Geometric uncertainty refers to the deviation of the geometric boundary from its ideal position, which may have a non-trivial impact on design performance. Since geometric uncertainty is embedded in the boundary which is dynamic and changes continuously in the optimization process, topology optimization under geometric uncertainty (TOGU) poses extreme difficulty to the already challenging topol...

Abstract. A new morphological multiscale method in 3D image processing is presented which combines the image processing methodology based on nonlinear diffusion equations and the theory of geometric evolution problems. Its aim is to smooth level sets of a 3D image while simultaneously preserving geometric features such as edges and corners on the level sets. This is obtained by an anisotropic c...

In this paper, we present appendices employed in the paper ”A geometric level-set formulation of a plasma-sheath interface” by the authors. Appendix A. Local existence of sheath solutions In this appendix, we present a series of a priori estimates for the approximate solutions constructed in Step 0 Step 7 in Section 7 and then give the proof Theorem 7.3. A.1. Basic a priori estimates. In this p...

We present a geometric approach for calculating integrals over irregular domains described by a level-set function. This procedure can be used to evaluate integrals over a lower dimensional interface and may be used to evaluate the contribution of singular source terms. This approach produces results that are second-order accurate and robust to the perturbation of the interface location on the ...

In this paper we describe and evaluate a geometric mass-preserving redistancing procedure for the level set function on general structured grids. The proposed algorithm is adapted from a recent finite element-based method and preserves the mass by means of a localized mass correction. A salient feature of the scheme is the absence of adjustable parameters. The algorithm is tested in two and thr...

In the previous paper [8] we have introduced notion of geometric directional bundle a singular space, in order to introduce global bi-Lipschitz invariants. Then posed question whether or not is stabilised as an operation acting on spaces. this give positive answer case where spaces are subanalytic sets, thus providing new invariant associated with sets.

The first part of this report describes the following result that, logarithmic approximation factor for hard capacitated set cover can be achieved from Wolsey's work [9], using a simpler and more intuitive analysis. We further show in our work, that O(log n) approximation factor can be achieved for the same problem by applying analysis of general set cover to analyze Wolsey's algorithm [5]. Thi...