pdes with variable coefficients that have a lot of applications e g the modeling of functionally graded materials the inhomogeneous materials obtained by 3 d printing and many others here we consider the 2 d wave and heat equations for isotropic and anisotropic inhomogeneous materials the idea of the extension to the case of pdes with variable coefficients is based on the representation of the stencil coefficients as functions of the mesh size this leads to the increase in the size of the local system of algebraic equations solved for each grid point of the new approach however this does not change the size of the global system of semidiscrete equations and practically does not increase the computational costs of the proposed technique similar to our previous technique the new 2 d approach with compact 9 point stencils uses trivial cartesian meshes for complex irregular domains and provides the fourth order of accuracy for the wave and heat equations with variable coefficients the calculation of the coefficients of the stencil equations is based on the minimization of the local truncation error of the stencil equations and yields the optimal order of accuracy of the new technique at similar 9 point stencils the accuracy of the new approach is much higher than that for the linear finite elements the numerical results for irregular domains show that at the same number of degrees of freedom the new approach is even much more accurate than the high order up to the third order finite elements with much wider stencils the wave and heat equations are uniformly treated with the new approach