7,005 research outputs found
An isogeometric analysis for elliptic homogenization problems
A novel and efficient approach which is based on the framework of
isogeometric analysis for elliptic homogenization problems is proposed. These
problems possess highly oscillating coefficients leading to extremely high
computational expenses while using traditional finite element methods. The
isogeometric analysis heterogeneous multiscale method (IGA-HMM) investigated in
this paper is regarded as an alternative approach to the standard Finite
Element Heterogeneous Multiscale Method (FE-HMM) which is currently an
effective framework to solve these problems. The method utilizes non-uniform
rational B-splines (NURBS) in both macro and micro levels instead of standard
Lagrange basis. Beside the ability to describe exactly the geometry, it
tremendously facilitates high-order macroscopic/microscopic discretizations
thanks to the flexibility of refinement and degree elevation with an arbitrary
continuity level provided by NURBS basis functions. A priori error estimates of
the discretization error coming from macro and micro meshes and optimal micro
refinement strategies for macro/micro NURBS basis functions of arbitrary orders
are derived. Numerical results show the excellent performance of the proposed
method
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Volume Modeling for Rapid Prototyping
The expanding workspace of Rapid Prototyping will draw on the new developments
in geometric modeling. Volume modeling has substantial advantages over other modeling
schemes to meet the emerging requirements of Rapid Prototyping technology. It provides us with
a new approach to design complex geometry and topology. The integration of the volume
modeling and Rapid Prototyping technology will help us to fully exploit RP's ability to fabricate
objects with complex structures. This paper addresses our research and practice in a volume
modeling system toward Rapid Prototyping. Novel techniques in volumetric data manipulation,
NURBS volume models and triangular facet generation over solid models are presented.
Computer models designed by this system and their corresponding DTM products are also
shown atthe end of this paper.Mechanical Engineerin
Isogeometric analysis applied to frictionless large deformation elastoplastic contact
This paper focuses on the application of isogeometric analysis to model frictionless large deformation contact between deformable bodies and rigid surfaces that may be represented by analytical functions. The contact constraints are satisfied exactly with the augmented Lagrangian method, and treated with a mortar-based approach combined with a simplified integration method to avoid segmentation of the contact surfaces. The spatial discretization of the deformable body is performed with NURBS and C0-continuous Lagrange polynomial elements. The numerical examples demonstrate that isogeometric surface discretization delivers more accurate and robust predictions of the response compared to Lagrange discretizations
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An exploration of the IGA method for efficient reservoir simulation
Novel numerical methods present exciting opportunities to improve the efficiency of reservoir simulators. Because potentially significant gains to computational speed and
accuracy may be obtained, it is worthwhile explore alternative computational algorithms
for both general and case-by-case application to the discretization of the equations of porous media flow, fluid-structure interaction, and/or production. In the present
work, the fairly new concept of isogeometric analysis (IGA) is evaluated for its suitability
to reservoir simulation via direct comparison with the industry standard finite difference (FD) method and 1st order standard finite element method (SFEM). To this end, two main studies are carried out to observe IGA’s performance with regards to geometrical modeling and ability to capture steep saturation fronts. The first study explores IGA’s ability to model complex reservoir geometries, observing L2 error convergence rates under a variety of refinement schemes. The numerical experimental setup includes an 'S' shaped line sink of varying curvature from which water is produced in a 2D homogenous domain. The accompanying study simplifies the domain to 1D, but adds in multiphase physics that traditionally introduce difficulties associated with modeling of a moving saturation front. Results overall demonstrate promise for the IGA method to be a particularly effective tool in handling geometrically difficult features while also managing typically challenging numerical phenomena.Petroleum and Geosystems Engineerin
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