Article
Engineering, Multidisciplinary
Jan Groselj, Marjeta Knez
Summary: The paper generalizes the classical C-1 Clough-Tocher spline space to C-1 spaces of higher degree, demonstrating their applicability in the finite element method. The considered spaces have optimal approximation power and are defined with additional smoothness enforced inside the triangles of the triangulation. Locally, the splines are expressed in the Bernstein-Bezier form, allowing for the utilization of geometric properties and computational techniques. Examples illustrate the straightforward solution of boundary problems with Galerkin discretization.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Mathematics, Applied
D. Barrera, S. Eddargani, M. J. Ibanez, S. Remogna
Summary: In this paper, a quasi-interpolation scheme is proposed on a uniform triangulation of type-1 with a Powell-Sabin refinement. Unlike the traditional construction of quasi-interpolation splines on the 6-split, the method described in this work does not require a set of appropriate basis functions. The resulting approximating splines are directly defined by setting their Bezier ordinates to suitable combinations of the given data values. Numerical tests are conducted to confirm the theoretical results.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Engineering, Biomedical
Busra Mutlu Ipek, Huseyin Oktay Altun, Kasim Oztoprak
Summary: In this study, a novel hybrid deep learning and SVM technique is applied to restructured EEG data, achieving outstanding performance and filling a gap in the literature regarding automatic detection of epileptic episodes.
BIOMEDICAL ENGINEERING-BIOMEDIZINISCHE TECHNIK
(2022)
Article
Computer Science, Interdisciplinary Applications
Min Zhang, Zhuang Zhao
Summary: In this paper, a simple fifth-order finite difference Hermite WENO (HWENO) scheme combined with a limiter is proposed for one-and two-dimensional hyperbolic conservation laws. The proposed HWENO scheme is simpler, more accurate, efficient, and has better resolution compared to the modified HWENO scheme. It also has a more compact spatial reconstructed stencil and is more efficient than other WENO schemes. Various benchmark numerical examples are presented to demonstrate the fifth-order accuracy, efficiency, high resolution, and robustness of the proposed HWENO scheme.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mathematics, Applied
Cedric Boulbe, Blaise Faugeras, Guillaume Gros, Francesca Rapetti
Summary: This paper investigates the axisymmetric equilibrium problem of a hot plasma in a tokamak. A non-overlapping mortar element approach is adopted, which couples C0 piece-wise linear Lagrange finite elements in a region without plasma and C1 piece-wise cubic reduced Hsieh-Clough-Tocher finite elements elsewhere, to approximate the magnetic flux field on a triangular mesh of the poloidal tokamak section. The inclusion of ferromagnetic parts is simplified by assuming their axisymmetric fit, and a new formulation of the Newton algorithm for problem solution is stated for both static and quasi-static evolution cases.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Computer Science, Interdisciplinary Applications
Ali Elarif, Blaise Faugeras, Francesca Rapetti
Summary: This study presents a numerical simulation technique that combines finite element method and triangular mesh to improve the accuracy of the equilibrium of the plasma in a tokamak and its coupling with resistive diffusion. The method achieves higher order regularity in the plasma-covered area while maintaining accuracy in meshing the geometric details in the rest of the computational domain.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Engineering, Chemical
Liang Li, Yapu Feng, Yanmeng Wang, Liuyong Pang, Jun Zhu
Summary: In this paper, we propose a fifth-order finite-difference Hermite weighted essentially non-oscillatory (HWENO) method for solving the Degasperis-Procesi (DP) equation. The DP equation is rewritten as a system of equations consisting of hyperbolic equations and elliptic equations by introducing an auxiliary variable. The auxiliary variable equations are solved using the Hermite interpolation, while the HWENO scheme is performed for the hyperbolic equations. The compactness of the spatial reconstruction stencil is the most important feature of the HWENO scheme, which achieves fifth-order accuracy with only three points, while the WENO method requires five points.
Article
Engineering, Civil
Manyu Xiao, Sougata Mukherjee, Balaji Raghavan, Subhrajit Dutta, Piotr Breitkopf, Weihong Zhang
Summary: This study investigates the effects of p-refinement in SIMP topology optimization, comparing optimized topologies, compliance values, and CPU clock time for various 2D classical benchmark problems.
Article
Computer Science, Interdisciplinary Applications
Andreas Thalhamer, Mathias Fleisch, Clara Schuecker, Peter Filipp Fuchs, Sandra Schlogl, Michael Berer
Summary: A Finite Element simulation-based optimization framework is proposed to create a predefined deformation behavior in metamaterials. The framework includes numerical homogenization, interpolation, and black-box optimization. The framework is tested on tri-antichiral metamaterials, exploring various combinations of optimization objectives and constraints.
ADVANCES IN ENGINEERING SOFTWARE
(2023)
Article
Computer Science, Interdisciplinary Applications
Ashish Bhole, Herve Guillard, Boniface Nkonga, Francesca Rapetti
Summary: Finite elements of class C-1 are used for computing magnetohydrodynamics instabilities in tokamak plasmas, and isoparametric approximations are employed to align the mesh with the magnetic field line. This numerical framework helps in understanding the operation of existing devices and predicting optimal strategies for the international ITER tokamak. However, a mesh-aligned isoparametric representation encounters issues near critical points of the magnetic field, which can be addressed by combining aligned and unaligned meshes.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2024)
Article
Engineering, Marine
Shen -Haw Ju, Cheng-Han Hsieh
Summary: This study developed an optimization procedure using Powell's method, which can optimize parameters in structural designs. The results suggest that specific architecture design and braking systems can effectively minimize the structural weight.
Article
Engineering, Civil
Zhenyu Wu, Dongdong Wang, Songyang Hou
Summary: This paper proposes a simple and unified method for developing arbitrary order Hermite shape functions of Euler-Bernoulli beam elements. The method utilizes the fact that the Hermite reproducing kernel meshfree shape functions degenerate to the interpolatory Hermite finite element shape functions under a proper choice of support sizes. Using this method, cubic, quintic, and septic Hermite beam elements are constructed, and the shape functions, mass and stiffness matrices, frequency errors, and higher order mass matrix formulation for these elements are presented.
INTERNATIONAL JOURNAL OF STRUCTURAL STABILITY AND DYNAMICS
(2023)
Article
Mathematics, Applied
Hiroki Ishizaka, Kenta Kobayashi, Ryo Suzuki, Takuya Tsuchiya
Summary: This paper discusses the importance of the maximum angle condition in error analysis of Lagrange interpolation on tetrahedrons, and presents an equivalent geometric condition as a replacement for the maximum angle condition.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Mathematics, Applied
Francesco Dell'Accio, Filomena Di Tommaso, Allal Guessab, Federico Nudo
Summary: In this paper, a new nonconforming finite element is presented, which is a polynomial enrichment of the standard triangular linear element. Based on this new element, an improvement of the triangular Shepard operator is proposed. It is proven that the order of the new approximation operator is at least cubic. Numerical experiments verify the accuracy of the proposed method.
APPLIED NUMERICAL MATHEMATICS
(2023)
Article
Mathematics, Applied
Juan Pablo Borthagaray, Ricardo H. Nochetto, Shuonan Wu, Jinchao Xu
Summary: We propose and analyze a robust Bramble-Pasciak-Xu (BPX) pre-conditioner for the integral fractional Laplacian on bounded Lipschitz domains. The additional scaling factor incorporated to the coarse levels ensures uniformly bounded condition numbers for quasi-uniform or graded bisection grids.
MATHEMATICS OF COMPUTATION
(2023)
Article
Mathematics, Applied
D. Barrera, S. Eddargani, A. Lamnii
Summary: This article defines a family of univariate many knot spline spaces of arbitrary degree on an initial partition that is refined by adding a point in each sub-interval. Additional regularity is imposed when necessary for splines of degrees 2r and 2r + 1 with arbitrary smoothness r. A B-spline-like basis is constructed using the Bernstein-Bezier representation for arbitrary degree. Various quasi-interpolation operators with optimal approximation orders are defined by establishing a Marsden's identity through blossoming.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
D. Barrera, S. Eddargani, M. J. Ibanez, A. Lamnii
Summary: This paper investigates the characterization of Powell-Sabin triangulations for constructing bivariate quartic splines of class C-2. The relationship between the triangle and edge split points obtained through refinement of each triangle is used to establish the result. A normalized representation of the splines in the C-2 space is provided for triangulations that meet the established characterization.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Mathematics, Applied
D. Barrera, M. Barton, I Chiarella, S. Remogna
Summary: This study investigates the use of Gaussian rules for splines in the Nystrom method, showing that the approximate solution of linear Fredholm integral equations computed using spline Gaussian quadrature rules converges to the exact solution for continuous kernels.
APPLIED NUMERICAL MATHEMATICS
(2022)
Article
Computer Science, Interdisciplinary Applications
D. Barrera, S. Eddargani, M. J. Ibanez, A. Lamnii
Summary: In this paper, a novel normalized B-spline-like representation is constructed for a C-2-continuous cubic spline space defined on a refined initial partition. The basis functions are compactly supported non-negative functions that are geometrically constructed and form a convex partition of unity. Through the introduction of control polynomial theory, a Marsden identity is derived, and several families of super-convergent quasi-interpolation operators are defined.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2022)
Article
Engineering, Electrical & Electronic
D. Maldonado, S. Aldana, M. B. Gonzalez, F. Jimenez-Molinos, M. J. Ibanez, D. Barrera, F. Campabadal, J. B. Roldan
Summary: This study analyzed the variability of resistive memories using advanced numerical techniques. New extraction methods were developed to obtain switching parameters and their appropriateness were checked against kinetic Monte Carlo simulations. The results showed that the variability of resistive memories depends on the numerical technique used, highlighting the importance of considering this issue in RS characterization and modeling studies.
MICROELECTRONIC ENGINEERING
(2022)
Article
Mathematics, Applied
Francisco J. Ariza-Lopez, Domingo Barrera, Salah Eddargani, Maria Jose Ibanez, Juan F. Reinoso
Summary: This paper presents a non-standard low-cost spline approximation method for approximating bivariate functions, which is then applied to Digital Elevation approximation. The accuracy of this method in the downscaling process is also studied.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics
Haithem Benharzallah, Abdelaziz Mennouni, Domingo Barrera
Summary: This paper presents a method that constructs C-1 continuous quasi-interpolating splines over Clough-Tocher refinement of a type-1 triangulation. The Bernstein-Bezier coefficients of these splines are directly defined from the known values of the function to be approximated, eliminating the need for a set of appropriate basis functions. The resulting quasi-interpolation operators can reproduce cubic polynomials. Numerical tests are conducted to demonstrate the performance of the approximation scheme.
Article
Mathematics, Applied
D. Barrera, S. Eddargani, A. Lamnii
Summary: The construction of C2 cubic spline quasi-interpolation schemes on a refined partition is discussed in this paper. These schemes are reduced in terms of degrees of freedom compared to those existing in the literature. Super-smoothing conditions are imposed to reduce them while preserving full smoothness and cubic precision. In addition, subdivision rules are provided using blossoming.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
D. Barrera, S. Eddargani, M. J. Ibanez, S. Remogna
Summary: In this paper, a quasi-interpolation scheme is proposed on a uniform triangulation of type-1 with a Powell-Sabin refinement. Unlike the traditional construction of quasi-interpolation splines on the 6-split, the method described in this work does not require a set of appropriate basis functions. The resulting approximating splines are directly defined by setting their Bezier ordinates to suitable combinations of the given data values. Numerical tests are conducted to confirm the theoretical results.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
D. Barrera, S. Eddargani, M. J. Ibanez, S. Remogna
Summary: In this paper, we propose a method for constructing univariate low-degree quasi-interpolating splines in the Bernstein basis, considering C1 and C2 smoothness, specific polynomial reproduction properties, and different sets of evaluation points. The splines are determined directly by setting their Bernstein-Bezier coefficients to appropriate combinations of the given data values. Furthermore, we obtain quasi-interpolating splines with special properties by imposing particular requirements in case of free parameters. Finally, we provide numerical tests to demonstrate the performance of the proposed methods.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Mathematics, Applied
M. -Y. Nour, A. Lamnii, A. Zidna, D. Barrera
Summary: A construction of Marsden's identity for UE-splines is developed and a complete proof is given. With the help of this identity, a new non-uniform quasi-interpolant that reproduces the spaces of polynomial, trigonometric and hyperbolic functions are defined. Efficient quadrature rules based on integrating these quasi-interpolation schemes are derived and analyzed. Then, a quadrature formula associated with non-uniform quasi-interpolation along with Nystrom's method is used to numerically solve Hammerstein and Fredholm integral equations. Numerical results that illustrate the effectiveness of these rules are presented.
APPLIED NUMERICAL MATHEMATICS
(2023)
Article
Mathematics, Applied
Ali Hashemian, Hanna Sliusarenko, Sara Remogna, Domingo Barrera, Michael Barton
Summary: We propose using spline Gauss quadrature rules with the Nystrom method to solve boundary value problems (BVPs). The method involves converting the corresponding partial differential equation inside a domain into a Fredholm integral equation of the second kind on the boundary using the concept of boundary integral equation (BIE). The results indicate that spline Gauss quadratures provide significantly more accurate approximations compared to traditional polynomial Gauss counterparts.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Mathematics, Applied
M. S. Bruzon, T. M. Garrido, R. de la Rosa
Summary: We study a family of generalized Zakharov-Kuznetsov modified equal width equations in (2+1)-dimensions involving an arbitrary function and three parameters. By using the Lie group theory, we classify the Lie point symmetries of these equations and obtain exact solutions. We also show that this family of equations admits local low-order multipliers and derive all local low-order conservation laws through the multiplier approach.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Dohee Jung, Changbum Chun
Summary: The paper presents a general approach to enhance the Pade iterations for computing the matrix sign function by selecting an arbitrary three-point family of methods based on weight functions. The approach leads to a multi-parameter family of iterations and allows for the discovery of new methods. Convergence and stability analysis as well as numerical experiments confirm the improved performance of the new methods.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Abhishek Yadav, Amit Setia, M. Thamban Nair
Summary: In this paper, we propose a Galerkin's residual-based numerical scheme for solving a system of Cauchy-type singular integral equations using Chebyshev polynomials. We prove the well-posedness of the system and derive a theoretical error bound and convergence order. The numerical examples validate the theoretical results.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Fernando Chacon-Gomez, M. Eugenia Cornejo, Jesus Medina, Eloisa Ramirez-Poussa
Summary: The use of decision rules allows for reliable extraction of information and inference of conclusions from relational databases, but the concepts of decision algorithms need to be extended in fuzzy environments.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Ilhame Amirali, Gabil M. Amiraliyev
Summary: This paper considers the one-dimensional initial-boundary problem for a pseudoparabolic equation with a time delay. To solve this problem numerically, a higher-order difference method is constructed and the error estimate for its solution is obtained. Based on the method of energy estimates, the fully discrete scheme is shown to be convergent of order four in space and of order two in time. The given numerical results illustrate the convergence and effectiveness of the numerical method.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Tong-tong Shang, Guo-ji Tang, Wen-sheng Jia
Summary: The goal of this paper is to investigate a class of linear complementarity problems over tensor-spaces, denoted by TLCP, which is an extension of the classical linear complementarity problem. First, two classes of structured tensors over tensor-spaces (i.e., T-R tensor and T-RO tensor) are introduced and some equivalent characterizations are discussed. Then, the lower bound and upper bound of the solutions in the sense of the infinity norm of the TLCP are obtained when the problem has a solution.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Fabio Difonzo, Pawel Przybylowicz, Yue Wu
Summary: This paper focuses on the existence, uniqueness, and approximation of solutions of delay differential equations (DDEs) with Caratheodory type right-hand side functions. It presents the construction of the randomized Euler scheme for DDEs and investigates its error. Furthermore, the paper reports the results of numerical experiments.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Priyanka Roy, Geetanjali Panda, Dong Qiu
Summary: In this article, a gradient based descent line search scheme is proposed for solving interval optimization problems under generalized Hukuhara differentiability. The innovation and importance of these concepts are presented from practical and computational perspectives. The necessary condition for existence of critical point is presented in inclusion form of interval-valued gradient. Suitable efficient descent direction is chosen based on the monotonic property of the interval-valued function and specific interval ordering. Mathematical convergence of the scheme is proved under the assumption of Inexact line search. The theoretical developments are implemented with a set of interval test problems in different dimensions. A possible application in finance is provided and solved by the proposed scheme.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Zhongqian Wang, Changqing Ye, Eric T. Chung
Summary: In this paper, the constrained energy minimizing generalized multiscale finite element method (CEM-GMsFEM) with mixed boundary conditions for elasticity equations in high contrast media is developed. The method offers advantages such as independence of target region's contrast from precision and significant impact of oversampling domain sizes on numerical accuracy. Furthermore, this is the first proof of convergence of CEM-GMsFEM with mixed boundary conditions for elasticity equations. Numerical experiments demonstrate the method's performance.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Samaneh Soradi-Zeid, Maryam Alipour
Summary: The Laguerre polynomials are a new set of basic functions used to solve a specific class of optimal control problems specified by integro-differential equations, namely IOCP. The corresponding operational matrices of derivatives are calculated to extend the solution of the problem in terms of Laguerre polynomials. By considering the basis functions and using the collocation method, the IOCP is simplified into solving a system of nonlinear algebraic equations. The proposed method has been proven to have an error bound and convergence analysis for the approximate optimal value of the performance index. Finally, examples are provided to demonstrate the validity and applicability of this technique.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Almudena P. Marquez, Maria L. Gandarias, Stephen C. Anco
Summary: A generalization of the KP equation involving higher-order dispersion is studied. The Lie point symmetries and conservation laws of the equation are obtained using Noether's theorem and the introduction of a potential. Sech-type line wave solutions are found and their features, including dark solitary waves on varying backgrounds, are discussed.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Susanne Saminger-Platz, Anna Kolesarova, Adam Seliga, Radko Mesiar, Erich Peter Klement
Summary: In this article, we study real functions defined on the unit square satisfying basic properties and explore the conditions for generating bivariate copulas using parameterized transformations and other constructions.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Lulu Tian, Nattaporn Chuenjarern, Hui Guo, Yang Yang
Summary: In this paper, a new local discontinuous Galerkin (LDG) algorithm is proposed to solve the incompressible Euler equation in two dimensions on overlapping meshes. The algorithm solves the vorticity, velocity field, and potential function on different meshes. The method employs overlapping meshes to ensure continuity of velocity along the interfaces of the primitive meshes, allowing for the application of upwind fluxes. The article introduces two sufficient conditions to maintain the maximum principle of vorticity.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Cheng Wang, Jilu Wang, Steven M. Wise, Zeyu Xia, Liwei Xu
Summary: In this paper, a temporally second-order accurate numerical scheme for the Cahn-Hilliard-Magnetohydrodynamics system of equations is proposed and analyzed. The scheme utilizes a modified Crank-Nicolson-type approximation for time discretization and a mixed finite element method for spatial discretization. The modified Crank-Nicolson approximation allows for mass conservation and energy stability analysis. Error estimates are derived for the phase field, velocity, and magnetic fields, and numerical examples are presented to validate the proposed scheme's theoretical results.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Mingyu He, Wenyuan Liao
Summary: This paper presents a numerical method for solving reaction-diffusion equations in spatially heterogeneous domains, which are commonly used to model biological applications. The method utilizes a fourth-order compact alternative directional implicit scheme based on Pade approximation-based operator splitting techniques. Stability analysis shows that the method is unconditionally stable, and numerical examples demonstrate its high efficiency and high order accuracy in both space and time.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
