Engineering Analysis via Distance Sampling

Date:Friday, March 20, 2009
Time:2:00pm - 3:00pm
Location:LBNL Bldg. 50B, Room 4205

Speaker:
Vadim Shapiro
Departments of Mechanical Engineering and Computer Sciences
University of Wisconsin-Madison

Abstract:
Dramatic advances in sensing technology, computing power, and
special purpose hardware point to a new era in geometric modeling
where point clouds and sampling increasingly dominate many
traditional geometric representations and algorithms. By contrast,
engineering analysis continues to rely on classical analytical
formulations and mesh-based solution techniques, that require
complex and error-prone conversions of geometric representations.
Building on seminal ideas of Kantorovich in 1950s and Rvachev's
theory of R-functions, we develop a meshfree reformulation of
engineering analysis that leads to a solution procedure consisting
of a sequence of geometric and functional sampling and composition
steps, followed by solving a system of algebraic equations. The
exposed computational pipeline is general in that it applies to any
unambiguous geometric representation supporting point membership
classification (PMC) and distance computations, and is efficient
enough to compete with mesh-based techniques such as finite element
analysis. The new approach allows computational engineering analysis
in situ for a wide range of digitally acquired models, as well as
traditional CAD designs.

    This is joint work with Igor Tsukanov and Michael Freytag.

Host of Seminar:
Horst Simon