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CHARMS: A Simple Framework for Adaptive Simulation
(Eitan Grinspun, Petr Krysl and Peter Schröder), ACM TOG, 2002 / Proceedings of SIGGRAPH 2002.
Abstract:
Finite element solvers are a basic component of simulation applications;
they are common in computer graphics, engineering, and medical simulations.
Although adaptive solvers can be of great value in reducing
the often high computational cost of simulations they are not
employed broadly. Indeed,
building adaptive solvers can be a daunting task
especially for 3D finite elements. In this paper we are introducing
a new approach to produce conforming, hierarchical, adaptive
refinement methods (CHARMS). The basic principle of our approach
is to refine basis functions, not elements. This removes a number of
implementation headaches associated with other approaches and is a
general technique independent of domain dimension (here 2D and 3D),
element type (eg, triangle, quad, tetrahedron, hexahedron), and
basis function order (piecewise linear, higher order B-splines, Loop
subdivision, etc.). The (un-)refinement algorithms are simple
and require little in terms of data structure support. We
demonstrate the versatility of our new approach through 2D and 3D examples,
including medical applications and thin-shell animations.
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