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An unconditionally energy stable method for binary incompressible heat conductive fluids based on the phase–field model Comput. Math. Appl. (IF 3.218) Pub Date : 20220810
Qing Xia, Junseok Kim, Binhu Xia, Yibao LiThis paper proposes an unconditionally energy stable method for incompressible heat conductive fluids under the phase–field framework. We combine the complicated system by the Navier–Stokes equation, Cahn–Hilliard equation, and heat transfer equation. A Crank–Nicolson type scheme is employed to discretize the governing equation with the secondorder temporal accuracy. The unconditional energy stability

A new nonconvex low rank minimization model to decompose an image into cartoon and texture components Comput. Math. Appl. (IF 3.218) Pub Date : 20220809
Riya Ruhela, Bhupendra Gupta, Subir Singh LambaDecomposition of an image into cartoon and texture components is frequently used in many image processing applications. Here, the cartoon component has been characterized by the frequently used total variation norm. However, it becomes very challenging to obtain the texture component due to the varying nature of the texture. In general, the texture component has oscillatory behavior locally or globally

Unsteady oblique stagnationpoint flow and heat transfer of fractional Maxwell fluid with convective derivative under modified pressure field Comput. Math. Appl. (IF 3.218) Pub Date : 20220809
Yu Bai, Xin Wang, Yan ZhangUnsteady oblique stagnationpoint flow and heat transfer of fractional Maxwell fluid with convective derivative towards an oscillating tensile plate are discussed in this paper. The fractional operator is introduced to material derivative for the first time to obtain a newly defined constitutive equation of Maxwell fluid. The Fourier's law is modified accordingly. The pressure gradient is innovatively

High precision implicit method for 3D quasilinear hyperbolic equations on a dissimilar domain: Application to 3D telegraphic equation Comput. Math. Appl. (IF 3.218) Pub Date : 20220805
R.K. Mohanty, Bishnu Pada Ghosh, Urvashi AroraIn this paper, we recommend a novel high accuracy compact threelevel implicit numerical method of order two in time and four in space using unequal mesh for the solution of 3D quasilinear hyperbolic equations on an irrational domain. The stability analysis of the model Telegraphic equation for unequal mesh has been discussed and it has been shown that the proposed method for Telegraphic equation

Error analysis of a SUPGstabilized PODROM method for convectiondiffusionreaction equations Comput. Math. Appl. (IF 3.218) Pub Date : 20220803
Volker John, Baptiste Moreau, Julia NovoA reduced order model (ROM) method based on proper orthogonal decomposition (POD) is analyzed for convectiondiffusionreaction equations. The streamlineupwind Petrov–Galerkin (SUPG) stabilization is used in the practically interesting case of dominant convection, both for the full order method (FOM) and the ROM simulations. The asymptotic choice of the stabilization parameter for the SUPGROM is

Virtual element methods for general linear elliptic interface problems on polygonal meshes with small edges Comput. Math. Appl. (IF 3.218) Pub Date : 20220803
Jai Tushar, Anil Kumar, Sarvesh KumarIn this article, we discuss and analyze a conforming virtual element discretization with boundary stabilization term proposed in Brenner and Sung (2018) [30] (suitable for small edges that appeared in the mesh generation) to approximate general linear elliptic problems with discontinuous diffusivity coefficient across the interface. One of the critical features of the proposed virtual element method

Developing and analyzing a finite element method for simulating wave propagation in graphenebased absorber Comput. Math. Appl. (IF 3.218) Pub Date : 20220803
Yunqing Huang, Jichun Li, Wei YangIn this paper, we are concerned about a graphenebased absorber model, which incorporates both the interband conductivity and intraband conductivity of the graphene. We first establish an energy identity and stability for the continuous model. Then we propose a finite element timedomain method for solving the model by edge elements. Numerical stability and optimal error estimate are proved for the

Analysis of a preconditioner for a membrane diffusion problem with the Kedem–Katchalsky transmission condition Comput. Math. Appl. (IF 3.218) Pub Date : 20220802
Piotr KrzyżanowskiA composite hp discontinuous Galerkin finite element discretization of a diffusion problem, where subdomains are separated by thin membranes, modeled by the Kedem–Katchalsky transmission condition, is considered. A preconditioner based on the additive Schwarz method is proved to have the condition number bounded independently of the mesh size, the membrane permeability and the diffusion coefficient

Battling Gibbs phenomenon: On finite element approximations of discontinuous solutions of PDEs Comput. Math. Appl. (IF 3.218) Pub Date : 20220802
Shun ZhangIn this paper, we want to clarify the Gibbs phenomenon when continuous and discontinuous finite elements are used to approximate discontinuous or nearly discontinuous PDE solutions from the approximation point of view. For a simple step function, we explicitly compute its continuous and discontinuous piecewise constant or linear projections on discontinuity matched or nonmatched meshes. For the simple

A comprehensive assessment of accuracy of adaptive integration of cut cells for laminar fluidstructure interaction problems Comput. Math. Appl. (IF 3.218) Pub Date : 20220801
Chennakesava Kadapa, Xinyu Wang, Yue MeiFinite element methods based on cutcells are becoming increasingly popular because of their advantages over formulations based on bodyfitted meshes for problems with moving interfaces. In such methods, the cells (or elements) which are cut by the interface between two different domains need to be integrated using special techniques in order to obtain optimal convergence rates and accurate fluxes

Adaptive parameter based matrix splitting iteration method for the large and sparse linear systems Comput. Math. Appl. (IF 3.218) Pub Date : 20220801
Yifen Ke, Changfeng MaFor the large and sparse linear systems, we utilize the efficient splittings of the system matrix and introduce an intermediate variable. The main contribution of this paper is that the adaptive parameter based matrix splitting iteration method is constructed from the view of numerical optimization and hybrid procedure to solve the derived equation instead. The novel method adopts the prediction and

Direct Numerical Simulation of pulsating flow effect on the distribution of noncircular particles with increased levels of complexity: IBLBM Comput. Math. Appl. (IF 3.218) Pub Date : 20220728
Amin Amiri Delouei, Sajjad Karimnejad, Fuli HeEquilibrium position, as well as dynamic patterns of suspended particles, plays a dominant role in particle manipulation of segregation, transporting, or sorting. The current paper aims to investigate the falling manners of noncircular particles in an enclosure while the pulsatile flow is involved as a counterflow. The directforcing immersed boundary method is coupled with the lattice Boltzmann

An effective secondorder scheme for the nonstationary incompressible magnetohydrodynamics equations Comput. Math. Appl. (IF 3.218) Pub Date : 20220727
Xiaojuan Shen, Yunqing Huang, Xiaojing DongWe are proposing the CrankNicolson/AdamsBashforth (CN/AB) algorithm for the nonstationary magnetohydrodynamic (MHD) equations. For time discretization, the time derivative terms are approximated by a firstorder Eulerbackward scheme, an implicit secondorder CrankNicolson scheme acting on linear terms, and an explicit AdamsBashforth scheme dealing with nonlinear terms. We use the finite element

Arbitrary highorder exponential integrators conservative schemes for the nonlinear GrossPitaevskii equation Comput. Math. Appl. (IF 3.218) Pub Date : 20220726
Yayun Fu, Dongdong Hu, Gengen ZhangIn this paper, we propose a family of highorder conservative schemes based on the exponential integrators technique and the symplectic RungeKutta method for solving the nonlinear GrossPitaevskii equation. By introducing generalized scalar auxiliary variable, the equation is equivalent to a new system with both mass and modified energy conservation laws. Then, a conservative semidiscrete exponential

Effective properties of twodimensional dispersed composites. Part II. Revision of selfconsistent methods Comput. Math. Appl. (IF 3.218) Pub Date : 20220721
Vladimir MityushevThe generalized alternating method of Schwarz was applied to boundary value problems for a multiply connected domain in the prior work Part I [62]. Approximate analytical formulas for the effective properties of dispersed composites with the exactly derived precision of their validity in concentration and in contrast parameter were derived. The present paper is devoted to comparison study of the formulas

Virtual element method on polyhedral meshes for biharmonic eigenvalues problems Comput. Math. Appl. (IF 3.218) Pub Date : 20220721
Franco Dassi, Iván VelásquezIn this paper we study a C1 Virtual Element Method (VEM) on polyhedral meshes for biharmonic eigenvalue problems in three dimensions. Optimal order error estimates for the eigenfunctions and a double order for the eigenvalues are obtained by using the approximation theory of compact selfadjoint operators. Finally, a set of tests will numerically prove the theoretical result of the proposed scheme

HomPINNs: Homotopy physicsinformed neural networks for learning multiple solutions of nonlinear elliptic differential equations Comput. Math. Appl. (IF 3.218) Pub Date : 20220720
Yao Huang, Wenrui Hao, Guang LinPhysicsinformed neural networks (PINNs) based machine learning is an emerging framework for solving nonlinear differential equations. However, due to the implicit regularity of neural network structure, PINNs can only find the flattest solution in most cases by minimizing the loss functions. In this paper, we combine PINNs with the homotopy continuation method, a classical numerical method to compute

A reducedorder fast reproducing kernel collocation method for nonlocal models with inhomogeneous volume constraints Comput. Math. Appl. (IF 3.218) Pub Date : 20220719
Jiashu Lu, Yufeng NieThis paper is concerned with the implementations of the meshfreebased reducedorder model (ROM) to timedependent nonlocal models with inhomogeneous volume constraints. Generally, when using ROM for nonlocal models, the projection of nonlocal volume constraints needs to be computed in every time step to handle the nonlocal boundary conditions. Up to now, only finite element methods (FEM) can work

The mass diffusive model of Svärd simplified to simulate nearly incompressible flows Comput. Math. Appl. (IF 3.218) Pub Date : 20220714
Adam Kajzer, Jacek PozorskiA model of viscous gas flows has recently been proposed by Svärd (2018) [27] as a remedy to some physical inconsistencies of the compressible NavierStokes equations. We adopt and simplify the model to handle nearly incompressible flows by neglecting the energy conservation law and imposing the isothermal equation of state. For the sake of accuracy and computational efficiency, the artificial speed

A unified analysis of fully mixed virtual element method for wormhole propagation arising in the petroleum engineering Comput. Math. Appl. (IF 3.218) Pub Date : 20220714
Mehdi Dehghan, Zeinab GharibiWormhole propagation, arising in petroleum engineering, is used to describe the distribution of acid and the increase of porosity in carbonate reservoir under the dissolution of injected acid and plays a very important role in the product enhancement of oil and gas reservoirs. In this paper, a fully mixed virtual element method (VEM) is employed to discretize this problem, in which mixed VEM is used

Anisotropic mesh adaptation for regionbased segmentation accounting for image spatial information Comput. Math. Appl. (IF 3.218) Pub Date : 20220713
Matteo Giacomini, Simona PerottoA finite elementbased image segmentation strategy enhanced by an anisotropic mesh adaptation procedure is presented. The methodology relies on a split Bregman algorithm for the minimisation of a regionbased energy functional and on an anisotropic recoverybased error estimate to drive mesh adaptation. More precisely, a Bayesian energy functional is considered to account for image spatial information

An enriched Galerkin method for the Stokes equations Comput. Math. Appl. (IF 3.218) Pub Date : 20220712
SonYoung Yi, Xiaozhe Hu, Sanghyun Lee, James H. AdlerWe present a new enriched Galerkin (EG) scheme for the Stokes equations based on piecewise linear elements for the velocity unknowns and piecewise constant elements for the pressure. The proposed EG method augments the conforming piecewise linear space for velocity by adding an additional degree of freedom which corresponds to one discontinuous linear basis function per element. Thus, the total number

A combined stabilized mixed finite element and discontinuous Galerkin method for coupled Stokes and Darcy flows with transport Comput. Math. Appl. (IF 3.218) Pub Date : 20220708
Junpeng Song, Hongxing RuiThis paper presents a combined stabilized mixed finite element and discontinuous Galerkin method for coupled StokesDarcy flows model with transport, where the fluid viscosity depends on the concentration. We use nonconforming piecewise linear CrouzeixRaviart (CR) element to approximate velocity, piecewise constant function to approximate pressure and the symmetric interior penalty Galerkin (SIPG)

ReLU deep neural networks from the hierarchical basis perspective Comput. Math. Appl. (IF 3.218) Pub Date : 20220708
Juncai He, Lin Li, Jinchao XuWe study ReLU deep neural networks (DNNs) by investigating their connections with the hierarchical basis method in finite element methods. First, we show that the approximation schemes of ReLU DNNs for x2 and xy are composition versions of the hierarchical basis approximation for these two functions. Based on this fact, we obtain a geometric interpretation and systematic proof for the approximation

Highorder methods for the option pricing under multivariate rough volatility models Comput. Math. Appl. (IF 3.218) Pub Date : 20220707
Zhengguang Shi, Pin Lyu, Jingtang MaThis paper studies the efficient methods for option pricing under multivariate rough volatility models. The characteristic functions of the asset logprice, which play important role in the option pricing under the multivariate rough volatility models, are determined by a system of parametric nonlinear fractional Riccati equations. This paper obtains the results on the existence, uniqueness and regularity

An efficient maximum bound principle preserving padaptive operatorsplitting method for threedimensional phase field shape transformation model Comput. Math. Appl. (IF 3.218) Pub Date : 20220707
Yan Wang, Xufeng Xiao, Xinlong FengIn this paper, a novel numerical algorithm for efficient modeling of threedimensional shape transformation governed by the modified AllenCahn (AC) equation is developed, which has important significance for computer science and graphics technology. The new idea of the proposed method is as follows. Firstly, the operator splitting method is used to decompose the threedimensional problem into a series

Investigation of a noniterative technique based on topological derivatives for fast localization of small conductivity inclusions Comput. Math. Appl. (IF 3.218) Pub Date : 20220706
WonKwang ParkIn this contribution, we consider a topological derivativebased noniterative technique for an inverse conductivity problem of localizing a smallconductivity inclusion completely embedded in a homogeneous domain via boundary measurement data. For this purpose, we derive the topological derivative by applying an asymptotic formula in the presence of a smalldiameter conductivity inclusion and establish

Highorder level set reinitialization for multiphase flow simulations based on unstructured grids Comput. Math. Appl. (IF 3.218) Pub Date : 20220706
Long Cu Ngo, QuangNgoc Dinh, Hyoung Gwon ChoiReinitialization is essential to maintaining the accuracy of the level set method at capturing interfaces. In this paper, a highorder reinitialization method for the level set function which has previously been developed for structured grids was extended to unstructured grids. The proposed method involves constructing a stencil of an unstructured grid to define a highorder polynomial that approximates

A posteriori error estimation for a C1 virtual element method of Kirchhoff plates Comput. Math. Appl. (IF 3.218) Pub Date : 20220705
Mingqing Chen, Jianguo Huang, Sen LinA residualtype a posteriori error estimation is developed for a C1conforming virtual element method (VEM) to solve a Kirchhoff plate bending problem. To derive the reliability and efficiency of the a posteriori error bound, the inverse inequalities and norm equivalence are developed over the underlying C1conforming virtual element space, and a weak interpolation operator together with its error

Unconditional stability of first and second orders implicit/explicit schemes for the natural convection equations Comput. Math. Appl. (IF 3.218) Pub Date : 20220630
Chuanjun Chen, Tong ZhangIn this paper, we consider and analyze the stability of three implicit/explicit (IMEX) schemes for the timedependent natural convection problem, these considered numerical schemes contain the first order backward Euler scheme, second order CrankNicolson IMEX scheme and BDF2AB2 combination. All numerical schemes deal with the linear terms implicitly and the nonlinear terms explicitly. Then the original

A fourthorder compact implicit immersed interface method for 2D Poisson interface problems Comput. Math. Appl. (IF 3.218) Pub Date : 20220629
Reymundo Itza Balam, Miguel Uh ZapataThis paper presents a fourthorder compact immersed interface method to solve twodimensional Poisson equations with discontinuous solutions on arbitrary domains divided by an interface. The compact scheme only employs a ninepoint stencil for each grid point on the computational domain. The new approach is based on an implicit formulation obtained from generalized Taylor series expansions, and it

A global convergent semismooth Newton method for semilinear elliptic optimal control problem Comput. Math. Appl. (IF 3.218) Pub Date : 20220629
Zemian Zhang, Xuesong Chen 
A vector penaltyprojection approach for the timedependent incompressible magnetohydrodynamics flows Comput. Math. Appl. (IF 3.218) Pub Date : 20220629
Huimin Ma, Pengzhan HuangIn this paper, we study a fully discrete vector penaltyprojection method for the timedependent incompressible magnetohydrodynamics flows. This fully discrete scheme is a combination of a mixed finite element approximation for spatial discretization and firstorder backward Euler for temporal discretization. Moreover, unconditionally energy stable is established, and error estimates for the fully

Theoretical analysis of the generalized finite difference method Comput. Math. Appl. (IF 3.218) Pub Date : 20220628
Zhiyin Zheng, Xiaolin LiThe generalized finite difference method (GFDM) is a typical meshless collocation method based on the Taylor series expansion and the moving least squares technique. In this paper, we first provide theoretical results of the meshless function approximation in the GFDM. Properties, stability and error estimation of the approximation are studied theoretically, and a stabilized approximation is proposed

Singular boundary method for 2D and 3D acoustic design sensitivity analysis Comput. Math. Appl. (IF 3.218) Pub Date : 20220623
Suifu Cheng, Fajie Wang, PoWei Li, Wenzhen QuIn this paper, a novel BurtonMillertype singular boundary method (BMSBM) formulation is proposed for the acoustic design sensitivity analysis, with the help of the direct differentiation method. The BurtonMiller formulation is employed to overcome the fictitious frequency problem in the numerical solutions of exterior acoustic problems. The simple empirical formulas are used to estimate the origin

Kalman filter temperature estimation with a photoacoustic observation model during the hyperthermia treatment of cancer Comput. Math. Appl. (IF 3.218) Pub Date : 20220623
Mohsen Alaeian, Helcio R.B. Orlande, Bernard LamienHyperthermia with laser heating can be a noninvasive treatment for tumors near the body surface. Thermal damage of tissues depends on temperature levels and time of exposure to high temperatures, thus requiring accurate techniques to measure the temperature in the target region of interest. In this computational work, we couple the laser hyperthermia treatment of cancer to the photoacoustic temperature

C1conforming variational discretization of the biharmonic wave equation Comput. Math. Appl. (IF 3.218) Pub Date : 20220623
Markus Bause, Maria Lymbery, Kevin OsthuesBiharmonic wave equations are of importance to various applications including thin plate analyses. The innovation of this work comes through the numerical approximation of their solutions by a C1conforming in space and time finite element approach. Therein, the smoothness properties of solutions to the continuous evolution problem are embodied. Time discretization is based on a combined Galerkin and

Global superconvergence analysis of nonconforming finite element method for time fractional reactiondiffusion problem with anisotropic data Comput. Math. Appl. (IF 3.218) Pub Date : 20220622
Yabing Wei, Shujuan Lü, Fenling Wang, F. Liu, Yanmin ZhaoIn this paper, a class of twodimensional (2D) time fractional reactiondiffusion equation is considered. The solution usually exhibits singularity at the initial moment and anisotropic behavior in the spatial direction. In response to these problems, we provide an effective numerical framework for analyzing the L2norm error, H1norm superclose property and H1norm global superconvergence result

Normal forms of double Hopf bifurcation for a reactiondiffusion system with delay and nonlocal spatial average and applications Comput. Math. Appl. (IF 3.218) Pub Date : 20220622
Shuhao Wu, Yongli Song, Qingyan ShiIn this paper, we are concerned with a reactiondiffusion model incorporating delay and nonlocal effects. The normal form of double Hopf bifurcation is derived. The diffusive model of pollen tube tip growth is discussed and numerical simulations show that spatially homogeneous and inhomogeneous periodic solutions can be both stable or connected by a heteroclinic orbit under certain conditions. In addition

Vibration analysis of variable fractional viscoelastic plate based on shifted Chebyshev wavelets algorithm Comput. Math. Appl. (IF 3.218) Pub Date : 20220620
Rongqi Dang, Aiming Yang, Yiming Chen, Yanqiao Wei, Chunxiao YuIn this paper, new and effective methods are provided for modeling and numerical simulation of viscoelastic plate, respectively. Viscoelastic plate is modeled by a variable fractional derivative model with better fitting effect and is numerically analyzed directly in time domain using shifted Chebyshev wavelets algorithm for the first time. A governing equation with three independent variables is established

Block symmetrictriangular preconditioners for generalized saddle point linear systems from piezoelectric equations Comput. Math. Appl. (IF 3.218) Pub Date : 20220615
QinQin Shen, Quan ShiBased on the symmetrictriangular (ST) decomposition technique, a class of block ST (BST) preconditioners are proposed for generalized saddle point linear systems arising from the meshfree discretization of piezoelectric equations. By applying the BST preconditioners, we first transform the generalized saddle point linear systems into symmetric positive definite ones, which then can be solved in a

A fully discrete twogrid method for the diffusive Peterlin viscoelastic model Comput. Math. Appl. (IF 3.218) Pub Date : 20220615
JingYu Yang, YaoLin Jiang, Jun LiWe present in this paper a fully discrete twogrid finite element method to solve the diffusive Peterlin viscoelastic model on the basis of studying the fully discrete standard finite element method. The fully discrete twogrid method involves solving small nonlinear coarse spatial grid systems and linear fine spatial grid systems with the same time step. Under the reasonable assumptions, it is proven

Reliability analysis of the uncertain heat conduction model Comput. Math. Appl. (IF 3.218) Pub Date : 20220615
Chenlei Tian, Ting Jin, Xiangfeng Yang, Qinyu LiuUncertainty theory has been demonstrated as a rigorous mathematical system to measure the reliability of products when there are few or no samples. Meanwhile, first hitting time, which is the first type of undetermined time appeared in history, has been extensively used in reliability analysis. Based upon it, this article mainly focuses on the reliability analysis of the uncertain heat equation through

Explicit highorder conservative exponential time differencing RungeKutta schemes for the twodimensional nonlinear Schrödinger equation Comput. Math. Appl. (IF 3.218) Pub Date : 20220615
Yayun Fu, Zhuangzhi XuIn this paper, we develop a class of explicit energypreserving RungeKutta schemes for solving the nonlinear Schrödinger equation based on the projection technique and the exponential time differencing method. First, we reformulate the equation to an equivalent system that possesses new quadratic energy via introducing an auxiliary variable. Then, we construct a family of fully discrete exponential

A nonintrusive neural network model order reduction algorithm for parameterized parabolic PDEs Comput. Math. Appl. (IF 3.218) Pub Date : 20220614
Tao Zhang, Hui Xu, Lei Guo, Xinlong FengReducedorder modeling based on projectiondriven neural network (PDNN) generally needs sufficient data set while physicsinformed machine learning (PINN) and physicsreinforced neural network (PRNN) take the reduced order systems into consideration. However, the physicsinformed machine learning technique used in these two methods gives rise to expensive time consumption for complex neural network

Improved error estimates of hybridizable interior penalty methods using a variable penalty for highly anisotropic diffusion problems Comput. Math. Appl. (IF 3.218) Pub Date : 20220614
Grégory Etangsale, Marwan Fahs, Vincent Fontaine, Nalitiana RajaonisonIn this paper, we derive improved a priori error estimates for families of hybridizable interior penalty discontinuous Galerkin (HIP) methods using a variable penalty for secondorder elliptic problems. The strategy is to use a penalization function of the form O(1/h1+δ), where h denotes the mesh size and δ is a userdependent parameter. We then quantify its direct impact on the convergence analysis

A wellbalanced discontinuous Galerkin method for the shallow water flows on erodible bottom Comput. Math. Appl. (IF 3.218) Pub Date : 20220610
Maojun Li, Rushuang Mu, Haiyun DongIn this paper, we investigate the shallow water (SW) flow over the erodible layer using a fully coupled mathematical model in twodimensional (2D) space. A wellbalanced discontinuous Galerkin (DG) scheme is proposed for solving the SW equations with sediment transport and bed evolution. To achieve the wellbalanced property of the numerical scheme easily, the nonlinear SW equations are first reformulated

Supercloseness and postprocessing of stabilizerfree weak Galerkin finite element approximations for parabolic problems Comput. Math. Appl. (IF 3.218) Pub Date : 20220613
Peng Zhu, Shenglan XieIn this paper we present a fully discrete stabilizerfree weak Galerkin (SFWG) finite element scheme for the approximation of the parabolic equations. The temporal variable is discretized by the second order CrankNicolson scheme; the spatial variables are discretized by a stabilizerfree weak Galerkin finite element method. The stability and supercloseness convergence of both the semidiscrete SFWG

Computational study of magnetoconvective nonNewtonian nanofluid slip flow over a stretching/shrinking sheet embedded in a porous medium Comput. Math. Appl. (IF 3.218) Pub Date : 20220610
Adebowale Martins Obalalu, Adebayo Olusegun Ajala, Akintayo Oladimeji Akindele, Olayinka Akeem Oladapo, Olajide Olatunbosun Akintayo, Oluwatosin Muinat JimohA Steady flow of twodimensional magnetohydrodynamic nonNewtonian fluid over a stretching/shrinking sheet in the presence of nanoparticles is exemplified theoretically and numerically. In this problem, we have considered the thermal radiation and adjust the hot fluid along with the lower surface of the wall namely convective boundarylayer slip. To the best of the authors' knowledge, this parameter

Convolutional neural network based simulation and analysis for backward stochastic partial differential equations Comput. Math. Appl. (IF 3.218) Pub Date : 20220610
Wanyang DaiWe develop a generic convolutional neural network (CNN) based numerical scheme to simulate the 2tuple adapted strong solution to a unified system of backward stochastic partial differential equations (BSPDEs) driven by Brownian motions, which can be used to model many realworld system dynamics such as optimal control and differential game problems. The dynamics of the scheme is modeled by a CNN

A new finite difference mapped unequalsized WENO scheme for HamiltonJacobi equations Comput. Math. Appl. (IF 3.218) Pub Date : 20220610
Liang Li, Jun ZhuIn this paper, a new fifthorder finite difference mapped unequalsized weighted essentially nonoscillatory (MUSWENO) scheme is proposed for solving HamiltonJacobi equations in multidimensions. This new MUSWENO scheme uses the same widest spatial stencils as that of the classical same order finite difference WENO scheme [19], and could obtain smaller truncation errors and optimal fifthorder accuracy

Stochastic heat equation: Numerical positivity and almost surely exponential stability Comput. Math. Appl. (IF 3.218) Pub Date : 20220609
Xiaochen Yang, Zhanwen Yang, Chiping ZhangIn this paper, the numerical positivity and almost surely exponential stability of the stochastic heat equation are discussed. The finite difference method and the splitstep backward Euler are considered for spatial and temporal, respectively. Motivated from physical applications such as temperature, finance and so on, positivity has real significance, which is volatilized by some common numerical

Numerical approximation of optimal convex and rotationally symmetric shapes for an eigenvalue problem arising in optimal insulation Comput. Math. Appl. (IF 3.218) Pub Date : 20220609
Sören Bartels, Hedwig Keller, Gerd WachsmuthWe are interested in the optimization of convex domains under a PDE constraint. Due to the difficulties of approximating convex domains in R3, the restriction to rotationally symmetric domains is used to reduce shape optimization problems to a twodimensional setting. For the optimization of an eigenvalue arising in a problem of optimal insulation, the existence of an optimal domain is proven. An algorithm

Partially pivoted ACA based acceleration of the energetic BEM for timedomain acoustic and elastic waves exterior problems Comput. Math. Appl. (IF 3.218) Pub Date : 20220609
A. Aimi, L. Desiderio, G. Di CredicoWe consider acoustic and elastic wave propagation problems in 2D unbounded domains, reformulated in terms of spacetime Boundary Integral Equations (BIEs). For their numerical solution, we employ a weak formulation related to the energy of the system and we discretize the weak problems by a Galerkintype Boundary Element Method (BEM): this approach, called Energetic BEM, has revealed accurate and stable

An investigation of the multimode RichtmyerMeshkov instability at a gas/HE interface using Pagosa Comput. Math. Appl. (IF 3.218) Pub Date : 20220609
Jinlian Ren, David Culp, Brandon Smith, Xia MaIn this work, we present a hydrocode Pagosa and explore the RichtmyerMeshkov Instability (RMI) at an air/high explosive (HE) interface for the first time that is important but has not received much attention yet in the high explosive safety field. Thus, the presented Pagosa can be expected to predict the whole deflagrationtodetonation transition (DDT) process in future. In Pagosa, spatial discretization

Bend 3d mixed virtual element method for Darcy problems Comput. Math. Appl. (IF 3.218) Pub Date : 20220609
Franco Dassi, Alessio Fumagalli, Anna Scotti, Giuseppe VaccaIn this study, we propose a virtual element scheme to solve the Darcy problem in three physical dimensions. The main novelty is that curved elements are naturally handled without any degradation of the solution accuracy. Indeed, in presence of curved boundaries, or internal interfaces, the geometrical error introduced by planar approximations may dominate the convergence rate limiting the benefit of

Temporal convergence of extrapolated BDF2 scheme for the MaxwellLandauLifshitz equations Comput. Math. Appl. (IF 3.218) Pub Date : 20220608
Shuaifei Hu, Guomei Zhao, Rong AnThe MaxwellLandauLifshitz equations are used to describe certain electromagnetic phenomena and are a strongly nonlinear parabolic system. This paper focuses on the optimal error estimates of a linearized secondorder BDF semidiscrete scheme for the numerical approximation of the solution to the MaxwellLandauLifshitz equations. The proposed algorithm is a semiimplicit scheme by using the extrapolation

A wellbalanced RungeKutta discontinuous Galerkin method for the Euler equations in isothermal hydrostatic state under gravitational field Comput. Math. Appl. (IF 3.218) Pub Date : 20220607
Ziming Chen, Yingjuan Zhang, Gang Li, Shouguo QianThis article presents a wellbalanced RungeKutta discontinuous Galerkin method for the Euler equations with gravitation and in the isothermal hydrostatic state. To achieve the wellbalanced feature, we develop a decomposition algorithm backed by a novel auxiliary function. Using the decomposition algorithm, we successfully build wellbalanced numerical fluxes and achieve novel discretizations to the

Deformable models for image segmentation: A critical review of achievements and future challenges Comput. Math. Appl. (IF 3.218) Pub Date : 20220607
Ankit Kumar, Subit Kumar JainImage segmentation is a fundamental and tedious task of computer vision. Because of inherent noise and intensity inhomogeneity in realworld images, it remains a difficult problem in practical applications such as image analysis, scene understanding, object detection, and many others. Several mathematical models proposed for image segmentation in the past few decades with an effective policy. Among

Fully implicit local timestepping methods for advectiondiffusion problems in mixed formulations Comput. Math. Appl. (IF 3.218) Pub Date : 20220607
ThiThaoPhuong HoangThis paper is concerned with numerical solution of transport problems in heterogeneous porous media. A semidiscrete continuousintime formulation of the linear advectiondiffusion equation is obtained by using a mixed hybrid finite element method, in which the flux variable represents both the advective and diffusive flux, and the Lagrange multiplier arising from the hybridization is used for the