On filter boundary conditions in topology optimization

Shape Optimization Problems with Robin Conditions on the Free Boundary

We provide a free discontinuity approach to a class of shape optimization problems involving Robin conditions on the free boundary. More precisely, we identify a large family of domains on which such problems are well posed in a way that the extended problem can be considered a relaxed version of the corresponding one on regular domains, we prove existence of a solution and obtain some qualitat...

Global Theory of Quantum Boundary Conditions and Topology Change

We analyze the global theory of boundary conditions for a constrained quantum system with classical configuration space a compact Riemannian manifold M with regular boundary Γ = ∂M . The space M of self-adjoint extensions of the covariant Laplacian on M is shown to have interesting geometrical and topological properties which are related to the different topological closures of M . In this sens...

Boundary filter optimization for segmentation-based subband coding

This paper presents boundary optimization techniques for the nonexpansive decomposition of arbitrary-length signals with multirate filterbanks. Both biorthogonal and paraunitary filterbanks are considered. The paper shows how matching moments and orthonormality can be imposed as additional conditions during the boundary filter optimization process. It provides direct solutions to the problem of...

On Stochastic Structural Topology Optimization

We consider structural topology optimization problems including unilateral constraints arising from, for example, non-penetration conditions in contact mechanics or noncompression conditions for elastic ropes. To construct more realistic models and to hedge off possible failures or inefficient behaviour of optimal structures, we allow parameters (for example, loads) defining the problem to be s...

On the Boundary Between Mereology and Topology