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Isogeometric Analysis with Piece-wise Constant Test Functions by Paszynski, Maciej is a scholarly article available to read on EtoBox.

What is Isogeometric Analysis with Piece-wise Constant Test Functions about?

We focus on the finite element method computations with higher-order C1 continuity basis functions that preserve the partition of unity. We show that the rows of the system of linear equations can be combined, and the test functions can be sum up to 1 using the partition of unity property at the quadrature points. Thus, the test functions in higher continuity IGA can be set to piece-wise constants. This formulation is equivalent to testing with piece-wise constant basis functions, with supports span over some parts of the domain. The resulting method is a Petrov-Galerkin formulation with piece-wise constant test functions. This observation has the following consequences. The numerical integration cost can be reduced because we do not need to evaluate the test functions since they are equal to 1. This observation is valid for any basis functions preserving the partition of unity property. It is independent of the problem dimension and geometry of the computational domain. It also can be used in time-dependent problems, e.g., in the explicit dynamics computations, where we can reduce the cost of generation of the right-hand side. This summation of test functions can be performed for

Author

Paszynski, Maciej

Published

2019

Language

EN