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Geometry-independent field approximation for spline-based finite element methods - Generalised IGA

In isogeometric analysis, the same spline representation is employed for the geometry and

for the field variables solutions. In this paper, we propose a new approximation scheme called

Geometry-Independent Field Approximation ( GIFA for short) where the spline spaces used for the

geometry and the field variables can be chosen independently. In the proposed method, for a given

computational domain with spline form, the solution field can have a different spline representation.

The proposed method has the following features: (1) It is possible to flexibly choose between

different spline spaces with different properties to better represent the solution of the PDE, e.g.

the continuity of the solution field. (2) For the case of multi-patches, the continuity condition

between neighboring patches on the solution field can be automatically guaranteed without setting

additional constraint conditions in the linear system. (3) Refinement operations by knot insertion

and degree elevation are performed directly on the spline space of the solution field, independently

of the spline space of the geometry of the domain, which saves some computing costs and facilitates

the subsequence shape optimization operation. The GIFA method with PHT-spline solution field

and NURBS geometry is investigated for two-dimensional heat conduction problem to show the

effectiveness of the proposed approach.


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