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This paper deals with the implementation of high order semi-Lagrangian particle methods to handle high dimensional Vlasov–Poisson systems. It is based on recent developments in the numerical analysis of particle methods and the paper focuses on specific algorithmic features to handle large dimensions. The methods are tested with uniform particle distributions in particular against a recent multi-resolution wavelet based method on a 4D plasma instability case and a 6D gravitational case. Conservation properties, accuracy and computational costs are monitored. The excellent accuracy/cost trade-off shown by the method opens new perspective for accurate simulations of high dimensional kinetic equations by particle methods. [ABSTRACT FROM AUTHOR]

In this paper, a combined numerical and experimental method, called Extended Load Confluence Algorithm, is presented to accurately predict the dynamic response of non-periodic structures when little or no information about the applied loads is available. This approach, which falls into the category of Shape Sensing methods, inputs limited experimental information acquired from sensors to a mapping algorithm that predicts the response at unmeasured locations. The proposed algorithm consists of three major cores: an experimental core for data acquisition, a numerical core based on Finite Element Method for modeling the structure, and a mapping algorithm that improves the numerical model based on a modal approach in the frequency domain. The robustness and precision of the proposed algorithm are verified through numerical and experimental examples. The results of this paper demonstrate that without a precise knowledge of the loads acting on the structure, the dynamic behavior of the system can be predicted in an effective and precise manner after just a few iterations. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new multiscale representation of surfaces using tight wavelet frames. Both triangular and quadrilateral (quad) surfaces are considered. The multiscale representation for triangulated surfaces is generalized from the non-tensor-product tight wavelet frame representation of functions (of two variables) that were introduced in [1] , while the tensor-product tight frames of continuous linear B-spline from [63] are used for quad surfaces representation. As one of many possible applications of such representation, we consider surface denoising as an example at the end of the paper. We propose an analysis based surface denoising model for triangular and quad surfaces. Fast numerical algorithms are also proposed, which is different from the algorithms used in image restoration [50,52] due to the nonlinear nature of the proposed tight wavelet frame transforms on surfaces. [ABSTRACT FROM AUTHOR]

One of the main aims of second order cyclostationary (CS2) analysis is the estimation of the full spectral correlation, allowing the identification of different CS2 components in a signal and their characterisation in terms of both spectral frequency f and cyclic frequency α . Unfortunately, traditional estimators of the full spectral correlation (e.g. averaged cyclic periodogram) are highly computationally expensive and hence their application has been quite limited. On the other hand, fast envelope-based CS2 indicators (e.g. cyclic modulation spectrum, CMS) are bound by a cyclic-spectral form of the uncertainty principle, which limits the extent of the cyclic frequency axis α max at approximately the value chosen for the spectral frequency axis resolution Δ f . A recent work has however introduced a ground-breaking approach resulting in a fast algorithm for the calculation of the spectral correlation. This approach is based on the calculation of a series of CMS-like quantities, each scanning a different cyclic-frequency band, given a certain spectral frequency resolution. The superposition of all these quantities allows covering a larger α -band breaking the constraint between maximum cyclic frequency α max and spectral frequency axis resolution Δ f , at a limited computational cost. In this paper a new algorithm for the calculation of the same fast spectral correlation is introduced, resulting in a further computational efficiency gain, and a simplification of the computational procedure. [ABSTRACT FROM AUTHOR]

In this paper we study the ℓ 1 -penalized partial likelihood estimator for the sparse high-dimensional Cox proportional hazards model. In particular, we investigate how the ℓ 1 -penalized partial likelihood estimation recovers the sparsity pattern and the conditions under which the sign support consistency is guaranteed. We establish sign recovery consistency and ℓ ∞ -error bounds for the Lasso partial likelihood estimator under suitable and interpretable conditions, including mutual incoherence conditions. More importantly, we show that the conditions of the incoherence and bounds on the minimal non-zero coefficients are necessary, which provides significant and instructional implications for understanding the Lasso for the Cox model. Numerical studies are presented to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract It is known that, for systems of initial-value problems, algorithms using adaptive information perform much better in the worst case setting than the algorithms using nonadaptive information. In the latter case, lower and upper complexity bounds significantly depend on the number of equations. However, in contrast with adaptive information, existing lower and upper complexity bounds for nonadaptive information are not asymptotically tight. In this paper, we close the gap in the complexity exponents, showing asymptotically matching bounds for nonadaptive standard information, as well as for a more general class of nonadaptive linear information. [ABSTRACT FROM AUTHOR]

In this paper, a segregated algorithm is proposed to suppress high-frequency oscillations in the velocity field for incompressible flows. In this context, a new velocity formula based on a reconstruction of face fluxes is defined eliminating high-frequency errors. In analogy to the Rhie–Chow interpolation, this approach is equivalent to including a flux-based pressure gradient with a velocity diffusion in the momentum equation. In order to guarantee second-order accuracy of the numerical solver, a set of conditions are defined for the reconstruction operator. To arrive at the final formulation, an outlook over the state of the art regarding velocity reconstruction procedures is presented comparing them through an error analysis. A new operator is then obtained by means of a flux difference minimization satisfying the required spatial accuracy. The accuracy of the new algorithm is analyzed by performing mesh convergence studies for unsteady Navier–Stokes problems with analytical solutions. The stabilization properties of the solver are then tested in a problem where spurious numerical oscillations arise for the velocity field. The results show a remarkable performance of the proposed technique eliminating high-frequency errors without losing accuracy. [ABSTRACT FROM AUTHOR]

This paper presents a stable numerical algorithm for the Brinkman equations by using weak Galerkin (WG) finite element methods. The Brinkman equations can be viewed mathematically as a combination of the Stokes and Darcy equations which model fluid flow in a multi-physics environment, such as flow in complex porous media with a permeability coefficient highly varying in the simulation domain. In such applications, the flow is dominated by Darcy in some regions and by Stokes in others. It is well known that the usual Stokes stable elements do not work well for Darcy flow and vice versa. The challenge of this study is on the design of numerical schemes which are stable for both the Stokes and the Darcy equations. This paper shows that the WG finite element method is capable of meeting this challenge by providing a numerical scheme that is stable and accurate for both Darcy and the Stokes dominated flows. Error estimates of optimal order are established for the corresponding WG finite element solutions. The paper also presents some numerical experiments that demonstrate the robustness, reliability, flexibility and accuracy of the WG method for the Brinkman equations. [ABSTRACT FROM AUTHOR]

In this paper we propose an algorithm for load balancing in distributed data centers based on game theory. We model the load balancing problem as a non-cooperative game among the front-end proxy servers. We model the operating cost associated with a data center as a weighted linear combination of the energy cost and the latency cost. We propose a non-cooperative load balancing game with the objective of minimizing the operating cost and obtain the structure of Nash equilibrium. Based on this structure, a distributed load balancing algorithm is designed. We compare the performance of the proposed algorithm with the existing approaches. Numerical results demonstrate that the solution achieved by the proposed algorithm approximates the global optimal solution in terms of the cost and it also ensures fairness among the users. [ABSTRACT FROM AUTHOR]

The standard method for constructing generating vectors for good lattice point sets is the component-by-component construction. Numerical experiments have shown that the generating vectors found by these constructions sometimes tend to have recurring components, which can lead to the problem of having projections with all lattice points lying on the main diagonal. In this paper we combine methods of Dick and Kritzer to avoid this problem with a reduced fast component-by-component construction. That is, we give a variation of the standard component-by-component construction which avoids repeated components and simultaneously results in a considerable speed-up in comparison to the standard construction. [ABSTRACT FROM AUTHOR]

Abstract: When one solves PDEs modelling physical phenomena, it is of great importance to take physical constraints into account. More precisely, numerical schemes have to be designed such that discrete solutions satisfy the same constraints as exact solutions. For instance, the underlying physical assumptions for the Euler equations are the positivity of both density and pressure variables. We consider in this paper an unstructured vertex-based tesselation in . Given a MUSCL finite volume scheme and given a reconstruction method (including a limiting process), the point is to determine whether the overall scheme ensures the positivity. The present work is issued from seminal papers from Perthame and Shu (On positivity preserving finite volume schemes for Euler equations, Numer. Math. 73 (1996) 119–130) and Berthon (Robustness of MUSCL schemes for 2D unstructured meshes, J. Comput. Phys. 218 (2) (2006) 495–509). They proved in different frameworks that under assumptions on the corresponding one-dimensional numerical flux, a suitable CFL condition guarantees that density and pressure remain positive. We first analyse Berthon’s method by presenting the ins and outs. We then propose a more general approach adding non geometric degrees of freedom. This approach includes an optimization procedure in order to make the CFL condition explicit and as less restrictive as possible. The reconstruction method is handled independently by means of τ-limiters and of an additional damping parameter. An algorithm is provided in order to specify the adjustments to make in a preexisting code based on a certain numerical flux. Numerical simulations are carried out to prove the accuracy of the method and its ability to deal with low densities and pressures. [Copyright &y& Elsevier]

Time–frequency analysis for non-linear and non-stationary signals is extraordinarily challenging. To capture features in these signals, it is necessary for the analysis methods to be local, adaptive and stable. In recent years, decomposition based analysis methods, such as the empirical mode decomposition (EMD) technique pioneered by Huang et al., were developed by different research groups. These methods decompose a signal into a finite number of components on which the time–frequency analysis can be applied more effectively. In this paper we consider the Iterative Filtering (IF) approach as an alternative to EMD. We provide sufficient conditions on the filters that ensure the convergence of IF applied to any L 2 signal. Then we propose a new technique, the Adaptive Local Iterative Filtering (ALIF) method, which uses the IF strategy together with an adaptive and data driven filter length selection to achieve the decomposition. Furthermore we design smooth filters with compact support from solutions of Fokker–Planck equations (FP filters) that can be used within both IF and ALIF methods. These filters fulfill the derived sufficient conditions for the convergence of the IF algorithm. Numerical examples are given to demonstrate the performance and stability of IF and ALIF techniques with FP filters. In addition, in order to have a complete and truly local analysis toolbox for non-linear and non-stationary signals, we propose new definitions for the instantaneous frequency and phase which depend exclusively on local properties of a signal. [ABSTRACT FROM AUTHOR]

Abstract: A systematic approach is presented for constructing higher-order immersed boundary and ghost fluid methods for CFD in general, and fluid–structure interaction problems in particular. Such methods are gaining popularity because they simplify a number of computational issues. These range from gridding the fluid domain, to designing and implementing Eulerian-based algorithms for challenging fluid–structure applications characterized by large structural motions and deformations or topological changes. However, because they typically operate on non body-fitted grids, immersed boundary and ghost fluid methods also complicate other issues such as the treatment of wall boundary conditions in general, and fluid–structure transmission conditions in particular. These methods also tend to be at best first-order space-accurate at the immersed interfaces. In some cases, they are also provably inconsistent at these locations. A methodology is presented in this paper for addressing this issue. It is developed for inviscid flows and prescribed structural motions. For the sake of clarity, but without any loss of generality, this methodology is described in one and two dimensions. However, its extensions to flow-induced structural motions and three dimensions are straightforward. The proposed methodology leads to a departure from the current practice of populating ghost fluid values independently from the chosen spatial discretization scheme. Instead, it accounts for the pattern and properties of a preferred higher-order discretization scheme, and attributes ghost values as to preserve the formal order of spatial accuracy of this scheme. It is illustrated in this paper by its application to various finite difference and finite volume methods. Its impact is also demonstrated by one- and two-dimensional numerical experiments that confirm its theoretically proven ability to preserve higher-order spatial accuracy, including in the vicinity of the immersed interfaces. [Copyright &y& Elsevier]

Abstract: This paper proposes an algorithm for matrix minimum-distance projection, with respect to a metric induced from an inner product that is the sum of inner products of column vectors, onto the collection of all matrices with their rows restricted in closed convex sets. This algorithm produces a sequence of matrices by modifying a matrix row by row, over and over again. It is shown that the sequence is convergent, and it converges to the desired projection. The implementation of the algorithm for multivariate isotonic regressions and numerical examples are also presented in the paper. [Copyright &y& Elsevier]

Abstract: In this paper, we tackle the modeling and numerical simulation of sprays and aerosols, that is dilute gas–droplet flows for which polydispersity description is of paramount importance. Starting from a kinetic description for point particles experiencing transport either at the carrier phase velocity for aerosols or at their own velocity for sprays as well as evaporation, we focus on an Eulerian high order moment method in size and consider a system of partial differential equations (PDEs) on a vector of successive integer size moments of order 0 to N, N >2, over a compact size interval. There exists a stumbling block for the usual approaches using high order moment methods resolved with high order finite volume methods: the transport algorithm does not preserve the moment space. Indeed, reconstruction of moments by polynomials inside computational cells coupled to the evolution algorithm can create N-dimensional vectors which fail to be moment vectors: it is impossible to find a size distribution for which there are the moments. We thus propose a new approach as well as an algorithm which is second order in space and time with very limited numerical diffusion and allows to accurately describe the advection process and naturally preserves the moment space. The algorithm also leads to a natural coupling with a recently designed algorithm for evaporation which also preserves the moment space; thus polydispersity is accounted for in the evaporation and advection process, very accurately and at a very reasonable computational cost. These modeling and algorithmic tools are referred to as the Eulerian Multi Size Moment (EMSM) model. We show that such an approach is very competitive compared to multi-fluid approaches, where the size phase space is discretized into several sections and low order moment methods are used in each section, as well as with other existing high order moment methods. An accuracy study assesses the order of the method as well as the low level of numerical diffusion on structured meshes. Whereas the extension to unstructured meshes is provided, we focus in this paper on cartesian meshes and two 2D test-cases are presented: Taylor–Green vortices and turbulent free jets, where the accuracy and efficiency of the approach are assessed. [Copyright &y& Elsevier]

Abstract: In this paper, we will present a generalization for a minimization problem from I. Daubechies, M. Defrise, and C. DeMol (2004) . This generalization is useful for solving many practical problems in which more than one constraint are involved. In this regard, we will conclude the findings of many papers (most of which are on image processing) from this generalization. It is hoped that the approach proposed in this paper will be a suitable reference for some applied works where multi-frames, multi-wavelets, or multi-constraints are present in linear inverse problems. [Copyright &y& Elsevier]

Abstract: In a recent paper (Cucker et al., 2008 ) we analyzed a numerical algorithm for computing the number of real zeros of a polynomial system. The analysis relied on a condition number for the input system f. In this paper we look at as a random variable derived from imposing a probability measure on the space of polynomial systems and give bounds for both the tail and the expected value . [Copyright &y& Elsevier]

Abstract: Modeling of laser-plasma wakefield accelerators in an optimal frame of reference has been shown to produce orders of magnitude speed-up of calculations from first principles. Obtaining these speedups required mitigation of a high-frequency instability that otherwise limits effectiveness. In this paper, methods are presented which mitigated the observed instability, including an electromagnetic solver with tunable coefficients, its extension to accommodate Perfectly Matched Layers and Friedman’s damping algorithms, as well as an efficient large bandwidth digital filter. It is observed that choosing the frame of the wake as the frame of reference allows for higher levels of filtering or damping than is possible in other frames for the same accuracy. Detailed testing also revealed the existence of a singular time step at which the instability level is minimized, independently of numerical dispersion. A combination of the techniques presented in this paper prove to be very efficient at controlling the instability, allowing for efficient direct modeling of 10GeV class laser plasma accelerator stages. The methods developed in this paper may have broader application, to other Lorentz-boosted simulations and Particle-In-Cell simulations in general. [Copyright &y& Elsevier]

Abstract: This paper proposes a novel segmentation method based on the scale space techniques endowed with a feature stability approach. The novelty of the paper is the lifetime of the space-scale blobs measured not only by their presence and disappearance but by the stability of the features characterizing the objects of interest as well. Our numerical experiments show that the algorithm outperforms the conventional space scale algorithm applied to variable size and variable shape objects. The proposed algorithm can be used as a preprocessing step in object or pattern recognition applications to produce seeds for more accurate image segmentation methods such as the snakes or the level set techniques. [Copyright &y& Elsevier]

Abstract: This paper investigates the dispersion relations of axisymmetric wave propagation in initially twisted bi-material compound cylinders, within the scope of the piecewise homogeneous body model, utilizing 3D linearized wave propagation theory in an initially stressed body. It is assumed that the constituents of the compound cylinder are isotropic and homogeneous. The corresponding eigen-value problem is formulated and the solution method for this problem as well as the algorithm for obtaining the numerical results is developed. The numerical results illustrate the influence of the initial twisting of the compound cylinder on the dispersion of the axisymmetric wave propagation as presented and discussed in the present paper. In particular, it is established that as a result of the existence of the initial twisting, at least in one constituent of the considered compound cylinder, the axisymmetric longitudinal and torsional waves cannot propagate separately, i.e. the new type axisymmetric waves, which differ from the axisymmetric torsional and longitudinal waves, must appear. [Copyright &y& Elsevier]

Abstract: Given an matrix A and a positive integer k, we describe a randomized procedure for the approximation of A with a matrix Z of rank k. The procedure relies on applying to a collection of l random vectors, where l is an integer equal to or slightly greater than k; the scheme is efficient whenever A and can be applied rapidly to arbitrary vectors. The discrepancy between A and Z is of the same order as times the st greatest singular value of A, with negligible probability of even moderately large deviations. The actual estimates derived in the paper are fairly complicated, but are simpler when is a fixed small nonnegative integer. For example, according to one of our estimates for , the probability that the spectral norm is greater than is less than . The paper contains a number of estimates for , including several that are stronger (but more detailed) than the preceding example; some of the estimates are effectively independent of m. Thus, given a matrix A of limited numerical rank, such that both A and can be applied rapidly to arbitrary vectors, the scheme provides a simple, efficient means for constructing an accurate approximation to a singular value decomposition of A. Furthermore, the algorithm presented here operates reliably independently of the structure of the matrix A. The results are illustrated via several numerical examples. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we compute and manipulate the support of monomial resolutions based on iterated mapping cones. We derive in this way algorithms to obtain homological and numerical invariants of monomial ideals without actually computing their resolution. Our computations include Betti diagrams, Hilbert series and irreducible decompositions. The algorithms derived by the method presented in the paper are efficient in practice as shown by experiments. [Copyright &y& Elsevier]

Abstract: This paper describes the algorithms and functionality of a new module developed to support overset grid assembly associated with performing time-dependent and adaptive moving body calculations of external aerodynamic flows using a multi-solver paradigm (i.e. different CFD solvers in different parts of the computational domain). We use the term “domain connectivity” in this paper to denote all the procedures that are involved in an overset grid assembly, and the module developed is referred henceforth as the domain-connectivity module. The domain-connectivity module coordinates the data transfer between different solvers applied in different parts of the computational domain – body fitted structured or unstructured to capture viscous near-wall effects, and Cartesian adaptive mesh refinement to capture effects away from the wall. The execution of the CFD solvers and the domain-connectivity module are orchestrated by a Python-based computational infrastructure. The domain-connectivity module is fully parallel and performs all its operations (identification of grid overlaps and determination of data interpolation strategy) on the partitioned grid data. In addition, the domain connectivity procedures are completely automated such that no user intervention or manual input is necessary. The capabilities and performance of the package are presented for several test problems, including flow over a NACA 0015 wing and an AGARD A2 slotted airfoil, hover simulation of a scaled V-22 rotor, and dynamic simulation of a UH-60A rotor in forward flight. A modification to the algorithm for improved domain connectivity solutions in problems with tight tolerances as well as heterogeneous grid clustering is also presented. [Copyright &y& Elsevier]

Abstract: In this paper we analyze the equilibrium limit of the constitutive model for two-phase granular mixtures introduced in Papalexandris (2004) , and develop an algorithm for its numerical approximation. At, equilibrium, the constitutive model reduces to a strongly coupled, overdetermined system of quasilinear elliptic partial differential equations with respect to the pressure and the volume fraction of the solid granular phase. First we carry a perturbation analysis based on standard hydrostatic-type scaling arguments which reduces the complexity of the coupling of the equations. The perturbed system is then supplemented by an appropriate compatibility condition which arises from the properties of the gradient operator. Further, based on the Helmholtz decomposition and Ladyzhenskaya’s decomposition theorem, we develop a projection-type, Successive-Over-Relaxation numerical method. This method is general enough and can be applied to a variety of continuum models of complex mixtures and mixtures with micro-structure. We also prove that this method is both stable and consistent hence, under standard assumptions, convergent. The paper concludes with the presentation of representative numerical results. [Copyright &y& Elsevier]

Abstract: Building upon a recent existence result of Kuo and Sloan, this paper presents a component-by-component algorithm for constructing the m points of a quasi-Monte Carlo (QMC) rule for numerical integration over the d-fold product of unit spheres . Our construction is as follows: starting with a well-chosen generating point set of m points on , the algorithm chooses a permutation of this generating point set for each sphere, one sphere at a time, so that the projection of the m QMC points onto each sphere is the same, and is just the generating point set but with the points occurring in a different order. Understandably, the quality of our QMC rule depends on the quality of both the generating point set and the successive permutations. This paper contains two key results. Firstly, assuming that the worst-case error for the generating point set in a certain Sobolev space satisfies a certain estimate, we prove inductively that the resulting QMC rule satisfies the existence result for the worst-case error bound in a d-dimensional weighted Sobolev space established non-constructively by Kuo and Sloan: specifically, the worst-case error of our QMC rule is bounded from above by , where is independent of m and d, provided that the sum of the weights is bounded independently of d. Secondly, we show that the desired estimate for the generating point set on is automatically satisfied for m sufficiently large by a spherical n-design with points (if such spherical designs exist) and by a spherical n-design with points if slightly stronger assumptions are made on the smoothness of the weighted function space. The latter task involves techniques developed by Hesse and Sloan for numerical integration in Sobolev spaces on . The construction cost for the component-by-component algorithm grows only linearly with d. However, a complete search over all permutations at each step of the construction is infeasible, thus a randomized version of the algorithm is recommended in practice. [Copyright &y& Elsevier]

Abstract: The present paper describes an iterative procedure for BEM–BEM coupling. The paper presents suitable interface conditions and algorithms for iteratively coupling sub-domains modeled by three different boundary element time-domain formulations, namely: acoustic and elastodynamic BEM formulations based on time-dependent Green’s functions and non-linear time-domain approach which employs elastostatic Green’s functions and therefore requires domain discretization. Two examples are analyzed and at the end of the paper conclusions of the study are presented. [Copyright &y& Elsevier]

Abstract: The basic principle of feedforward noise cancellation for broadband active noise reduction is based on the availability of a reliable measurement of the noise source. Reliability is compromised in case the noise measurement is acoustically coupled to the actual active noise cancellation (ANC), as stability and performance of the feedforward compensation becomes ambiguous. This paper presents a framework to recursively estimate a feedforward filter in the presence of acoustic coupling, addressing both stability and performance of the active feedforward noise cancellation algorithm. The framework is based on fractional model representations in which a feedforward filter is parameterized by coprime factorization. Conditions on the parameterization of the coprime factorization formulated by the existence of a stable perturbation enables stability in the presence of acoustic coupling. In addition, the paper shows how the stable perturbation can be estimated on-line via a recursive least-squares estimation of a generalized FIR filter to improve the performance of the feedforward filter for ANC. [Copyright &y& Elsevier]

Abstract: This paper introduces a robust algorithm to determine the interfacial tension (γ) from pendant drop profiles using the Galerkin finite element method (γ-PD-FEM) to solve the axisymmetric form of the Young–Laplace (YL) equation. In this algorithm, the theoretical profiles are generated by solving the spherical coordinate form of the YL equation. γ-PD-FEM also solves for the parameter estimates by minimizing the difference between the theoretical and experimental surface functions, . This technique is compared to the widely used method of converting the YL equation to the three arc length-based (ALB) first-order ODEs developed by Bashforth and Adams (BA) in 1883, or as denoted in this paper, the γ-PD-BA method. The drop apex is the initial condition for the γ-PD-BA algorithm and the integration is terminated at a specified location along the drop profile. In contrast to techniques based on the BA approach, computation of the theoretical drop profile in γ-PD-FEM is obtained from a second-order ordinary differential equation and requires boundary conditions at the drop apex and at the contact line of the drop to the nozzle. By incorporating both boundary conditions into the problem formulation, the algorithm can also determine if the drop shape is at static equilibrium. Results to be presented include an outline of the computer algorithm, and comparison of γ values obtained from the γ-PD-FEM and the traditional γ-PD-BA method using simulated and experimental drop profile data sets. [Copyright &y& Elsevier]

The formation of shock waves in solutions of hyperbolic conservation laws calls for locally adaptive numerical solution algorithms and requires a practical tool for identifying where adaption is needed. In this paper, a new smoothness indicator (SI) is used to identify “rough” solution regions and is implemented in locally adaptive algorithms. The SI is based on the weak local truncation error of the approximate solution. It was recently reported in S. Karni and A. Kurganov, Local error analysis for approximate solutions of hyperbolic conservation laws, where error analysis and convergence properties were established. The present paper is concerned with its implementation in scheme adaption and mesh adaption algorithms. The SI provides a general framework for adaption and is not restricted to a particular discretization scheme. The implementation in this paper uses the central-upwind scheme of A. Kurganov, S. Noelle, and G. Petrova, SIAM J. Sci. Comput.23, 707 (2001). The extension of the SI to two space dimensions is given. Numerical results in one and two space dimensions demonstrate the robustness of the proposed SI and its potential in reducing computational costs and improving the resolution of the solution. [Copyright &y& Elsevier]

Mumford showed that Schottky subgroups of PGL ( 2 , K ) give rise to certain curves, now called Mumford curves, over a non-archimedean field K . Such curves are foundational to subjects dealing with non-archimedean varieties, including Berkovich theory and tropical geometry. We develop and implement numerical algorithms for Mumford curves over the field of p -adic numbers. A crucial and difficult step is finding a good set of generators for a Schottky group, a problem solved in this paper. This result allows us to design and implement algorithms for tasks such as: approximating the period matrices of the Jacobians of Mumford curves; computing the Berkovich skeleta of their analytifications; and approximating points in canonical embeddings. We also discuss specific methods and future work for hyperelliptic Mumford curves. [ABSTRACT FROM AUTHOR]

In this paper, some numerical algorithms (spectral collocation method, block spectral collocation method, boundary value method, block boundary value method, implicit Runge–Kutta method, diagonally implicit Runge–Kutta method and total variation diminishing Runge–Kutta method) are used to solve the highly oscillatory second-order initial value problems. We first derive these methods for the first-order initial value problems, and then extend these methods to the highly oscillatory nonlinear systems by matrix analysis methods. These new methods preserve the accuracy of the original methods and the main advantages of these new methods are low storage requirements and high efficiency. Extensive numerical results are presented to demonstrate the convergence properties of these methods. [ABSTRACT FROM AUTHOR]

Fourier extensions have been shown to be an effective means for the approximation of smooth, nonperiodic functions on bounded intervals given their values on an equispaced, or in general, scattered grid. Related to this method are two parameters. These are the extension parameter T (the ratio of the size of the extended domain to the physical domain) and the oversampling ratio η (the number of sampling nodes per Fourier mode). The purpose of this paper is to investigate how the choice of these parameters affects the accuracy and stability of the approximation. Our main contribution is to document the following interesting phenomenon: namely, if the desired condition number of the algorithm is fixed in advance, then the particular choice of such parameters makes little difference to the algorithm's accuracy. As a result, one is free to choose T without concern that it is suboptimal. In particular, one may use the value T=2 - which corresponds to the case where the extended domain is precisely twice the size of the physical domain - for which there is known to be a fast algorithm for computing the approximation. In addition, we determine the resolution power (points-per-wavelength) of the approximation to be equal to Tη, and address the trade-off between resolution power and stability. [ABSTRACT FROM AUTHOR]

Abstract: This is a research expository paper regarding superparameterization, a class of multi-scale numerical methods designed to cope with the intermittent multi-scale effects of inhomogeneous geophysical turbulence where energy often inverse-cascades from the unresolved scales to the large scales through the effects of waves, jets, vortices, and latent heat release from moist processes. Original as well as sparse space–time superparameterization algorithms are discussed for the important case of moist atmospheric convection including the role of multi-scale asymptotic methods in providing self-consistent constraints on superparameterization algorithms and related deterministic and stochastic multi-cloud parameterizations. Test models for the statistical numerical analysis of superparameterization algorithms are discussed both to elucidate the performance of the basic algorithms and to test their potential role in efficient multi-scale data assimilation. The very recent development of grid-free seamless stochastic superparameterization methods for geophysical turbulence appropriate for “eddy-permitting” mesoscale ocean turbulence is presented here including a general formulation and illustrative applications to two-layer quasigeostrophic turbulence, and another difficult test case involving one-dimensional models of dispersive wave turbulence. This last test case has randomly generated solitons as coherent structures which collapse and radiate wave energy back to the larger scales, resulting in strong direct and inverse turbulent energy cascades. [Copyright &y& Elsevier]

Abstract: Stable partitioned algorithms for fluid–structure interaction (FSI) problems are developed and analyzed in this two-part paper. Part I describes an algorithm for incompressible flow coupled with compressible elastic solids, while Part II discusses an algorithm for incompressible flow coupled with structural shells. The numerical approach described here for structural shells uses Robin (mixed) interface conditions for the pressure and velocity in the fluid which are derived directly from the governing equations. The resulting added-mass partitioned (AMP) algorithm is stable even for very light structures, requires no sub-iterations per time step, and is second-order accurate. The stability and accuracy of the AMP algorithm is evaluated for linearized FSI model problems. A normal mode analysis is performed to show that the new AMP algorithm is stable, even for the case of very light structures when added-mass effects are large. Exact traveling wave solutions are derived for the FSI model problems, and these solutions are used to verify the stability and accuracy of the corresponding numerical results obtained from the AMP algorithm for the cases of light, medium and heavy structures. A summary comparison of the AMP algorithm developed here and the one in Part I is provided. [Copyright &y& Elsevier]

Abstract: The paper describes an algorithm for PDE-constrained optimization that controls numerical errors using error estimates and grid adaptation during the optimization process. A key aspect of the algorithm is the use of adjoint variables to estimate errors in the first-order optimality conditions. Multilevel optimization is used to drive the optimality conditions and their estimated errors below a specified tolerance. The error estimate requires two additional adjoint solutions, but only at the beginning and end of each optimization cycle. Moreover, the adjoint systems can be formed and solved with limited additional infrastructure beyond that found in typical PDE-constrained optimization algorithms. The approach is general and can accommodate both reduced-space and full-space formulations of the optimization problem. The algorithm is illustrated using the inverse design of a nozzle constrained by the quasi-one-dimensional Euler equations. [Copyright &y& Elsevier]

Abstract: The pseudo-spectral analytical time-domain (PSATD) particle-in-cell (PIC) algorithm solves the vacuum Maxwellʼs equations exactly, has no Courant time-step limit (as conventionally defined), and offers substantial flexibility in plasma and particle beam simulations. It is, however, not free of the usual numerical instabilities, including the numerical Cherenkov instability, when applied to relativistic beam simulations. This paper derives and solves the numerical dispersion relation for the PSATD algorithm and compares the results with corresponding behavior of the more conventional pseudo-spectral time-domain (PSTD) and finite difference time-domain (FDTD) algorithms. In general, PSATD offers superior stability properties over a reasonable range of time steps. More importantly, one version of the PSATD algorithm, when combined with digital filtering, is almost completely free of the numerical Cherenkov instability for time steps (scaled to the speed of light) comparable to or smaller than the axial cell size. [Copyright &y& Elsevier]

Abstract: In this paper, a novel algorithm for incompressible flows of two-phase granular mixtures is proposed. The algorithm constitutes a generalization of projection-type methods to multi-phase flows and employs a predictor–corrector time-marching scheme. For the computation of the phasial pressures, a Poisson equation and a second-order elliptic PDE with variable coefficients are solved at both the prediction and the correction stage. Further, the algorithm is combined with a regularization scheme for the numerical treatment of material interfaces which are a common characteristic of the flows of interest. The efficiency and robustness of the proposed algorithm are illustrated via numerical simulations of unsteady two-dimensional shear flows for a reference mixture of beach sand and water. [Copyright &y& Elsevier]

Abstract: In this paper, a simple method for detection of multiple edge cracks in Euler–Bernoulli beams having two different types of cracks is presented based on energy equations. Each crack is modeled as a massless rotational spring using Linear Elastic Fracture Mechanics (LEFM) theory, and a relationship among natural frequencies, crack locations and stiffness of equivalent springs is demonstrated. In the procedure, for detection of m cracks in a beam, 3m equations and natural frequencies of healthy and cracked beam in two different directions are needed as input to the algorithm. The main accomplishment of the presented algorithm is the capability to detect the location, severity and type of each crack in a multi-cracked beam. Concise and simple calculations along with accuracy are other advantages of this method. A number of numerical examples for cantilever beams including one and two cracks are presented to validate the method. [Copyright &y& Elsevier]

Abstract: Explicit time stepping renders many high-resolution computational schemes to become less efficient when dealing with non-uniform grids typical of many aeroacoustic applications. Asynchronous time stepping, i.e., updating the solution in different cell sizes according to their local rates, is known to be a promising way to improve the efficiency of explicit time-stepping methods without compromise in accuracy. In the present paper, a new asynchronous time-stepping algorithm is developed for the Compact Accurately Boundary-Adjusting high-REsolution Technique (CABARET) Euler method. This allows to significantly speedup the original single-step CABARET method with non-uniform grids and improves its accuracy at the same time. Numerical examples are provided and issues associated with the method performance on various grid resolutions are discussed. [Copyright &y& Elsevier]

CG_DESCENT is a state-of-the-art algorithm to solve large-scale unconstrained minimization problems. However, research activities on CG_DESCENT in some other scenarios are relatively fewer. In this paper, by combining with the projection method of Solodov and Svaiter, we extend CG_DESCENT to solve large-scale nonlinear convex constrained monotone equations. The proposed method does not require the Jacobian information, even though it does not store any matrix at each iteration. It thus has the potential to solve large-scale non-smooth problems. Under some mild conditions, we show that the proposed method converges globally. Primary numerical results illustrate that the proposed method works quite well. Moreover, we also extend this method to solve the -norm regularized problems to decode a sparse signal in compressive sensing. Performance comparisons show that the proposed method is practical, efficient and competitive with the compared ones. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we present a new algorithm based on Cartesian meshes for the numerical approximation of kinetic models set in an arbitrary geometry. Due to the high dimensional property of kinetic models, numerical algorithms based on unstructured meshes are not really appropriate since most of numerical methods (semi-Lagrangian, spectral methods) are particularly efficient on structured grids. Here we propose to adapt the inverse Lax–Wendroff procedure, which has been recently introduced for conservation laws [21], for kinetic equations. Numerical simulations in and based on this approach are proposed for Boltzmann type operators (BGK, ES-BGK models). [Copyright &y& Elsevier]

• A linearly operator splitting algorithm is proposed for the nonlocal VCH equation. • The energy stabilities for both subproblems are proved. • The stability and convergence of the operator splitting algorithm are studied. • A semi-implicit SDC method is further used to improve time accuracy. Recently, the viscous Cahn-Hilliard (VCH) equation has been proposed as a phenomenological continuum model for phase separation in glass and polymer systems where intermolecular friction forces become important. Compared with the classical local VCH model, the nonlocal VCH model equipped with nonlocal diffusion operator can describe more practical phenomena for modeling phase transitions of microstructures in materials. This paper presents a high order fast explicit method based on operator splitting and spectral deferred correction (SDC) for solving the nonlocal VCH equation. We start with a second-order operator splitting spectral scheme, which is based on the Fourier spectral method and the strong stability preserving Runge-Kutta (SSP-RK) method. The scheme takes advantage of applying the fast Fourier transform (FFT) and avoiding nonlinear iteration. The stability and convergence analysis of the obtained numerical scheme are analyzed. To improve the temporal accuracy, the semi-implicit SDC method is then introduced. Various numerical simulations are performed to validate the accuracy and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents the results of shaking table tests on adjacent structures controlled by passive and semi-active MR dampers. The aim was to demonstrate experimentally the effectiveness of passive and semi-active strategies in reducing structural vibrations due to seismic excitation. The physical model at issue was represented by two adjacent steel structures, respectively of 4 and 2 levels, connected at the second level by a MR damper. When the device operated in semi-active mode, an ON–OFF control algorithm, derived by the Lyapunov stability theory, was implemented and experimentally validated. Since the experimentation concerned adjacent structures, two control objectives have been reached: global and selective protection. In case of global protection, the attention was focused on protecting both structures, whereas, in case of selective protection, the attention was focused on protecting only one structure. For each objective the effectiveness of passive control has been compared with the situation of no control and then the effectiveness of semi-active control has been compared with the passive one. The quantities directly compared have been: measured displacements, accelerations and force–displacement of the MR damper, moreover some global response quantities have been estimated from experimental measures, which are the base share force and the base bending moment, the input energy and the energy dissipated by the device. In order to evaluate the effectiveness of the control action in both passive and semi-active case, an energy index EDI, previously defined and already often applied numerically, has been utilized. The aspects investigated in the experimentation have been: the implementation and validation of the control algorithm for selective and global protection, the MR damper input voltage influence, the kind of seismic input and its intensity. [Copyright &y& Elsevier]

Abstract: In this paper we present a technique for shape reconstruction based on the topological and shape gradients. The shape in consideration is a solution of an inverse conductivity problem. To solve such a problem numerically, we compute the topological gradient of a Kohn–Vogelius-type cost function when the domain under consideration is perturbed by the introduction of a small inclusion instead of a hole. The reconstruction is done by considering the shape as a superposition of very thin elliptic inclusions to get a first approximation. Then, we use a gradient-type algorithm to perform a good reconstruction. Various numerical experiments of single and multiple inclusions demonstrate the viability of the designed algorithm. [Copyright &y& Elsevier]

Abstract: In this paper, we derive a series of local structure-preserving algorithms for the “good” Boussinesq equation, including multisymplectic geometric structure-preserving algorithms, local energy-preserving algorithms and local momentum-preserving algorithms. The outstanding advantage of the proposed algorithms is that they conserve these local structures in any time-space region exactly. For example, the proposed local energy-preserving algorithms preserve the local energy conservation law in any local domain. Therefore, the local structure-preserving algorithms overcome the shortage of global structure-preserving algorithms on the boundary conditions. Especially, with suitable boundary conditions such as periodic or homogeneous boundary conditions, the local structure-preserving algorithms will be global structure-preserving algorithms. Numerical results verify the theoretical analysis. [Copyright &y& Elsevier]

Abstract: This paper presents a method for the identification of loads applied to a structure, using the concept of response transmissibility. The authors propose to perform the identification of the loads in two steps: the first identifies the number of forces and their location using an algorithm of “search for number and position”, based on the response transmissibility concept; the second step consists of the reconstruction of the load vector. To carry out the first step, a complete description of the structure in terms of degrees-of-freedom will be assumed and a numerical model (usually a finite element one) is built. In order to perform the identification of the number of forces and their location, the proposed algorithm combines both the dynamic responses experimentally measured and the transmissibility matrices obtained from the numerical model. The regeneration of the load vector is achieved during the second step, once the number of loads and their location are known, combining the dynamic responses obtained experimentally with the transmissibility matrix from the numerical model. A series of simulated and experimental results on a free–free beam are presented to illustrate the procedure. [Copyright &y& Elsevier]

Abstract: This paper is concerned with spectral Galerkin algorithms for solving high even-order two point boundary value problems in one dimension subject to homogeneous and nonhomogeneous boundary conditions. The proposed algorithms are extended to solve two-dimensional high even-order differential equations. The key to the efficiency of these algorithms is to construct compact combinations of Chebyshev polynomials of the third and fourth kinds as basis functions. The algorithms lead to linear systems with specially structured matrices that can be efficiently inverted. Numerical examples are included to demonstrate the validity and applicability of the proposed algorithms, and some comparisons with some other methods are made. [Copyright &y& Elsevier]

Abstract: The paper presents a detailed numerical study of an iterative solution to 3-D sound-hard acoustic scattering problems at high frequency considering the Combined Field Integral Equation (CFIE). We propose a combination of an OSRC preconditioning technique and a Fast Multipole Method which leads to a fast and efficient algorithm independently of both a frequency increase and a mesh refinement. The OSRC-preconditioned CFIE exhibits very interesting spectral properties even for trapping domains. Moreover, this analytic preconditioner shows highly-desirable advantages: sparse structure, ease of implementation and low additional computational cost. We first investigate the numerical behavior of the eigenvalues of the related integral operators, CFIE and OSRC-preconditioned CFIE, in order to illustrate the influence of the proposed preconditioner. We then apply the resolution algorithm to various and significant test-cases using a GMRES solver. The OSRC-preconditioning technique is combined to a Fast Multipole Method in order to deal with high-frequency 3-D cases. This variety of tests validates the effectiveness of the method and fully justifies the interest of such a combination. [Copyright &y& Elsevier]

Abstract: Jacobian-free Newton–Krylov (JFNK) method is an effective algorithm for solving large scale nonlinear equations. One of the most important advantages of JFNK method is that there is no necessity to form and store the Jacobian matrix of the nonlinear system when JFNK method is employed. However, an approximation of the Jacobian is needed for the purpose of preconditioning. In this paper, JFNK method is employed to solve a class of non-equilibrium radiation diffusion coupled to material thermal conduction equations, and two preconditioners are designed by linearizing the equations in two methods. Numerical results show that the two preconditioning methods can improve the convergence behavior and efficiency of JFNK method. [Copyright &y& Elsevier]