arXiv - CS - Numerical Analysis最新文献_第4页

A generalized formulation for gradient schemes in unstructured finite volume method 非结构化有限体积法中梯度方案的通用表述方法

arXiv - CS - Numerical Analysis Pub Date : 2024-02-09 DOI: arxiv-2402.06199

Mandeep Deka, Ashwani Assam, Ganesh Natarajan

引用次数: 0

HAMLET: Graph Transformer Neural Operator for Partial Differential Equations HAMLET：偏微分方程图变换器神经算子

arXiv - CS - Numerical Analysis Pub Date : 2024-02-05 DOI: arxiv-2402.03541

Andrey Bryutkin, Jiahao Huang, Zhongying Deng, Guang Yang, Carola-Bibiane Schönlieb, Angelica Aviles-Rivero

引用次数: 0

Parallelization Strategies for the Randomized Kaczmarz Algorithm on Large-Scale Dense Systems 大规模密集系统上的随机卡兹马兹算法并行化策略

arXiv - CS - Numerical Analysis Pub Date : 2024-01-30 DOI: arxiv-2401.17474

Inês Ferreira, Juan A. Acebrón, José Monteiro

{"title":"Parallelization Strategies for the Randomized Kaczmarz Algorithm on Large-Scale Dense Systems","authors":"Inês Ferreira, Juan A. Acebrón, José Monteiro","doi":"arxiv-2401.17474","DOIUrl":"https://doi.org/arxiv-2401.17474","url":null,"abstract":"The Kaczmarz algorithm is an iterative technique designed to solve consistent\u0000linear systems of equations. It falls within the category of row-action\u0000methods, focusing on handling one equation per iteration. This characteristic\u0000makes it especially useful in solving very large systems. The recent\u0000introduction of a randomized version, the Randomized Kaczmarz method, renewed\u0000interest in the algorithm, leading to the development of numerous variations.\u0000Subsequently, parallel implementations for both the original and Randomized\u0000Kaczmarz method have since then been proposed. However, previous work has\u0000addressed sparse linear systems, whereas we focus on solving dense systems. In\u0000this paper, we explore in detail approaches to parallelizing the Kaczmarz\u0000method for both shared and distributed memory for large dense systems. In\u0000particular, we implemented the Randomized Kaczmarz with Averaging (RKA) method\u0000that, for inconsistent systems, unlike the standard Randomized Kaczmarz\u0000algorithm, reduces the final error of the solution. While efficient\u0000parallelization of this algorithm is not achievable, we introduce a block\u0000version of the averaging method that can outperform the RKA method.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139656767","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Efficient reference configuration formulation in fully nonlinear poroelastic media 全非线性孔弹性介质中的高效参考构型公式

arXiv - CS - Numerical Analysis Pub Date : 2024-01-25 DOI: arxiv-2401.14536

Nicolás A. Barnafi, Argyrios Petras, Luca Gerardo-Giorda

{"title":"Efficient reference configuration formulation in fully nonlinear poroelastic media","authors":"Nicolás A. Barnafi, Argyrios Petras, Luca Gerardo-Giorda","doi":"arxiv-2401.14536","DOIUrl":"https://doi.org/arxiv-2401.14536","url":null,"abstract":"Typical pipelines for model geometry generation in computational biomedicine\u0000stem from images, which are usually considered to be at rest, despite the\u0000object being in mechanical equilibrium under several forces. We refer to the\u0000stress-free geometry computation as the reference configuration problem, and in\u0000this work we extend such a formulation to the theory of fully nonlinear\u0000poroelastic media. The main steps are (i) writing the equations in terms of the\u0000reference porosity and (ii) defining a time dependent problem whose steady\u0000state solution is the reference porosity. This problem can be computationally\u0000challenging as it can require several hundreds of iterations to converge, so we\u0000propose the use of Anderson acceleration to speed up this procedure. Our\u0000evidence shows that this strategy can reduce the number of iterations up to\u000080%. In addition, we note that a primal formulation of the nonlinear mass\u0000conservation equations is not consistent due to the presence of second order\u0000derivatives of the displacement, which we alleviate through adequate mixed\u0000formulations. All claims are validated through numerical simulations in both\u0000idealized and realistic scenarios.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":"181 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139584308","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Projection-based model order reduction for prestressed concrete with an application to the standard section of a nuclear containment building 基于投影的预应力混凝土模型阶次缩减，应用于核安全壳建筑的标准部分

arXiv - CS - Numerical Analysis Pub Date : 2024-01-10 DOI: arxiv-2401.05098

Eki Agouzal, Jean-Philippe Argaud, Michel Bergmann, Guilhem Ferté, Sylvie Michel-Ponnelle, Tommaso Taddei

{"title":"Projection-based model order reduction for prestressed concrete with an application to the standard section of a nuclear containment building","authors":"Eki Agouzal, Jean-Philippe Argaud, Michel Bergmann, Guilhem Ferté, Sylvie Michel-Ponnelle, Tommaso Taddei","doi":"arxiv-2401.05098","DOIUrl":"https://doi.org/arxiv-2401.05098","url":null,"abstract":"We propose a projection-based model order reduction procedure for the ageing\u0000of large prestressed concrete structures. Our work is motivated by applications\u0000in the nuclear industry, particularly in the simulation of containment\u0000buildings. Such numerical simulations involve a multi-modeling approach: a\u0000three-dimensional nonlinear thermo-hydro-visco-elastic rheological model is\u0000used for concrete; and prestressing cables are described by a one-dimensional\u0000linear thermo-elastic behavior. A kinematic linkage is performed in order to\u0000connect the concrete nodes and the steel nodes: coincident points in each\u0000material are assumed to have the same displacement. We develop an adaptive\u0000algorithm based on a Proper Orthogonal Decomposition (POD) in time and greedy\u0000in parameter to build a reduced order model (ROM). The nonlinearity of the\u0000operator entails that the computational cost of the ROM assembly scales with\u0000the size of the high-fidelity model. We develop an hyper-reduction strategy\u0000based on empirical quadrature to bypass this computational bottleneck: our\u0000approach relies on the construction of a reduced mesh to speed up online\u0000assembly costs of the ROM. We provide numerical results for a standard section\u0000of a double-walled containment building using a qualified and broadly-used\u0000industrial grade finite element solver for structural mechanics\u0000(code$_$aster).","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":"85 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139422799","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On Lattice Boltzmann Methods based on vector-kinetic models for hyperbolic partial differential equations 基于双曲偏微分方程向量动力学模型的格点玻尔兹曼方法

arXiv - CS - Numerical Analysis Pub Date : 2024-01-08 DOI: arxiv-2401.03952

Megala Anandan, S. V. Raghurama Rao

{"title":"On Lattice Boltzmann Methods based on vector-kinetic models for hyperbolic partial differential equations","authors":"Megala Anandan, S. V. Raghurama Rao","doi":"arxiv-2401.03952","DOIUrl":"https://doi.org/arxiv-2401.03952","url":null,"abstract":"In this paper, we are concerned about the lattice Boltzmann methods (LBMs)\u0000based on vector-kinetic models for hyperbolic partial differential equations.\u0000In addition to usual lattice Boltzmann equation (LBE) derived by explicit\u0000discretisation of vector-kinetic equation (VKE), we also consider LBE derived\u0000by semi-implicit discretisation of VKE and compare the relaxation factors of\u0000both. We study the properties such as H-inequality, total variation boundedness\u0000and positivity of both the LBEs, and infer that the LBE due to semi-implicit\u0000discretisation naturally satisfies all the properties while the LBE due to\u0000explicit discretisation requires more restrictive condition on relaxation\u0000factor compared to the usual condition obtained from Chapman-Enskog expansion.\u0000We also derive the macroscopic finite difference form of the LBEs, and utilise\u0000it to establish the consistency of LBEs with the hyperbolic system. Further, we\u0000extend this LBM framework to hyperbolic conservation laws with source terms,\u0000such that there is no spurious numerical convection due to imbalance between\u0000convection and source terms. We also present a D$2$Q$9$ model that allows\u0000upwinding even along diagonal directions in addition to the usual upwinding\u0000along coordinate directions. The different aspects of the results are validated\u0000numerically on standard benchmark problems.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139409065","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

CG-Kit: Code Generation Toolkit for Performant and Maintainable Variants of Source Code Applied to Flash-X Hydrodynamics Simulations CG-Kit：适用于 Flash-X 流体动力学模拟的代码生成工具包，用于源代码的性能和可维护变量

arXiv - CS - Numerical Analysis Pub Date : 2024-01-07 DOI: arxiv-2401.03378

Johann Rudi, Youngjun Lee, Aidan H. Chadha, Mohamed Wahib, Klaus Weide, Jared P. O'Neal, Anshu Dubey

{"title":"CG-Kit: Code Generation Toolkit for Performant and Maintainable Variants of Source Code Applied to Flash-X Hydrodynamics Simulations","authors":"Johann Rudi, Youngjun Lee, Aidan H. Chadha, Mohamed Wahib, Klaus Weide, Jared P. O'Neal, Anshu Dubey","doi":"arxiv-2401.03378","DOIUrl":"https://doi.org/arxiv-2401.03378","url":null,"abstract":"CG-Kit is a new code generation toolkit that we propose as a solution for\u0000portability and maintainability for scientific computing applications. The\u0000development of CG-Kit is rooted in the urgent need created by the shifting\u0000landscape of high-performance computing platforms and the algorithmic\u0000complexities of a particular large-scale multiphysics application: Flash-X.\u0000This combination leads to unique challenges including handling an existing\u0000large code base in Fortran and/or C/C++, subdivision of code into a great\u0000variety of units supporting a wide range of physics and numerical methods,\u0000different parallelization techniques for distributed- and shared-memory systems\u0000and accelerator devices, and heterogeneity of computing platforms requiring\u0000coexisting variants of parallel algorithms. The challenges demand that\u0000developers determine custom abstractions and granularity for code generation.\u0000CG-Kit tackles this with standalone tools that can be combined into highly\u0000specific and, we argue, highly effective portability and maintainability tool\u0000chains. Here we present the design of our new tools: parametrized source trees,\u0000control flow graphs, and recipes. The tools are implemented in Python. Although\u0000the tools are agnostic to the programming language of the source code, we focus\u0000on C/C++ and Fortran. Code generation experiments demonstrate the generation of\u0000variants of parallel algorithms: first, multithreaded variants of the basic\u0000AXPY operation (scalar-vector addition and vector-vector multiplication) to\u0000introduce the application of CG-Kit tool chains; and second, variants of\u0000parallel algorithms within a hydrodynamics solver, called Spark, from Flash-X\u0000that operates on block-structured adaptive meshes. In summary, code generated\u0000by CG-Kit achieves a reduction by over 60% of the original C/C++/Fortran source\u0000code.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":"37 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139409773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Asynchronous multiplicative coarse-space correction 异步乘法粗空间校正

arXiv - CS - Numerical Analysis Pub Date : 2023-12-19 DOI: arxiv-2312.12053

Guillaume Gbikpi-Benissan, Frédéric Magoulès

引用次数: 0

Transformed Primal-Dual Methods with Variable-Preconditioners 带可变预调器的变换原始-双重方法

arXiv - CS - Numerical Analysis Pub Date : 2023-12-19 DOI: arxiv-2312.12355

Long Chen, Ruchi Guo, Jingrong Wei

引用次数: 0

Robust algorithms for limit load and shear strength reduction methods 极限载荷和剪切强度降低方法的稳健算法

arXiv - CS - Numerical Analysis Pub Date : 2023-12-19 DOI: arxiv-2312.12170

Stanislav Sysala

引用次数: 0