Computers & Mathematics with Applications最新文献

{"title":"On nonlinear magnetic field solvers using local Quasi-Newton updates","authors":"H. Egger ,&nbsp;F. Engertsberger ,&nbsp;L. Domenig ,&nbsp;K. Roppert ,&nbsp;M. Kaltenbacher","doi":"10.1016/j.camwa.2025.01.033","DOIUrl":"10.1016/j.camwa.2025.01.033","url":null,"abstract":"<div><div>Fixed-point or Newton-methods are typically employed for the numerical solution of nonlinear systems arising from discretization of nonlinear magnetic field problems. We here discuss an alternative strategy which uses Quasi-Newton updates locally, at every material point, to construct appropriate linearizations of the material behavior during the nonlinear iteration. The resulting scheme shows similar fast convergence as the Newton-method but, like the fixed-point methods, does not require derivative information of the underlying material law. As a consequence, the method can be used for the efficient solution of models with hysteresis which involve nonsmooth material behavior. The implementation of the proposed scheme can be realized in standard finite-element codes in parallel to the fixed-point and the Newton method. A full convergence analysis of all three methods is established proving global mesh-independent convergence. The theoretical results and the performance of the nonlinear iterative schemes are evaluated by computational tests for a typical benchmark problem.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"183 ","pages":"Pages 20-31"},"PeriodicalIF":2.9,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143102666","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":"Accelerating simulations of turbulent flows over waves leveraging GPU parallelization","authors":"Anqing Xuan,&nbsp;Ziyan Ren,&nbsp;Lian Shen","doi":"10.1016/j.camwa.2025.01.031","DOIUrl":"10.1016/j.camwa.2025.01.031","url":null,"abstract":"<div><div>We present a highly efficient solver, accelerated by graphics processing units (GPUs), for simulations of turbulent flows over wave surfaces. The solver employs a boundary-fitted curvilinear grid, which is horizontally discretized by a Fourier-based pseudospectral scheme, enabling accurate and efficient resolution of turbulence motions and wave geometry effects across scales. Our GPU implementation incorporates optimizations including kernel fusion for computing derivatives using the fast Fourier transform and a mixed-precision iterative solver for the pressure Poisson equation. A parallel tridiagonal solver is developed to solve the batched systems arising from the iterative Poisson solver on multiple GPUs. Our GPU solver is validated against a canonical problem of turbulence over waves, demonstrating the solver's accuracy. Performance tests indicate substantial speed improvement of up to 80% enabled by the proposed optimizations. Good parallel scalability suggests the solver's capability for large-scale simulations of turbulent flows over waves.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"183 ","pages":"Pages 1-19"},"PeriodicalIF":2.9,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143102665","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":"Efficient spectral method for the fourth order elliptic equation with a variable coefficient on the unit disc","authors":"Suna Ma","doi":"10.1016/j.camwa.2025.01.023","DOIUrl":"10.1016/j.camwa.2025.01.023","url":null,"abstract":"<div><div>In this paper, an efficient spectral-Galerkin method is proposed to solve the fourth order elliptic equation with a variable coefficient on the unit disc. The efficiency of the method is rest with the use of properly designed orthogonal polynomials as basis functions, which preserve the block-diagonal matrix structure of the discretized system with a constant coefficient and also work well with the general variable coefficient. Further, the three-term recurrence relation for orthogonal polynomials on the unit disc is explored to reduce the computational complexity of assembling the mass matrix. Then optimal error estimates are established. Finally, numerical experiments are carried out to illustrate the effectiveness of the proposed spectral method.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"181 ","pages":"Pages 340-350"},"PeriodicalIF":2.9,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143125217","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 mass and charge conservative fully discrete scheme for a 3D diffuse interface model of the two-phase inductionless MHD flows","authors":"Xiaorong Wang ,&nbsp;Xuerui Mao ,&nbsp;Shipeng Mao ,&nbsp;Xiaoming He","doi":"10.1016/j.camwa.2025.01.020","DOIUrl":"10.1016/j.camwa.2025.01.020","url":null,"abstract":"<div><div>In this paper, we study the phase field model on a three-dimensional bounded domain for a two-phase, incompressible, inductionless magnetohydrodynamic (MHD) system, which is important for many engineering applications. To efficiently and accurately solve this multi-physics nonlinear system, we present a fully discrete scheme that ensures both mass and charge conservation. Making use of the discrete energy law, we demonstrate that the fully discrete scheme satisfies unconditional energy stability. Subsequently, by utilizing the Leray-Schauder principle, we establish the existence of solutions to the discrete scheme. As both mesh size and time step size tend to zero, we prove that the discrete solutions converge to the weak solution of the continuous problem. Finally, several three-dimensional numerical experiments, including the accuracy test, the bubble coalescence, the drop deformation and the Kelvin-Helmholtz (KH) instability, are performed to validate the reliability and efficiency of the proposed numerical scheme.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"182 ","pages":"Pages 139-162"},"PeriodicalIF":2.9,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143055378","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 reduced-order model for segregated fluid-structure interaction solvers in an ALE approach at high Reynolds number","authors":"Valentin Nkana Ngan ,&nbsp;Giovanni Stabile ,&nbsp;Andrea Mola ,&nbsp;Gianluigi Rozza","doi":"10.1016/j.camwa.2025.01.004","DOIUrl":"10.1016/j.camwa.2025.01.004","url":null,"abstract":"<div><div>This study introduces a first step for constructing a hybrid reduced-order models (ROMs) for segregated fluid-structure interaction in an Arbitrary Lagrangian-Eulerian (ALE) approach at a high Reynolds number using the Finite Volume Method (FVM). The ROM is driven by proper orthogonal decomposition (POD) with hybrid techniques that combines the classical Galerkin projection and two data-driven methods (radial basis networks, and neural networks/ long short term memory). Results demonstrate the ROM's ability to accurately capture the physics of fluid-structure interaction phenomena. This approach is validated through a case study focusing on flow-induced vibration (FIV) of a pitch-plunge airfoil at a high Reynolds number (<span><math><mi>R</mi><mi>e</mi><mo>=</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>7</mn></mrow></msup></math></span>).</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"180 ","pages":"Pages 299-321"},"PeriodicalIF":2.9,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143055382","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":"Block ω-circulant preconditioners for parabolic equations","authors":"Po Yin Fung,&nbsp;Sean Y. Hon","doi":"10.1016/j.camwa.2025.01.019","DOIUrl":"10.1016/j.camwa.2025.01.019","url":null,"abstract":"<div><div>In this study, a novel class of block <em>ω</em>-circulant preconditioners is developed for the all-at-once linear system that emerges from solving parabolic equations using first and second order discretization schemes for time. We establish a unifying preconditioning framework for <em>ω</em>-circulant preconditioners, extending and modifying the preconditioning approach recently proposed in (Zhang and Xu, 2024 <span><span>[27]</span></span>) and integrating some existing results in the literature. The proposed preconditioners leverage fast Fourier transforms for efficient diagonalization, facilitating parallel-in-time execution. Theoretically, these preconditioners ensure that eigenvalue clustering around ±1 is achieved, fostering fast convergence under the minimal residual method. Furthermore, when using the generalized minimal residual method, the effectiveness of these preconditioners is supported by the singular value clustering at unity. Numerical experiments validate the performance of the developed preconditioning strategies.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"182 ","pages":"Pages 122-138"},"PeriodicalIF":2.9,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143020141","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 staggered discontinuous Galerkin method for solving SN transport equation on arbitrary polygonal grids","authors":"Deng Wang ,&nbsp;Zupeng Jia","doi":"10.1016/j.camwa.2025.01.018","DOIUrl":"10.1016/j.camwa.2025.01.018","url":null,"abstract":"<div><div>This paper proposes a staggered discontinuous Galerkin (SDG) method for solving the 2D <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>N</mi></mrow></msub></math></span> transport equation on arbitrary polygonal mesh. The new method allows rough grids such as highly distorted quadrilateral grids and general polygonal grids. More importantly, it is numerical flux free, different from the standard discontinuous Galerkin (DG) method using upwind flux, and thus gains the advantage of not demanding a sweeping algorithm to determine the computational ordering of all elements. The sweeping process not only requires a significant amount of computation, but also encounters deadlocks due to the presence of cycles in the corresponding directed graph on deformed three-dimensional polyhedral meshes. Additionally, there are challenges with sweeping stability on curved meshes. Our method naturally avoids these problems such that it can be generalized to high-order schemes on curved meshes. Convergence of the new method is analyzed in the linear case, and we have shown that it is optimally convergent for sufficiently smooth transport solution and appropriate total cross section. Numerical results are consistent with the theoretical analysis. The tests also show that our method employing linear elements can maintain second-order accuracy on rough grids mentioned earlier, demonstrating good robustness, and be able to model material interfaces with sharp changes of the angular flux. Moreover, the asymptotic-preserving property can be observed by scaling the cross section parameter in the thick diffusive limit problem. A test employing quadratic elements is also provided, which preliminarily demonstrates the feasibility and effectiveness of our method in higher-order scenarios.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"182 ","pages":"Pages 102-121"},"PeriodicalIF":2.9,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143020191","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 handy tool for assessing tetrahedron-based finite-cell methods and for numerical simulations in spheroidal domains","authors":"Andrés León Baldelli ,&nbsp;Vitoriano Ruas ,&nbsp;Marco Antonio Silva Ramos","doi":"10.1016/j.camwa.2025.01.017","DOIUrl":"10.1016/j.camwa.2025.01.017","url":null,"abstract":"<div><div>A straightforward procedure is presented for the generation of finite-cell meshes consisting of tetrahedrons for curved domains, whose boundary can be expressed in spherical coordinates with origin at a suitable location in its interior. Besides the equation of the boundary, the generation of the mesh depends only on an integer parameter, whose value is associated with its degree of refinement. Several examples indicate that the meshes of a given domain form a quasi-uniform family of partitions, as the value of the integer parameter increases. Mesh quality is optimal in the case of a ball but it remains quite correct as the shape of the domain moves away from perfect sphericity, with a gradual but in all natural downgrade. The procedure is a handy tool for an a priori order-checking of a new finite-cell method, as applied to a given type of boundary value problem posed in curved domains. A MATLAB code was developed to implement this tetrahedrization procedure for domains with three symmetry planes.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"181 ","pages":"Pages 323-339"},"PeriodicalIF":2.9,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143020142","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":"Simulation of cartesian cut-cell technique for modeling turbulent flow in asymmetric diffusers using various turbulence models","authors":"A.S. Dawood ,&nbsp;A.S. Amer ,&nbsp;R.M. Abumandour ,&nbsp;W.A. El-Askary","doi":"10.1016/j.camwa.2025.01.015","DOIUrl":"10.1016/j.camwa.2025.01.015","url":null,"abstract":"<div><div>The process of accurately predicting the behavior of the separated turbulent flow requires extraordinary efforts, whether it is choosing the appropriate computational mesh or using the appropriate turbulence model for that. The present study introduces a comparative numerical investigation for predicting the behavior of turbulent-separated flow in asymmetric diffusers. Numerical simulation using a finite volume approach of incompressible Reynolds Averaged Navier Stokes equations (RANS) with three turbulence models (Standard <span><math><mrow><mi>k</mi><mo>−</mo><mrow><mi>ε</mi></mrow></mrow></math></span>, Chen-kim, and modified Chen-kim) is here performed in a self-developed FORTRAN code. The treatment of asymmetric diffusers poses challenges due to the complex flow behavior and geometry. To address this, a developed cartesian cut-cell technique is employed, which provides compatibility with solid boundaries and efficiently handles complex geometries This developed cut-cell technique is checked to treat its ability to predict complex turbulent flow with the presence of strong pressure gradient for correctness and convergence, as well as testing the proposed turbulence-models performance. So, verifications are performed by comparing the present computational results of asymmetric-diffuser flow characteristics with available experimental and LES data. The proposed models reveal acceptable agreements in most cases, especially the modified Chen-kim model, which shows a great match with the experimental and LES results for all flow characteristics. The standard k-ε model fails to predict the flow-separation well in most comparisons. Extended computational studies are also introduced to investigate the effects of diffuser cant angles (4 to 15°) and area ratio (2.4 to 7) on the diffuser flow behavior using the successfully modified Chen-kim turbulence model. The parametric study reveals that these two factors strongly affect the diffuser performance, where the pressure recovery, skin friction coefficients, and separation bubble size are provided.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"182 ","pages":"Pages 84-101"},"PeriodicalIF":2.9,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143020188","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":"Analysis of the Picard-Newton finite element iteration for the stationary incompressible inductionless MHD equations","authors":"Xiaodi Zhang ,&nbsp;Meiying Zhang ,&nbsp;Xianghai Zhou","doi":"10.1016/j.camwa.2025.01.016","DOIUrl":"10.1016/j.camwa.2025.01.016","url":null,"abstract":"<div><div>In this paper, we propose and analyze the Picard-Newton finite element iteration for the stationary incompressible inductionless magnetohydrodynamics (MHD) equations. In finite element discretization, the hydrodynamic unknowns are approximated by stable finite element pairs, and the electromagnetic system is discretized by using the face-volume pairs. To solve the nonlinear discretized problem efficiently, our method consists of first applying the Picard iteration and then applying the Newton iteration. The Picard-Newton iteration is proved to be globally stable under the uniqueness condition and quadratically convergent under the stronger uniqueness condition. Thanks to the improved stability property, this solver has a larger convergence basin than the usual Newton iteration. Numerical tests confirm our theoretical analysis and show that the Picard-Newton iteration dramatically excels both the Picard and Newton iterations in several benchmark problems.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"182 ","pages":"Pages 46-65"},"PeriodicalIF":2.9,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143020189","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}