Computers & Mathematics with Applications最新文献

{"title":"A parallel algorithm for the inversion of matrices with simultaneously diagonalizable blocks","authors":"Dimitrios S. Lazaridis,&nbsp;Konstantinos A. Draziotis,&nbsp;Nikolaos L. Tsitsas","doi":"10.1016/j.camwa.2024.09.014","DOIUrl":"10.1016/j.camwa.2024.09.014","url":null,"abstract":"<div><div>Block matrices with simultaneously diagonalizable blocks arise in diverse application areas, including, e.g., numerical methods for engineering based on partial differential equations as well as network synchronization, cryptography and control theory. In the present paper, we develop a parallel algorithm for the inversion of <span><math><mi>m</mi><mo>×</mo><mi>m</mi></math></span> block matrices with simultaneously-diagonalizable blocks of order <em>n</em>. First, a sequential version of the algorithm is presented and its computational complexity is determined. Then, a parallelization of the algorithm is implemented and analyzed. The complexity of the derived parallel algorithm is expressed as a function of <em>m</em> and <em>n</em> as well as of the number <em>μ</em> of utilized CPU threads. Results of numerical experiments demonstrate the CPU time superiority of the parallel algorithm versus the respective sequential version and a standard inversion method applied to the original block matrix. An efficient parallelizable procedure to compute the determinants of such block matrices is also described. Numerical examples are presented for using the developed serial and parallel inversion algorithms for boundary-value problems involving transmission problems for the Helmholtz partial differential equation in piecewise homogeneous media.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"174 ","pages":"Pages 340-351"},"PeriodicalIF":2.9,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142421917","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Convergence analysis of novel discontinuous Galerkin methods for a convection dominated problem","authors":"Satyajith Bommana Boyana ,&nbsp;Thomas Lewis ,&nbsp;Sijing Liu ,&nbsp;Yi Zhang","doi":"10.1016/j.camwa.2024.09.027","DOIUrl":"10.1016/j.camwa.2024.09.027","url":null,"abstract":"<div><div>In this paper, we propose and analyze a numerically stable and convergent scheme for a convection-diffusion-reaction equation in the convection-dominated regime. Discontinuous Galerkin (DG) methods are considered since standard finite element methods for the convection-dominated equation cause spurious oscillations. We choose to follow a DG finite element differential calculus framework introduced in Feng et al. (2016) and approximate the infinite-dimensional operators in the equation with the finite-dimensional DG differential operators. Specifically, we construct the numerical method by using the dual-wind discontinuous Galerkin (DWDG) formulation for the diffusive term and the average discrete gradient operator for the convective term along with standard DG stabilization. We prove that the method converges optimally in the convection-dominated regime. Numerical results are provided to support the theoretical findings.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"175 ","pages":"Pages 224-235"},"PeriodicalIF":2.9,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142419164","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modified upwind finite volume scheme with second-order Lagrange multiplier method for dimensionally reduced transport model in intersecting fractured porous media","authors":"Wei Liu ,&nbsp;Zhifeng Wang ,&nbsp;Gexian Fan ,&nbsp;Yingxue Song","doi":"10.1016/j.camwa.2024.09.024","DOIUrl":"10.1016/j.camwa.2024.09.024","url":null,"abstract":"<div><div>In this paper, a dimensionally reduced model is introduced to express the solute transport in the porous media containing with intersecting fractures, in which the fractures are treated as dimensionally reduced manifolds with respect to the dimensions of surrounding media. The transmission conditions can be used to describe the physical behavior of concentration and flux. We construct a hybrid-dimensional finite volume method involving BDF2 time discretization and modified upwind scheme for advection-dominated diffusion model. Fully space-time second-order convergence rate is deduced on the staggered nonuniform grids based on the error estimates of coupling terms. The numerical tests are presented to show that the proposed finite volume method can handle reduced model in porous media with multiple L-shaped, crossing and bifurcated fractures efficiently and flexibly. In addition, the Lagrange multiplier approach is developed to construct bound preserving schemes for dimensionally reduced advection-dominated diffusion model in intersecting fractured porous media.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"175 ","pages":"Pages 202-223"},"PeriodicalIF":2.9,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142419163","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Flow through a prosthetic mechanical aortic valve: Numerical model and experimental study","authors":"Marcin Nowak ,&nbsp;Eduardo Divo ,&nbsp;Tomasz Borkowski ,&nbsp;Ewelina Marciniak ,&nbsp;Marek Rojczyk ,&nbsp;Ryszard Białecki","doi":"10.1016/j.camwa.2024.09.010","DOIUrl":"10.1016/j.camwa.2024.09.010","url":null,"abstract":"<div><div>This research presents a numerical model dedicated for virtual patient diagnostics in the field of synthetic valve implantation. The model operates based on computational fluid dynamics solver with implemented rigid body motion solver. Characteristic indicators related to the prosthetic valve were determined to assess the correctness of cardiac system operation after implantation. A novel approach for dynamic time discretization was developed for reliable and time-efficient calculation. The solver efficiency and computational savings due to application of the developed time-discretization scheme is discussed. Numerical results were validated using experimental data acquired from a test rig, including mass flow meter, pressure transducers, and valve holder designed for this purpose. Multivariant analysis of the model constant was performed towards different levels of the valve resistance to motion. The in-house algorithm was prepared to automatically determine the prosthetic valve position from fast camera images.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"175 ","pages":"Pages 184-201"},"PeriodicalIF":2.9,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142326523","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A hybrid lattice Boltzmann and finite difference method for two-phase flows with soluble surfactants","authors":"Yan Ba ,&nbsp;Haihu Liu ,&nbsp;Wenqiang Li ,&nbsp;Wenjing Yang","doi":"10.1016/j.camwa.2024.09.022","DOIUrl":"10.1016/j.camwa.2024.09.022","url":null,"abstract":"<div><div>A hybrid method is developed to simulate two-phase flows with soluble surfactants. In this method, the interface and bulk surfactant concentration equations of diffuse-interface form, which include source terms to consider surfactant adsorption and desorption dynamics, are solved in the entire fluid domain by the finite difference method, while two-phase flows are solved by a lattice Boltzmann color-gradient model, which can accurately simulate binary fluids with unequal densities. The flow and interface surfactant concentration fields are coupled by a modified Langmuir equation of state, which allows for surfactant concentration beyond critical micelle concentration. The capability and accuracy of the hybrid method are first validated by simulating three numerical examples, including the adsorption of bulk surfactants onto the interface of a stationary droplet, the droplet migration in a constant surfactant gradient, and the deformation of a surfactant-laden droplet in a simple shear flow, in which the numerical results are compared with theoretical solutions and available literature data. Then, the hybrid method is applied to simulate the buoyancy-driven bubble rise in a surfactant solution, in which the influence of surfactants is identified for varying wall confinement, density ratio, Eotvos number and Biot number. It is found that surfactants exhibit a retardation effect on the bubble rise due to the Marangoni stress that resists interface motion, and the retardation effect weakens as the Eotvos or Biot number increases. We further show that the weakened retardation effect at higher Biot numbers is attributed to a decreased non-uniform effect of surfactants at the interface. By comparing with the Cahn-Hilliard phase-field method, we also show that the present method conserves the mass for each fluid, improves numerical stability especially at high density ratio and Eotvos number, and does not need the selection of free parameters, thus breaking the limitations of the existing method.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"174 ","pages":"Pages 325-339"},"PeriodicalIF":2.9,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142327241","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimized five-by-five block preconditioning for efficient GMRES convergence in curvature-based image deblurring","authors":"Shahbaz Ahmad","doi":"10.1016/j.camwa.2024.09.026","DOIUrl":"10.1016/j.camwa.2024.09.026","url":null,"abstract":"<div><div>We introduce an enhanced preconditioning technique designed to expedite the convergence of Krylov subspace methods when dealing with non-linear systems of equations featuring a block five-by-five format. This scenario often arises in the context of cell centered finite difference discretizations applied to the mean curvature based image deblurring problem. A thorough spectral analysis of the preconditioned matrices reveals a favorable eigenvalue distribution, leading to accelerated convergence of preconditioned Generalized Minimal Residual (GMRES) methods. Furthermore, we present numerical experiments to showcase the effectiveness of this preconditioner when combined with the flexible GMRES solver for addressing non-linear systems of equations originating from a image deblurring problems. Codes can be obtained at <span><span>https://github.com/shahbaz1982/Preconditioning</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"175 ","pages":"Pages 174-183"},"PeriodicalIF":2.9,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142326369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The asymptotic preserving unified gas kinetic scheme for the multi-scale kinetic SIR epidemic model","authors":"Xiaojing Xu ,&nbsp;Wenjun Sun ,&nbsp;Qi Li","doi":"10.1016/j.camwa.2024.09.021","DOIUrl":"10.1016/j.camwa.2024.09.021","url":null,"abstract":"<div><div>In this paper, we present an asymptotic preserving scheme for the two-dimensional space-dependent and multi-scale kinetic SIR epidemic model which is widely used to model the spread of infectious diseases in populations. The scheme combines a discrete ordinate method for the velocity variables and finite volume method for the spatial and time variables. The idea of unified gas kinetic scheme (UGKS) is used to construct the numerical boundary fluxes which needs the formal integral solutions of the model. Due to the coupling of the three transfer equations in the SIR model, it is difficult to obtain these integral solutions dependently. We decouple the system by constructing the fluxes in a separate way. Then following the framework of UGKS we can obtain the macro auxiliary quantities which is needed in the scheme. Thus the SIR model can be solved in the sequential way. In addition, we can show numerically that the scheme is second-order accurate both in space and time. Moreover, it can not only capture the solution of the diffusion limit equations without requiring the cell size and time step being related to the smallness of the scaling parameters, but also resolve the solution in hyperbolic regime in a natural way. Furthermore, the positive property of the UGKS is analyzed in detail, and through adding time step constraint conditions and applying nodal limiters together, the positive UGKS, called <span><math><mi>P</mi><mi>P</mi><mi>U</mi><mi>G</mi><mi>K</mi><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn><mo>−</mo><mi>o</mi><mi>r</mi><mi>d</mi><mi>e</mi><mi>r</mi></mrow></msup></math></span>, is obtained. Moreover, in order release the time step constraints in the diffusion regime, a temporal first-order accuracy positive preserving UGKS, called <span><math><mi>P</mi><mi>P</mi><mi>U</mi><mi>G</mi><mi>K</mi><msup><mrow><mi>S</mi></mrow><mrow><mn>1</mn><mo>−</mo><mi>o</mi><mi>r</mi><mi>d</mi><mi>e</mi><mi>r</mi></mrow></msup></math></span>, is proposed. Finally, several numerical tests are included to validate the performance of the proposed schemes.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"174 ","pages":"Pages 298-324"},"PeriodicalIF":2.9,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142323875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Robust boundary integral equations for the solution of elastic scattering problems via Helmholtz decompositions","authors":"Víctor Domínguez ,&nbsp;Catalin Turc","doi":"10.1016/j.camwa.2024.09.013","DOIUrl":"10.1016/j.camwa.2024.09.013","url":null,"abstract":"<div><div>Helmholtz decompositions of the elastic fields open up new avenues for the solution of linear elastic scattering problems via boundary integral equations (BIE) (Dong et al. (2021) <span><span>[20]</span></span>). The main appeal of this approach is that the ensuing systems of BIE feature only integral operators associated with the Helmholtz equation. However, these BIE involve non standard boundary integral operators that do not result after the application of either the Dirichlet or the Neumann trace to Helmholtz single and double layer potentials. Rather, the Helmholtz decomposition approach leads to BIE formulations of elastic scattering problems with Neumann boundary conditions that involve boundary traces of the Hessians of Helmholtz layer potential. As a consequence, the classical combined field approach applied in the framework of the Helmholtz decompositions leads to BIE formulations which, although robust, are not of the second kind. Following the regularizing methodology introduced in Boubendir et al. (2015) <span><span>[6]</span></span> we design and analyze novel robust Helmholtz decomposition BIE for the solution of elastic scattering that are of the second kind in the case of smooth scatterers in two dimensions. We present a variety of numerical results based on Nyström discretizations that illustrate the good performance of the second kind regularized formulations in connections to iterative solvers.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"175 ","pages":"Pages 152-173"},"PeriodicalIF":2.9,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142323861","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A mixed virtual element method for the two-dimensional Navier-Stokes equations in stream-function formulation","authors":"Xi Zhang ,&nbsp;Minfu Feng","doi":"10.1016/j.camwa.2024.09.020","DOIUrl":"10.1016/j.camwa.2024.09.020","url":null,"abstract":"<div><div>This work presents the formulation and analysis of a <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>−</mo></math></span> conforming mixed virtual element method (VEM) for the two-dimensional stationary incompressible Navier-Stokes (NS) equations in stream-function formulation. By representing the velocity field as the curl of a stream function, we recast the second-order NS system into a fourth-order nonlinear equation for the scalar stream function, inherently satisfying the incompressibility constraint. Introducing a vorticity variable enables construction of <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>−</mo></math></span> conforming VEM spaces for both stream function and vorticity and circumventing stringent <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>−</mo></math></span> continuity constraints. The proposed method provides an initial exploration of stream function-vorticity discretizations on general polygonal meshes using the flexible VEM of arbitrary order. Existence and uniqueness of discrete solutions are established theoretically under a small data assumption. Optimal error estimates are then derived in the energy norm for the stream function, <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>−</mo></math></span> norm for the stream function and <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo></math></span> norm for the vorticity, rigorously demonstrating convergence. Numerical results validate the error analysis and illustrate the accuracy and robustness of the mixed VEM for simulation of incompressible flows on complex geometries.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"175 ","pages":"Pages 119-137"},"PeriodicalIF":2.9,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142315169","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A hybrid model for accurate prediction of composite longitudinal elastic modulus","authors":"Ilige S. Hage","doi":"10.1016/j.camwa.2024.09.019","DOIUrl":"10.1016/j.camwa.2024.09.019","url":null,"abstract":"<div><div>This research presents a novel hybrid model that integrates a physical-based empirical model with an Artificial Neural Network (ANN) to accurately predict the longitudinal modulus of elasticity for composites under compression. The study focuses on a composite material with a pore inclusion within an ABS plastic matrix, exploring various pore volumes, orientations, and shapes. As part of the proposed hybrid model, a regression-type neural network was trained in MATLAB® to predict and correct discrepancies between the Generalized Stiffness Formulation (GSF) homogenization-based modeling method and the collected compression experimental test results. Using MATLAB® neural network, random error datasets were used to train the feed-forward neural network, and the remaining error datasets were used for validating the performance of the proposed hybrid modeling scheme.</div><div>The hybrid model demonstrated superior performance, achieving the lowest Mean Error (ME) of 0.1684864, Mean Absolute Error (MAE) of 1.051846, Mean Squared Error (MSE) of 3.500952, and highest R-squared of 0.998797. The proposed hybrid model outperformed both the Generalized Stiffness Formulation (GSF) and standalone ANN models. The significant improvement in prediction accuracy underscores the novelty and robustness of the hybrid approach in composite material modeling. Furthermore, this method can be used to refine any existing physical model by focusing on improving these established models to match experimental results and reducing the discrepancies, which offers a more efficient and attractive strategy for accurate predictions.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"174 ","pages":"Pages 287-297"},"PeriodicalIF":2.9,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142314493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}