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Highlights • A finite-buffer vacation queue with batch Markovian arrival process has been analyzed. • The server is subjected to serve under gated-limited service discipline. • Proposed analysis is based on the successive substitution and the supplementary variable method. • The results have been matched with the corresponding infinite-buffer queue. • Numerical results are presented for different service- and vacation-time distributions. Abstract This paper analyzes the finite-buffer single server queue with vacation(s). It is assumed that the arrivals follow a batch Markovian arrival process (BMAP) and the server serves customers according to a non-exhaustive type gated-limited service discipline. It has been also considered that the service and vacation distributions possess rational Laplace-Stieltjes transformation (LST) as these types of distributions may approximate many other distributions appeared in queueing literature. Among several batch acceptance/rejection strategies, the partial batch acceptance strategy is discussed in this paper. The service limit L (1 ≤ L ≤ N) is considered to be fixed, where N is the buffer-capacity excluding the one in service. It is assumed that in each busy period the server continues to serve until either L customers out of those that were waiting at the start of the busy period are served or the queue empties, whichever occurs first. The queue-length distribution at vacation termination/service completion epochs is determined by solving a set of linear simultaneous equations. The successive substitution method is used in the steady-state equations embedded at vacation termination/service completion epochs. The distribution of the queue-length at an arbitrary epoch has been obtained using the supplementary variable technique. The queue-length distributions at pre-arrival and post-departure epoch are also obtained. The results of the corresponding infinite-buffer queueing model have been analyzed briefly and matched with the previous model. Net profit function per unit of time is derived and an optimal service limit and buffer-capacity are obtained from a maximal expected profit. Some numerical results are presented in tabular and graphical forms. [ABSTRACT FROM AUTHOR]

The search for multivariate quadrature rules of minimal size with a specified polynomial accuracy has been the topic of many years of research. Finding such a rule allows accurate integration of moments, which play a central role in many aspects of scientific computing with complex models. The contribution of this paper is twofold. First, we provide novel mathematical analysis of the polynomial quadrature problem that provides a lower bound for the minimal possible number of nodes in a polynomial rule with specified accuracy. We give concrete but simplistic multivariate examples where a minimal quadrature rule can be designed that achieves this lower bound, along with situations that showcase when it is not possible to achieve this lower bound. Our second contribution is the formulation of an algorithm that is able to efficiently generate multivariate quadrature rules with positive weights on non-tensorial domains. Our tests show success of this procedure in up to 20 dimensions. We test our method on applications to dimension reduction and chemical kinetics problems, including comparisons against popular alternatives such as sparse grids, Monte Carlo and quasi Monte Carlo sequences, and Stroud rules. The quadrature rules computed in this paper outperform these alternatives in almost all scenarios. [ABSTRACT FROM AUTHOR]

This paper estimates stress intensity factors of rotating solid disks or cylinders with a radial crack subjected to a uniform tension at their outer surface and a uniform temperature change through the body. Material properties of the cylinder are assumed to obey from the power law through the radius of the cylinder. The cracks are assumed to be small and located radially at center, inside or edge of the body. The stress intensity factors are obtained applying an approximate method and using the proper geometric functions for combination of the thermomechanical stresses. The method proposed in this paper is imposed to isotropic FG plates with an edge slanted crack to quantify the difference between present method and numerical methods given in the literature review. Also, the SIFs obtained for the non-homogeneous cylinder are reduced to the homogeneous one and are compared with the corresponding exact solution of isotropic materials. [ABSTRACT FROM AUTHOR]

Abstract Field experiments of solute transport through heterogeneous porous and fractured media show that the growth of contaminant plumes may convert between diffusive states. In this paper, we propose a multi-term time–space variable-order fractional advection–diffusion model (MTT-SVO-FADM) to describe the underlying transport dynamics. We consider a numerical approach based on the implicit numerical method for numerical solution of this model. A fully-discrete numerical scheme is developed by using the classical finite difference method. The unconditional stability and convergence of the scheme are discussed and theoretically proved. We use a modified grid approximation method (MGAM) to estimate the model's parameters. The MTT-SVO-FADM is then applied to describe transient dispersion observed at a field tracer test and four numerical experiments. The results show that this model can simulate the experimental data more accurately and can efficiently quantify these transitions. Highlights • A multi-term time–space variable-order fractional advection–diffusion model is proposed. • A fully-discrete numerical scheme is developed. • The unconditional stability and convergence of the scheme are discussed and proved. • A modified grid approximation method is used to estimate the model's parameters. • This model is applied to describe transient dispersion observed at a field tracer test and four numerical experiments. [ABSTRACT FROM AUTHOR]

Abstract In this paper, our main aim is to investigate the stability and strong convergence of an implicit numerical approximations for neutral-type stochastic differential equations with superlinearly growing coefficients. After providing moment boundedness and exponential stability for the exact solutions, we show that the backward Euler–Maruyama numerical method preserves stability and boundedness of moments, and the numerical approximations converge strongly to the true solutions for sufficiently small step size. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we construct wavelet tight frames with n vanishing moments for Dubuc–Deslauriers 2 n -point semi-regular interpolatory subdivision schemes. Our motivation for this construction is its practical use for further regularity analysis of wide classes of semi-regular subdivision. Our constructive tools are local eigenvalue convergence analysis for semi-regular Dubuc–Deslauriers subdivision, the Unitary Extension Principle and the generalization of the Oblique Extension Principle to the irregular setting by Chui, He and Stöckler. This group of authors derives suitable approximation of the inverse Gramian for irregular B-spline subdivision. Our main contribution is the derivation of the appropriate approximation of the inverse Gramian for the semi-regular Dubuc–Deslauriers scaling functions ensuring n vanishing moments of the corresponding framelets. [ABSTRACT FROM AUTHOR]

Abstract This paper deals with the a priori error analysis for a convection-dominated diffusion 2D problem, when applying the HDG method on a family of anisotropic triangulations. It is known that in this case, boundary or interior layers may appear. Therefore, it is important to resolve these layers in order to recover, if possible, the expected order of approximation. In this work, we extend the use of HDG method on anisotropic meshes. In this context, when the discrete local spaces are polynomials of degree k ≥ 0 , this approach is able to recover an order of convergence k + 1 2 in L 2 for all the variables, under certain assumptions on the stabilization parameter and family of triangulations. Numerical examples confirm our theoretical results. Highlights • We develop an a priori error analysis for a HDG scheme defined on anisotropic meshes that are made of triangles. • We require that the family of triangulations satisfy the maximum angle condition, which is usual in this case. • We include numerical examples that validate our theoretical results. [ABSTRACT FROM AUTHOR]

Highlights • The Sturm sequence number is applied to adaptively determine the number of the lowest modes that need to be calculated. • The complementary part of contribution of the computed modes is approximated by a partial sum of a convergent power series. • The number of items in the partial sum are adaptively determined by the highest excitation frequency only. • The resulting expressions are efficient for the entire range of excitation frequencies of interest. • The proposed method can significantly reduce the computational cost. Abstract This paper presents a numerical method for calculating the frequency response and its sensitivity of an undamped system in a frequency interval. The Sturm sequence number is first used to adaptively determine the number of the lowest modes that need to be calculated. The corresponding modes can be computed by the Lanczos or subspace iteration methods. The complementary portion of contribution of these computed modes is then transformed into the solution to a new system by using the mass orthogonality. The solution of the new system is approximated by the partial sum of the convergent power series of the excitation frequencies, and the number of items therein can be adaptively determined by utilizing only the highest excitation frequency. The sensitivity expression of the frequency response is also established. The resulting expressions of the frequency response and its sensitivity are valid for the entire range of excitation frequencies of interest. By changing only the excitation frequency, we can obtain frequency responses and their sensitivities. This computational methodology is illustrated by its applications to two examples. The results show that the proposed method can remarkably reduce the CPU time required by the direct method. [ABSTRACT FROM AUTHOR]

Abstract This work proposes a locally stabilized central difference method for time domain analyses, which performs considering the relation between the adopted temporal and spatial discretizations. Here, the standard expressions of the Central Difference Method (CDM) are considered to approximate the time derivatives of the incognita field, and the local (or element) matrices of the spatially discretized model are modified, if the stability criterion of the CDM is not locally fulfilled. Thus, a locally defined time marching methodology is provided, which may be up to fourth order accurate, has guaranteed stability, enhanced precision, and is highly efficient and versatile. The new technique may be stated as a semi-explicit/explicit approach; in this context, just reduced systems of equations have to be dealt with in the analyses and iterative procedures are never required, when nonlinear models are focused. In addition, the new technique is also very simple to implement and entirely automatized, requiring no decision or expertise from the user. Numerical results are presented along the paper, illustrating the performance and effectiveness of the new approach. Highlights • An effective time-marching procedure is proposed for nonlinear dynamics. • It is locally defined, introducing modified elements to guarantee stability. • The method has enhanced accuracy, it is simple and entirely automatized. • It enables reduced solver efforts and it stands as a non-iterative procedure. [ABSTRACT FROM AUTHOR]

Abstract This paper was dealt with buckling and post-buckling behavior of short thin-walled Z-columns made of a carbon-epoxy laminate, subjected to eccentric compressive load. The buckling mode and the buckling load of real structures versus load eccentricity were discussed. The study involved both experimental tests were carried out on real laminated structures and numerical simulations by the finite element method. The buckling load of real structures was determined by approximation methods on the basis of experimental and numerical post-buckling equilibrium paths of the structure. Additionally, in numerical simulations, the bifurcation load value was determined by solving an eigen problem. In all cases, experimental findings and numerical results show high agreement. The study determined the quantitative influence of the direction and value of compressive load eccentricity on the buckling load and rigidity of the structure in the post-buckling state. [ABSTRACT FROM AUTHOR]

Abstract This paper introduces a high-order time stepping scheme, that is based on using Fourier spectral in space and a fourth-order diagonal Padé approximation to the matrix exponential function for solving multi-dimensional space-fractional reaction–diffusion equations. The resulting time stepping scheme is developed based on an exponential time differencing approach such that it alleviates solving a large non-linear system at each time step while maintaining the stability of the scheme. The non-locality of the fractional operator in some other numerical schemes for these equations leads to full and dense matrices. This scheme is able to overcome such computational inefficiency due to the full diagonal representation of the fractional operator. It also attains spectral convergence for multiple spatial dimensions. The stability of the scheme is discussed through the investigation of the amplification symbol and plotting its stability regions, which provides an indication of the stability of the method. The convergence analysis is performed empirically to show that the scheme is fourth-order accurate in time, as expected. Numerical experiments on reaction–diffusion systems with application to pattern formation are discussed to show the effect of the fractional order in space-fractional reaction–diffusion equations and to validate the effectiveness of the scheme. [ABSTRACT FROM AUTHOR]

The efficient solution of coupled PDEs/ODEs problems arising in cardiac electrophysiology is of key importance whenever interested to study the electrical behavior of the tissue for several instances of relevant physical and/or geometrical parameters. This poses significant challenges to reduced order modeling (ROM) techniques –such as the reduced basis method –traditionally employed when dealing with the repeated solution of parameter dependent differential equations. Indeed, the nonlinear nature of the problem, the presence of moving fronts in the solution, and the high sensitivity of this latter to parameter variations, make the application of standard ROM techniques very problematic. In this paper we propose a local ROM built through a k -means clustering in the state space of the snapshots for both the solution and the nonlinear term. Several comparisons among alternative local ROMs on a benchmark test case show the effectivity of the proposed approach. Finally, the application to a parametrized problem set on an idealized left-ventricle geometry shows the capability of the proposed ROM to face complex problems. [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 propose an iterative numerical method for approximating solutions of fractional integral equations of the second kind, based on Picard iteration and a suitable quadrature formula. Under certain conditions, we prove the existence and uniqueness of the solution and give error estimates of the approximations. Numerical examples are given, which illustrate the good approximations. [ABSTRACT FROM AUTHOR]

This paper is devoted to construct approximations of the probability density function of the non-autonomous first-order homogeneous linear random differential equation, where the initial condition and the diffusion coefficient are assumed to be a random variable and a stochastic process, respectively. We combine Random Variable Transformation technique and Karhunen–Loève expansion to construct reliable approximations under general conditions. Several numerical examples illustrate our theoretical findings. [ABSTRACT FROM AUTHOR]

This paper is on numerical treatment of problems that describe high contrast composite materials with complex geometry. In particular, a heterogeneous domain decomposition method for a class of diffusion problems with rapidly oscillating coefficients that also have large variation of values within the domain is proposed. The method combines a FEM discretization in one subdomain with an asymptotic representation of the Dirichlet to Neumann map for the other subdomain. Numerical results that demonstrate the feasibility of the proposed approach are also provided. [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]

Particle-based methods based on material models using spheres can provide good approximations for many physical phenomena at both the micro and macroscales. The point of departure for the simulations, in general, is a dense arrangement of spherical particles (sphere pack) inside a given container. For generic domains, the generation of a sphere pack may be complex and time-consuming, especially if the pack must comply with a prescribed sphere size distribution and the stability requirements of the simulation. The primary goal of this paper is to present an efficient algorithm that is capable of producing packs with millions of spheres following a statistical sphere size distribution inside complex arbitrary domains. This algorithm uses a new strategy to ensure that the sphere size distribution is preserved even when large particles are rejected in the growing process. The paper also presents numerical results that enable an evaluation of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The paper presents a numerical procedure for solving a class of optimal control problems for heterogeneous systems. The latter are described by parameterized systems of ordinary differential equations, coupled by integrals along the parameter space. Such problems arise in economics, demography, epidemiology, management of biological resources, etc. The numerical procedure includes discretization and a gradient projection method for solving the resulting discrete problem. A main point of the paper is the performed error analysis, which is based on the property of metric regularity of the system of necessary optimality conditions associated with the considered problem. [ABSTRACT FROM AUTHOR]

In this paper, we propose an a posteriori error estimator for the numerical approximation of a stochastic magnetostatic problem, whose solution depends on the spatial variable but also on a stochastic one. The spatial discretization is performed with finite elements and the stochastic one with a polynomial chaos expansion. As a consequence, the numerical error results from these two levels of discretization. In this paper, we propose an error estimator that takes into account these two sources of error, and which is evaluated from the residuals. [ABSTRACT FROM AUTHOR]

This paper reports a multiscale asymptotic analysis and computation for predicting heat transfer performance of periodic porous materials with radiation boundary condition. In these porous materials thermal radiation effect at micro-scale have an important impact on the macroscopic temperature field, which is our particular interest in this study. The multiscale asymptotic expansions for computing temperature field of the problem are constructed, and associated explicit convergence rates are obtained on some regularity hypothesis. Finally, the corresponding finite element algorithms based on the multiscale method are brought forward and some numerical results are given in details. The numerical tests indicate that the developed method is feasible and valid for predicting the heat transfer performance of periodic porous materials, and support the approximate convergence results proposed in this paper. [ABSTRACT FROM AUTHOR]

This paper is concerned with the solution of large-scale linear discrete ill-posed problems. The determination of a meaningful approximate solution of these problems requires regularization. We discuss regularization by the Tikhonov method and by truncated iteration. The choice of regularization matrix in Tikhonov regularization may significantly affect the quality of the computed approximate solution. The present paper describes the construction of square regularization matrices from finite difference equations with a focus on the boundary conditions. The regularization matrices considered have a structure that makes them easy to apply in iterative methods, including methods based on the Arnoldi process. Numerical examples illustrate the properties and effectiveness of the regularization matrices described. [ABSTRACT FROM AUTHOR]

The problem of spinning-up an axially symmetric spacecraft subjected to an external torque constant in magnitude and parallel to the symmetry axis is considered. The existing exact analytic solution for an axially symmetric body is applied for the first time to this problem. The proposed solution is valid for any initial conditions of attitude and angular velocity and for any length of time and rotation amplitude. Furthermore, the proposed solution can be numerically evaluated up to any desired level of accuracy. Numerical experiments and comparison with an existing approximated solution and with the integration of the equations of motion are reported in the paper. Finally, a new approximated solution obtained from the exact one is introduced in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we significantly extend the applicability of state-of-the-art ELDP (equations for linearizing discrete product terms) method by providing a new linearization to handle more complicated non-linear terms involving both of discrete and bounded continuous variables. A general class of “representable programming problems” is formally proposed for a much wider range of engineering applications. Moreover, by exploiting the logarithmic feature embedded in the discrete structure, we present an enhanced linear reformulation model which requires half an order fewer equations than the original ELDP. Computational experiments on various engineering design problems support the superior computational efficiency of the proposed linearization reformulation in solving engineering optimization problems with discrete and bounded continuous variables. [ABSTRACT FROM AUTHOR]

This paper gives a theoretical proof that the one dimensional (1D) Willis-form equations with displacement coupling terms can retain time synchronization under spatial transformations. This is also supported by a numerical example that compares the distributions of the wave velocities of an inhomogeneous material calculated by the Willis-form equations and the classical elastodynamic equations, respectively. It further demonstrates that the classical elastodynamic equations are good approximations of the Willis-form equations only when the wave frequency is sufficiently high. These findings serve as additional evidence of the validity of the Willis-form equations for inhomogeneous media. [ABSTRACT FROM AUTHOR]

In this paper a time-fractional Black–Scholes equation is examined. We transform the initial value problem into an equivalent integral–differential equation with a weakly singular kernel and use an integral discretization scheme on an adapted mesh for the time discretization. A rigorous analysis about the convergence of the time discretization scheme is given by taking account of the possibly singular behavior of the exact solution and first-order convergence with respect to the time variable is proved. For overcoming the possibly nonphysical oscillation in the computed solution caused by the degeneracy of the Black–Scholes differential operator, we employ a central difference scheme on a piecewise uniform mesh for the spatial discretization. It is proved that the scheme is stable and second-order convergent with respect to the spatial variable. Numerical experiments support these theoretical results. [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]

In this paper, the dynamics of a viscoelastic plate resting on a viscoelastic Winkler foundation and traversed by a moving mass is studied. The Laplace transform is employed to derive the governing equation of the problem. Thereafter, an analytical-numerical method is proposed in order to determine the dynamic response of the plate. The method is based on transforming the governing partial differential equation into a new solvable system of linear ordinary differential equations. To that extent, the proposed solution proves to be applicable to plates made of any viscoelastic material and with various boundary conditions. Moreover, the moving mass may travel at any arbitrary trajectory with no restriction. The capability of the method is demonstrated through several illustrative examples, wherein a comprehensive parametric study is performed to investigate the effect of various parameters on the response of the system. A comparison between the results obtained by the complete moving mass approach with those coming from the approximate solutions is also carried out. The comparative study suggests that neglecting the inertia of the moving mass in the problems where a relatively heavy mass is traveling at high speeds on a plate with a low level of viscosity leads, in general, to an unsafe design. Additionally, ignoring the effect of convective accelerations in the moving mass formulation results in an overly uneconomical design in most cases. However, for large values of viscosity, the accuracy of the approximate methods further improves, and those methods can be used to reasonably estimate the response. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a Cauchy problem associated with Helmholtz-type equation in an infinite “strip”. This is a classical severely ill-posed problem, i.e., the solution (if it exists) does not depend continuously on the data (or Cauchy data), a small perturbation in the data can cause a dramatically large error in the solution for 0 < x ≤ 1 . The stability of the solution is restored by using a wavelet regularization method. Moreover, some sharp stable estimates between the exact solution and its approximation in H r ( R ) -norm is also provided and the numerical examples show that the method works effectively. [ABSTRACT FROM AUTHOR]

In this paper, we study efficient numerical integrators for linear and nonlinear systems of highly oscillatory second-order ordinary differential equations. The systems are reformulated as a first-order system, which is then transformed to adiabatic variables. The solution of the transformed system is a smoother function which is more accessible to numerical approximation than the original system. We develop Filon-type methods for linear systems by approximating the integral as a linear combination of function values and derivatives. We then present a special combination of Filon-type methods and waveform relaxation methods for nonlinear systems. Both types of methods can be used with far larger step sizes than those required by traditional schemes and their performance drastically improves as frequency grows, as are illustrated by numerical experiments. [ABSTRACT FROM AUTHOR]

Abstract: Few papers look at the asymptotic boundedness of numerical solutions of stochastic differential equations (SDEs). One of the open questions is whether numerical approximations can reproduce the boundedness property of the underlying SDEs. In this paper, we give positive answer to this question. Firstly we discuss the asymptotic moment upper bound of the Itô type SDEs and show that the Euler–Maruyama (EM) method is capable to preserve the boundedness property for SDEs with the linear growth condition on both drift and diffusion coefficients. But under the weaker assumption, the one-sided Lipschitz, on the drift coefficient, the EM method fails to work. We then show that the backward EM method can work in this situation. [Copyright &y& Elsevier]

Abstract: This paper addresses the numerical approximation of fluid–structure interaction (FSI) problems through the arbitrary Lagrangian Eulerian (ALE) framework, high-order methods and a Dirichlet–Newmann approach for the coupling. The paper is divided into two main parts. The first part concerns the discretization method for the FSI problem. We introduce an improved ALE map, capable of handling curved geometries in 2D and 3D in a unified manner, that is based on a local differential operator. We also propose a minimal continuous interior penalty (CIP) stabilization term for the fluid discretization that accounts for a smaller computational effort, while stabilizing the flow regime. The second part is dedicated to validating our numerical strategy through a benchmark and some applications to blood flow in arteries. [Copyright &y& Elsevier]

In this paper a numerical procedure to generate approximations to periodic traveling wave profiles of some nonlinear dispersive wave systems is introduced. The method is based on a suitable modification of a fixed point algorithm of Petviashvili type and solves several drawbacks of some previous algorithms presented in the literature. By way of illustration, the method is applied to generate numerically periodic traveling waves of two problems of interest: the fractional KdV type equations and the extended Boussinesq system. [ABSTRACT FROM AUTHOR]

Current material point method (MPM) particle updates use a PIC approach, a FLIP approach, or a linear combination of PIC and FLIP. A PIC update filters velocity in each time step, which causes unwanted numerical diffusion, while FLIP eliminates that diffusion, but may retain too much noise. This paper develops a new particle update termed XPIC( m ) (for eXtended PIC of order m ) because it generalizes PIC updates. XPIC(1) is identical to current PIC methods, but higher orders of XPIC( m ) address the over filtering and numerical diffusion of PIC, while still filtering out noise caused by the nontrivial null space of the extrapolation matrix used in MPM. As m → ∞ , XPIC( m ) converges to a modified FLIP update with orthogonal removal of null space noise. The frequency response and filtering properties of XPIC( m ) are investigated and several numerical examples demonstrate its advantages over other update methods. [ABSTRACT FROM AUTHOR]

The exact reliability of a complicated network system is usually difficult to determine, and numerical approximations may play a crucial role in indicating the reliable probability that a system is still operational under a specified suite of conditions. In this paper, we establish upper and lower bounds on the first-order subsystem reliability of bubblesort networks using the probabilistic fault model. Numerical results show that the curves of upper- and lower-bounded reliability are in good agreement, especially when the node reliability is at a low level. [ABSTRACT FROM AUTHOR]

This paper presents a semigroup approach for inverse source problems for the abstract heat equation, when the measured output data is given in subject to the integral overspecification over the spatial domain. The existence of a solution to the inverse source problem is shown in appropriate function spaces and a representation formula for the solution is proposed. Such representation permits the derivation of sufficient conditions for the uniqueness of the solution. Also an approximation method based on the optimal homotopy analysis method (OHAM) is designed, and the error estimates are discussed using graphical analysis. Moreover, we conjecture that our approach can be applied for the determination of a control parameter in an inverse problem with integral overspecialization data. The proposed algorithm is examined through various numerical examples for the reconstruction of continuous sources and the determination of a control parameter in parabolic equations. The accuracy and stability of the method are discussed and compared with several finite-difference techniques. Computational results show efficiency and high accuracy of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, a new nonconforming immersed finite element (IFE) method on triangular Cartesian meshes is developed for solving planar elasticity interface problems. The proposed IFE method possesses optimal approximation property for both compressible and nearly incompressible problems. Its degree of freedom is much less than those of existing finite element methods for the same problem. Moreover, the method is robust with respect to the shape of the interface and its location relative to the domain and the underlying mesh. Both theory and numerical experiments are presented to demonstrate the effectiveness of the new method. Theoretically, the unisolvent property and the consistency of the IFE space are proved. Experimentally, extensive numerical examples are given to show that the approximation orders in L 2 norm and semi- H 1 norm are optimal under various Lamé parameters settings and different interface geometry configurations. [ABSTRACT FROM AUTHOR]

In this paper, we consider the mixed finite element method of the plane elasticity equations based on the Hellinger–Reissner variational principle. Low order mixed finite element spaces are used to approximate the stress and the displacement. Based on the local polynomial projection stabilization method, we present a stabilization scheme for the pairs to overcome the lack of the inf–sup condition. The stability is proved and the error estimate is derived. At last, two numerical examples are implemented to test the stability and effectiveness of the proposed method. These pairs are very convenient in the numerical implementation for the mixed form of the plane elasticity equations. [ABSTRACT FROM AUTHOR]

Solving elliptic equations with interfaces has wide applications in engineering and science. The real world problems are mostly in three dimensions, while an efficient and accurate solver is a challenge. Some existing methods that work well in two dimensions are too complicated to be generalized to three dimensions. Although traditional finite element method using body-fitted grid is well-established, the expensive cost of mesh generation is an issue. In this paper, an efficient non-traditional finite element method with non-body-fitted grids is proposed to solve elliptic interface problems. The special cases when the interface cuts though grid points are handled carefully, rather than perturbing the cutting point away to apply the method for general case. Both Dirichlet and Neumann boundary conditions are considered. Numerical experiments show that this method is approximately second order accurate in the L ∞ norm and L 2 norm for piecewise smooth solutions. The large sparse matrix for our linear system also has nice structure and properties. [ABSTRACT FROM AUTHOR]

This paper introduces a new disjunctive formulation for the simultaneous optimization and heat integration of systems with variable inlet and outlet temperatures in process streams as well as the possibility of selecting and using different utilities. The starting point is the original compact formulation of the Pinch Location Method, however, instead of approximating the “maximum” operator with smooth, but non-convex functions, these operators are modeled by means of a disjunction. The new formulation has shown to have equal or lower relaxation gap than the best alternative reformulation, thus reducing computational time and numerical problems related to non-convex approximations. [ABSTRACT FROM AUTHOR]

In this paper we propose some modifications in the schemes for the iterative splitting techniques defined in Geiser (2009) for partial differential equations and introduce the parallel version of these modified algorithms. Theoretical results related to the order of the iterative splitting for these schemes are obtained. In the numerical experiments we compare the obtained results by applying iterative methods to approximate the solutions of the nonlinear systems obtained from the discretization of the splitting techniques to the mixed convection–diffusion Burgers’ equation and a momentum equation that models a viscous flow. The differential equations in each splitting interval are solved by the back-Euler–Newton algorithm using sparse matrices. [ABSTRACT FROM AUTHOR]

Abstract: This paper improves on generalized properties of a family of iterative methods to compute the approximate inverses of square matrices originally proposed in [1]. And while the methods of [1] can be used to compute the inner inverses of any matrix, it has not been proved that these sequences converge (in norm) to a fixed inner inverse of the matrix. In this paper, it is proved that the sequences indeed are convergent to a fixed inner inverse of the matrix which is the Moore–Penrose inverse of the matrix. The convergence proof of these sequences is given by fundamental matrix calculus, and numerical experiments show that the third-order iterations are as good as the second-order iterations. [Copyright &y& Elsevier]

Abstract: In this paper numerical methods for solving stochastic differential equations with Markovian switching (SDEwMSs) are developed by pathwise approximation. The proposed family of strong predictor–corrector Euler–Maruyama methods is designed to overcome the propagation of errors during the simulation of an approximate path. This paper not only shows the strong convergence of the numerical solution to the exact solution but also reveals the order of the error under some conditions on the coefficient functions. A natural analogue of the -stability criterion is studied. Numerical examples are given to illustrate the computational efficiency of the new predictor–corrector Euler–Maruyama approximation. [Copyright &y& Elsevier]

In this paper a numerical method for the computation of the approximate least common multiple (ALCM) of a set of several univariate real polynomials is presented. The most important characteristic of the proposed method is that it avoids root finding procedures and computations involving the greatest common divisor (GCD). Conversely, it is based on the algebraic construction of a special matrix which contains key data from the original set of polynomials and leads to the formulation of a linear system which provides the degree and the coefficients of the ALCM using low-rank approximation techniques and numerical optimization tools particularly in the presence of inaccurate data. The numerical stability and complexity of the method are analysed, and a comparison with other methods is provided. [ABSTRACT FROM AUTHOR]

In this paper we consider the numerical approximations of the nonstationary 1D flow of a compressible micropolar fluid, which is in the thermodynamical sense perfect and polytropic. The flow equations are considered in the Eulerian formulation. It is proved that the inviscid micropolar flow equations are hyperbolic and the corresponding eigensystem is determined. The numerical approximations are based on the upwind Roe solver applied to the inviscid part of the flux, while the viscous part of the flux is approximated by using central differences. Numerical results for the inviscid flow show that the numerical schemes approximate the solutions very accurately. The numerical tests for the viscous and heat-conducting flow are also performed. [ABSTRACT FROM AUTHOR]

This paper proposes a full grid interval collocation method (FGICM) and a sparse grid interval collocation method (SGICM) to solve the uncertain heat convection-diffusion problem with interval input parameters in material properties, applied loads and boundary conditions. The Legendre polynomial series is adopted to approximate the functional dependency of temperature response with respect to the interval parameters. In the process of calculating the expansion coefficients, FGICM evaluates the deterministic solutions directly on the full tensor product grids, while the Smolyak sparse grids are reconstructed in SGICM to avoid the curse of dimensionality. The eventual lower and upper bounds of temperature responses are easily predicted based on the continuously-differentiable property of the approximate function. Comparing results with traditional Monte Carlo simulations and perturbation method, the numerical example evidences the remarkable accuracy and effectiveness of the proposed methods for interval temperature field prediction in engineering. [ABSTRACT FROM AUTHOR]