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COMPUTER SCIENCE (1221 journals)                  1 2 3 4 5 6 7 | Last

Showing 1 - 200 of 872 Journals sorted alphabetically
3D Printing and Additive Manufacturing     Full-text available via subscription   (Followers: 21)
Abakós     Open Access   (Followers: 4)
ACM Computing Surveys     Hybrid Journal   (Followers: 29)
ACM Journal on Computing and Cultural Heritage     Hybrid Journal   (Followers: 8)
ACM Journal on Emerging Technologies in Computing Systems     Hybrid Journal   (Followers: 16)
ACM Transactions on Accessible Computing (TACCESS)     Hybrid Journal   (Followers: 3)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 15)
ACM Transactions on Applied Perception (TAP)     Hybrid Journal   (Followers: 5)
ACM Transactions on Architecture and Code Optimization (TACO)     Hybrid Journal   (Followers: 9)
ACM Transactions on Autonomous and Adaptive Systems (TAAS)     Hybrid Journal   (Followers: 9)
ACM Transactions on Computation Theory (TOCT)     Hybrid Journal   (Followers: 12)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 3)
ACM Transactions on Computer Systems (TOCS)     Hybrid Journal   (Followers: 18)
ACM Transactions on Computer-Human Interaction     Hybrid Journal   (Followers: 15)
ACM Transactions on Computing Education (TOCE)     Hybrid Journal   (Followers: 6)
ACM Transactions on Design Automation of Electronic Systems (TODAES)     Hybrid Journal   (Followers: 6)
ACM Transactions on Economics and Computation     Hybrid Journal   (Followers: 1)
ACM Transactions on Embedded Computing Systems (TECS)     Hybrid Journal   (Followers: 3)
ACM Transactions on Information Systems (TOIS)     Hybrid Journal   (Followers: 20)
ACM Transactions on Intelligent Systems and Technology (TIST)     Hybrid Journal   (Followers: 8)
ACM Transactions on Interactive Intelligent Systems (TiiS)     Hybrid Journal   (Followers: 3)
ACM Transactions on Multimedia Computing, Communications, and Applications (TOMCCAP)     Hybrid Journal   (Followers: 9)
ACM Transactions on Reconfigurable Technology and Systems (TRETS)     Hybrid Journal   (Followers: 6)
ACM Transactions on Sensor Networks (TOSN)     Hybrid Journal   (Followers: 8)
ACM Transactions on Speech and Language Processing (TSLP)     Hybrid Journal   (Followers: 9)
ACM Transactions on Storage     Hybrid Journal  
ACS Applied Materials & Interfaces     Hybrid Journal   (Followers: 32)
Acta Automatica Sinica     Full-text available via subscription   (Followers: 2)
Acta Informatica Malaysia     Open Access  
Acta Universitatis Cibiniensis. Technical Series     Open Access  
Ad Hoc Networks     Hybrid Journal   (Followers: 11)
Adaptive Behavior     Hybrid Journal   (Followers: 10)
Advanced Engineering Materials     Hybrid Journal   (Followers: 28)
Advanced Science Letters     Full-text available via subscription   (Followers: 11)
Advances in Adaptive Data Analysis     Hybrid Journal   (Followers: 7)
Advances in Artificial Intelligence     Open Access   (Followers: 15)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 4)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 19)
Advances in Computer Engineering     Open Access   (Followers: 4)
Advances in Computer Science : an International Journal     Open Access   (Followers: 14)
Advances in Computing     Open Access   (Followers: 2)
Advances in Data Analysis and Classification     Hybrid Journal   (Followers: 55)
Advances in Engineering Software     Hybrid Journal   (Followers: 28)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 14)
Advances in Human Factors/Ergonomics     Full-text available via subscription   (Followers: 22)
Advances in Human-Computer Interaction     Open Access   (Followers: 20)
Advances in Materials Science     Open Access   (Followers: 14)
Advances in Operations Research     Open Access   (Followers: 12)
Advances in Parallel Computing     Full-text available via subscription   (Followers: 7)
Advances in Porous Media     Full-text available via subscription   (Followers: 5)
Advances in Remote Sensing     Open Access   (Followers: 49)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
Advances in Technology Innovation     Open Access   (Followers: 6)
AEU - International Journal of Electronics and Communications     Hybrid Journal   (Followers: 8)
African Journal of Information and Communication     Open Access   (Followers: 9)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
AI EDAM     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 12)
AIS Transactions on Human-Computer Interaction     Open Access   (Followers: 6)
Algebras and Representation Theory     Hybrid Journal   (Followers: 1)
Algorithms     Open Access   (Followers: 11)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 5)
American Journal of Computational Mathematics     Open Access   (Followers: 4)
American Journal of Information Systems     Open Access   (Followers: 6)
American Journal of Sensor Technology     Open Access   (Followers: 4)
Anais da Academia Brasileira de Ciências     Open Access   (Followers: 2)
Analog Integrated Circuits and Signal Processing     Hybrid Journal   (Followers: 7)
Analysis in Theory and Applications     Hybrid Journal   (Followers: 1)
Animation Practice, Process & Production     Hybrid Journal   (Followers: 5)
Annals of Combinatorics     Hybrid Journal   (Followers: 4)
Annals of Data Science     Hybrid Journal   (Followers: 12)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 13)
Annals of Pure and Applied Logic     Open Access   (Followers: 3)
Annals of Software Engineering     Hybrid Journal   (Followers: 13)
Annals of West University of Timisoara - Mathematics and Computer Science     Open Access  
Annual Reviews in Control     Hybrid Journal   (Followers: 8)
Anuario Americanista Europeo     Open Access  
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applied and Computational Harmonic Analysis     Full-text available via subscription   (Followers: 1)
Applied Artificial Intelligence: An International Journal     Hybrid Journal   (Followers: 12)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 13)
Applied Computer Systems     Open Access   (Followers: 2)
Applied Informatics     Open Access  
Applied Mathematics and Computation     Hybrid Journal   (Followers: 33)
Applied Medical Informatics     Open Access   (Followers: 10)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Soft Computing     Hybrid Journal   (Followers: 16)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 5)
Applied System Innovation     Open Access  
Architectural Theory Review     Hybrid Journal   (Followers: 3)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 5)
Archive of Numerical Software     Open Access  
Archives and Museum Informatics     Hybrid Journal   (Followers: 144)
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
arq: Architectural Research Quarterly     Hybrid Journal   (Followers: 8)
Artifact     Hybrid Journal   (Followers: 2)
Artificial Life     Hybrid Journal   (Followers: 7)
Asia Pacific Journal on Computational Engineering     Open Access  
Asia-Pacific Journal of Information Technology and Multimedia     Open Access   (Followers: 1)
Asian Journal of Computer Science and Information Technology     Open Access  
Asian Journal of Control     Hybrid Journal  
Assembly Automation     Hybrid Journal   (Followers: 2)
at - Automatisierungstechnik     Hybrid Journal   (Followers: 1)
Australian Educational Computing     Open Access   (Followers: 1)
Automatic Control and Computer Sciences     Hybrid Journal   (Followers: 5)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Automatica     Hybrid Journal   (Followers: 13)
Automation in Construction     Hybrid Journal   (Followers: 7)
Autonomous Mental Development, IEEE Transactions on     Hybrid Journal   (Followers: 8)
Basin Research     Hybrid Journal   (Followers: 5)
Behaviour & Information Technology     Hybrid Journal   (Followers: 52)
Big Data and Cognitive Computing     Open Access   (Followers: 2)
Biodiversity Information Science and Standards     Open Access  
Bioinformatics     Hybrid Journal   (Followers: 308)
Biomedical Engineering     Hybrid Journal   (Followers: 16)
Biomedical Engineering and Computational Biology     Open Access   (Followers: 13)
Biomedical Engineering, IEEE Reviews in     Full-text available via subscription   (Followers: 20)
Biomedical Engineering, IEEE Transactions on     Hybrid Journal   (Followers: 35)
Briefings in Bioinformatics     Hybrid Journal   (Followers: 49)
British Journal of Educational Technology     Hybrid Journal   (Followers: 146)
Broadcasting, IEEE Transactions on     Hybrid Journal   (Followers: 12)
c't Magazin fuer Computertechnik     Full-text available via subscription   (Followers: 1)
CALCOLO     Hybrid Journal  
Calphad     Hybrid Journal   (Followers: 2)
Canadian Journal of Electrical and Computer Engineering     Full-text available via subscription   (Followers: 15)
Capturing Intelligence     Full-text available via subscription  
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 2)
Cell Communication and Signaling     Open Access   (Followers: 2)
Central European Journal of Computer Science     Hybrid Journal   (Followers: 5)
CERN IdeaSquare Journal of Experimental Innovation     Open Access   (Followers: 3)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
Chemometrics and Intelligent Laboratory Systems     Hybrid Journal   (Followers: 15)
ChemSusChem     Hybrid Journal   (Followers: 7)
China Communications     Full-text available via subscription   (Followers: 8)
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
CIN Computers Informatics Nursing     Hybrid Journal   (Followers: 11)
Circuits and Systems     Open Access   (Followers: 15)
Clean Air Journal     Full-text available via subscription   (Followers: 1)
CLEI Electronic Journal     Open Access  
Clin-Alert     Hybrid Journal   (Followers: 1)
Clinical eHealth     Open Access  
Cluster Computing     Hybrid Journal   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 14)
Communication Methods and Measures     Hybrid Journal   (Followers: 12)
Communication Theory     Hybrid Journal   (Followers: 23)
Communications Engineer     Hybrid Journal   (Followers: 1)
Communications in Algebra     Hybrid Journal   (Followers: 3)
Communications in Computational Physics     Full-text available via subscription   (Followers: 2)
Communications in Information Science and Management Engineering     Open Access   (Followers: 4)
Communications in Partial Differential Equations     Hybrid Journal   (Followers: 3)
Communications of the ACM     Full-text available via subscription   (Followers: 51)
Communications of the Association for Information Systems     Open Access   (Followers: 16)
COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering     Hybrid Journal   (Followers: 3)
Complex & Intelligent Systems     Open Access   (Followers: 1)
Complex Adaptive Systems Modeling     Open Access  
Complex Analysis and Operator Theory     Hybrid Journal   (Followers: 2)
Complexity     Hybrid Journal   (Followers: 6)
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 8)
Computación y Sistemas     Open Access  
Computation     Open Access   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 3)
Computational and Mathematical Biophysics     Open Access   (Followers: 1)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational and Structural Biotechnology Journal     Open Access   (Followers: 2)
Computational and Theoretical Chemistry     Hybrid Journal   (Followers: 9)
Computational Astrophysics and Cosmology     Open Access   (Followers: 1)
Computational Biology and Chemistry     Hybrid Journal   (Followers: 12)
Computational Chemistry     Open Access   (Followers: 2)
Computational Cognitive Science     Open Access   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Condensed Matter     Open Access  
Computational Ecology and Software     Open Access   (Followers: 9)
Computational Economics     Hybrid Journal   (Followers: 9)
Computational Geosciences     Hybrid Journal   (Followers: 17)
Computational Linguistics     Open Access   (Followers: 23)
Computational Management Science     Hybrid Journal  
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 5)
Computational Methods and Function Theory     Hybrid Journal  
Computational Molecular Bioscience     Open Access   (Followers: 2)
Computational Optimization and Applications     Hybrid Journal   (Followers: 8)
Computational Particle Mechanics     Hybrid Journal   (Followers: 1)
Computational Research     Open Access   (Followers: 1)
Computational Science and Discovery     Full-text available via subscription   (Followers: 2)
Computational Science and Techniques     Open Access  
Computational Statistics     Hybrid Journal   (Followers: 14)
Computational Statistics & Data Analysis     Hybrid Journal   (Followers: 30)
Computer     Full-text available via subscription   (Followers: 99)
Computer Aided Surgery     Open Access   (Followers: 6)
Computer Applications in Engineering Education     Hybrid Journal   (Followers: 8)
Computer Communications     Hybrid Journal   (Followers: 16)
Computer Journal     Hybrid Journal   (Followers: 9)

        1 2 3 4 5 6 7 | Last

Journal Cover
Advances in Computational Mathematics
Journal Prestige (SJR): 0.812
Citation Impact (citeScore): 1
Number of Followers: 19  
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1572-9044 - ISSN (Online) 1019-7168
Published by Springer-Verlag Homepage  [2349 journals]
  • Adaptive mesh selection asymptotically guarantees a prescribed local error
           for systems of initial value problems
    • Authors: Bolesław Kacewicz
      Pages: 1325 - 1344
      Abstract: We study potential advantages of adaptive mesh point selection for the solution of systems of initial value problems. For an optimal order discretization method, we propose an algorithm for successive selection of the mesh points, which only requires evaluations of the right-hand side function. The selection (asymptotically) guarantees that the maximum local error of the method does not exceed a prescribed level. The usage of the algorithm is not restricted to the chosen method; it can also be applied with any method from a general class. We provide a rigorous analysis of the cost of the proposed algorithm. It is shown that the cost is almost minimal, up to absolute constants, among all mesh selection algorithms. For illustration, we specify the advantage of the adaptive mesh over the uniform one. Efficiency of the adaptive algorithm results from automatic adjustment of the successive mesh points to the local behavior of the solution. Some numerical results illustrating theoretical findings are reported.
      PubDate: 2018-10-01
      DOI: 10.1007/s10444-017-9584-2
      Issue No: Vol. 44, No. 5 (2018)
  • A phase field approach to shape optimization in Navier–Stokes flow with
           integral state constraints
    • Authors: Harald Garcke; Michael Hinze; Christian Kahle; Kei Fong Lam
      Pages: 1345 - 1383
      Abstract: We consider the shape optimization of an object in Navier–Stokes flow by employing a combined phase field and porous medium approach, along with additional perimeter regularization. By considering integral control and state constraints, we extend the results of earlier works concerning the existence of optimal shapes and the derivation of first order optimality conditions. The control variable is a phase field function that prescribes the shape and topology of the object, while the state variables are the velocity and the pressure of the fluid. In our analysis, we cover a multitude of constraints which include constraints on the center of mass, the volume of the fluid region, and the total potential power of the object. Finally, we present numerical results of the optimization problem that is solved using the variable metric projection type (VMPT) method proposed by Blank and Rupprecht, where we consider one example of topology optimization without constraints and one example of maximizing the lift of the object with a state constraint, as well as a comparison with earlier results for the drag minimization.
      PubDate: 2018-10-01
      DOI: 10.1007/s10444-018-9586-8
      Issue No: Vol. 44, No. 5 (2018)
  • Second-kind integral equations for the Laplace-Beltrami problem on
           surfaces in three dimensions
    • Authors: Michael O’Neil
      Pages: 1385 - 1409
      Abstract: The Laplace-Beltrami problem ΔΓψ = f has several applications in mathematical physics, differential geometry, machine learning, and topology. In this work, we present novel second-kind integral equations for its solution which obviate the need for constructing a suitable parametrix to approximate the in-surface Green’s function. The resulting integral equations are well-conditioned and compatible with standard fast multipole methods and iterative linear algebraic solvers, as well as more modern fast direct solvers. Using layer-potential identities known as Calderón projectors, the Laplace-Beltrami operator can be pre-conditioned from the left and/or right to obtain second-kind integral equations. We demonstrate the accuracy and stability of the scheme in several numerical examples along surfaces described by curvilinear triangles.
      PubDate: 2018-10-01
      DOI: 10.1007/s10444-018-9587-7
      Issue No: Vol. 44, No. 5 (2018)
  • Efficient construction of 2-chains representing a basis of H 2 ( Ω ¯ ,
           ∂ Ω ; ℤ ) $H_{2}(\overline {\Omega }, \partial {\Omega }; \mathbb
    • Authors: Ana Alonso Rodríguez; Enrico Bertolazzi; Riccardo Ghiloni; Ruben Specogna
      Pages: 1411 - 1440
      Abstract: We present an efficient algorithm for the construction of a basis of \(H_{2}(\overline {\Omega },\partial {\Omega };\mathbb {Z})\) via the Poincaré-Lefschetz duality theorem. Denoting by g the first Betti number of \(\overline {\Omega }\) the idea is to find, first g different 1-boundaries of \(\overline {\Omega }\) with supports contained in ∂Ω whose homology classes in \(\mathbb {R}^{3} \setminus {\Omega }\) form a basis of \(H_{1}(\mathbb {R}^{3} \setminus {\Omega };\mathbb {Z})\) , and then to construct a set of 2-chains in \(\overline {\Omega }\) having these 1-boundaries as their boundaries. The Poincaré-Lefschetz duality theorem ensures that the relative homology classes of these 2-chains in \(\overline {\Omega }\) modulo ∂Ω form a basis of \(H_{2}(\overline {\Omega },\partial {\Omega };\mathbb {Z})\) . We devise a simple procedure for the construction of the required set of 1-boundaries of \(\overline {\Omega }\) that, combined with a fast algorithm for the construction of 2-chains with prescribed boundary, allows the efficient computation of a basis of \(H_{2}(\overline {\Omega },\partial {\Omega };\mathbb {Z})\) via this very natural approach. Some numerical experiments show the efficiency of the method and its performance comparing with other algorithms.
      PubDate: 2018-10-01
      DOI: 10.1007/s10444-018-9588-6
      Issue No: Vol. 44, No. 5 (2018)
  • Uniform asymptotic expansions for Laguerre polynomials and related
           confluent hypergeometric functions
    • Authors: T. M. Dunster; A. Gil; J. Segura
      Pages: 1441 - 1474
      Abstract: Uniform asymptotic expansions involving exponential and Airy functions are obtained for Laguerre polynomials \(L_{n}^{(\alpha )}(x)\) , as well as complementary confluent hypergeometric functions. The expansions are valid for n large and α small or large, uniformly for unbounded real and complex values of x. The new expansions extend the range of computability of \(L_{n}^{(\alpha )}(x)\) compared to previous expansions, in particular with respect to higher terms and large values of α. Numerical evidence of their accuracy for real and complex values of x is provided.
      PubDate: 2018-10-01
      DOI: 10.1007/s10444-018-9589-5
      Issue No: Vol. 44, No. 5 (2018)
  • Large deformation shape uncertainty quantification in acoustic scattering
    • Authors: R. Hiptmair; L. Scarabosio; C. Schillings; Ch. Schwab
      Pages: 1475 - 1518
      Abstract: We address shape uncertainty quantification for the two-dimensional Helmholtz transmission problem, where the shape of the scatterer is the only source of uncertainty. In the framework of the so-called deterministic approach, we provide a high-dimensional parametrization for the interface. Each domain configuration is mapped to a nominal configuration, obtaining a problem on a fixed domain with stochastic coefficients. To compute surrogate models and statistics of quantities of interest, we apply an adaptive, anisotropic Smolyak algorithm, which allows to attain high convergence rates that are independent of the number of dimensions activated in the parameter space. We also develop a regularity theory with respect to the spatial variable, with norm bounds that are independent of the parametric dimension. The techniques and theory presented in this paper can be easily generalized to any elliptic problem on a stochastic domain.
      PubDate: 2018-10-01
      DOI: 10.1007/s10444-018-9594-8
      Issue No: Vol. 44, No. 5 (2018)
  • Approximately dual Gabor frames and almost perfect reconstruction based on
           a class of window functions
    • Authors: Ole Christensen; Augustus J. E. M. Janssen; Hong Oh Kim; Rae Young Kim
      Pages: 1519 - 1535
      Abstract: It is a well-known problem in Gabor analysis how to construct explicitly given dual frames associated with a given frame. In this paper we will consider a class of window functions for which approximately dual windows can be calculated explicitly. The method makes it possible to get arbitrarily close to perfect reconstruction by allowing the modulation parameter to vary. Explicit estimates for the deviation from perfect reconstruction are provided for some of the standard functions in Gabor analysis, e.g., the Gaussian and the two-sided exponential function.
      PubDate: 2018-10-01
      DOI: 10.1007/s10444-018-9595-7
      Issue No: Vol. 44, No. 5 (2018)
  • Expanded mixed FEM with lowest order RT elements for nonlinear and
           nonlocal parabolic problems
    • Authors: Nisha Sharma; Amiya K. Pani; Kapil K. Sharma
      Pages: 1537 - 1571
      Abstract: In this paper, an expanded mixed finite element method with lowest order Raviart Thomas elements is developed and analyzed for a class of nonlinear and nonlocal parabolic problems. After obtaining some regularity results for the exact solution, a priori error estimates for the semidiscrete problem are established. Based on a linearized backward Euler method, a complete discrete scheme is proposed and a variant of Brouwer’s fixed point theorem is used to derive an existence of a fully discrete solution. Further, a priori error estimates for the fully discrete scheme are established. Finally, numerical experiments are conducted to confirm our theoretical findings.
      PubDate: 2018-10-01
      DOI: 10.1007/s10444-018-9596-6
      Issue No: Vol. 44, No. 5 (2018)
  • Linear second order in time energy stable schemes for hydrodynamic models
           of binary mixtures based on a spatially pseudospectral approximation
    • Authors: Yuezheng Gong; Jia Zhao; Qi Wang
      Pages: 1573 - 1600
      Abstract: We develop two linear, second order energy stable schemes for solving the governing system of partial differential equations of a hydrodynamic phase field model of binary fluid mixtures. We first apply the Fourier pseudo-spectral approximation to the partial differential equations in space to obtain a semi-discrete, time-dependent, ordinary differential and algebraic equation (DAE) system, which preserves the energy dissipation law at the semi-discrete level. Then, we discretize the DAE system by the Crank-Nicolson (CN) and the second-order backward differentiation/extrapolation (BDF/EP) method in time, respectively, to obtain two fully discrete systems. We show that the CN method preserves the energy dissipation law while the BDF/EP method does not preserve it exactly but respects the energy dissipation property of the hydrodynamic model. The two new fully discrete schemes are linear, unconditional stable, second order accurate in time and high order in space, and uniquely solvable as linear systems. Numerical examples are presented to show the convergence property as well as the efficiency and accuracy of the new schemes in simulating mixing dynamics of binary polymeric solutions.
      PubDate: 2018-10-01
      DOI: 10.1007/s10444-018-9597-5
      Issue No: Vol. 44, No. 5 (2018)
  • A fully discrete Galerkin method for Abel-type integral equations
    • Authors: Urs Vögeli; Khadijeh Nedaiasl; Stefan A. Sauter
      Pages: 1601 - 1626
      Abstract: In this paper, we present a Galerkin method for Abel-type integral equation with a general class of kernel. Stability and quasi-optimal convergence estimates are derived in fractional-order Sobolev norms. The fully-discrete Galerkin method is defined by employing simple tensor-Gauss quadrature. We develop a corresponding perturbation analysis which allows to keep the number of quadrature points small. Numerical experiments have been performed which illustrate the sharpness of the theoretical estimates and the sensitivity of the solution with respect to some parameters in the equation.
      PubDate: 2018-10-01
      DOI: 10.1007/s10444-018-9598-4
      Issue No: Vol. 44, No. 5 (2018)
  • Rational frames of minimal twist along space curves under specified
           boundary conditions
    • Authors: Rida T. Farouki; Hwan Pyo Moon
      Pages: 1627 - 1650
      Abstract: An adapted orthonormal frame (f1(ξ),f2(ξ),f3(ξ)) on a space curve r(ξ), ξ ∈ [ 0, 1 ] comprises the curve tangent \(\mathbf {f}_{1}(\xi ) =\mathbf {r}^{\prime }(\xi )/ \mathbf {r}^{\prime }(\xi ) \) and two unit vectors f2(ξ),f3(ξ) that span the normal plane. The variation of this frame is specified by its angular velocity Ω = Ω1f1 + Ω2f2 + Ω3f3, and the twist of the framed curve is the integral of the component Ω1 with respect to arc length. A minimal twist frame (MTF) has the least possible twist value, subject to prescribed initial and final orientations f2(0),f3(0) and f2(1),f3(1) of the normal–plane vectors. Employing the Euler–Rodrigues frame (ERF) — a rational adapted frame defined on spatial Pythagorean–hodograph curves — as an intermediary, an exact expression for an MTF with Ω1 = constant is derived. However, since this involves rather complicated transcendental terms, a construction of rational MTFs is proposed by the imposition of a rational rotation on the ERF normal–plane vectors. For spatial PH quintics, it is shown that rational MTFs compatible with the boundary conditions can be constructed, with only modest deviations of Ω1 about the mean value, by a rational quartic normal–plane rotation of the ERF. If necessary, subdivision methods can be invoked to ensure that the rational MTF is free of inflections, or to more accurately approximate a constant Ω1. The procedure is summarized by an algorithm outline, and illustrated by a representative selection of computed examples.
      PubDate: 2018-10-01
      DOI: 10.1007/s10444-018-9599-3
      Issue No: Vol. 44, No. 5 (2018)
  • Randomized algorithms for distributed computation of principal component
           analysis and singular value decomposition
    • Authors: Huamin Li; Yuval Kluger; Mark Tygert
      Pages: 1651 - 1672
      Abstract: Randomized algorithms provide solutions to two ubiquitous problems: (1) the distributed calculation of a principal component analysis or singular value decomposition of a highly rectangular matrix, and (2) the distributed calculation of a low-rank approximation (in the form of a singular value decomposition) to an arbitrary matrix. Carefully honed algorithms yield results that are uniformly superior to those of the stock, deterministic implementations in Spark (the popular platform for distributed computation); in particular, whereas the stock software will without warning return left singular vectors that are far from numerically orthonormal, a significantly burnished randomized implementation generates left singular vectors that are numerically orthonormal to nearly the machine precision.
      PubDate: 2018-10-01
      DOI: 10.1007/s10444-018-9600-1
      Issue No: Vol. 44, No. 5 (2018)
  • Left Lie reduction for curves in homogeneous spaces
    • Authors: Erchuan Zhang; Lyle Noakes
      Pages: 1673 - 1686
      Abstract: Let H be a closed subgroup of a connected finite-dimensional Lie group G, where the canonical projection π : G → G/H is a Riemannian submersion with respect to a bi-invariant Riemannian metric on G. Given a C∞ curve x : [a, b] → G/H, let \(\tilde {x}:[a,b]\rightarrow G\) be the horizontal lifting of x with \(\tilde {x}(a)=e\) , where e denotes the identity of G. When (G, H) is a Riemannian symmetric pair, we prove that the left Lie reduction \(V(t):=\tilde x(t)^{-1}\dot {\tilde x}(t)\) of \(\dot {\tilde x}(t)\) for t ∈ [a, b] can be identified with the parallel pullbackP(t) of the velocity vector \(\dot {x}(t)\) from x(t) to x(a) along x. Then left Lie reductions are used to investigate Riemannian cubics, Riemannian cubics in tension and elastica in homogeneous spaces G/H. Simplifications of reduced equations are found when (G, H) is a Riemannian symmetric pair. These equations are compared with equations known for curves in Lie groups, focusing on the special case of Riemannian cubics in the 3-dimensional unit sphere S3.
      PubDate: 2018-10-01
      DOI: 10.1007/s10444-018-9601-0
      Issue No: Vol. 44, No. 5 (2018)
  • Linear hybrid-variable methods for advection equations
    • Authors: Xianyi Zeng
      Abstract: We propose a general hybrid-variable (HV) framework to solve linear advection equations by utilizing both cell-average approximations and nodal approximations. The construction is carried out for 1D problems, where the spatial discretization for cell averages is obtained from the integral form of the governing equation whereas that for nodal values is constructed using hybrid-variable discrete differential operators (HV-DDO); explicit Runge-Kutta methods are employed for marching the solutions in time. We demonstrate the connection between the HV-DDO and Hermite interpolation polynomials, and show that it can be constructed to arbitrary order of accuracy. In particular, we derive explicit formula for the coefficients to achieve the optimal order of accuracy given any compact stencil of the HV-DDO. The superconvergence of the proposed HV methods is then proved: these methods have one-order higher spatial accuracy than the designed order of the HV-DDO; in contrast, for conventional methods that only utilize one type of variables, the two orders are the same. Hence, the proposed method can potentially achieve higher-order accuracy given the same computational cost, comparing to existing finite difference methods. We then prove the linear stability of sample HV methods with up to fifth-order accuracy in the case of Cauchy problems. Next, we demonstrate how the HV methods can be extended to 2D problems as well as nonlinear conservation laws with smooth solutions. The performance of the sample HV methods are assessed by extensive 1D and 2D benchmark tests of linear advection equations, the nonlinear Euler equations, and the nonlinear Buckely-Leverett equation.
      PubDate: 2018-11-10
      DOI: 10.1007/s10444-018-9647-z
  • Collocation methods for general Riemann-Liouville two-point boundary value
    • Authors: Hui Liang; Martin Stynes
      Abstract: General Riemann-Liouville linear two-point boundary value problems of order αp, where n − 1 < αp < n for some positive integer n, are investigated on the interval [0,b]. It is shown first that the natural degree of regularity to impose on the solution y of the problem is \(y\in C^{n-2}[0,b]\) and \(D^{\alpha _{p}-1}y\in C[0,b]\) , with further restrictions on the behavior of the derivatives of y(n− 2) (these regularity conditions differ significantly from the natural regularity conditions in the corresponding Caputo problem). From this regularity, it is deduced that the most general choice of boundary conditions possible is \(y(0) = y^{\prime }(0) = {\dots } = y^{(n-2)}(0) = 0\) and \({\sum }_{j = 0}^{n_{1}}\beta _{j}y^{(j)}(b_{1}) =\gamma \) for some constants βj and γ, with b1 ∈ (0,b] and \(n_{1}\in \{0, 1, \dots , n-1\}\) . A wide class of transformations of the problem into weakly singular Volterra integral equations (VIEs) is then investigated; the aim is to choose the transformation that will yield the most accurate results when the VIE is solved using a collocation method with piecewise polynomials. Error estimates are derived for this method and for its iterated variant. Numerical results are given to support the theoretical conclusions.
      PubDate: 2018-11-08
      DOI: 10.1007/s10444-018-9645-1
  • Model reduction of complex dynamical systems
    • Authors: Peter Benner; Heike Faßbender; Michael Hinze; Tatjana Stykel; Ralf Zimmermann
      PubDate: 2018-10-30
      DOI: 10.1007/s10444-018-9640-6
  • Adaptive estimation for nonlinear systems using reproducing kernel Hilbert
    • Authors: Parag Bobade; Suprotim Majumdar; Savio Pereira; Andrew J. Kurdila; John B. Ferris
      Abstract: This paper extends a conventional, general framework for online adaptive estimation problems for systems governed by unknown or uncertain nonlinear ordinary differential equations. The central feature of the theory introduced in this paper represents the unknown function as a member of a reproducing kernel Hilbert space (RKHS) and defines a distributed parameter system (DPS) that governs state estimates and estimates of the unknown function. Under the assumption that full state measurements are available, this paper (1) derives sufficient conditions for the existence and stability of the infinite dimensional online estimation problem, (2) derives existence and stability of finite dimensional approximations of the infinite dimensional approximations, and (3) determines sufficient conditions for the convergence of finite dimensional approximations to the infinite dimensional online estimates. A new condition for persistency of excitation in a RKHS in terms of its evaluation functionals is introduced in the paper that enables proof of convergence of the finite dimensional approximations of the unknown function in the RKHS. This paper studies two particular choices of the RKHS, those that are generated by exponential functions and those that are generated by multiscale kernels defined from a multiresolution analysis.
      PubDate: 2018-10-30
      DOI: 10.1007/s10444-018-9639-z
  • Hybrid asymptotic/numerical methods for the evaluation of layer heat
           potentials in two dimensions
    • Authors: Jun Wang; Leslie Greengard
      Abstract: We present a hybrid asymptotic/numerical method for the accurate computation of single- and double-layer heat potentials in two dimensions. It has been shown in previous work that simple quadrature schemes suffer from a phenomenon called “geometrically induced stiffness,” meaning that formally high-order accurate methods require excessively small time steps before the rapid convergence rate is observed. This can be overcome by analytic integration in time, requiring the evaluation of a collection of spatial boundary integral operators with non-physical, weakly singular kernels. In our hybrid scheme, we combine a local asymptotic approximation with the evaluation of a few boundary integral operators involving only Gaussian kernels, which are easily accelerated by a new version of the fast Gauss transform. This new scheme is robust, avoids geometrically induced stiffness, and is easy to use in the presence of moving geometries. Its extension to three dimensions is natural and straightforward, and should permit layer heat potentials to become flexible and powerful tools for modeling diffusion processes.
      PubDate: 2018-10-24
      DOI: 10.1007/s10444-018-9641-5
  • Fokker-Planck equation driven by asymmetric Lévy motion
    • Authors: Xiao Wang; Wenpeng Shang; Xiaofan Li; Jinqiao Duan; Yanghong Huang
      Abstract: Non-Gaussian Lévy noises are present in many models for understanding underlining principles of physics, finance, biology, and more. In this work, we consider the Fokker-Planck equation (FPE) due to one-dimensional asymmetric Lévy motion, which is a non-local partial differential equation. We present an accurate numerical quadrature for the singular integrals in the non-local FPE and develop a fast summation method to reduce the order of the complexity from O(J2) to \(O(J\log J)\) in one time step, where J is the number of unknowns. We also provide conditions under which the numerical schemes satisfy maximum principle. Our numerical method is validated by comparing with exact solutions for special cases. We also discuss the properties of the probability density functions and the effects of various factors on the solutions, including the stability index, the skewness parameter, the drift term, the Gaussian and non-Gaussian noises, and the domain size.
      PubDate: 2018-10-24
      DOI: 10.1007/s10444-018-9642-4
  • Asymptotically optimal approximation of some stochastic integrals and its
           applications to the strong second-order methods
    • Authors: Xiao Tang; Aiguo Xiao
      Abstract: This study concerns the approximation of some stochastic integrals used in the strong second-order methods for several classes of stochastic differential equations. An explicit construction of the asymptotically optimal approximation (in the mean-square sense) to these stochastic integrals is proposed based on a Karhunen-Loève expansion of a Wiener process. This asymptotically optimal approximation is more efficient by comparison with the Fourier series approximation introduced by Kloeden and Platen (1992) and the Taylor approximation introduced by Milstein and Tretyakov (2004). In the numerical test part, we replace the stochastic integrals appearing in the strong second-order methods with our corresponding approximations. The numerical results show that those strong second-order methods can perform very well by using our approximation method.
      PubDate: 2018-10-24
      DOI: 10.1007/s10444-018-9638-0
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