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Analysis of a fractional-step parareal algorithm for the incompressible Navier-Stokes equations Comput. Math. Appl. (IF 2.9) Pub Date : 2024-03-04 Zhen Miao, Ren-Hao Zhang, Wei-Wei Han, Yao-Lin Jiang
This paper analyzes a parareal approach based on fractional-step methods for the nonstationary Navier-Stokes equations. As an efficient parallel computing framework, the coarse propagator often determines the performance of the parareal algorithm. We present a parareal algorithm using the fractional-step method, a very efficient time discrete scheme for the Naiver-Stokes equations, as the coarse propagator
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Stress mixed polyhedral finite elements for two-scale elasticity models with relaxed symmetry Comput. Math. Appl. (IF 2.9) Pub Date : 2024-03-04 Philippe R.B. Devloo, Jeferson W.D. Fernandes, Sônia M. Gomes, Nathan Shauer
We consider two-scale stress mixed finite element elasticity models using H(div)-conforming tensor approximations for the stress variable, whilst displacement and rotation fields are introduced to impose divergence and symmetry constraints. The variables are searched in composite FE spaces based on polyhedral subdomains, formed by the conglomeration of local shape-regular micro partitions. The two-scale
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Convergence analysis of an IMEX scheme for an integro-differential equation with inexact boundary arising in option pricing with stochastic intensity jumps Comput. Math. Appl. (IF 2.9) Pub Date : 2024-03-01 Yong Chen
In this paper, we are concerned with the convergence rates of an implicit-explicit (IMEX) difference scheme for solving a two-dimensional partial integro-differential equation (PIDE) with an inexact boundary which arises in option pricing with stochastic intensity jumps. First, the IMEX scheme is proposed to solve the two-dimensional PIDE and its inexact boundary governed by a one-dimensional PIDE
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An efficient computational technique for solving a time-fractional reaction-subdiffusion model in 2D space Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-29 Trishna Kumari, Pradip Roul
The solution of time fractional reaction-subdiffusion (TFRS) equation with the Caputo time fractional derivative of order ∈ (0, 1), in general, exhibits a mild singularity at the initial time. In this article, we propose an efficient numerical technique based on a graded mesh in time to overcome the singular behavior of the solution at . In this technique, the temporal fractional derivative is approximated
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A neutrally buoyant particle motion in a double-lid-driven square cavity Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-29 Qinglan Zhai, Lin Zheng, Song Zheng, Hutao Cui
A neutrally buoyant circular particle motion in a double lid-driven cavity flow (LDCF) is investigated by immersed moving boundary based lattice Boltzmann method, where the top and bottom walls move with constant velocities. To understand the mechanism of particle motion in double LDCF, the influence of the moving wall velocity ratio , initial position, particle size, and Reynolds number on the trajectory
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An implicit lattice Boltzmann flux solver with a projection-based interpolation scheme for the convection-diffusion equation Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-28 Peng Hong, Chuanshan Dai, Guiling Wang, Haiyan Lei
This paper proposes a novel matrix assembly method called dummy scalar triplet to construct the implicit lattice Boltzmann flux solver (LBFS). The implicit discretize scheme enables the LBFS to use a time step far exceeding the Courant-Friedrichs-Lewy condition limit. Therefore, the computational efficiency and the applicability of LBFS are significantly enhanced, especially in solving complex geometry
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A lowest order stabilization-free mixed Virtual Element Method Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-28 Andrea Borio, Carlo Lovadina, Francesca Marcon, Michele Visinoni
We initiate the design and the analysis of stabilization-free Virtual Element Methods for the Poisson problem written in mixed form. A Virtual Element version of the lowest order Raviart-Thomas Finite Element is considered. To reduce the computational costs, a suitable projection on the gradients of harmonic polynomials is employed. A complete theoretical analysis of stability and convergence is developed
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A warm-start FE-dABCD algorithm for elliptic optimal control problems with constraints on the control and the gradient of the state Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-27 Zixuan Chen, Xiaoliang Song, Xiaotong Chen, Bo Yu
In this paper, elliptic control problems with the integral constraint on the gradient of the state and the box constraint on the control are considered. The optimality conditions for the problem are proved. To numerically solve the problem, a finite element duality-based inexact majorized accelerated block coordinate descent (FE-dABCD) algorithm is proposed. Specifically, both the state and the control
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An ADI Crank-Nicolson orthogonal spline collocation method for 2D parabolic problems with an interface Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-27 Santosh Kumar Bhal, P. Danumjaya, G. Fairweather
A modification of the alternating direction implicit (ADI) Crank-Nicolson orthogonal spline collocation method for 2D parabolic problems to handle problems with an interface is described. For the spatial discretization, piecewise Hermite cubics are used in one direction and piecewise cubic monomials in the other direction. The time discretization is performed using a Crank-Nicolson approach. In each
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Optimization-based, property-preserving algorithm for passive tracer transport Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-27 Kara Peterson, Pavel Bochev, Denis Ridzal
We present a new optimization-based property-preserving algorithm for passive tracer transport. The algorithm utilizes a semi-Lagrangian approach based on incremental remapping of the mass and the total tracer. However, unlike traditional semi-Lagrangian schemes, which remap the density and the tracer mixing ratio through monotone reconstruction or flux correction, we utilize an optimization-based
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Convergence analysis of virtual element method for the electric interface model on polygonal meshes with small edges Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-26 Naresh Kumar, Jai Tushar, J.Y. Yuan
A conforming virtual element method is studied for approximating the solution of a pulsed electric interface model on polygonal meshes with small edges or faces, which traditional virtual and finite element methods cannot easily handle. One of the significant advantages of this virtual element method is to generate interface-conforming meshes efficiently exploiting polygonal meshes and hanging nodes
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A stochastic method for solving time-fractional differential equations Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-26 Nicolas L. Guidotti, Juan A. Acebrón, José Monteiro
We present a stochastic method for efficiently computing the solution of time-fractional partial differential equations (fPDEs) that model anomalous diffusion problems of the subdiffusive type. After discretizing the fPDE in space, the ensuing system of fractional linear equations is solved resorting to a Monte Carlo evaluation of the corresponding Mittag-Leffler matrix function. This is accomplished
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Isogeometric dual reciprocity BEM for solving time-domain acoustic wave problems Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-26 Senlin Zhang, Bo Yu, Leilei Chen, Haojie Lian, Stephane P.A. Bordas
In this paper, an isogeometric dual reciprocity boundary element method (IG-DRBEM) is proposed for the time-domain acoustic wave problem in 3D infinite domain. The fundamental solution of the potential problem is used to establish the boundary-domain integral equation, which avoids the problem of solving the coefficient matrix repeatedly at different times. On the one hand, in order to maintain the
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Enhancement of coupled immersed boundary–finite volume lattice Boltzmann method (IB–FVLBM) using least–square aided “ghost–cell” techniques Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-22 Yong Wang, Jun Cao, Chengwen Zhong
In this paper, a new hybrid numerical approach is presented that couples “ghost cell” based immersed boundary (IB) method with the finite volume lattice Boltzmann method (FVLBM). In the implementation process, the grid cells are classified into three types, i.e., “”, “” and “”, where the “” is the first layer of “” near the “”. As the wall boundary condition is reflected in the “”, the high–accuracy
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Piecewise DMD for oscillatory and Turing spatio-temporal dynamics Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-22 Alessandro Alla, Angela Monti, Ivonne Sgura
Dynamic Mode Decomposition (DMD) is an equation-free method that aims at reconstructing the best linear fit from temporal datasets. In this paper, we show that DMD does not provide accurate approximation for datasets describing oscillatory dynamics, like spiral waves, relaxation oscillations and spatio-temporal Turing instability. Inspired by the classical “divide and conquer” approach, we propose
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A new approach for recovering the gradient and a posteriori error estimates Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-20 Mohamed Barakat, Waheed Zahra, Ahmed Elsaid
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A singular boundary method for transient coupled dynamic thermoelastic analysis Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-20 Linlin Sun, Qing Zhang, Zhikang Chen, Xing Wei
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An unconditionally stable modified leapfrog method for Maxwell's equation in Kerr-type nonlinear media Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-20 Meng Chen, Rong Gao, Linghua Kong
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A very robust MMALE method based on a novel VoF method for two-dimensional compressible fluid flows Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-19 Bojiao Sha, Zupeng Jia
The Volume of Fluid (VoF) method stands out as a widely utilized tool for capturing interfaces in the numerical simulation of multimaterial fluid flow. Numerous efforts have been invested in enhancing its accuracy and efficiency, including the development of analytic reconstruction methods. Despite these advancements, there exists a continued need for further improvements in the accuracy, efficiency
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Smoothed particle hydrodynamics with diffusive flux for advection–diffusion equation with discontinuities Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-15 Zewei Sun, Qingzhi Hou, Arris S. Tijsseling, Jijian Lian, Jianguo Wei
The advection-diffusion equation (ADE) with variable diffusion coefficient can be written in a flux form to avoid rewriting the diffusion term with a drift. However, for solving the flux-form ADE using smoothed particle hydrodynamics (SPH), a double first-order derivative approximation has to be used to approximate the diffusion term, which creates non-physical oscillations at any discontinuities.
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A reduced-order Schwarz domain decomposition method based on POD for the convection-diffusion equation Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-15 Junpeng Song, Hongxing Rui
The Schwarz domain decomposition (SDD) method is known for its high efficacy in solving large-scale systems of partial differential equations, primarily due to its parallelizability. However, the method's reliance on iteration introduces substantial computational expenses. In this study, we propose a reduced-order Schwarz domain decomposition (ROSDD) method tailored specifically for the convection-diffusion
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The Carleman convexification method for Hamilton-Jacobi equations Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-15 Huynh P.N. Le, Thuy T. Le, Loc H. Nguyen
We propose a new globally convergent numerical method to compute solution Hamilton-Jacobi equations defined in , , on a truncated bounded domain. This method is named the Carleman convexification method. By Carleman convexification, we mean that we use a Carleman weight function to convexify the conventional least squares mismatch functional. We will prove a new version of the convexification theorem
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Error analysis of vector penalty-projection method with second order accuracy for incompressible magnetohydrodynamic system Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-14 Zijun Du, Haiyan Su, Xinlong Feng
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Nodal integral method to solve the two-dimensional, time-dependent, incompressible Navier-Stokes equations in curvilinear coordinates Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-14 Ibrahim Jarrah
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Optimization of stacking sequence for quadrilateral laminated composite plates with curved edges based on Kriging Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-14 Weiping Wang, Qingshan Wang, Rui Zhong, Xianjie Shi, Liming Chen
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Efficient numerical methods for models of evolving interfaces enhanced with a small curvature term Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-14 Katarína Lacková, Peter Frolkovič
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Continuous data assimilation of a discretized barotropic vorticity model of geophysical flow Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-14 Mine Akbas, Amanda E. Diegel, Leo G. Rebholz
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Planar curve registration using Bayesian inversion Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-14 Andreas Bock, Colin J. Cotter, Robert C. Kirby
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A block upper triangular preconditioner with two parameters for saddle-point problems Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-13 Xiao-Yong Xiao, Cha-Sheng Wang
In this paper, a simple preconditioner with two parameters (SPTP) is introduced for solving a class of saddle-point problems. The SPTP preconditioner is block upper triangular and does not contain the approximate matrix of the Schur complement matrix. Theoretical analyses on the sufficient conditions under which the SPTP iterative sequence converges to the unique solution, are given in detail. Convergence
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Non-smooth solutions of time-fractional Allen–Cahn problems via novel operational matrix based semi-spectral method with convergence analysis Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-13 Muhammad Usman, Muhammad Hamid, Dianchen Lu, Zhengdi Zhang
The fractional-order nonlinear Allen Cahn problem frequently appears in the process of phase separation in multi-component alloy systems, including order-disorder transitions. Due to its huge involvement, its accurate solutions become a challenging task among researchers. In this context, this article addresses a novel operational-based scheme to capture the accurate solutions of the fractional-order
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A variant of the discrete gradient method for the solution of the semilinear wave equation under different boundary conditions Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-12 Kai Liu, Mingqian Zhang, Xiong You
In this paper, energy-preserving schemes based upon the discrete gradient are used to numerically solve the semilinear wave equation under periodic boundary conditions, Dirichlet boundary conditions and Neumann boundary conditions. Both the integral form and the evolutionary behaviour of the energy depend on the associated boundary conditions. The wave equations are semi-discretized in different manners
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An adaptive finite element method for distributed elliptic optimal control problems with variable energy regularization Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-12 Ulrich Langer, Richard Löscher, Olaf Steinbach, Huidong Yang
We analyze the finite element discretization of distributed elliptic optimal control problems with variable energy regularization, where the usual norm regularization term with a constant regularization parameter is replaced by a suitable representation of the energy norm in involving a variable, mesh-dependent regularization parameter . It turns out that the error between the computed finite element
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Enhanced cascaded lattice Boltzmann model for multiphase flow simulations at large density ratio Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-12 Yunjie Xu, Linlin Tian, Chunling Zhu, Ning Zhao
In recent years, the pseudopotential multiphase lattice Boltzmann method (LBM) has been widely applied in the numerical simulations of complex multiphase flow. However, numerical stability at high Weber () and Reynolds () numbers seriously restricts its application. In the present work, the pseudopotential multiphase LBM is developed by introducing the entropic stabilizers to the cascaded collision
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Auxiliary splines space preconditioning for B-splines finite elements: The case of H(curl,Ω) and (div,Ω) elliptic problems Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-12 A. El Akri, K. Jbilou, A. Ratnani
This paper presents a study of large linear systems resulting from the regular -splines finite element discretization of the and elliptic problems on unit square/cube domains. We consider systems subject to both homogeneous essential and natural boundary conditions. Our objective is to develop a preconditioning strategy that is optimal and robust, based on the Auxiliary Space Preconditioning method
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Analytical and numerical insights into wildfire dynamics: Exploring the advection–diffusion–reaction model Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-09 Cordula Reisch, Adrián Navas-Montilla, Ilhan Özgen-Xian
Understanding the dynamics of wildfire is crucial for developing management and intervention strategies. Mathematical and computational models can be used to improve our understanding of wildfire processes and dynamics. This paper presents a systematic study of a widely used advection–diffusion–reaction wildfire model with non-linear coupling. The importance of single mechanisms is discovered by analysing
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Physical informed neural networks with soft and hard boundary constraints for solving advection-diffusion equations using Fourier expansions Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-09 Xi'an Li, Jiaxin Deng, Jinran Wu, Shaotong Zhang, Weide Li, You-Gan Wang
Deep learning methods have gained considerable interest in the numerical solution of various partial differential equations (PDEs). One particular focus is physics-informed neural networks (PINN), which integrate physical principles into neural networks. This transforms the process of solving PDEs into optimization problems for neural networks. To address a collection of advection-diffusion equations
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Nonlocal Cahn-Hilliard type model for image inpainting Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-09 Dandan Jiang, Mejdi Azaiez, Alain Miranville, Chuanju Xu
This paper proposes a Cahn-Hilliard type inpainting model equipped with a nonlocal diffusion operator. A rigorous analysis of the well-posedness of the stationary solution is established using Schauder's fixed point theory. We construct a time stepping scheme based on the convex splitting method with the nonlocal term treated implicitly and the fidelity term treated explicitly. We prove the consistency
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Comparisons of two iteration methods for time-harmonic parabolic optimal control problems Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-08 Li-Dan Liao, Xia Ai, Rui-Xia Li, Di-Gen Li, Wei Xu
In this article, based on the structural properties of the coefficient matrix obtained through the discretization of constrained optimal control problems under the time-harmonic parabolic equation, we propose and compare two types of algorithms, namely the Optimized PU (OPU) method and the optimized double-step (ODS) method. It can be theoretically proven that both of these iterative methods have a
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A DPG method for planar div-curl problems Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-07 Jiaqi Li, Leszek Demkowicz
The div-curl system arises in many fields including electromagnetism and fluid dynamics. We are particularly interested in the div-curl problem in 2D multiply-connected domains, as a simplified model of flow around airfoils. In such domains, well-posedness of the problem depends on the prescription of additional line integrals (circulation), apart from standard boundary conditions. We apply the DPG
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Operator approximation of the wave equation based on deep learning of Green's function Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-07 Ziad Aldirany, Régis Cottereau, Marc Laforest, Serge Prudhomme
Deep operator networks (DeepONets) have demonstrated their capability of approximating nonlinear operators for initial- and boundary-value problems. One attractive feature of DeepONets is their versatility since they do not rely on prior knowledge about the solution structure of a problem and can thus be directly applied to a large class of problems. However, training the parameters of the networks
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Efficient Legendre-Laguerre spectral element methods for problems on unbounded domains with diagonalization technique Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-06 Xuhong Yu, Xiaoyang Wang
Based on the generalized matrix eigenvalue decomposition technique, two kinds of basis functions are constructed, which are simultaneously orthogonal in both - and -inner products, and lead to diagonal systems for second order problems. Then we construct mixed Legendre-Laguerre spectral element methods for solving high oscillation or steep gradient solutions problems on unbounded domains, which reduce
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Numerical analysis of a variational-hemivariational inequality governed by the Stokes equations Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-05 Qichang Xiao, Xiaoliang Cheng, Kewei Liang, Hailing Xuan
A variational-hemivariational inequality that describes stationary Stokes equations for the incompressible fluid with mixed nonlinear boundary conditions is studied. We discuss the equivalence of different weak formulations together with the results on unique solvability. The mixed finite element method of P1b/P1 pair is used to discretize the inequality problem and error bounds are derived. Numerical
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An explicitness-preserving IMEX-split multiderivative method Comput. Math. Appl. (IF 2.9) Pub Date : 2024-01-31 Eleni Theodosiou, Jochen Schütz, David Seal
In the last decade, multi-derivative schemes for ordinary differential equations (ODE), i.e., schemes not only using the ODE's flux, but also derivatives thereof, have seen renewed interest in various applications. In (Schütz and Seal, 2021) [33], the authors have introduced a two-derivative method for applications where a clear distinction can be made between stiff (to be treated implicitly) and non-stiff
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A general numerical method for solving the three-dimensional hyperbolic heat conduction equation on unstructured grids Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-02 Huizhi He, Xiaobing Zhang
The non-Fourier heat transfer model has gained significant attention in practical engineering applications, particularly under extreme conditions. However, solving the three-dimensional non-Fourier hyperbolic heat conduction equation remains a challenge. A method for solving the three-dimensional Maxwell-Cattaneo-Vernotte hyperbolic heat conduction equation on unstructured grids is proposed, where
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Mixed variational formulations of virtual elements for the polyharmonic operator (−Δ) Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-02 Franco Dassi, David Mora, Carlos Reales, Iván Velásquez
In this work we will present a method of virtual elements to approximate the solution of a polyharmonic problem . We will consider auxiliary unknowns when , and auxiliary unknowns for . In the first case (), we will solve fourth order problems and a second order one. In the even case, only fourth-order problems have to be solved. Virtual element conforming discretizations are written for each fourth-order
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Hybrid numerical method for the Allen–Cahn equation on nonuniform grids Comput. Math. Appl. (IF 2.9) Pub Date : 2024-02-01 Hyundong Kim, Gyeonggyu Lee, Seungyoon Kang, Seokjun Ham, Youngjin Hwang, Junseok Kim
In this article, we present a hybrid numerical scheme for solving the Allen–Cahn (AC) equation on a nonuniform mesh. The AC equation represents a model for antiphase domain coarsening in a binary mixture. To solve the AC equation on nonuniform grids, the AC equation is split into linear and nonlinear terms applying the operator splitting method. As the first step, the nonlinear term is solved using
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Convergence of a continuous Galerkin method for hyperbolic-parabolic systems Comput. Math. Appl. (IF 2.9) Pub Date : 2024-01-26 Markus Bause, Mathias Anselmann, Uwe Köcher, Florin A. Radu
We study the numerical approximation by space-time finite element methods of a coupled hyperbolic-parabolic system modeling, for instance, poro- and thermoelasticity. The equations are rewritten as a first-order system in time. Discretizations by continuous Galerkin methods in time and inf-sup stable pairs of finite element spaces for the spatial variables are investigated. Optimal order error estimates
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Experimental analysis and numerical simulation of ignition delay time of diesel fuel using a shock tube Comput. Math. Appl. (IF 2.9) Pub Date : 2024-01-23 Claudio Marcio Santana, Jose Eduardo Mautone Barros
The present work consisted in developing a computational routine for prediction and characterization ignition delay time, pressure, temperature generated and energy released in the combustion process in a shock tube. Mathematical modeling considered the high-pressure region of the shock tube known as the conducted section. The Lazarus code compiler was used to generate the unstructured triangular meshes
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A novel numerical inverse technique for multi-parameter time fractional radially symmetric anomalous diffusion problem with initial singularity Comput. Math. Appl. (IF 2.9) Pub Date : 2024-01-25 Wenping Fan, Hao Cheng
In this paper, the multi-parameter time fractional radially symmetric anomalous diffusion model used in porous media with initial singularity is considered. Both the direct numerical solution problem and the multi-parameter identification inverse problem are studied. Given the singularity in the initial time, a stable numerical scheme on nonuniform grid mesh is derived by using the L2−1σ method. To
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Error analysis for finite element approximation of parabolic Neumann boundary control problems Comput. Math. Appl. (IF 2.9) Pub Date : 2024-01-26 Ram Manohar
Our aim is to study a posteriori error estimates for the finite element method of the parabolic boundary control problems on a bounded convex polygonal domain. For discretization, piecewise linear and continuous finite elements are used to approximate the state and the adjoint-state variables, while piecewise constant functions are employed to approximate the control variable. The backward Euler implicit
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A mathematical interpolation bounce back wall modeled lattice Boltzmann method based on hierarchical Cartesian mesh applied to 30P30N airfoil aeroacoustics simulation Comput. Math. Appl. (IF 2.9) Pub Date : 2024-01-23 Wen-zhi Liang, Pei-qing Liu, Jin Zhang, Shu-tong Yang, Qiu-lin Qu
Wall-modeled large eddy simulation (WMLES) is considered to be a powerful method in high Reynolds number wall-bounded fluid dynamics calculations. However, little research on aero-acoustic simulation by lattice Boltzmann method (LBM) combined with LES considering wall model has been found. Moreover, the discussion of the dominant geometric parameters of the wall model, which is dedicated to curved
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Hierarchical higher-order dynamic mode decomposition for clustering and feature selection Comput. Math. Appl. (IF 2.9) Pub Date : 2024-01-23 Adrián Corrochano, Giuseppe D'Alessio, Alessandro Parente, Soledad Le Clainche
This article introduces a novel, fully data-driven method for forming reduced order models (ROMs) in complex flow databases that consist of a large number of variables. The algorithm utilizes higher order dynamic mode decomposition (HODMD), a modal decomposition method, to identify the main frequencies and associated patterns that govern the flow dynamics. By incorporating various normalization techniques
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Approximation of the derivatives beyond Taylor expansion Comput. Math. Appl. (IF 2.9) Pub Date : 2024-01-23 Qiuyan Xu, Zhiyong Liu
Different from the construction process of the traditional finite difference method, we derive a large class of high-accuracy methods for approximating derivatives. Since Taylor expansion is avoided, the requirement for function smoothness in the new methods is greatly reduced. We analyze the approximation errors of the proposed methods and compare their approximation effects. As a typical application
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A monotone diffusion scheme for 3D general meshes: Application to radiation hydrodynamics in the equilibrium diffusion limit Comput. Math. Appl. (IF 2.9) Pub Date : 2024-01-24 Pierre Anguill, Xavier Blanc, Emmanuel Labourasse
We propose in this article a monotone finite volume diffusion scheme on 3D general meshes for the radiation hydrodynamics. Primary unknowns are averaged value over the cells of the mesh. It requires the evaluation of intermediate unknowns located at the vertices of the mesh. These vertex unknowns are computed using an interpolation method. In a second step, the scheme is made monotone by combining
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Multiscale optimization via enhanced multilevel PCA-based control space reduction for electrical impedance tomography imaging Comput. Math. Appl. (IF 2.9) Pub Date : 2024-01-24 Maria M.F.M. Chun, Briana L. Edwards, Vladislav Bukshtynov
An efficient computational approach for imaging binary-type physical properties suitable for various models in biomedical applications is developed and validated. The proposed methodology includes gradient-based multiscale optimization with multilevel control space reduction based on principal component analysis, optimal switching between the fine and coarse scales, and their effective re-parameterization
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A discrete Hermite moments based multiple-relaxation-time lattice Boltzmann model for convection-diffusion equations Comput. Math. Appl. (IF 2.9) Pub Date : 2024-01-23 Yao Wu, Zhenhua Chai, Xiaolei Yuan, Xiuya Guo, Baochang Shi
In this work, a multiple-relaxation-time lattice Boltzmann (MRT-LB) model based on discrete Hermite moments is proposed for nonlinear convection-diffusion equations (NCDEs). First, we use the block-weighted orthogonality of Hermite matrix to give a general expression of equilibrium distribution function (EDF) with adjustable parameter . This expression is suitable for NCDEs and Navier-Stokes equations