134 research outputs found
Suitably graded THB-spline refinement and coarsening: Towards an adaptive isogeometric analysis of additive manufacturing processes
In the present work we introduce a complete set of algorithms to efficiently
perform adaptive refinement and coarsening by exploiting truncated hierarchical
B-splines (THB-splines) defined on suitably graded isogeometric meshes, that
are called admissible mesh configurations. We apply the proposed algorithms to
two-dimensional linear heat transfer problems with localized moving heat
source, as simplified models for additive manufacturing applications. We first
verify the accuracy of the admissible adaptive scheme with respect to an
overkilled solution, for then comparing our results with similar schemes which
consider different refinement and coarsening algorithms, with or without taking
into account grading parameters. This study shows that the THB-spline
admissible solution delivers an optimal discretization for what concerns not
only the accuracy of the approximation, but also the (reduced) number of
degrees of freedom per time step. In the last example we investigate the
capability of the algorithms to approximate the thermal history of the problem
for a more complicated source path. The comparison with uniform and
non-admissible hierarchical meshes demonstrates that also in this case our
adaptive scheme returns the desired accuracy while strongly improving the
computational efficiency.Comment: 20 pages, 12 figure
Variational Multiscale Stabilization and the Exponential Decay of Fine-scale Correctors
This paper addresses the variational multiscale stabilization of standard
finite element methods for linear partial differential equations that exhibit
multiscale features. The stabilization is of Petrov-Galerkin type with a
standard finite element trial space and a problem-dependent test space based on
pre-computed fine-scale correctors. The exponential decay of these correctors
and their localisation to local cell problems is rigorously justified. The
stabilization eliminates scale-dependent pre-asymptotic effects as they appear
for standard finite element discretizations of highly oscillatory problems,
e.g., the poor approximation in homogenization problems or the pollution
effect in high-frequency acoustic scattering
Certified Reduced Basis Method for Affinely Parametric Isogeometric Analysis NURBS Approximation
In this work we apply reduced basis methods for parametric PDEs to an isogeometric formulation based on NURBS. We propose an integrated and complete work pipeline from CAD to parametrization of domain geometry, then from full order to certified reduced basis solution. IsoGeometric Analysis (IGA), as well as reduced basis methods for parametric PDEs growing research themes in scientific computing and computational mechanics. Their combination enhances the solution of some class of problems, especially the ones characterized by parametrized geometries. This work shows that it is also possible for some class of problems to deal with affine geometrical parametrization combined with a NURBS IGA formulation. In this work we show a certification of accuracy and a complete integration between IGA formulation and parametric certified greedy RB formulation by introducing two numerical examples in heat transfer with different parametrization
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