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In this paper, we develop the Hermite-type virtual element method to solve the second order problem. A Hermite-type virtual element of degree ≥3 is constructed, which can be taken as an extension of classical Hermite finite element to polygonal meshes. For this virtual element, we rigorously prove some inverse inequalities and the boundedness of basis functions. Further, we prove the interpolation error estimates. Based on a computable H 1 -projection, we give the discrete formulation and prove the optimal convergence for the Hermite-type virtual element method. Finally, we show some numerical results to verify the convergence of Hermite-type virtual element. Additionally, compared with other virtual elements, both theoretical analysis and numerical experiments demonstrate that the Hermite-type virtual element has fewer global degrees of freedom and results in significant computational savings. [ABSTRACT FROM AUTHOR]

This paper proposes and analyzes a stabilized embedded discontinuous Galerkin (EDG) method for linear elasticity problems. A stabilized term is added in the scheme to ensure locking-free approximations. With a special designed interpolation, we prove the Stokes stable elements in space [ H 0 1 (Ω) ] d × L 0 2 (Ω) are also stable in [ H D 1 (Ω) ] d × L 2 (Ω) on general simplicial mesh, and therefore, we prove the underlying EDG method is robust in the sense that the derived a priori error estimates are optimal and uniform with respect to the Lamé constant λ. Numerical experiments are provided to verify the theoretical results. [ABSTRACT FROM AUTHOR]

This paper presents a thorough experimental/numerical validation of optimised multi-material structures fabricated by material jetting technology. The proposed methodology uses, on the one hand, non-uniform rational basis spline (NURBS) entities to represent the geometric descriptor associated with each material phase constituting the continuum and, on the other hand, a general multi-phase material interpolation scheme to penalise the stiffness tensor of the structure. Two design requirements are included in the problem formulation: the lightness and the minimum length scale of each material phase. The influence of the integer parameters intervening in the definition of the NURBS entity and the influence of different combinations of material phases on the optimised solutions are investigated. The proposed approach is applied to 2D and 3D benchmark structures subjected to prescribed displacements representative of a three-point bending test. Based on the result of the topology optimisation process one of the optimised solutions, balancing the requirements of structural stiffness, lightness, and manufacturing constraints, is selected, manufactured and tested. A comparison between experimental and numerical results (obtained by non-linear analyses) is carried out to show the effectiveness of the approach. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a construction of Marsden's identity for UAH B-splines (i.e. Uniform Algebraic Hyperbolic B-splines) is developed and a clear proof is given. With the help of this identity, quasi-interpolant schemes that produce the space of algebraic hyperbolic functions are derived. Efficient quadrature rules, based on integrating some of these quasi-interpolant schemes, are constructed and studied. Numerical results that illustrate the effectiveness of these rules are presented. [ABSTRACT FROM AUTHOR]

Abstract In this paper, controllability and observability matrices for pseudo upper or lower triangular multi-order fractional systems are derived. It is demonstrated that these systems are controllable and observable if and only if their controllability and observability matrices are full rank. In other words, the rank of these matrices should be equal to the inner dimension of their corresponding state space realizations. To reduce the computational complexities, these matrices are converted to simplified matrices with smaller dimensions. Numerical examples are provided to show the usefulness of the mentioned matrices for controllability and observability analysis of this case of multi-order fractional systems. These examples clarify that the duality concept is not necessarily true for these special systems. Highlights • Controllability and observability matrices for pseudo upper and lower triangular multi-order fractional systems are proposed. • The proposed matrices do not depend on the fractional orders. • The optimum dimensions of the proposed matrices are extracted. [ABSTRACT FROM AUTHOR]

Abstract In this paper, the superconvergence analysis of a two-grid method (TGM) is established for the semilinear parabolic equations. Based on the combination of the interpolation and Ritz projection technique, an important ingredient in the method, the superclose estimates in the H 1 -norm are deduced for the backward Euler fully-discrete TGM scheme. Moreover, through the interpolated postprocessing approach, the corresponding global superconvergence result is derived. Finally, some numerical results are provided to confirm the theoretical analysis, and also show that the computing cost of the proposed TGM is only half of the conventional Galerkin finite element methods (FEMs). [ABSTRACT FROM AUTHOR]

A. Horn's problem concerns finding two self adjoint matrices, so that A , B , and A + B have prescribed spectrum. In this paper, we show how it connects to an interpolation problem for two variable real zero polynomials and a tracial moment problem. In addition, we outline an algorithm to construct a pair ( A , B ) . [ABSTRACT FROM AUTHOR]

In this paper, we consider the numerical solution of the time fractional Fokker-Planck equation. We propose a spectral collocation method in both temporal and spatial discretizations with a spectral expansion of Jacobi interpolation polynomial for this equation. The convergence of the method is rigorously established. Numerical tests are carried out to confirm the theoretical results. [ABSTRACT FROM AUTHOR]

The aim of this paper is a construction of parametric polynomial interpolants of a circular arc possessing maximal geometric smoothness. Two boundary points of a circular arc are interpolated together with higher order geometric data. Construction of interpolants is done via a complex factorization of the implicit unit circle equation. The problem is reduced to solving only one nonlinear equation determined by a monotone function and the existence of the solution is proven for any degree of the interpolating polynomial. Precise starting points for the Newton–Raphson type iteration methods are provided and the best solutions are then given in a closed form. Interpolation by parametric polynomials of degree up to six is discussed in detail and numerical examples confirming theoretical results are included. [ABSTRACT FROM AUTHOR]

In this paper, a new approach of superconvergent estimate of bilinear finite element is established for two-dimensional time-fractional diffusion equation under fully-discrete scheme. The novelty of this approach is the combination technique of the interpolation and Ritz projection as well as the superclose estimate in H 1 -norm between them, which avoids the difficulty of constructing a postprocessing operator for Ritz projection operator, and reduces the regularity requirement of the exact solution. At the same time, three numerical examples are carried out to verify the theoretical analysis. [ABSTRACT FROM AUTHOR]

Interpolation operators are important for many applications in scientific computing. During numerical simulations and especially in the context of anisotropic mesh adaptation, with highly stretched elements, the interpolation step is crucial. However, it reduces conservation of important physical quantities and leads to errors that spoil the solution accuracy. In this paper we present a globally conservative method suitable for both interpolations on unstructured fixed and adaptive anisotropic meshes. It consists in combining an a posteriori error estimator that minimizes the interpolation error of the finite element solution followed by an interpolation with restrictions method that conserves physical properties of the field being interpolated. Several numerical examples, in 2D and 3D, are presented and validated to illustrate the efficiency of the approach. [ABSTRACT FROM AUTHOR]

This paper proposes a packet loss concealment (PLC) method based on redundant information to enhance speech quality under severe network conditions as well as a new model to simulate packet loss effect, end-to-end transmission delay, and jitter on the concealment process. Our proposed method increases the efficiency of the standard ITU-T G.722.2 by improving the quality of the decoded speech under random frame loss conditions over packet-switched networks. The new method achieves a MUltiple Stimuli with Hidden Reference and Anchor (MUSHRA) value exceeding 48.7 at a 20% packet loss ratio (PLR). Numerical analysis indicates that our method outperforms existing alternatives and can be successfully used, even in severe propagation scenarios at the expense of an increase in processing requirements. • The proposed method allows a good recovery of portions where there are transitions of pitch. • The proposed method allows a good recovery of portions between voiced/unvoiced portions. • We proposed a packet loss model to simulate the packet loss. • It also simulates the influence of end-to-end transmission delay and jitter. • We have used EMBSD and MUSHRA as subjective and objective metrics. • The average latency is linearly dependent on the jitter value. [ABSTRACT FROM AUTHOR]

This paper proposes a novel curve modeling method based on an envelope curve template. As the theoretical basis for the envelope template, a family of interpolating curves is generated by repeated interpolation of the given data points. On this basis, a family of one-parameter interpolating cylindrical surfaces is introduced, and then the envelope condition and its envelope surface are given, and the directrix of which serves as the prototype for curve modeling. After analyzing the geometric properties of the directrix of the envelope, the continuity conditions of two adjacent curve segments at the common point are derived. At a technical level, an envelope curve template is constructed, and the expected G 2 or C 2 composite curves can be obtained utilizing the envelope template sweeping over the data points. [ABSTRACT FROM AUTHOR]

A theorem of Hoischen states that given a positive continuous function ε : R n → R , an unbounded sequence 0 ≤ c 1 ≤ c 2 ≤ … and a closed discrete set T ⊆ R n , any C ∞ function g : R n → R can be approximated by an entire function f so that for k = 0 , 1 , 2 , …  , for all x ∈ R n such that | x | ≥ c k , and for each multi-index α such that | α | ≤ k , (a) | ( D α f ) ( x ) − ( D α g ) ( x ) | < ε ( x ) ; (b) ( D α f ) ( x ) = ( D α g ) ( x ) if x ∈ T . In this paper, we show that if C ⊆ R n + 1 is meager, A ⊆ R n is countable and disjoint from T , and for each multi-index α and p ∈ A we are given a countable dense set A p , α ⊆ R , then we can require also that (c) ( D α f ) ( p ) ∈ A p , α for p ∈ A and α any multi-index; (d) if x ∉ T , q = ( D α f ) ( x ) and there are values of p ∈ A arbitrarily close to x for which q ∈ A p , α , then there are values of p ∈ A arbitrarily close to x for which q = ( D α f ) ( p ) ; (e) for each α , { x ∈ R n : ( x , ( D α f ) ( x ) ) ∈ C } is meager in R n . Clause (d) is a surjectivity property whose full statement in the text also allows for finding solutions in A to equations of the form q = h ⁎ ( x , ( D α f ) ( x ) ) under similar assumptions, where h ( x , y ) = ( x , h ⁎ ( x , y ) ) is one of countably many given fiber-preserving homeomorphisms of open subsets of R n + 1 ≅ R n × R . We also prove a weaker corresponding result with “meager” replaced by “Lebesgue null.” In this context, the approximating function is C ∞ rather than entire, and we do not know whether it can be taken to be entire. The first result builds on earlier work of the author which deduced special cases of it from forcing theorems using absoluteness arguments. The proofs here do not use forcing. [ABSTRACT FROM AUTHOR]

We present a simple and effective Chebyshev polynomial scheme (CPS) combined with the method of fundamental solutions (MFS) and the equilibrated collocation Trefftz method for the numerical solutions of inhomogeneous elliptic partial differential equations (PDEs). In this paper, CPS is applied in a two-step approach. First, Chebyshev polynomials are used to approximate a particular solution of a PDE. Chebyshev nodes which are the roots of Chebyshev polynomials are used in the polynomial interpolation due to its spectral convergence. Then the resulting homogeneous equation is solved by boundary type methods including the MFS and the equilibrated collocation Trefftz method. Numerical results for problems on various irregular domains show that our proposed scheme is highly accurate and efficient. [ABSTRACT FROM AUTHOR]

Image resolution enhancement or super-resolution (SR) problem generates a high resolution (HR) image from one or a set of low resolution (LR) images. In the past two decades, a wide variety of resolution enhancement algorithms have been proposed. These methods are confined to small scaling factors. This paper presents a novel single image resolution enhancement algorithm in wavelet domain which operates at high scaling factors. First, we perform subband decomposition on the input LR image by using discrete wavelet transform (DWT). It decomposes the LR image into different frequency subbands namely low-low (LL), low-high (LH), high-low (HL) and high-high (HH). In parallel we apply sparse representation based interpolation method on the LR image. Next, we process the three high frequency subbands in wavelet domain by applying bicubic interpolation. Finally, the interpolated high frequency subbands in addition to the sparse recovered solution are combined to produce a HR image using inverse discrete wavelet transform (IDWT). Experiments on different LR test images demonstrate that our approach produces relatively less artifacts compared to the existing methods. [ABSTRACT FROM AUTHOR]

Piecewise biquadratic B-Spline surface satisfying biharmonic condition is studied in this paper. By applying biharmonic PDE, biquadratic B-Spline surface is fully determined by boundary control vertices. A linear system for solving inner control vertices is established. Its coefficient matrix is block tridiagonal and the proof of non-singularity of coefficient matrix is presented under the condition that all knots do not coincide with each other. A few examples are given to show the effectiveness of piecewise biharmonic biquadratic B-Spline surface. An interpolation method on given boundary points is presented if boundary curves are open. [ABSTRACT FROM AUTHOR]

In this paper we investigate the problem of interpolating a B-spline curve network, in order to create a surface satisfying such a constraint and defined by blending functions spanning the space of bivariate C 1 quadratic splines on criss–cross triangulations. We prove the existence and uniqueness of the surface, providing a constructive algorithm for its generation. We also present numerical and graphical results and comparisons with other methods. [ABSTRACT FROM AUTHOR]

The Strong Discontinuity embedded Approach (SDA) has proved to be a robust numerical method for simulating fracture of quasi-brittle materials such as glass and concrete. Three different numerical formulations are used in the SDA: (i) Statically Optimal Symmetric (SOS), (ii) Kinematically Optimal Symmetric (KOS), (iii) Statically and Kinematically Optimal Nonsymmetric (SKON). While the SOS formulation (standard version) of the SDA is simple for coding and provides good numerical stability (considering standard Galerkin method), several researchers have pointed out that this formulation encounters serious stress-locking. In this paper, an SOS formulation of the SDA is presented, considering elements with linear and quadratic interpolation for the displacement field. The performance of the proposed model of crack simulation is investigated by re-analysis of a pulling test, a three-point bending test, and an L-shaped panel with prescribed crack paths. The obtained results show that elements with linear interpolation encounter significant stress-locking, whereas elements with quadratic interpolation give good results without locking. Based on the eight-node quadrilateral element, which showed the best performance in the aforementioned re-analysis of the tests, an energy-based crack-tracking strategy, originally used in the framework of the XFEM, is modified and implemented into the SDA model. Several numerical benchmark tests, including an L-shaped panel test, a tension-shear test, a notched panel test, four-point bending tests with single and double notches, and a pull-out test are performed, illustrating the good performance with respected to the SDA model and the robustness of the proposed crack-tracking strategy. [ABSTRACT FROM AUTHOR]

Using reversible data hiding (RDH) we can hide our secret data into a cover image and the receiver can restore both the secret data and the original image. It has wide application in medical imagery, military imagery where no distortion of original cover is allowed. Hong and Chen proposed a RDH scheme based on interpolation and histogram shifting. In their scheme reference pixels are not used for data embedding which leads to low capacity. Huang et al. modified this scheme and proposed a high capacity RDH scheme in which prediction errors are used for data embedding. In this paper we propose a further modification to the scheme of Huang et al. based on directional interpolation. Directional interpolation yields a better approximation to the original pixel which improves the capacity of embedding. The effectiveness of the proposed scheme is tested using standard test images and the proposed scheme gives better results in terms of embedding capacity and visual quality compared to Huang et al. scheme. [ABSTRACT FROM AUTHOR]

This paper deals with the numerical analysis of a finite element projection-based VMS turbulence model that includes general non-linear wall laws. Only a single mesh and interpolation operators on a virtual coarser mesh are needed to implement the model. We include a projection-stabilization of pressure to use the same interpolation for velocity and pressure. Good accuracy is obtained with benchmark turbulent flow problems on coarse grids, that justify the interest of this approach. Also, the model solves smooth flows with optimal accuracy. [ABSTRACT FROM AUTHOR]

This paper presents a method to design servo controllers for flexible ball screw drives with time-varying dynamics, which are mainly due to the time-varying table position and the workpiece mass. A gain-scheduled H∞ loop shaping controller is designed to achieve high tracking performance against the dynamic variations. H∞ loop shaping design procedure incorporates open loop shaping by a set of compensators to obtain performance/robust stability tradeoffs. The interpolating gain-scheduled controller is obtained by interpolating the state space model of the linear time-invariant (LTI) controllers estimated for fixed values of the scheduling parameters and a linear least squares problem can be solved. The proposed controller has been compared with P/PI with velocity and acceleration feedforward and adaptive backstepping sliding mode control experimentally. The experimental results indicate that the tracking performance has been improved and the robustness for time-varying dynamics has been achieved with the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper presents a biarc-based subdivision scheme for space curve interpolation. Given a sequence of space points, or a sequence of space points and tangent vectors, the scheme produces a smooth curve interpolating all input points by iteratively inserting new points and computing new tangent vectors. For each step of subdivision, the newly inserted point corresponding to an existing edge is a specified joint point of a biarc curve which interpolates the two end points and the tangents. A provisional tangent is also assigned to the newly inserted point. Each of the tangents for the following subdivision step is further updated as a linear blending of the provisional tangent and the tangent at the respective point of a circle passing through the local point and its two adjacent points. If adjacent four initial points and their initial reference tangent vectors are sampled from a spherical surface, the limit curve segment between the middle two initial points exactly lies on the same spherical surface. The biarc based subdivision scheme is proved to be G 1 continuous with a nice convexity preserving property. Numerical examples also show that the limit curves are G 2 continuous and fair. Several examples are given to demonstrate the excellent properties of the scheme. [ABSTRACT FROM AUTHOR]

As a truly boundary-type meshless method, the hybrid boundary node method (HdBNM) does not require ‘boundary element mesh’, either for the purpose of interpolation of the solution variables or for the integration of ‘energy’. In this paper, the HdBNM is coupled with the finite element method (FEM) for predicting the mechanical behaviors of reinforced concrete. The steel bars are considered as body forces in the concrete. A bond model is presented to simulate the bond-slip between the concrete and steels using fictitious spring elements. The computational scale and cost for meshing can be further reduced. Numerical examples, in 2D and 3D cases, demonstrate the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, the center finite difference (CFD) method for the elliptic equation is deduced by the P 1 -element and the first-order discrete partial differential equation over the dual element K ∗ in the 1D or 2D domain. Next, the coefficient matrix of the CFD method is explicitly reduced and the H 1 -stability and convergence of the CFD solution u h is provided. Furthermore, the H 1 -super-convergence of u h to I h u is obtained under the case of the almost-uniform mesh. Based on the H 1 -super-convergence of u h to I h u , the optimal L 2 -error estimate of the numerical solution u h and the H 1 -super-convergence error estimate of the interpolation solution I 2 h 2 u h are derived respectively. Finally, some numerical tests are made to show the analytical results of the CFD method. [ABSTRACT FROM AUTHOR]

Cubic biarcs are the natural counterpart, in the context of the PH spatial Hermite interpolation, of piecewise quadratics for Hermite interpolation of standard parametric curves. Recently, it has been shown that, spatial Hermite interpolation can be always treated with PH cubic biarcs, providing an interesting alternative to the use of higher degrees, see Bastl et al. (2014) . Beside the parameter value at the joint of the two arcs, which is typically free in any scheme of this kind, two free angular parameters remain. They should be automatically fixed by some suitable criterion in order to ensure the generation of interpolants with a reasonable shape. In this paper, an alternative to the constant choice of free parameters presented in Bastl et al. (2014) is proposed. It consists of an extension of the so called CC selection strategy introduced in Farouki et al. (2008) to the biarc setting. Such strategy is fully data-dependent, does not require any special configuration of the coordinate system and it guarantees the PH cubic reproduction when such kind of the interpolant exists. Moreover, the obtained scheme possesses other two important features, i.e. it is third order accurate and gives the possibility to control the torsion sign of the produced interpolant, in case with the introduction of an additional tension parameter relaxing the smoothness from C 1 to G 1 . The numerical results, based also on the straightforward spline extension of the scheme, confirm the developed theoretical analysis. [ABSTRACT FROM AUTHOR]