2015/01/20 by Francisco Javier Ramírez-Gil, Ramírez-Gil, Francisco Javier, Marcos de Sales Guerra Tsuzuki +3
Computer Science · Engineering · Physics and Astronomy · #35Q68 #65N30 #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Computational Engineering #Distributed #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Computer and information sciences #FOS: Mathematics #Finance #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Parallel #Performance (cs.PF) #and Cluster Computing (cs.DC) #and Science (cs.CE)
paper · pdf · doi:10.48550/arxiv.1501.04784
openalex publication_date 2015/01/20 · openalex created_date 2022/09/05 · openalex updated_date 2026/08/01
The finite element method (FEM) has several computational steps to\nnumerically solve a particular problem, to which many efforts have been\ndirected to accelerate the solution stage of the linear system of equations.\nHowever, the finite element matrix construction, which is also time-consuming\nfor unstructured meshes, has been less investigated. The generation of the\nglobal finite element matrix is performed in two steps, computing the local\nmatrices by numerical integration and assembling them into a global system,\nwhich has traditionally been done in serial computing. This work presents a\nfast technique to construct the global finite element matrix that arises by\nsolving the Poisson's equation in a three-dimensional domain. The proposed\nmethodology consists in computing the numerical integration, due to its\nintrinsic parallel opportunities, in the graphics processing unit (GPU) and\ncomputing the matrix assembly, due to its intrinsic serial operations, in the\ncentral processing unit (CPU). In the numerical integration, only the lower\ntriangular part of each local stiffness matrix is computed thanks to its\nsymmetry, which saves GPU memory and computing time. As a result of symmetry,\nthe global sparse matrix also contains non-zero elements only in its lower\ntriangular part, which reduces the assembly operations and memory usage. This\nmethodology allows generating the global sparse matrix from any unstructured\nfinite element mesh size on GPUs with little memory capacity, only limited by\nthe CPU memory.\n