National Institute of Standards and Technology における超伝導研究及び生活

Three-dimensional geometry and topology. Volume 1, by William P. Thurston, (edited by Sylvio Levy). Princeton Mathematical Series, 35. £29.95. 1997. ISBN 0-691-08304-5 (Princeton University Press).

Definition. A (topological) n-manifold M is a Hausdorff topological space with a countable basis of open sets, such that each point of M lies in an open set homeomorphic to R or R+ = {(x1, . . . , xn) ∈ R n : xn ≥ 0}. The boundary ∂M of M is the set of points not having neighbourhoods homeomorphic to R. The set M − ∂M is the interior of M , denoted int(M). If M is compact and ∂M = ∅, then M is closed.

Three-dimensional manifolds

https://orbilu.uni.lu/bitstream/10993/28037/1/1-s2.0-S0045782516304832-main.pdf

Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth

We review the treatment of trimmed geometries in the context of design, data exchange, and computational simulation. Such models are omnipresent in current engineering modeling and play a key role for the integration of design and analysis. The problems induced by trimming are often underestimated due to the conceptional simplicity of the procedure. In this work, several challenges and pitfalls are described.

/pdf/a-review-of-trimming-in-isogeometric-analysis-challenges-4bj7mwwi2t.pdf

Benjamin Marussig

Papers

A Review of Trimming in Isogeometric Analysis: Challenges, Data Exchange and Simulation Aspects

Fast isogeometric boundary element method based on independent field approximation

Isogeometric Boundary Element analysis with elasto-plastic inclusions. Part 1: Plane problems

Stable isogeometric analysis of trimmed geometries

A simple approach to the numerical simulation with trimmed CAD surfaces