A Variational Level Set Approach for Surface Area Minimization of Triply Periodic Surfaces

Details A Variational Level Set Approach for Surface Area Minimization of Triply Periodic Surfaces A Variational Level Set Approach for Surface Area Minimization of Triply Periodic Surfaces

2006-06-14

arxiv.org/abs/math/0606345v1

Mathematics

Optimization and Control

28 pages, 16 figures, 3 tables

Scientific paper

In this paper, we study triply periodic surfaces with minimal surface area under a constraint in the volume fraction of the regions (phases) that the surface separates. Using a variational level set method formulation, we present a theoretical characterization of and a numerical algorithm for computing these surfaces. We use our theoretical and computational formulation to study the optimality of the Schwartz P, Schwartz D, and Schoen G surfaces when the volume fractions of the two phases are equal and explore the properties of optimal structures when the volume fractions of the two phases not equal. Due to the computational cost of the fully, three-dimensional shape optimization problem, we implement our numerical simulations using a parallel level set method software package.

Affiliated with

Also associated with

No associations

Rating

A Variational Level Set Approach for Surface Area Minimization of Triply Periodic Surfaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Variational Level Set Approach for Surface Area Minimization of Triply Periodic Surfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Variational Level Set Approach for Surface Area Minimization of Triply Periodic Surfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-197279