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arXiv 2024年

作者： Pramanik, R. Park, M. Ren, Z. Sitti, M. Verstappen, R.W.C.P. Onck, P.R. Computational & Numerical Mathematics Group Bernoulli Institute for Mathematics Computer Science & Artificial Intelligence University of Groningen Netherlands Physical Intelligence Department Max Planck Institute for Intelligent Systems Stuttgart Germany School of Mechanical Engineering and Automation Beihang University Beijing China Institute for Biomedical Engineering ETH Zurich Zurich Switzerland School of Medicine College of Engineering Koc University Istanbul Turkey Micromechanics Group Zernike Institute for Advanced Materials University of Groningen Netherlands

Miniaturized magnetic soft robots have shown extraordinary capabilities of contactless manipulation, complex path maneuvering, precise localization, and quick actuation, which have equipped them to cater to challenging biomedical applications such as targeted drug delivery, internal wound healing, and laparoscopic surgery. However, despite their successful fabrication by several different research groups, a thorough design strategy encompassing the optimized kinematic performance of the three fundamental biomimetic swimming modes at miniaturized length scales has not been reported till now. Here, we resolve this by designing magnetic soft robotic swimmers (MSRSs) from the class of helical and undulatory low Reynolds number (Re) swimmers using a fully coupled, experimentally calibrated computational fluid dynamics model. We study (and compare) their swimming performance, and report their steady-state swimming speed for different non-dimensional numbers that capture the competition by magnetic loading, non-linear elastic deformation and viscous solid-fluid coupling. We investigate their stability for different initial spatial orientations to ensure robustness during real-life applications. Our results show that the helical’finger-shaped’ swimmer is, by far, the fastest low Re swimmer in terms of body lengths per cycle, but that the undulatory’carangiform’ swimmer proved to be the most versatile, bidirectional swimmer with maximum stability. © 2024, CC BY-NC-ND.

关键词： Reynolds number

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Common Fixed Point of the Commutative F-contraction Self-mappings

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International Journal of Applied and Computational mathematics 2021年第4期7卷 1-10页

作者： Chebel, Zoheir Boureghda, Abdellatif Department of Mathematics Faculty of Mathematics and Computer Science Mohamed El Bachir El Ibrahimi University Bordj Bou Arreridj 34031 Algeria ETA Laboratory Electronics Department University of Bordj Bou Arreridj El Anasser Bordj Bou Arreridj 34031 Algeria Département de Mathématiques IRIMAS Université de Haute Alsace 6 Rue des Frères lumière Mulhouse Cedex 68093 France Laboratory of Fundamental and Numerical Mathematics Faculty of Sciences Ferhat Abbas University Sétif 19137 Algeria

The purpose of this paper is to introduce and study a concept, called F-contraction mappings which generalize Lipschtzian mappings. They form a class that is wider than the Lipschtzian mappings. Moreover, we establish a new approach to obtain a common fixed point theorem for two commuting mappings, in order to get an equivalent theorem to G. Jungck’s result (Am Math Mon 83:261–263, 1976). Our result is illustrated by examples and generalizes Banach contraction theorem. The two joined theorems of both G. Jungck and ours are realised and some applications in the ball are derived from. © 2021, The Author(s), under exclusive licence to Springer Nature India Private Limited.

关键词： Common fixed point Fixed point theorems Lipschitzian mapping

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Finite element methods respecting the discrete maximum principle for convection-diffusion equations

arXiv

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arXiv 2022年

作者： Barrenechea, Gabriel R. John, Volker Knobloch, Petr Department of Mathematics and Statistics University of Strathclyde 26 Richmond Street GlasgowG1 1XH United Kingdom Mohrenstr. 29 Berlin10117 Germany Freie Universität Berlin Department of Mathematics and Computer Science Arnimallee 6 Berlin14195 Germany Department of Numerical Mathematics Faculty of Mathematics and Physics Charles University Sokolovská 83 Praha 818675 Czech Republic

Convection-diffusion-reaction equations model the conservation of scalar quantities. From the analytic point of view, solution of these equations satisfy under certain conditions maximum principles, which represent physical bounds of the solution. That the same bounds are respected by numerical approximations of the solution is often of utmost importance in practice. The mathematical formulation of this property, which contributes to the physical consistency of a method, is called Discrete Maximum Principle (DMP). In many applications, convection dominates diffusion by several orders of magnitude. It is well known that standard discretizations typically do not satisfy the DMP in this convection-dominated regime. In fact, in this case, it turns out to be a challenging problem to construct discretizations that, on the one hand, respect the DMP and, on the other hand, compute accurate solutions. This paper presents a survey on finite element methods, with a main focus on the convection-dominated regime, that satisfy a local or a global DMP. The concepts of the underlying numerical analysis are discussed. The survey reveals that for the steady-state problem there are only a few discretizations, all of them nonlinear, that at the same time satisfy the DMP and compute reasonably accurate solutions, e.g., algebraically stabilized schemes. Moreover, most of these discretizations have been developed in recent years, showing the enormous progress that has been achieved lately. Methods based on algebraic stabilization, nonlinear and linear ones, are currently as well the only finite element methods that combine the satisfaction of the global DMP and accurate numerical results for the evolutionary equations in the convection-dominated *** Codes 65N30, 65M60 © 2022, CC BY-NC-ND.

关键词： Finite element method

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A MULTISCALE MODEL FOR WEAKLY NONLINEAR SHALLOW WATER WAVES OVER PERIODIC BATHYMETRY

arXiv

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arXiv 2023年

作者： Ketcheson, David I. Lóczi, Lajos Russo, Giovanni Thuwal23955-6900 Saudi Arabia Department of Numerical Analysis ELTE Eötvös Loránd University Pázmány P. s. 1/C BudapestH-1117 Hungary Department of Analysis and Operations Research BME Budapest University of Technology and Economics Hungary Department of Mathematics and Computer Science University of Catania Viale A. Doria 6 Catania95125 Italy

We study the behavior of shallow water waves over periodically-varying bathymetry, based on the first-order hyperbolic Saint-Venant equations. Although solutions of this system are known to generally exhibit wave breaking, numerical experiments suggest a different behavior in the presence of periodic bathymetry. Starting from the first-order variable-coefficient hyperbolic system, we apply a multiple-scale perturbation approach in order to derive a system of constant-coefficient high-order partial differential equations whose solution approximates that of the original system. The high-order system turns out to be dispersive and exhibits solitary-wave formation, in close agreement with direct numerical simulations of the original system. We show that the constant-coefficient homogenized system can be used to study the properties of solitary waves and to conduct efficient numerical simulations. Copyright © 2023, The Authors. All rights reserved.

关键词： Bathymetry

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Chimney Height, a Determining Factor in the Dispersion of Pollutants and Their Concentration

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World Journal of Engineering and Technology 2021年第1期9卷 173-193页

作者： Neyva Maria Lopes Romeiro Eliandro Rodrigues Cirilo Paulo Laerte Natti Letícia Mayumi Doy Okamoto Tainá Julianotti Department of Mathematics State University of Londrina and Member of the Simulation and Numerical Analysis Laboratory—LabSan Paraná Brazil Graduated in Computer Science State University of Londrina Paraná Brazil Master’s Student Applied and Computational Mathematics—PGMAC State University of Londrina Paraná Brazil

This work proposes a way of modelling two-dimensional complex meshes using elliptic equations, which the computational grid coincides with the problem geometry, making computational processing more suitable. A multiblock technique was used in order to achieve a better representation of the problem domain. In this way, numerical simulations of the movement and dispersion of pollutant emissions in the atmosphere are presented in the generated domains, using the Navier-Stokes pollutant transport equations. The curvilinear coordinates and the finite difference method are used for the discretization. The model was verified in two tests. In the first test, three cases were proposed, with geometries containing a chimney followed by an obstacle, using different chimney heights, and the obstacle height was fixed. The test aims to verify the vortices appearance, in the blocks, to obtain agreement with as presented in the literature. In the second test, the geometry is described by a chimney and an obstacle that represents one of the mountains in the valley. The performed tests made possible to verify that the height of the chimney can be considered a determining factor to describe the dispersion of pollutants, as well as their concentration in the proximity of industrial areas.

关键词： Atmosphere Valley Multiblock Navier-Stokes Transport Equation

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Shooting-projection method for a small object moving under the influence of a force 10

Shooting-projection method for a small object moving under t...

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202 10th International Conference on Engineering mathematics and Physics, ICEMP 2021

作者： Filipov, S.M. Faragó, I. Avdzhieva, A. Department of Computer Science Faculty of Chemical and System Engineering University of Chemical Technology and Metallurgy 8 St. Kliment Ohridski Blvd. Sofia1756 Bulgaria Department of Differential Equations Institute of Mathematics Budapest University of Technology and Economics MTA-ELTE Research Group Egry József u. 1 Budapest1111 Hungary Department of Numerical Methods Faculty of Mathematics and Informatics Sofia University St. Kliment Ohridski 5 James Bourchier Blvd. Sofia1164 Bulgaria

We consider a small object in 3D moving under the influence of a force that may depend explicitly on time, on the position of the object, and on its velocity. The equations of motion of classical mechanics are assumed to hold. If the position of the object is specified at some initial and some final time, obtaining the trajectory of the object requires the solution of a two-point boundary value problem. To solve the problem various numerical technics can be applied. This paper extends the recently proposed shooting-projection method to 3D. We introduce a Lagrangian from which, applying the principle of least action, the projection trajectory is derived. Analysis of the action reveals the meaning of the projection trajectory. Using the shooting-projection method, the considered two-point boundary value problem is solved for the case of a projectile motion in the presence of air resistance and wind. © 2021 Institute of Physics Publishing. All rights reserved.

关键词： Trajectories

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On algebraically stabilized schemes for convection–diffusion–reaction problems

arXiv

引用

arXiv 2021年

作者： John, Volker Knobloch, Petr Mohrenstr. 39 Berlin10117 Germany Department of Mathematics and Computer Science Freie Universität Berlin Arnimallee 6 Berlin14195 Germany Department of Numerical Mathematics Faculty of Mathematics and Physics Charles University Sokolovská 83 Praha 818675 Czech Republic

An abstract framework is developed that enables the analysis of algebraically stabilized discretizations in a unified way. This framework is applied to a discretization of this kind for convection–diffusion–reaction equations. The definition of this scheme contains a new limiter that improves a standard one in such a way that local and global discrete maximum principles are satisfied on arbitrary simplicial *** Codes 65N12, 65N30 © 2021, CC BY.

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Local Fourier Analysis of a space-time multigrid method for DG-SEM for the linear advection equation

arXiv

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arXiv 2021年

作者： Versbach, Lea M. Birken, Philipp Linders, Viktor Gassner, Gregor Centre for Mathematical Sciences Numerical Analysis Lund University Lund Sweden Center for Data and Simulation Sciences Department of Mathematics and Computer Science Weyertal 86-90 Köln50931 Germany

In this paper we present a Local Fourier Analysis of a space-time multigrid solver for a hyperbolic test problem. The space-time discretization is based on arbitrarily high order discontinuous Galerkin spectral element methods in time and a first order finite volume method in space. We apply a block Jacobi smoother and consider coarsening in space-time, as well as temporal coarsening only. Asymptotic convergence factors for the smoother and the two-grid method for both coarsening strategies are presented. For high CFL numbers, the convergence factors for both strategies are 0.5 for first order, and 0.375 for second order accurate temporal approximations. numerical experiments in one and two spatial dimensions for space-time DG-SEM discretizations of varying order gives even better convergence rates of around 0.3 and 0.25 for sufficiently high CFL *** Codes 65M55, 65M22, 65M60, 65T99 © 2021, CC BY-SA.

关键词： Fourier analysis

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Analysis of Communication and Network Securities Using the Concepts of Complex Picture Fuzzy Relations

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Computational Intelligence and Neuroscience 2021年 2021卷 9427492页

作者： Nasir, Abdul Jan, Naeem Khan, Sami Ullah Gumaei, Abdu Alothaim, Abdulrahman Department of Mathematics Institute of Numerical Sciences Gomal University Dera Ismail Khan Khyber Pakhtunkhwa29050 Pakistan Computer Science Department Faculty of Applied Sciences Taiz University Taiz6803 Yemen STC's Artificial Intelligence Chair Department of Information Systems College of Computer and Information Sciences King Saud University Riyadh11543 Saudi Arabia

In our lives, we cannot avoid the uncertainty. Randomness, rough knowledge, and vagueness lead us to uncertainty. In mathematics, the fuzzy set (FS) theory and logics are used to model uncertain events. This article defines a new concept of complex picture fuzzy relation (CPFR) in the field of FS theory. In addition, the types of CPFRs are also discussed to make the paper more fruitful. Today's complex network architecture faces the ever-changing threats. The cyber-attackers are always trying to discover, catch, and exploit the weaknesses in the networks. So, the security measures are essential to avoid and dismantle such threats. The CPFR has a vast structure composed of levels of membership, abstinence, and nonmembership which models uncertainty better than any other structures in the theory. Moreover, a CPFR has the ability to cope with multivariable problems. Therefore, this article proposes modeling techniques based on the complex picture fuzzy information which are used to study the effectiveness and ineffectiveness of different network securities against several threats and cyber-attack practices. Moreover, the strength and preeminence of the proposed methods are verified by studying their comparison with the existing methods. © 2021 Abdul Nasir et al.

关键词： Uncertainty analysis

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Structured Matrices in numerical Linear Algebra 1

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丛书名： Springer INdAM Series

2019年

作者： Dario Andrea Bini Fabio Di Benedetto Eugene Tyrtyshnikov Marc Van Barel

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