Proceedings for the ICASE Workshop on Heterogeneous Boundary Conditions

Domain Decomposition is a complex problem with many interesting aspects. The choice of decomposition can be made based on many different criteria, and the choice of interface of internal boundary conditions are numerous. The various regions under study may have different dynamical balances, indicating that different physical processes are dominating the flow in these regions. This conference was called in recognition of the need to more clearly define the nature of these complex problems. This proceedings is a collection of the presentations and the discussion groups

Information-based complexity, feedback and dynamics in convex programming

We study the intrinsic limitations of sequential convex optimization through the lens of feedback information theory. In the oracle model of optimization, an algorithm queries an {\em oracle} for noisy information about the unknown objective function, and the goal is to (approximately) minimize every function in a given class using as few queries as possible. We show that, in order for a function to be optimized, the algorithm must be able to accumulate enough information about the objective. This, in turn, puts limits on the speed of optimization under specific assumptions on the oracle and the type of feedback. Our techniques are akin to the ones used in statistical literature to obtain minimax lower bounds on the risks of estimation procedures; the notable difference is that, unlike in the case of i.i.d. data, a sequential optimization algorithm can gather observations in a {\em controlled} manner, so that the amount of information at each step is allowed to change in time. In particular, we show that optimization algorithms often obey the law of diminishing returns: the signal-to-noise ratio drops as the optimization algorithm approaches the optimum. To underscore the generality of the tools, we use our approach to derive fundamental lower bounds for a certain active learning problem. Overall, the present work connects the intuitive notions of information in optimization, experimental design, estimation, and active learning to the quantitative notion of Shannon information.Comment: final version; to appear in IEEE Transactions on Information Theor

Finite-element-based generalized impedance boundary condition for modeling plasmonic nanostructures

The superior ability of plasmonic structures to manipulate light has propelled their extensive applications in nanophotonics techniques and devices. Computational electromagnetics plays a critical role in characterizing and optimizing the nanometallic structures. In this paper, a general numerical algorithm, which is different from the commonly used discrete dipole approximation, the finite-difference time-domain, and the surface integral equation (SIE) method, is proposed to model plasmonic nanostructures. In this algorithm, the generalized impedance boundary condition (GIBC) based on the finite element method (FEM) is formulated and converted to the SIE. The plasmonic nanostructures with arbitrary inhomogeneity and shapes are modeled by the FEM. Their complex electromagnetic interactions are accurately described by the SIE method. As a result, the near field of plasmonic nanostructures can be accurately calculated. The higher order basis functions, together with the multifrontal massively parallel sparse direct solver, are involved to provide a higher order accurate and fast solver. © 2011 IEEE.published_or_final_versio

Finite element based generalized impedance boundary condition for complicated em calculation

In this paper, a finite element based generalized impedance boundary condition (FEM-GIBC) is proposed to solve complicated electromagnetic (EM) problems. Complex structures with arbitrary inhomogeneity and shapes are modeled with the finite element method, and their scattering contributions are transformed to generalized impedance conditions on their boundaries. For each sub-domain, a special GIBC can be established and it is only related to the structures in this domain. Hence, for finite periodic structures, a representative GIBC can be formulated at the boundary of a unit cell. After the GIBC at each boundary is established, the electromagnetic coupling between each impedance boundary can be calculated by the boundary integral equations (BIE) and accelerated with the multilevel fast multipole algorithm (MLFMA). © 2011 IEEE.published_or_final_versionThe 2011 IEEE International Symposium on Antennas and Propagation (APSURSI), Spokane, WA., 3-8 July 2011. In IEEE APSURSI Digest, 2011, p. 2700-270

An efficient rotation-free triangle for drape/cloth simulations - Part I: model improvement, dynamic simulation and adaptive remeshing

This series of two papers aim to improve the rotation-free (RF) triangle model previously developed by the authors and apply it for drape/cloth simulations. To avoid a previously un-observed drawback, the membrane strain obtained from the three-node displacement interpolation is replaced by the one obtained from the six-node interpolation. Dynamic simulations are made possible by explicit time integration. Instead of using dense structural meshes, the quality of draped patterns is improved by global adaptive remeshing. The works in this paper provide important and necessary techniques for practical applications of the RF triangle in the drape simulation. In part II, other techniques including collision handling and garment construction are further discussed and some practical applications of garments on still and moving human body model would be presented.postprin

Moving/deforming mesh techniques for computational fluid dynamics and heat transfer

This report represents a summary of a Laboratory Directed Research and Development (LDRD) project to develop general purpose unstructured grid techniques for solving free and moving boundary problems in computational fluid dynamics and heat transfer. Both control volume finite element and Galerkin finite element techniques were utilized. A very robust technique for keeping the deforming mesh from tangling was implemented; the mesh was treated as a fictitious elastic body. Sample results for an ablating nose tip and buoyancy driven flow in a box are presented. References to additional publications resulting from this work are included