Computers & Mathematics with Applications最新文献

{"title":"Mathematical and numerical analysis of reduced order interface conditions and augmented finite elements for mixed dimensional problems","authors":"Muriel Boulakia ,&nbsp;Céline Grandmont ,&nbsp;Fabien Lespagnol ,&nbsp;Paolo Zunino","doi":"10.1016/j.camwa.2024.10.028","DOIUrl":"10.1016/j.camwa.2024.10.028","url":null,"abstract":"<div><div>In this paper, we are interested in the mathematical properties of methods based on a fictitious domain approach combined with reduced-order interface coupling conditions, which have been recently introduced to simulate 3D-1D fluid-structure or structure-structure coupled problems. To give insights on the approximation properties of these methods, we investigate them in a simplified setting by considering the Poisson problem in a two-dimensional domain with non-homogeneous Dirichlet boundary conditions on small inclusions. The approximated reduced problem is obtained using a fictitious domain approach combined with a projection on a Fourier finite-dimensional space of the Lagrange multiplier associated to the Dirichlet boundary constraints, obtaining in this way a Poisson problem with defective interface conditions. After analyzing the existence of a solution of the reduced problem, we prove its convergence towards the original full problem, when the size of the holes tends towards zero, with a rate which depends on the number of modes of the finite-dimensional space. In particular, our estimates highlight the fact that to obtain a good convergence on the Lagrange multiplier, one needs to consider more modes than the first Fourier mode (constant mode). This is a key issue when one wants to deal with real coupled problems, such as fluid-structure problems for instance. Next, the numerical discretization of the reduced problem using the finite element method is analyzed in the case where the computational mesh does not fit the small inclusion interface. As is standard for these types of problem, the convergence of the solution is not optimal due to the lack of regularity of the solution. Moreover, convergence exhibits a well-known locking effect when the mesh size and the inclusion size are of the same order of magnitude. This locking effect is more apparent when increasing the number of modes and affects the Lagrange multiplier convergence rate more heavily. To resolve these issues, we propose and analyze a stabilized method and an enriched method for which additional basis functions are added without changing the approximation space of the Lagrange multiplier. Finally, the properties of numerical strategies are illustrated by numerical experiments.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"175 ","pages":"Pages 536-569"},"PeriodicalIF":2.9,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142555006","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 nonconforming extended virtual element method for Stokes interface problems","authors":"Yuxiang Huang ,&nbsp;Feng Wang ,&nbsp;Jinru Chen","doi":"10.1016/j.camwa.2024.10.027","DOIUrl":"10.1016/j.camwa.2024.10.027","url":null,"abstract":"<div><div>In this paper, we propose a nonconforming extended virtual element method, which combines the extended finite element method with the nonconforming virtual element method, for solving Stokes interface problems with the unfitted-interface mesh. By introducing some stabilization terms and penalty terms, as well as some special terms defined on non-cut edges of interface elements in the discrete bilinear form, we prove the discrete inf-sup condition and obtain optimal error estimates. It is shown that all results are not only independent of the mesh size and the viscosity coefficient, but also the interface position. Numerical experiments are performed to verify theoretical results.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"175 ","pages":"Pages 509-535"},"PeriodicalIF":2.9,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142555005","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 iterative spectral algorithms for smooth solutions of time-fractional nonlinear diffusion problems and convergence analysis","authors":"Muhammad Usman ,&nbsp;Muhammad Hamid ,&nbsp;Dianchen Lu ,&nbsp;Zhengdi Zhang ,&nbsp;Wojciech Sumelka","doi":"10.1016/j.camwa.2024.10.015","DOIUrl":"10.1016/j.camwa.2024.10.015","url":null,"abstract":"<div><div>Nonlinear time-fractional diffusion problems, a significant class of parabolic-type problems, appear in various diffusion phenomena that seem extensively in nature. Such physical problems arise in numerous fields, such as phase transition, filtration, biochemistry, and dynamics of biological groups. Because of its massive involvement, its accurate solutions have become a challenging task among researchers. In this framework, this article proposed two operational-based robust iterative spectral schemes for accurate solutions of the nonlinear time-fractional diffusion problems. Temporal and spatial variables are approximated using Vieta-Lucas polynomials, and derivative operators are approximated using novel operational matrices. The approximated solution, novel operational matrices, and uniform collection points convert the problem into a system of nonlinear equations. Here, two robust methods, namely Picard's iterative and Newton's, are incorporated to tackle a nonlinear system of equations. Some problems are considered in authenticating the present methods' accuracy, credibility, and reliability. An inclusive comparative study demonstrates that the proposed computational schemes are effective, accurate, and well-matched to find the numerical solutions to the problems mentioned above. The proposed methods improve the accuracy of numerical solutions from 27 % to 100 % when <span><math><mrow><mi>M</mi><mo>&gt;</mo><mn>2</mn></mrow></math></span> as compared to the existing results. The suggested methods' convergence, error bound, and stability are investigated theoretically and numerically.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"175 ","pages":"Pages 487-508"},"PeriodicalIF":2.9,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142538691","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":"Generalised adaptive cross approximation for convolution quadrature based boundary element formulation","authors":"A.M. Haider ,&nbsp;S. Rjasanow ,&nbsp;M. Schanz","doi":"10.1016/j.camwa.2024.10.025","DOIUrl":"10.1016/j.camwa.2024.10.025","url":null,"abstract":"<div><div>The acoustic wave equation is solved in time domain with a boundary element formulation. The time discretisation is performed with the generalised convolution quadrature method and for the spatial approximation standard lowest order elements are used. Collocation and Galerkin methods are applied. In the interest of increasing the efficiency of the boundary element method, a low-rank approximation such as the adaptive cross approximation (ACA) is carried out. We discuss a generalisation of the ACA to approximate a three-dimensional array of data, i.e., usual boundary element matrices at several complex frequencies. This method is used within the generalised convolution quadrature (gCQ) method to obtain a real time domain formulation. The behaviour of the proposed method is studied with three examples, a unit cube, a unit cube with a reentrant corner, and a unit ball. The properties of the method are preserved in the data sparse representation and a significant reduction in storage is obtained.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"175 ","pages":"Pages 470-486"},"PeriodicalIF":2.9,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530310","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":"Innovative discretizations of PDEs: Towards an accurate representation of the reality","authors":"Fleurianne Bertrand,&nbsp;Daniele Boffi,&nbsp;Alexander Düster,&nbsp;Jean-Luc Guermond,&nbsp;Norbert Heuer,&nbsp;Jichun Li,&nbsp;Waldemar Rachowicz","doi":"10.1016/j.camwa.2024.10.013","DOIUrl":"10.1016/j.camwa.2024.10.013","url":null,"abstract":"","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"176 ","pages":"Pages 221-223"},"PeriodicalIF":2.9,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142528145","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-priori and a-posteriori error estimates for discontinuous Galerkin method of the Maxwell eigenvalue problem","authors":"Jun Zhang ,&nbsp;Zijiang Luo ,&nbsp;Jiayu Han ,&nbsp;Hu Chen","doi":"10.1016/j.camwa.2024.10.026","DOIUrl":"10.1016/j.camwa.2024.10.026","url":null,"abstract":"<div><div>This paper is devoted to a-priori and a-posteriori error analysis of discontinuous Galerkin (DG) method for the Maxwell eigenvalue problem. The discrete compactness of DG space is proved so that the Babuška and Osborn spectral approximation theory can be applicable in the a-priori error analysis. Then we prove the optimal error estimates for DG eigenfunctions in mesh-dependent norm and DG eigenvalues. A special contribution of this work is to prove that the error in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-norm for smooth eigenfunctions is of higher order than that in mesh-dependent norm, so that the DG eigenvalues can approximate the true eigenvalues from upper. Another contribution of this work is to provide a-posteriori error analysis for the DG method. A reliable a-posteriori error estimator is analyzed. The upper bound property of DG eigenvalues and the robustness of adaptive methods are verified through numerical experiments.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"176 ","pages":"Pages 190-201"},"PeriodicalIF":2.9,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142528061","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":"Fully parallel and pipelined sparse direct solver for large symmetric indefinite finite element problems","authors":"Yujie Wang ,&nbsp;Shengquan Wang ,&nbsp;Yong Cai ,&nbsp;Guidong Wang ,&nbsp;Guangyao Li","doi":"10.1016/j.camwa.2024.10.017","DOIUrl":"10.1016/j.camwa.2024.10.017","url":null,"abstract":"<div><div>Sparse linear system solving is a primary computational cost in large-scale finite element analysis, and improving its performance is a key technological challenge in this field. Real-world engineering problems involve diverse materials, elements, and connectivity relationships, making it difficult for iterative methods to handle their global stiffness matrices. Direct methods, owing to their robustness, emerge as the preferred choice. In this paper, a novel block-based supernodal LDL^T numerical factorization method is introduced. The computational process is disassembled into distinct tasks, and the dependency relationships between these tasks are expressed via a directed acyclic graph to guide the calculation sequence. Based on this approach, a global task pool and local task stack are established to store task queues, enhancing data reuse and multicore collaboration efficiency. Additionally, an effective task dispatch and work-stealing mechanism is implemented to prevent performance degradation caused by load imbalances. Numerical experiments, including a publicly available matrix test set and real-world engineering finite element problems, are conducted to compare the parallel performances of the Pardiso, MUMPS, and proposed solver. The results illustrate that the proposed solver performs significantly better than the other solvers when handling various types of sparse matrices and diverse architectures of multicore processors.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"175 ","pages":"Pages 447-469"},"PeriodicalIF":2.9,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142529732","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 least-squares Fourier frame method for nonlocal diffusion models on arbitrary domains","authors":"Mengxia Shen ,&nbsp;Haiyong Wang","doi":"10.1016/j.camwa.2024.10.024","DOIUrl":"10.1016/j.camwa.2024.10.024","url":null,"abstract":"<div><div>We introduce a least-squares Fourier frame method for solving nonlocal diffusion models with Dirichlet volume constraint on arbitrary domains. The mathematical structure of a frame rather than a basis allows using a discrete least-squares approximation on irregular domains and imposing non-periodic boundary conditions. The method has inherited the one-dimensional integral expression of Fourier symbols of the nonlocal diffusion operator from Fourier spectral methods for any <em>d</em> spatial dimensions. High precision of its solution can be achieved via a direct solver such as pivoted QR decomposition even though the corresponding system is extremely ill-conditioned, due to the redundancy in the frame. The extension of AZ algorithm improves the complexity of solving the rectangular linear system to <span><math><mi>O</mi><mo>(</mo><mi>N</mi><msup><mrow><mi>log</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>⁡</mo><mi>N</mi><mo>)</mo></math></span> for 1<em>d</em> problems and <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></msup><msup><mrow><mi>log</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>⁡</mo><mi>N</mi><mo>)</mo></math></span> for 2<em>d</em> problems, compared with <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>N</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></math></span> of the direct solvers, where <em>N</em> is the number of degrees of freedom. We present ample numerical experiments to show the flexibility, fast convergence and asymptotical compatibility of the proposed method.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"175 ","pages":"Pages 433-446"},"PeriodicalIF":2.9,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530295","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 local projection stabilised HHO method for the Oseen problem","authors":"Gouranga Mallik ,&nbsp;Rahul Biswas ,&nbsp;Thirupathi Gudi","doi":"10.1016/j.camwa.2024.10.030","DOIUrl":"10.1016/j.camwa.2024.10.030","url":null,"abstract":"<div><div>In this article, we consider a local projection stabilisation for a Hybrid High-Order (HHO) approximation of the Oseen problem. We prove an existence-uniqueness result under a stronger SUPG-like norm. We improve the stability and provide error estimation in stronger norm for convection dominated Oseen problem. We also derive an optimal order error estimate under the SUPG-like norm for equal-order polynomial discretisation of velocity and pressure spaces. Numerical experiments are performed to validate the theoretical results.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"176 ","pages":"Pages 202-220"},"PeriodicalIF":2.9,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142528144","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":"Special Issue: Advanced COmputational Methods in ENgineering (ACOMEN 2022)","authors":"Maarten Arnst,&nbsp;Christophe Geuzaine,&nbsp;Ludovic Noels,&nbsp;Jean-Philippe Ponthot","doi":"10.1016/j.camwa.2024.10.012","DOIUrl":"10.1016/j.camwa.2024.10.012","url":null,"abstract":"","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"176 ","pages":"Page 189"},"PeriodicalIF":2.9,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142528146","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}