Geometric programming: a programming approach to geometric design
ACM Transactions on Graphics (TOG)
Chain models and finite elements analysis: an executable CHAINS formulation of plane stress
Computer Aided Geometric Design - Special issue on grid generation, finite elements, and geometric design
Splitting a complex of convex polytopes in any dimension
Proceedings of the twelfth annual symposium on Computational geometry
Journal of Computational Physics
A multivector data structure for differential forms and equations
Mathematics and Computers in Simulation
Progressive dimension-independent Boolean operations
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Matrix-Based Multigrid: Theory and Applications
Matrix-Based Multigrid: Theory and Applications
Discrete physics using metrized chains
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
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Computational science and engineering are dominated by field problems. Traditionally, engineering practice involves repeated iterations of shape design (i.e., shaping and modeling of material properties), simulation of the physical field, evaluation of the result, and re-design. In this paper, we propose a specific interpretation of the algebraic-topological formulation of field problems, which is conceptually simple, physically sound, computational effective and comprehensive. In the proposed approach, physical information is attached to an adaptive, full-dimensional decomposition of the domain of interest. Giving preeminence to the cells of highest dimension allows us to generate the geometry and to simulate the physics simultaneously. We will also demonstrate that our formulation removes artificial constraints on the shape of discrete elements and unifies commonly unrelated methods in a single computational framework. This framework, by using an efficient graph-representation of the domain of interest, unifies several geometric and physical finite formulations, and supports local progressive refinement (and coarsening) effected only where and when required.