iMechanica - Implicit boundary representation
https://imechanica.org/taxonomy/term/9748
enAn Alternative to IGA: Level Set based Finite Element Analysis Directly from CAD: Finite Elements on Implicit Domains
https://imechanica.org/node/16521
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/5089">extended finite element method</a></div><div class="field-item odd"><a href="/taxonomy/term/6437">Isogeometric Analysis</a></div><div class="field-item even"><a href="/taxonomy/term/8533">Level set method</a></div><div class="field-item odd"><a href="/taxonomy/term/8787">IGA</a></div><div class="field-item even"><a href="/taxonomy/term/9745">CAD-analysis</a></div><div class="field-item odd"><a href="/taxonomy/term/9746">Curved boundary and sharp edges</a></div><div class="field-item even"><a href="/taxonomy/term/9747">Dirichlet</a></div><div class="field-item odd"><a href="/taxonomy/term/9748">Implicit boundary representation</a></div><div class="field-item even"><a href="/taxonomy/term/9749">Boundary representations</a></div><div class="field-item odd"><a href="/taxonomy/term/9750">Curved boundary</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>
<a href="http://orbilu.uni.lu/handle/10993/12915">http://orbilu.uni.lu/handle/10993/12915</a> <a href="http://orbilu.uni.lu/bitstream/10993/12915/1/2011implicitDomainFEM_CMAME.pdf">http://orbilu.uni.lu/bitstream/10993/12915/1/2011implicitDomainFEM_CMAME...</a>
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In this paper, we present some novel results and ideas for robust and<br />
accurate implicit representation of geometric surfaces in finite element<br />
analysis. The novel contributions of this paper are threefold: (1)<br />
describe and validate a method to represent arbitrary parametric<br />
surfaces implicitly; (2) represent arbitrary solids implicitly,<br />
including sharp features using level sets and boolean operations; (3)<br />
impose arbitrary Dirichlet and Neumann boundary conditions on the<br />
resulting implicitly defined boundaries. The methods proposed do not<br />
require local refinement of the finite element mesh in regions of high<br />
curvature, ensure the independence of the domain's volume on the mesh,<br />
do not rely on boundary regularization, and are well suited to methods<br />
based on fixed grids such as the extended finite element method (XFEM).<br />
Numerical examples are presented to demonstrate the robustness and<br />
effectiveness of the proposed approach and show that it is possible to<br />
achieve optimal convergence rates using a fully implicit representation<br />
of object boundaries. This approach is one step in the desired direction<br />
of tying numerical simulations to computer aided design (CAD),<br />
similarly to the isogeometric analysis paradigm.
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</div></div></div>Thu, 01 May 2014 07:47:43 +0000Stephane Bordas16521 at https://imechanica.orghttps://imechanica.org/node/16521#commentshttps://imechanica.org/crss/node/16521Error | iMechanica