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  Subjects -> MATHEMATICS (Total: 874 journals)
    - APPLIED MATHEMATICS (71 journals)
    - GEOMETRY AND TOPOLOGY (19 journals)
    - MATHEMATICS (647 journals)
    - MATHEMATICS (GENERAL) (41 journals)
    - NUMERICAL ANALYSIS (19 journals)
    - PROBABILITIES AND MATH STATISTICS (77 journals)

MATHEMATICS (647 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 3)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 2)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 7)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 16)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 4)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 21)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 11)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 5)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 5)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 3)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 7)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 15)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 1)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 10)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 1)
Advances in Materials Sciences     Open Access   (Followers: 16)
Advances in Mathematical Physics     Open Access   (Followers: 6)
Advances in Mathematics     Full-text available via subscription   (Followers: 10)
Advances in Numerical Analysis     Open Access   (Followers: 4)
Advances in Operations Research     Open Access   (Followers: 11)
Advances in Porous Media     Full-text available via subscription   (Followers: 4)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 5)
Advances in Pure Mathematics     Open Access   (Followers: 4)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 7)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 3)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Full-text available via subscription   (Followers: 5)
Algorithms     Open Access   (Followers: 9)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Biostatistics     Open Access   (Followers: 9)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 3)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 7)
American Journal of Operations Research     Open Access   (Followers: 5)
American Mathematical Monthly     Full-text available via subscription   (Followers: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 7)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis     Hybrid Journal   (Followers: 2)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 4)
Analysis Mathematica     Full-text available via subscription  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales UMCS, Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 8)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription  
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 6)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 5)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 1)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 12)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 4)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 4)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access  
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 2)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 1)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 4)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 18)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Journal of Current Engineering & Maths     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 2)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access  
Baltic International Yearbook of Cognition, Logic and Communication     Open Access  
Basin Research     Hybrid Journal   (Followers: 3)
BIBECHANA     Open Access  
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 21)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 7)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 1)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 17)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal  
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
ChemSusChem     Hybrid Journal   (Followers: 7)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Clean Air Journal     Full-text available via subscription   (Followers: 2)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Full-text available via subscription   (Followers: 2)
COMBINATORICA     Hybrid Journal  
Combustion Theory and Modelling     Hybrid Journal   (Followers: 13)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 1)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 9)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 2)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 4)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 5)
Concrete Operators     Open Access   (Followers: 4)
Confluentes Mathematici     Hybrid Journal  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 14)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 12)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 29)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 2)
Discrete Mathematics     Hybrid Journal   (Followers: 7)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 3)
Energy for Sustainable Development     Hybrid Journal   (Followers: 9)
Enseñanza de las Ciencias : Revista de Investigación y Experiencias Didácticas     Open Access  
Ensino da Matemática em Debate     Open Access  
Entropy     Open Access   (Followers: 5)
ESAIM: Control Optimisation and Calculus of Variations     Full-text available via subscription   (Followers: 1)
European Journal of Combinatorics     Full-text available via subscription   (Followers: 4)
European Journal of Mathematics     Hybrid Journal   (Followers: 1)
European Scientific Journal     Open Access   (Followers: 2)
Experimental Mathematics     Hybrid Journal   (Followers: 3)
Expositiones Mathematicae     Hybrid Journal   (Followers: 2)
Facta Universitatis, Series : Mathematics and Informatics     Open Access  
Fasciculi Mathematici     Open Access  
Finite Fields and Their Applications     Full-text available via subscription   (Followers: 4)
Fixed Point Theory and Applications     Open Access   (Followers: 1)
Formalized Mathematics     Open Access   (Followers: 2)
Foundations and Trends® in Econometrics     Full-text available via subscription   (Followers: 4)

        1 2 3 4 | Last

Journal Cover Computers & Mathematics with Applications
  [SJR: 1.092]   [H-I: 84]   [5 followers]  Follow
    
   Full-text available via subscription Subscription journal
   ISSN (Print) 0898-1221
   Published by Elsevier Homepage  [3042 journals]
  • A remark on finite element schemes for nearly incompressible elasticity
    • Abstract: Publication date: Available online 20 June 2017
      Source:Computers & Mathematics with Applications
      Author(s): Daniele Boffi, Rolf Stenberg
      In this paper we discuss mixed finite element methods for nearly incompressible elasticity. We show that if a method uses the hydrostatic pressure as unknown, then the finite element spaces have to satisfy the condition of the ellipticity on the kernel, in addition to the well-known Babuška–Brezzi condition. Some known elements are proved to satisfy this condition.

      PubDate: 2017-06-20T16:49:54Z
       
  • On conservation laws by Lie symmetry analysis for (2+1)-dimensional
           Bogoyavlensky–Konopelchenko equation in wave propagation
    • Abstract: Publication date: Available online 19 June 2017
      Source:Computers & Mathematics with Applications
      Author(s): S. Saha Ray
      In this paper, using the Lie group analysis method, the infinitesimal generators for (2+1)-dimensional Bogoyavlensky–Konopelchenko equation are obtained. The new concept of nonlinear self-adjointness of differential equations is used for construction of nonlocal conservation laws. The conservation laws for the (2+1)-dimensional Bogoyavlensky–Konopelchenko equation are obtained by using the new conservation theorem method and the formal Lagrangian approach. Transforming this equation into a system of equations involving with two dependent variables, it has been shown that the resultant system of equations is quasi self-adjoint and finally the new nonlocal conservation laws are constructed by using the Lie symmetry operators.

      PubDate: 2017-06-20T16:49:54Z
       
  • Construction of DPG Fortin operators for second order problems
    • Abstract: Publication date: Available online 19 June 2017
      Source:Computers & Mathematics with Applications
      Author(s): Sriram Nagaraj, Socratis Petrides, Leszek F. Demkowicz
      The use of “ideal” optimal test functions in a Petrov–Galerkin scheme guarantees the discrete stability of the variational problem. However, in practice, the computation of the ideal optimal test functions is computationally intractable. In this paper, we study the effect of using approximate, “practical” test functions on the stability of the DPG (discontinuous Petrov–Galerkin) method and the change in stability between the “ideal” and “practical” cases is analyzed by constructing a Fortin operator. We highlight the construction of an “optimal” DPG Fortin operator for H 1 and H ( div ) spaces; the continuity constant of the Fortin operator is a measure of the loss of stability between the ideal and practical DPG methods. We take a two-pronged approach: first, we develop a numerical procedure to estimate an upper bound on the continuity constant of the Fortin operator in terms of the inf–sup constant γ h of an auxiliary problem. Second, we construct a sequence of approximate Fortin operators and exactly compute the continuity constants of the approximate operators, which provide a lower bound on the exact Fortin continuity constant. Our results shed light not only on the change in stability by using practical test functions, but also indicate how stability varies with the approximation order p and the enrichment order Δ p . The latter has important ramifications when one wishes to pursue local h p -adaptivity.

      PubDate: 2017-06-20T16:49:54Z
       
  • Hybrid Laplace transform and finite difference methods for pricing
           American options under complex models
    • Abstract: Publication date: Available online 19 June 2017
      Source:Computers & Mathematics with Applications
      Author(s): Jingtang Ma, Zhiqiang Zhou, Zhenyu Cui
      In this paper, we propose a hybrid Laplace transform and finite difference method to price (finite-maturity) American options, which is applicable to a wide variety of asset price models including the constant elasticity of variance (CEV), hyper-exponential jump–diffusion (HEJD), Markov regime switching models, and the finite moment log stable (FMLS) models. We first apply Laplace transforms to free boundary partial differential equations (PDEs) or fractional partial differential equations (FPDEs) governing the American option prices with respect to time, and obtain second order ordinary differential equations (ODEs) or fractional differential equations (FDEs) with free boundary, which is named as the early exercise boundary in the American option pricing. Then, we develop an iterative algorithm based on finite difference methods to solve the ODEs or FDEs together with the unknown free boundary values in the Laplace space. Both the early exercise boundary and the prices of American options are recovered through inverse Laplace transforms. Numerical examples demonstrate the accuracy and efficiency of the method in CEV, HEJD, Markov regime switching models and the FMLS models.

      PubDate: 2017-06-20T16:49:54Z
       
  • On preconditioned generalized shift-splitting iteration methods for saddle
           point problems
    • Abstract: Publication date: Available online 19 June 2017
      Source:Computers & Mathematics with Applications
      Author(s): Yang Cao, Shu-Xin Miao, Zhi-Ru Ren
      We study a preconditioned generalized shift-splitting iteration method for solving saddle point problems. The unconditional convergence theory of the preconditioned generalized shift-splitting iteration method is established. When the splitting matrix is used as a preconditioner, we analyze eigenvalue distribution of the preconditioned saddle point matrix. It is proved that complex eigenvalues having nonzero imaginary parts of the preconditioned matrix are located in an intersection of two circles and the real parts of all eigenvalues of the preconditioned matrix are located in a positive interval. Numerical experiments are used to verify our theoretical results and illustrate effectiveness of the proposed iteration method and the corresponding splitting preconditioner.

      PubDate: 2017-06-20T16:49:54Z
       
  • On the virtual element method for topology optimization on polygonal
           meshes: A numerical study
    • Abstract: Publication date: Available online 17 June 2017
      Source:Computers & Mathematics with Applications
      Author(s): P.F. Antonietti, M. Bruggi, S. Scacchi, M. Verani
      It is well known that the solution of topology optimization problems may be affected both by the geometric properties of the computational mesh, which can steer the minimization process towards local (and non-physical) minima, and by the accuracy of the method employed to discretize the underlying differential problem, which may not be able to correctly capture the physics of the problem. In light of the above remarks, in this paper we consider polygonal meshes and employ the virtual element method (VEM) to solve two classes of paradigmatic topology optimization problems, one governed by nearly-incompressible and compressible linear elasticity and the other by Stokes equations. Several numerical results show the virtues of our polygonal VEM based approach with respect to more standard methods.

      PubDate: 2017-06-20T16:49:54Z
       
  • A discontinuous Galerkin method for stochastic Cahn–Hilliard
           equations
    • Abstract: Publication date: Available online 16 June 2017
      Source:Computers & Mathematics with Applications
      Author(s): Chen Li, Ruibin Qin, Ju Ming, Zhongming Wang
      In this paper, a discontinuous Galerkin method for the stochastic Cahn-Hilliard equation with additive random noise, which preserves the conservation of mass, is investigated. Numerical analysis and error estimates are carried out for the linearized stochastic Cahn-Hilliard equation. The effects of the noises on the accuracy of our scheme are also presented. Numerical examples simulated by Monte Carlo method for both linear and nonlinear stochastic Cahn-Hilliard equations are presented to illustrate the convergence rate and validate our conclusion.

      PubDate: 2017-06-20T16:49:54Z
       
  • A posteriori error estimates for a Virtual Element Method for the Steklov
           eigenvalue problem
    • Abstract: Publication date: Available online 9 June 2017
      Source:Computers & Mathematics with Applications
      Author(s): David Mora, Gonzalo Rivera, Rodolfo Rodríguez
      The paper deals with the a posteriori error analysis of a virtual element method for the Steklov eigenvalue problem. The virtual element method has the advantage of using general polygonal meshes, which allows implementing efficiently mesh refinement strategies. We introduce a residual type a posteriori error estimator and prove its reliability and global efficiency. Local efficiency estimates also hold, although in some elements they involve boundary terms that are not known to be locally negligible. We use the corresponding error estimator to drive an adaptive scheme. Finally, we report the results of a couple of numerical tests, that allow us to assess the performance of this approach.

      PubDate: 2017-06-10T16:34:42Z
       
  • Isotropic and anisotropic total variation regularization in electrical
           impedance tomography
    • Abstract: Publication date: Available online 9 June 2017
      Source:Computers & Mathematics with Applications
      Author(s): Gerardo González, Ville Kolehmainen, Aku Seppänen
      This paper focuses on studying the effects of isotropic and anisotropic total variation (TV) regularization in electrical impedance tomography (EIT). A characteristic difference between these two widely used TV regularization methods is that the isotropic TV is rotationally invariant and the anisotropic TV is not. The rotational variance of the anisotropic TV is known to cause geometric distortions by favoring edge orientations that are aligned with co-ordinate axes. In many applications, such as transmission tomography problems, these distortions often play only a minor role in the overall accuracy of reconstructed images, because the measurement data is sensitive to the shapes of the edges in the imaged domain. In EIT and other diffusive image modalities, however, the data is severely less sensitive to the fine details of edges, and it is an open question how large impact the selection of the TV regularization variant has on the reconstructed images. In this work, this effect is investigated based on a set of experiments. The results demonstrate that the choice between isotropic and anisotropic TV regularization indeed has a significant impact on the properties of EIT reconstructions; especially, the tendency of the anisotropic TV to favor edges aligned with co-ordinate axes is shown to yield large geometric distortions in EIT reconstructions.

      PubDate: 2017-06-10T16:34:42Z
       
  • On the solitary waves, breather waves and rogue waves to a generalized
           (3+1)-dimensional Kadomtsev–Petviashvili equation
    • Abstract: Publication date: Available online 7 June 2017
      Source:Computers & Mathematics with Applications
      Author(s): Xiu-Bin Wang, Shou-Fu Tian, Hui Yan, Tian Tian Zhang
      Under investigation in this work is a generalized ( 3 + 1 )-dimensional Kadomtsev–Petviashvili (GKP) equation, which can describe many nonlinear phenomena in fluid dynamics. By virtue of the Bell’s polynomials, an effective and straightforward way is presented to explicitly construct its bilinear form and soliton solution. Furthermore, based on the bilinear formalism and the extended homoclinic test method, the kinky breather wave solutions and rational breather wave solutions of the equation are well constructed. It is hoped that our results can be used to enrich the dynamical behavior of the ( 3 + 1 )-dimensional nonlinear wave fields.

      PubDate: 2017-06-10T16:34:42Z
       
  • A comparative study of the axisymmetric lattice Boltzmann models under the
           incompressible limit
    • Abstract: Publication date: Available online 7 June 2017
      Source:Computers & Mathematics with Applications
      Author(s): Liangqi Zhang, Shiliang Yang, Zhong Zeng, Jie Chen, Lingquan Wang, Jia Wei Chew
      A comparative study on four axisymmetric lattice Boltzmann (LB) models, namely, the kinetic theory based model by Guo et al. (2009), the consistent model by Li et al. (2010), the centered scheme model by Zhou (2011), and our model (based on applying the centered scheme to the Guo et al. (2009) model), is conducted both theoretically and numerically. The finite difference interpretation of the LB method by Junk (2001) is applied to evaluate the accuracy of the models under the incompressible limit. Particularly, the finite difference stencils adopted for the spatial gradient terms in the macroscopic axisymmetric Navier–Stokes (N–S) equations are compared. Besides, the numerical performance (i.e., the numerical accuracy, stability and the convergence efficiency) of the models is compared by two benchmark tests, namely, the unsteady-state Womersley flow and the cylindrical cavity flow. The numerical results accord well with the theoretical analysis. Additionally, it is also found that the numerical stability of the axisymmetric LB models is effectively improved by removing the effects from the non-hydrodynamic variables.

      PubDate: 2017-06-10T16:34:42Z
       
  • Iterative differential quadrature solutions for Bratu problem
    • Abstract: Publication date: 15 July 2017
      Source:Computers & Mathematics with Applications, Volume 74, Issue 2
      Author(s): Ola Ragb, L.F. Seddek, M.S. Matbuly
      A numerical scheme based on differential quadrature methods, is introduced for solving Bratu problem. The problem is firstly reduced to an iterative one. Then, both of differential quadrature method (DQM) and moving least squares differential quadrature method (MLSDQM) are applied to solve iteratively the nonlinear problem. The proposed scheme successfully computes multiple solutions to Bratu’s problem. The obtained results agree with the 1D and 2D closed forms. Further a parametric study is introduced to investigate the computational characteristics of the proposed scheme.

      PubDate: 2017-06-06T16:30:40Z
       
  • A note on the Gaussons of some new logarithmic evolution equations
    • Abstract: Publication date: 15 July 2017
      Source:Computers & Mathematics with Applications, Volume 74, Issue 2
      Author(s): Jianping Yu, Yongli Sun
      In this paper, we study the Gaussian solitary waves for some nonlinear evolution equations with logarithmic nonlinearities. These studied logarithmic evolution equations are the generalized logarithmic BBM equations, the logarithmic ( 2 + 1 ) -dimensional KP-like equations, the logarithmic ( 3 + 1 ) -dimensional KP-like equations, the generalized logarithmic ( 2 + 1 ) -dimensional Klein-Gordon equations and the generalized logarithmic ( 3 + 1 ) -dimensional Klein-Gordon equations. We not only prove that they possess Gaussons: solitary wave solutions of Gaussian shape but also derive the relationships among the parameters.

      PubDate: 2017-06-06T16:30:40Z
       
  • The existence and the concentration behavior of normalized solutions for
           the L2-critical Schrödinger–Poisson system
    • Abstract: Publication date: 15 July 2017
      Source:Computers & Mathematics with Applications, Volume 74, Issue 2
      Author(s): Hongyu Ye
      In this paper, we study the existence and the concentration behavior of critical points for the following functional derived from the Schrödinger–Poisson system: E ( u ) = 1 2 ∫ R 3 ∇ u 2 + 1 4 ∫ R 3 ( x − 1 ∗ u 2 ) u 2 − 3 10 ∫ R 3 u 10 3 constrained on the L 2 -spheres S ( c ) = { u ∈ H 1 ( R 3 ) u 2 = c } when c > c ∗ = Q 2 , where Q is up to translations, the unique positive of − Δ Q + 2 3 Q = Q 4 3 Q in R 3 . As such constrained problem is L 2 -critical, E ( u ) is unbounded from below on S ( c ) when c > c ∗ and the existence of critical points constrained on S ( c ) is obtained by a mountain pass argument on S ( c ) . We show that there exists c 1 > ( 9 7 ) 3 4 c ∗ such that E ( u ) has at least one positive critical point restricted to S ( c ) for c ∗ < c ≤ c 1 . As c approaches c
      PubDate: 2017-06-06T16:30:40Z
       
  • Local RBF method for multi-dimensional partial differential equations
    • Abstract: Publication date: 15 July 2017
      Source:Computers & Mathematics with Applications, Volume 74, Issue 2
      Author(s): Imtiaz Ahmad, Siraj-ul-Islam, Abdul Q.M. Khaliq
      In this paper, a local meshless differential quadrature collocation method is utilized to solve multi-dimensional reaction–convection–diffusion PDEs numerically. In some cases, global version of the meshless method is considered as well. The meshless methods approximate solution on scattered and uniform nodes in both local and global sense. In the case of convection-dominated PDEs, the local meshless method is coupled with an upwind technique to avoid spurious oscillations. For this purpose, a physically motivated local domain is utilized in the flow direction. Both regular and irregular geometries are taken into consideration. Numerical experiments are performed to demonstrate effective applications and accuracy of the meshless method on regular and irregular domains.

      PubDate: 2017-06-06T16:30:40Z
       
  • Global solution of the critical Burgers equation in N Dimensions
    • Abstract: Publication date: 15 July 2017
      Source:Computers & Mathematics with Applications, Volume 74, Issue 2
      Author(s): Shaolei Ru, Jiecheng Chen
      In this paper, we first prove the local well-posedness of the fractional Burgers equations in N Dimensions. Combining the local well-posedness and the method of modulus of continuity, we show the global well-posedness of the N-D critical Burgers equation in critical Besov spaces B ̇ p , 1 N p ( R N ) with p ∈ [ N , ∞ ) .

      PubDate: 2017-06-06T16:30:40Z
       
  • Convergence estimates for a plane elasticity problem solved by the
           Galerkin boundary integral formulation with NURBS
    • Abstract: Publication date: 15 July 2017
      Source:Computers & Mathematics with Applications, Volume 74, Issue 2
      Author(s): Andrzej Karafiat
      A classical mixed boundary-value problem of linear elasticity in two dimensions in the Galerkin boundary integral formulation is considered. We prove a-priori error estimates of the solution to this problem by the isogeometric adaptive method using NURBS. The estimates include approximation of the boundary of the domain.

      PubDate: 2017-06-06T16:30:40Z
       
  • A new fourth-order compact scheme for the Navier–Stokes equations in
           irregular domains
    • Abstract: Publication date: 1 July 2017
      Source:Computers & Mathematics with Applications, Volume 74, Issue 1
      Author(s): D. Fishelov
      We present a high-order finite difference scheme for Navier–Stokes equations in irregular domains. The scheme is an extension of a fourth-order scheme for Navier–Stokes equations in streamfunction formulation on a rectangular domain (Ben-Artzi et al., 2010). The discretization offered here contains two types of interior points. The first is regular interior points, where all eight neighboring points of a grid point are inside the domain and not too close to the boundary. The second is interior points where at least one of the closest eight neighbors is outside the computational domain or too close to the boundary. In the second case we design discrete operators which approximate spatial derivatives of the streamfunction on irregular meshes, using discretizations of pure derivatives in the x , y and along the diagonals of the element.

      PubDate: 2017-05-26T14:42:33Z
       
  • Computational time and domain size analysis of porous media flows using
           the lattice Boltzmann method
    • Abstract: Publication date: 1 July 2017
      Source:Computers & Mathematics with Applications, Volume 74, Issue 1
      Author(s): Mayken Espinoza-Andaluz, Martin Andersson, Bengt Sundén
      The purpose of this study is to investigate the computational time required to describe the fluid flow behavior through a porous medium and its relation to the corresponding domain size. The fluid flow behavior is recovered using the lattice Boltzmann method (LBM). The selected methodology has been applied because of its feasibility for mimicking the fluid flow behavior in complex geometries and moving boundaries. In this study, three different porosities are selected to calculate, for several sizes domain, the required computational time to reach the steady state. Two different cases are implemented: (1) increasing the transversal area, but keeping the layer thickness as a constant, and (2) increasing the total volume of the pore domain by increasing all the dimensions of the volume equally. The porous media are digitally generated by placing the solid obstacles randomly, but uniformly distributed in the whole domain. Several relationships relating the computational time, domain size and porosity are proposed. Additionally, an expression that relates the hydraulic tortuosity to the porosity is proposed.

      PubDate: 2017-05-26T14:42:33Z
       
  • Multi-domain muffin tin finite element density functional calculations for
           small molecules
    • Abstract: Publication date: 1 July 2017
      Source:Computers & Mathematics with Applications, Volume 74, Issue 1
      Author(s): Moritz Braun, Kingsley O. Obodo
      In this contribution a multi domain finite element density functional code for molecules is presented. The method makes use of higher order elements to enforce the continuity of the orbitals between the spherical domains and the interstitial domain. The salient computational details of the algorithm are described in some detail. Results of calculations for the orbital energies of methane, ethane, water, ammonia and benzene are given and compared with those obtained using GPAW.

      PubDate: 2017-05-26T14:42:33Z
       
  • Anisotropic hp-mesh optimization technique based on the continuous mesh
           and error models
    • Abstract: Publication date: 1 July 2017
      Source:Computers & Mathematics with Applications, Volume 74, Issue 1
      Author(s): Vít Dolejší, Georg May, Filip Roskovec, Pavel Solin
      We develop a new mesh adaptive technique for the numerical solution of partial differential equations (PDEs) using the h p -version of the finite element method ( h p -FEM). The technique uses a combination of approximation and interpolation error estimates to generate anisotropic triangular elements as well as appropriate polynomial approximation degrees. We present a h p -version of the continuous mesh model as well as the continuous error model which are used for the formulation of a mesh optimization problem. Solving the optimization problem leads to h p -mesh with the smallest number of degrees of freedom, under the constraint that the approximate solution has an error estimate below a given tolerance. Further, we propose an iterative algorithm to find a suitable anisotropic h p -mesh in the sense of the mesh optimization problem. Several numerical examples demonstrating the efficiency and applicability of the new method are presented.

      PubDate: 2017-05-26T14:42:33Z
       
  • Numerical modeling of pseudo-homogeneous fluid flow in a pipe with leaks
    • Abstract: Publication date: 1 July 2017
      Source:Computers & Mathematics with Applications, Volume 74, Issue 1
      Author(s): L. Molina-Espinosa, C.G. Aguilar-Madera, E.C. Herrera-Hernández, C. Verde
      This work deals with the numerical modeling of single-phase flow in a pipe with one leak. The mathematical model governing mass, momentum and energy transport was established containing three coupled partial differential equations. These governing equations were numerically solved by discretizing time and space with backward finite differences, leading to one implicit scheme at every time step. The numerical solution was validated with available lab data obtaining good agreement. We present relevant results as the time behavior of upstream and downstream flow and pressure, while varying the leak location. Besides, we also show the temperature, pressure and flow profiles along the pipe when the leak is located near the inlet and outlet of the pipe. The predictive capabilities of the numerical model are remarkable to simulate the transient state of volumetric flow rate and pressure when a single leak is provoked at the pipe. A future application of our numerical scheme is for rapid automatic detection of loss of containment in pipes transporting valuable fluids as, for instance: oil, refined hydrocarbons, fuel, liquid catalysts, etc.

      PubDate: 2017-05-26T14:42:33Z
       
  • ParMooN—A modernized program package based on mapped finite elements
    • Abstract: Publication date: 1 July 2017
      Source:Computers & Mathematics with Applications, Volume 74, Issue 1
      Author(s): Ulrich Wilbrandt, Clemens Bartsch, Naveed Ahmed, Najib Alia, Felix Anker, Laura Blank, Alfonso Caiazzo, Sashikumaar Ganesan, Swetlana Giere, Gunar Matthies, Raviteja Meesala, Abdus Shamim, Jagannath Venkatesan, Volker John
      ParMooN is a program package for the numerical solution of elliptic and parabolic partial differential equations. It inherits the distinct features of its predecessor MooNMD (John and Matthies, 2004): strict decoupling of geometry and finite element spaces, implementation of mapped finite elements as their definition can be found in textbooks, and a geometric multigrid preconditioner with the option to use different finite element spaces on different levels of the multigrid hierarchy. After having presented some thoughts about in-house research codes, this paper focuses on aspects of the parallelization for a distributed memory environment, which is the main novelty of ParMooN. Numerical studies, performed on compute servers, assess the efficiency of the parallelized geometric multigrid preconditioner in comparison with some parallel solvers that are available in the library PETSc. The results of these studies give a first indication whether the cumbersome implementation of the parallelized geometric multigrid method was worthwhile or not.

      PubDate: 2017-05-26T14:42:33Z
       
  • Design and control for torque ripple reduction of a 3-phase switched
           reluctance motor
    • Abstract: Publication date: 1 July 2017
      Source:Computers & Mathematics with Applications, Volume 74, Issue 1
      Author(s): Dániel Marcsa, Miklós Kuczmann
      A major problem in switched reluctance motor is torque ripple, which causes undesirable acoustic noise and vibration. This work focuses on reducing the undesirable torque ripple in 6/4-pole three-phase switched reluctance motor by geometry modification and using control technique. The proposed method combined the specially skewed rotor pole shape with instantaneous torque control with sinusoidal torque sharing function. The results of geometry modification are analysed through the three-dimensional finite element simulation to determine the appropriate skewing angle. The drive performances of conventional and modified motor are compared through the simulations. The effectiveness of the proposed method is also demonstrated and verified by the simulations.

      PubDate: 2017-05-26T14:42:33Z
       
  • Comparison of different FETI preconditioners for elastoplasticity
    • Abstract: Publication date: 1 July 2017
      Source:Computers & Mathematics with Applications, Volume 74, Issue 1
      Author(s): Martin Čermák, Václav Hapla, Jakub Kružík, Alexandros Markopoulos, Alena Vašatová
      This paper illustrates parallel solution of elastoplastic problems with hardening based on the TFETI domain decomposition method with several preconditioning strategies. We consider von Mises plasticity with isotropic hardening using the return mapping concept for one time step. To treat nonlinearity and nonsmoothness, we use the semismooth Newton method. In each Newton iteration, we solve a linear system of equations using the TFETI domain decomposition method with lumped, Dirichlet, or no preconditioner. Our PERMON software is used for the numerical experiments. The observed times and numbers of iterations are backed up by the regular condition number estimates. Both preconditioners accelerate the solution process in terms of the convergence rate. For the worst conditioned benchmark, the most expensive Dirichlet preconditioner gives the lowest computational times. This lets us suggest the Dirichlet preconditioner as the default choice for engineering problems.

      PubDate: 2017-05-26T14:42:33Z
       
  • High performance shallow water kernels for parallel overland flow
           simulations based on FullSWOF2D
    • Abstract: Publication date: 1 July 2017
      Source:Computers & Mathematics with Applications, Volume 74, Issue 1
      Author(s): Roland Wittmann, Hans-Joachim Bungartz, Philipp Neumann
      We describe code optimization and parallelization procedures applied to the sequential overland flow solver FullSWOF2D. Major difficulties when simulating overland flows comprise dealing with high resolution datasets of large scale areas which either cannot be computed on a single node either due to limited amount of memory or due to too many (time step) iterations resulting from the CFL condition. We address these issues in terms of two major contributions. First, we demonstrate a generic step-by-step transformation of the second order finite volume scheme in FullSWOF2D towards MPI parallelization. Second, the computational kernels are optimized by the use of templates and a portable vectorization approach. We discuss the load imbalance of the flux computation due to dry and wet cells and propose a solution using an efficient cell counting approach. Finally, scalability results are shown for different test scenarios along with a flood simulation benchmark using the Shaheen II supercomputer.

      PubDate: 2017-05-26T14:42:33Z
       
  • Parallelization of the multi-level hp-adaptive finite cell method
    • Abstract: Publication date: 1 July 2017
      Source:Computers & Mathematics with Applications, Volume 74, Issue 1
      Author(s): John N. Jomo, Nils Zander, Mohamed Elhaddad, Ali Özcan, Stefan Kollmannsberger, Ralf-Peter Mundani, Ernst Rank
      The multi-level h p -refinement scheme is a powerful extension of the finite element method that allows local mesh adaptation without the trouble of constraining hanging nodes. This is achieved through hierarchical high-order overlay meshes, a h p -scheme based on spatial refinement by superposition. An efficient parallelization of this method using standard domain decomposition approaches in combination with ghost elements faces the challenge of a large basis function support resulting from the overlay structure and is in many cases not feasible. In this contribution, a parallelization strategy for the multi-level h p -scheme is presented that is adapted to the scheme’s simple hierarchical structure. By distributing the computational domain among processes on the granularity of the active leaf elements and utilizing shared mesh data structures, good parallel performance is achieved, as redundant computations on ghost elements are avoided. We show the scheme’s parallel scalability for problems with a few hundred elements per process. Furthermore, the scheme is used in conjunction with the finite cell method to perform numerical simulations on domains of complex shape.

      PubDate: 2017-05-26T14:42:33Z
       
  • Validation of numerical solution of diffusive part in a
           reaction–diffusion model
    • Abstract: Publication date: 1 July 2017
      Source:Computers & Mathematics with Applications, Volume 74, Issue 1
      Author(s): E.C. Herrera-Hernández, M. Núñez-López, J.A. González-Calderón
      In this work, we present a methodological procedure to validate the numerical solution of the diffusive part in a reaction–diffusion model. Uniform explicit finite differences method is used to generate the solution in a confined circular domain with boundary condition of zero flux. For the validation of the numerical solution, we consider three different criteria applied to normal diffusion and sub-diffusive cases: (i) the moments of concentration, ​(ii) decay of the concentration at the origin and (iii) the mass conservation. The numerical solution fulfills the validation criteria of moments and concentration decay at the origin only in the long-term. The mass conservation criterion is fulfilled when the initial condition is imposed close to the border, whereas when it is set near to the origin a dependence on the diffusion rate appears. Pattern formation is presented after validating the numerical solution for normal diffusive case. Good agreement of stationary spatial pattern against reported results is observed.

      PubDate: 2017-05-26T14:42:33Z
       
  • Boundary element quadrature schemes for multi- and many-core architectures
    • Abstract: Publication date: 1 July 2017
      Source:Computers & Mathematics with Applications, Volume 74, Issue 1
      Author(s): Jan Zapletal, Michal Merta, Lukáš Malý
      In the paper we study the performance of the regularized boundary element quadrature routines implemented in the BEM4I library developed by the authors. Apart from the results obtained on the classical multi-core architecture represented by the Intel Xeon processors we concentrate on the portability of the code to the many-core family Intel Xeon Phi. Contrary to the GP-GPU programming accelerating many scientific codes, the standard x86 architecture of the Xeon Phi processors allows to reuse the already existing multi-core implementation. Although in many cases a simple recompilation would lead to an inefficient utilization of the Xeon Phi, the effort invested in the optimization usually leads to a better performance on the multi-core Xeon processors as well. This makes the Xeon Phi an interesting platform for scientists developing a software library aimed at both modern portable PCs and high performance computing environments. Here we focus at the manually vectorized assembly of the local element contributions and the parallel assembly of the global matrices on shared memory systems. Due to the quadratic complexity of the standard assembly we also present an assembly sparsified by the adaptive cross approximation based on the same acceleration techniques. The numerical results performed on the Xeon multi-core processor and two generations of the Xeon Phi many-core platform validate the proposed implementation and highlight the importance of vectorization necessary to exploit the features of modern hardware.

      PubDate: 2017-05-26T14:42:33Z
       
  • Fast algorithms for intersection of non-matching grids using Plücker
           coordinates
    • Abstract: Publication date: 1 July 2017
      Source:Computers & Mathematics with Applications, Volume 74, Issue 1
      Author(s): Jan Březina, Pavel Exner
      The XFEM and Mortar methods can be used in combination with non-matching or non-conforming grids to deal with problems on complex geometries. However the information about the mesh intersection must be provided. We present algorithms for intersections between 1d and 2d unstructured multi component simplicial meshes and their intersections with a background unstructured 3d mesh. A common algorithm based on the advancing front technique is used for the efficient selection of candidate pairs among simplicial elements. Bounding interval hierarchy (BIH) of axes aligned bounding boxes (AABB) of elements is used to initialize the front tracking algorithm. The family of element intersection algorithms is built upon a line–triangle intersection algorithm based on the Plücker coordinates. These algorithms combined with the advancing front technique can reuse the results of calculations performed on the neighboring elements and reduce the number of arithmetic operations. Barycentric coordinates on each of the intersecting elements are provided for every intersection point. Benchmarks of the element intersection algorithms are presented and three variants of the global intersection algorithm are compared on the meshes raising from hydrogeological applications.

      PubDate: 2017-05-26T14:42:33Z
       
  • Toward a GPU-aware comparison of explicit and implicit CFD simulations on
           structured meshes
    • Abstract: Publication date: 1 July 2017
      Source:Computers & Mathematics with Applications, Volume 74, Issue 1
      Author(s): Mohamed Aissa, Tom Verstraete, Cornelis Vuik
      A computational Fluid Dynamics (CFD) code for steady simulations solves a set of non-linear partial differential equations using an iterative time stepping process, which could follow an explicit or an implicit scheme. On the CPU, the difference between both time stepping methods with respect to stability and performance has been well covered in the literature. However, it has not been extended to consider modern high-performance computing systems such as Graphics Processing Units (GPU). In this work, we first present an implementation of the two time-stepping methods on the GPU, highlighting the different challenges on the programming approach. Then we introduce a classification of basic CFD operations, found on the degree of parallelism they expose, and study the potential of GPU acceleration for every class. The classification provides local speedups of basic operations, which are finally used to compare the performance of both methods on the GPU. The target of this work is to enable an informed-decision on the most efficient combination of hardware and method when facing a new application. Our findings prove, that the choice between explicit and implicit time integration relies mainly on the convergence of explicit solvers and the efficiency of preconditioners on the GPU.

      PubDate: 2017-05-26T14:42:33Z
       
  • Integrated framework for solving the convection diffusion equation on 2D
           Quad mesh relying on internal boundaries
    • Abstract: Publication date: 1 July 2017
      Source:Computers & Mathematics with Applications, Volume 74, Issue 1
      Author(s): Saúl E. Buitrago Boret, Oswaldo J. Jiménez P.
      The aim of this research is the design and implementation of an integrated framework to solve numerically the two-dimensional convection diffusion equations on non-rectangular grids formed only by quadrilaterals honoring the internal structures of an oil reservoir. The framework is composed of (1) a preprocessor of the internal boundaries of a 2D oil reservoir structure, (2) a 2D structural quadrilateral grid generator, (3) a solver of the 2D convection diffusion equation (CDE) on the grid, and (4) a visualization module to display the reservoir properties, wells and the simulation results on the grid. An example of typical structures corresponding to an areal view of a hydrocarbon reservoir is presented. Different scenarios were considered varying boundary conditions, source term, and diffusion constant fluid velocity. All the results are consistent with the physical interpretation of each configuration.

      PubDate: 2017-05-26T14:42:33Z
       
  • Numerical analysis of coupled heat and moisture transport in masonry
    • Abstract: Publication date: 1 July 2017
      Source:Computers & Mathematics with Applications, Volume 74, Issue 1
      Author(s): Tomáš Krejčí, Jaroslav Kruis, Michal Šejnoha, Tomáš Koudelka
      Coupled analysis of heat and moisture transport in real world masonry structures deserves a special attention because the spatial discretization by the finite element method leads usually to large number of degrees of freedom. Thin mortar layers and large bricks or stones have very different material properties and the finite element mesh has to be able to describe correct temperature and moisture fields in mortar and in its vicinity in the blocks. This paper describes two possible solutions of such problems. The first solution is based on the domain decomposition method executed on parallel computers, where the Schur complement method is used with respect to non-symmetric systems of algebraic equations. The second alternative method is the application of a multi-scale approach in connection with a processor farming method, where the whole structure is described by a reasonably coarse finite element mesh, called the macro-scale problem, and the material parameters are obtained from the lower-level problems, called the meso-scale problem, by a homogenization procedure. In this procedure, the macro-problem is assigned to the master processor and the meso-scale problems belong to the slave processors in the processor farm.

      PubDate: 2017-05-26T14:42:33Z
       
  • Optimum configuration for accurate simulations of chaotic porous media
           with Lattice Boltzmann Methods considering boundary conditions, lattice
           spacing and domain size
    • Abstract: Publication date: 15 June 2017
      Source:Computers & Mathematics with Applications, Volume 73, Issue 12
      Author(s): A. Gil, J.P.G. Galache, C. Godenschwager, U. Rüde
      Simulations of the flow field through chaotic porous media are powerful numerical challenges of special interest in science and technology. The simulations are usually done over representative samples which summarise the properties of the material. Several factors affect the accuracy of the results. Firstly the spatial resolution has to be fine enough to be able to capture the smallest geometrical details. Secondly the domain size has to be large enough to contain the large characteristic scale of the porous media. And finally the effects induced by the boundary conditions have to be diluted when more realistic options are not available. This is the case when the geometry is obtained by tomography and the periodic boundary conditions cannot be applied to delimit the sample because its geometry is not periodic. Impermeable boundary conditions are usually chosen to enclose the domain, forcing mass conservation. As a result, the flow field is over-restricted and the total pressure drop can be over-estimated. In this paper a new strategy is presented to optimise the computational resources consumption keeping the restrictions imposed by the accuracy criteria. The effects of the domain size, discretisation thickness and boundary condition disturbances are studied in detail. The study starts with the procedural generation of chaotic porous walls which mimics acicular mullite filters. An advantage of this process is the possibility to create periodic geometries. Periodicity permits the application of advanced techniques such as cyclic cross-correlations between the phase field and the velocity component fields without aliasing. From cross-correlation operations the large characteristic scale is obtained. The result is a lower threshold for the domain size. In second place a mesh independent study is done to find the upper threshold for the lattice spacing. The Minkowski–Bouligand fractal dimension of the fluid–solid interface corroborates the results. It has been demonstrated how the fractal dimension is a good candidate to replace the mesh independent study with lower computational cost for this type of problems. The last step is to compare the results obtained for a periodic geometry applying periodicity and symmetry as boundary conditions. Considering the periodic case as reference the resultant error is analysed. The explanation of the analysis includes how the intensity of the error changes in space and the limitations of symmetric boundary conditions.

      PubDate: 2017-05-16T14:24:11Z
       
  • Conjugate gradient least squares algorithm for solving the generalized
           coupled Sylvester matrix equations
    • Abstract: Publication date: 15 June 2017
      Source:Computers & Mathematics with Applications, Volume 73, Issue 12
      Author(s): Huamin Zhang, Hongcai Yin
      This paper discusses the conjugate gradient least squares algorithm for solving the generalized coupled Sylvester matrix equations ∑ j = 1 q A i j X j B i j = F i , i = 1 , 2 , … , p . We prove that if this system is consistent then the iterative solution converges to the exact solution and if this system is inconsistent then the iterative solution converges to the least squares solution within the finite iteration steps in the absence of the roundoff errors. Also by setting the initial iterative value properly we prove that the iterative solution converges to the least squares and minimum-norm solution.

      PubDate: 2017-05-16T14:24:11Z
       
  • An inverse source problem for a two parameter anomalous diffusion equation
           with nonlocal boundary conditions
    • Abstract: Publication date: 15 June 2017
      Source:Computers & Mathematics with Applications, Volume 73, Issue 12
      Author(s): Salman A. Malik, Sara Aziz
      We consider the inverse problem of determination of the solution and a source term for a time fractional diffusion equation in two dimensional space. The time fractional derivative is the Hilfer derivative. A bi-orthogonal system of functions in L 2 ( Ω ) , obtained from the associated non-self-adjoint spectral problem and its adjoint problem, is used to prove the existence and uniqueness of the solution of the inverse problem. The stability of the solution of the inverse problem on the given data is proved.

      PubDate: 2017-05-16T14:24:11Z
       
  • Multi-dimensional α-fractional diffusion–wave equation and some
           properties of its fundamental solution
    • Abstract: Publication date: 15 June 2017
      Source:Computers & Mathematics with Applications, Volume 73, Issue 12
      Author(s): Lyubomir Boyadjiev, Yuri Luchko
      In this paper, a multi-dimensional α -fractional diffusion–wave equation is introduced and the properties of its fundamental solution are studied. This equation can be deduced from the basic continuous time random walk equations and contains the Caputo time-fractional derivative of the order α / 2 and the Riesz space-fractional derivative of the order α so that the ratio of the derivatives orders is equal to one half as in the case of the conventional diffusion equation. It turns out that the α -fractional diffusion–wave equation inherits some properties of both the conventional diffusion equation and of the wave equation. In particular, in the one- and two-dimensional cases, the fundamental solution to the α -fractional diffusion–wave equation can be interpreted as a probability density function and the entropy production rate of the stochastic process governed by this equation is exactly the same as the case of the conventional diffusion equation. On the other hand, in the three-dimensional case this equation describes a kind of anomalous wave propagation with a time-dependent propagation phase velocity.

      PubDate: 2017-05-16T14:24:11Z
       
  • 3D axisymmetric MHD system with regularity in the swirl component of the
           vorticity
    • Abstract: Publication date: 15 June 2017
      Source:Computers & Mathematics with Applications, Volume 73, Issue 12
      Author(s): Zujin Zhang, Zheng-an Yao
      This paper concerns with the regularity criteria for the 3 D axisymmetric MHD system. It is proved that the control of swirl component of vorticity can ensure the smoothness of the solution.

      PubDate: 2017-05-16T14:24:11Z
       
  • A semismooth Newton method for a kind of HJB equation
    • Abstract: Publication date: 15 June 2017
      Source:Computers & Mathematics with Applications, Volume 73, Issue 12
      Author(s): Hong-Ru Xu, Shui-Lian Xie
      In this paper, we present a semismooth Newton method for a kind of HJB equation. By suitably choosing the initial iterative point, the method is proved to have monotone convergence. Moreover, the semismooth Newton method has local superlinear convergence rate. Some simple numerical results are reported.

      PubDate: 2017-05-16T14:24:11Z
       
  • Partial differential equations based simulations in multiple space
           dimensions
    • Abstract: Publication date: Available online 12 May 2017
      Source:Computers & Mathematics with Applications
      Author(s): José L. Galán-García, Gabriel Aguilera-Venegas


      PubDate: 2017-05-16T14:24:11Z
       
  • Some uniqueness, multiplicity and complete dynamics for a cooperative
           model
    • Abstract: Publication date: Available online 6 May 2017
      Source:Computers & Mathematics with Applications
      Author(s): Hailong Yuan, Jianhua Wu, Yanling Li
      In this paper, a two-species cooperative model with diffusion and under homogeneous Dirichlet boundary conditions is investigated. It is shown the existence, stability, uniqueness and multiplicity of positive solutions. In particular, we study the global asymptotical stability of the unique positive solution when a ∈ ( λ 1 ( − b θ d 1 + β θ d ) , ∞ ) and α is large. Our method of analysis is based on perturbation technique, the Lyapunov–Schmidt procedure and the bifurcation theory.

      PubDate: 2017-05-07T13:20:10Z
       
  • Galerkin finite element method for cancer invasion mathematical model
    • Abstract: Publication date: Available online 5 May 2017
      Source:Computers & Mathematics with Applications
      Author(s): Sashikumaar Ganesan, Shangerganesh Lingeshwaran
      A finite element scheme for the solution of a cancer invasion model is proposed. The cancer dynamics model consists of three coupled partial differential equations which describe the evolution of cancer cell density, extra cellular matrix and the matrix degrading enzymes. The model incorporates proliferation and haptotaxis effect of cancer cells, their interaction with extracellular matrix, the production of matrix degrading enzymes and consequent degradation of the extracellular matrix. The coupled partial differential equations are discretized in space with the standard Galerkin finite elements and in time with the Crank–Nicolson method. Moreover, the nonlinear terms in the coupled equations are treated semi-implicitly in the finite element scheme. The numerical scheme is validated with numerical results taken from the literature. In addition to the mesh convergence study, the effects of haptotactic rate, proliferation rate and remodelling rate of matrix components of the considered mathematical model are investigated.

      PubDate: 2017-05-07T13:20:10Z
       
  • A new accurate residual-based a posteriori error indicator for the BEM in
           2D-acoustics
    • Abstract: Publication date: Available online 2 May 2017
      Source:Computers & Mathematics with Applications
      Author(s): Marc Bakry, Sébastien Pernet, Francis Collino
      In this work we construct a new reliable, efficient and local a posteriori error estimate for the single layer and hyper-singular boundary integral equations associated to the Helmholtz equation in two dimensions. It uses a localization technique based on a generic operator Λ which is used to transport the residual into L 2 . Under appropriate conditions on the construction of Λ , we show that it is asymptotically exact with respect to the energy norm of the error. The single layer equation and the hyper-singular equation are treated separately. While the current analysis requires the boundary to be smooth, numerical experiments show that the new error estimators also perform well for non-smooth boundaries.

      PubDate: 2017-05-07T13:20:10Z
       
 
 
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