Efficient implementation of Galerkin meshfree methods for large-scale problems with an emphasis on maximum entropy approximants

•We propose a simple method to implement matrix assembly in Galerkin meshfree methods.•By looping over groups of quadrature points, performance is significantly improved.•We propose a method to efficiently store the maximum entropy basis functions.•It stores partial information, at the expense of a...

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Bibliographic Details
Published in:Computers & structures Vol. 150; pp. 52 - 62
Main Authors: Peco, Christian, Millán, Daniel, Rosolen, Adrian, Arroyo, Marino
Format: Journal Article Publication
Language:English
Published: Elsevier Ltd 01.04.2015
Subjects:
74 Mechanics of deformable solids
74S Numerical methods
Anàlisi numèrica
Assembly
Balancing
Basis functions
Classificació AMS
Code optimization
CONSTRUCTION
FINITE-ELEMENT-METHOD
FORMULATION
FRACTURE
Galerkin methods
INTERPOLANTS
KERNEL PARTICLE METHODS
Local maximum entropy
Matemàtiques i estadística
Matrix structure creation
Maximum entropy
Meshfree methods
MESHLESS METHODS
Mètodes numèrics
Numerical methods and algorithms
Optimal memory storage
PHASE-FIELD MODELS
Resistència de materials
SCHEMES
SEAMLESS BRIDGE
Sparse matrix efficient assembly
Stores
Strategy
Àrees temàtiques de la UPC
Local maximum entropy
Optimal memory storage
Sparse matrix efficient assembly
Code optimization
Meshfree methods
Matrix structure creation
ISSN:0045-7949, 1879-2243
Online Access:Get full text
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Summary:•We propose a simple method to implement matrix assembly in Galerkin meshfree methods.•By looping over groups of quadrature points, performance is significantly improved.•We propose a method to efficiently store the maximum entropy basis functions.•It stores partial information, at the expense of a negligible amount of extra operations. In Galerkin meshfree methods, because of a denser and unstructured connectivity, the creation and assembly of sparse matrices is expensive. Additionally, the cost of computing basis functions can be significant in problems requiring repetitive evaluations. We show that it is possible to overcome these two bottlenecks resorting to simple and effective algorithms. First, we create and fill the matrix by coarse-graining the connectivity between quadrature points and nodes. Second, we store only partial information about the basis functions, striking a balance between storage and computation. We show the performance of these strategies in relevant problems.
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ISSN:0045-7949
1879-2243
DOI:10.1016/j.compstruc.2014.12.005