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Weight‐adaptive isogeometric analysis for solving elastodynamic problems based on space‐time discretization approach
Author(s) -
Izadpanah E.,
Shojaee S.,
HamzeheiJavaran S.
Publication year - 2019
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6082
Subject(s) - discretization , mathematics , isogeometric analysis , dimension (graph theory) , minification , domain (mathematical analysis) , mathematical optimization , algorithm , mathematical analysis , finite element method , physics , pure mathematics , thermodynamics
Summary In this paper, a novel adaptive isogeometric analysis (IGA) is introduced and its application in the numerical solution of two‐dimensional elastodynamic problems based on the space‐time discretization (STD) approach is studied. In the STD approach, the time is considered as an additional dimension and is discretized the same as the spatial domain. The weights of control points play the main role in the proposed method. In the conventional IGA, the same set of weights is used in the modeling of geometric and solution spaces. The idea is to define two groups of weights: geometric and solution weights. Geometric weights are known and can be determined based on the position of control points, but the solution weights are considered to be unknown and can be determined using a proper strategy so that the accuracy of the solution is optimized. This strategy is based on the minimization of an error function. The results obtained from the proposed method are compared with those obtained from the conventional IGA.