Workshop on Advances in Computational Mathematics and Engineering
In honor of the contributions of M. Y. Hussaini
Event Information
WhenSeptember 28-29, 2012
WhereFlorida Center for Advanced Aero-Propulsion
Aero-Propulsion, Mechatronics and Energy Building (AME)
2003 Levy Ave., Engineering Campus

Friday, Sept 28, 2012

A. Sameh, Purdue University
Title: Scalable parallel sparse matrix computations

Sparse matrix computations arise in numerous computational engineering applications such as structural mechanics, fluid dynamics, fluid structure interaction, electromagnetics, and nanoelectronics. Unfortunately, minor modifications of current uniprocessor sparse matrix kernels and algorithms are not sufficient to ensure realizing high performance on parallel computing platforms. Often, one needs to design, afresh, sparse matrix primitives and algorithms capable of minimizing memory references and interprocessor communications. Only then one can achieve high parallel scalability on computing platforms consisting of a single multicore node or many such nodes. In this presentation, we address: (i) designing sparse matrix primitives such as sparse matrix vector multiplication, sparse matrix reordering (large graph manipulations) that exhibit high degree of parallel scalability, (ii) designing a hybrid sparse linear system solver that is more scalable than current parallel direct sparse solvers, and more robust than preconditioned iterative solvers, and (iii) designing a scalable generalized symmetric eigenvalue problem solver for obtaining a few eigenpairs. Numerical experiments that demonstrate the robustness and parallel scalability of both our primitives and solvers are presented and compared with their counterparts in the Intel Math Kernel Library (MKL), and with Sandia.s Trilinos library.

Joint work with M. Manguoglu (METU, Turkey), F. Saied (Purdue), and O. Schenk (Lugano, Switzerland).

D. Banks, University of Tennessee
Title: The Topology of Water Ensembles Near a Charged Nanotube Reveals the Polarity of the Charge

Surface science concerns molecular-scale behavior at the interface between two phases (such as solid and liquid) of materials. We wish to visualize such behavior using 3-dimensional (3D) graphics. The traditional approach, drawing atoms as spheres, creates an immediate problem: the 2D interface occludes the atoms on the far side, and the atoms on the near side to the observer occlude the interface.

We selected the regime of water near a charged nanotube as an example of solid-liquid interaction along a surface. The water-nanotube regime is of interest to biologists simulating the movement of biofluids through pores in a cell membrane, and to engineers designing membranes for filtering/desalinating water.

Near a nanotube, the orientation of water molecules is influenced by the nanotube's charge. The coarse-scale character of the orientations is readily seen in ordinary 3D visualizations of the color-coded atoms, with oxygen atoms preferentially positioned closer to a positively charged nanotube and hydrogen atoms preferentially positioned closer to a negatively charged nanotube. But the aggregate pose of the water molecules also possesses a nuanced symmetry that depends on the nanotube's polarity, not at all evident in the traditional 3D representation of spatial positions of the atoms.

We demonstrate a technique for visualizing the difference in aggregate orientation of molecular water near a charged nanotube by constructing ensemble coordinates for each water-nanotube couple. Within this ensemble space, reversal of the nanotube's charge alters both the shape and topology of hydrogen density surrounding an oxygen atom. The result demonstrates that 3D visualization using ensemble coordinates can distinguish subtle geometric changes along a fluid-solid interface, which offers a new tool for visual analysis of data resulting from computational simulations in this arena.

Talks Session A

A.1. A. Srivastava, Florida State University
Title: A Computational Framework for Statistical Shape Analysis

Shape analysis and modeling of 2D and 3D objects has important applications in many branches of science and engineering. The general goals in shape analysis include: derivation of efficient shape metrics, computation of shape templates, representation of dominant shape variability in a shape class, and development of probability models that characterize shape variation within and across classes. While past work on shape analysis is dominated by point representations -- finite sets of ordered or triangulated points on objects' boundaries -- the emphasis has lately shifted to continuous formulations.The shape analysis of parameterized curves and surfaces introduces an additional shape invariance, the re-parametrization group, in additional to the standard invariants of rigid motions and global scales. Treating re-parameterization as a tool for registration of points across objects, we incorporate this group in shape analysis, in the same way orientation is handled in Procrustes analysis. This framework provides proper metrics, geodesics, and sample statistics of shapes. These sample statistics are further useful in statistical modeling of shapes in different shape classes. I will demonstrate these ideas using applications from medical image analysis, protein structure analysis, 3D face recognition, and human activity recognition in videos.

A.2. G. Okten, Florida State University
Title:Sensitivity analysis, model reduction, and model robustness

Good things can happen if one can assess the sensitivity of a model with respect to its variables. This information can be used to reduce the dimension of the model which then helps develop more efficient computational algorithms. Sensitivity information can also be used to compare different models in terms of their robustness. I will discuss a technique known as Sobol' global sensitivity analysis, and give examples from fire spread modeling and weather derivatives that illustrate the practical use of sensitivity information.

A.3.W. Dewar, Florida State University
Title: Centrifugal Instability and Mixing in the California Undercurrent

A regional numerical study of the California Current System near Monterey Bay, California is conducted using both hydrostatic and non-hydrostatic models. Frequent sighting of strong anticyclones (Cuddies) have occurred in the area, and previous studies have identified it as an apparent region of strong unbalanced flow generation. Here by means of a down-scaling exercise, a domain just downstream of Point Sur is analyzed and argued to be a preferred site of diapycnal mixing. The scenario suggested by the simulations involves the generation of negative relative vorticity in a topographically attached boundary layer by interactions of the California Undercurrent with the California continental shelf break. At Point Sur, the current separates from the coast and moves into deep waters where it rapidly develops finite amplitude instabilities. These manifest as isopycnal overturnings, but in contrast to the normal Kelvin-Helmholtz paradigm for mixing, we argue the instability is primarily centrifugal. The evidence for this comes from comparisons of the model with linear results for ageostrophic instabilities.

Mixing increases the potential energy of the fluid, either by negatively buoyant fluids being lifted and positively buoyant fluids deepened by overturnings or buoyancy being conducted deeper into the fluid by explicit diffusion. We argue the regional potential energy generation near Point Sur in the upper few hundred meters is comparable to and possibly larger than that typically estimated for the open ocean. We compute diapycnal fluxes and estimate turbulent diffusivities in two ways; both argue mixing by centrifugal instability is characterized by diffusivities of (2-4)x10^-4 m^2/s.

A.4. G. Erlebacher, Florida State University Title: High-Order Finite-Element Earthquake Modeling on very large Clusters of GPUs

The late 1980s saw the advent of commodity platforms with specialized hardware to greatly speed up graphics and visualization algorithms. Since then, lower cost and improved performance has combined to produce a wide range of sophisticated algorithms, many of which run in real time. Over the years, the hardware vendors gave increasing control of the graphic pipeline to the user, and in so doing, spawned off a new industry seeking to capitalize on this new functionality, leading to new languages, new algorithms, and new applications. Naturally, it was only a matter of time before non-graphical applications were ported to the GPUs, leading to speedups of one to two orders of magnitude. The most popular languages running on the GPU today are CUDA (from NVidia) and OpenCL (Khronos Group), although there exists a plethora of specialized libraries and utilities to simplify implementations.

This talk presents the steps taken to port the spectral element code SpecFem3D, developed by Dimitri Komatitsch, to run on a large cluster of GPUs using CUDA. We discuss the special nature of parallelization on GPUs and some of the issues that had to be addressed to optimize the resulting code one a single and multiple GPUs. The talk concludes with some benchmarks.

Saturday, Sept 29, 2012

D. Katz, Duke University
Title: Modeling Interacting Transport Processes of HIV Virions and Anti-HIV Microbicide Molecules

Abstract: Infection by HIV begins when virions contact and bind to host cells that contain specific receptor molecules for them. The subsequent interactions between virions and host cells enable the virions to reproduce themselves, and systemic infection ensues. Sexually introduced virions migrate from their carrier fluids (typically semen) down into mucosal tissues which contain the host cells. The virions thus move through a fluid and two layers of mucosal tissue to initiate infection. Anti-HIV molecules can be introduced to act locally to inhibit the onset of infection. These molecules, termed microbicides, can act directly against virions in the original semen or host fluids (e.g. vaginal fluid), or within the mucosal tissues (by altering host cell receptivity to virions or virion receptivity to host cells). The microbicide molecules can be introduced via various delivery systems, or vehicles. The vehicles can be semi-solid (e.g. non-Newtonian gels) or solid (e.g. plastic intravaginal rings). It is possible to use the principles of transport theory to model the interacting migration processes of the HIV virions and anti-HIV microbicidal molecules. The primary processes are diffusion and fluid flow (convection). Coupled systems of partial differential equations arise, in which the domains are the different compartments (fluids, tissues) and the dependent variables are the concentrations of microbicide, infectious HIV virions and neutralized HIV virions. Solutions of these systems of equations have both fundamental biological and applied pharmacological value. They help us understand how the processes of HIV infection, and its local mitigation, work. They also can serve as tools to help design and evaluate candidate anti-HIV microbicide products. This talk will illustrate the creation and solution of the systems of equations, also termed compartmental models, and link results to current fundamental knowledge about HIV transmission and its mitigation. The talk will also illustrate the challenging but rewarding implementation of such theory in the practical world of microbicide molecule and vehicle design and evaluation.

Talks Session B

B.1. N. Cogan, Florida State University
Title: Hybrid Method for Stokes Flow with Interfaces with Several Applications

Stokes flow arises in a variety of biological applications where the interaction between the flow influences an immersed interface-either through physical forces or chemical signaling. Additional difficulties that are widespread is the extreme spatial heterogeneity and disparate time/space scales. We will discuss a numerical method that is a hybrid combination of the boundary integral method near the immersed interface and regularized Stokeslets for the far-field information. We show results for three different biological applications where the Stokes flow is an appropriate approximation to the flow.

B.2. M. Sussman, Florida State University
Title: A Coupled Level Set-Moment of Fluid Method for Incompressible Two-Phase Flows

We combine the multimaterial Moment-of-Fluid (MOF) developments of Ahn and Shashkov with the work of Kwatra et al for removing the acoustic time step restriction in order to solve multimaterial flows. The density ratio among each material can be very large (e.g. 1000:1). The multimaterial reconstruction is a volume preserving reconstruction which enables one to compute splashing of liquid against moving/deforming solids without loss of liquid volume. The mass weights found in the algorithm of Kwatra et al are computed directly from the multimaterial MOF reconstructed interface. Simulations of bubbles, drops, and jets are presented to validate the new method.

B.3. A. Uzun, Florida State University
Title:High-Fidelity Simulations of Complex High-Speed Flows

This talk will present sample applications of high-fidelity numerical simulations to complex problems that contain high-speed flow field phenomena. Example applications include prediction of noise generated by high-speed free/impinging jets and detailed simulation of resonance-enhanced micro-actuators that generate pulsed high-momentum supersonic micro-jets for flow/noise control applications. A large eddy simulation (LES) methodology based on high-fidelity numerical schemes developed for turbulence simulations and computational aeroacoustics (CAA) has been utilized to perform the simulations. This talk will present representative results from these calculations and make comparisons with available experimental measurements to assess the predictive capability of the simulations.

M. Haik, Virginia Tech
Title: Computational Experiments and Discoveries at the Nanoscale

Several applications of newly discovered carbon nanomaterials have emerged in the last two decades. This presentation utilizes numerical computations and preliminary experimental verifications to shed some light on two possible applications of these nanomaterials; future organic electronics and drug delivery for cancer treatment.

Origination from their minimal defect confined nanostructure exceptional thermal and electrical properties have been reported for two carbon allotropes; carbon nanotubes (CNTs) and graphite nanoplatelets (GNPs). However, it is well established that the incorporation of these species into polymeric matrices does not enhance the composite.s effective properties to the levels predicted by the composites theory bounds. To assess the electrical properties of these nanocomposites, a percolation model that utilizes electron tunneling phenomenon is simulated by utilizing tools from statistical physics. To establish their validity, the simulation predictions are compared with relevant findings published in the literature. The applicability of the proposed model is confirmed for both CNTs and GNPs. To predict the thermal properties of nanocomposites based on CNTs and GNPs, a statistical continuum based model originally developed for two-phase composite is adopted and extended to describe multiphase nanocomposites. The adopted model is a strong-contrast expansion which directly links the thermal properties of the composites to the thermal properties of its constituents by considering microstructural effects. For verification purposes the proposed model predictions are compared with finite element model calculations for composites comprising cylindrical and disk-shaped nanoparticles. Preliminary experimental measurements of the electrical and thermal properties of hybrid CNTs/GNPs/polymer nanocomposites will be presented.

The ability of CNTs to enter the cell membrane, acting as drug delivery vehicles for cancer treatment, has yielded plethora of experimental investigations, mostly with inconclusive results due to the wide spectra of carbon nanotubes structures. Due to the virtual impossibility of synthesizing CNTs with distinct chirality, this presentation offers a parametric study on the use of molecular dynamics to provide better insights on the effect of the carbon nanotube chirality and aspect ratio on the interaction with a lipid bilayer membrane. The simulation results revealed the presence of different time-evolving mechanisms that facilitate the CNT internalization within the cell membrane. Also, the different aspect ratios and the chirality affected the CNTs translocation through and adhesion to the lipid bilayer membrane.

Talks Session C

C.1. A. Croicu, Kennesaw State University
Title:Robust Airfoil Optimization Using Maximum Expected Value and Expected Maximum Value Approaches

Deterministic engineering design often leads to unexpected or physically unrealizable results. This is due to the fact that deterministic design is not able to capture the effects of even slight natural fluctuations of parameters. Deterministic transonic shape optimization is no exception: deterministic designs can result in dramatically inferior performance when the actual operating conditions are different from the design conditions used during a deterministic optimization procedure. The goal of this research is to overcome the off-design performance degradation of deterministic transonic shape optimization by using two different optimization approaches to produce robust designs. Two criteria, the well-known maximum/minimum expected value criterion (MEV) and the alternative expected maximum/minimum value criterion (EMV), are studied and applied to improve an initial Royal Aircraft Q2 Establishment 2822 design. It turns out that EMV is much easier to implement than MEV, given a deterministic optimization code, and may provide a promising method for optimizing design shapes under uncertainty.

C.2. M. Navon, Florida State University
Title: The Tale of Three Papers

Three papers written in collaboration with Professor Hussaini and inspired by him are briefly discussed. One is in computational fluid dynamics field, namely a problem of controlling vortex shedding behind a cylinder (through suction/blowing on the cylinder surface) governed by the unsteady two-dimensional incompressible Navier.Stokes equations space discretized by finite-volume approximation with time-dependent boundary conditions

The second is a topic of applied mathematics related to the so-called perfectly matched layer (PML) as an absorbing boundary condition. The equations are obtained in this layer by splitting the shallow water equations in the coordinate directions and introducing the absorption coefficients.

The performance of the PML as an absorbing boundary treatment is demonstrated using a commonly employed bell-shaped Gaussian initially introduced at the center of the domain.

Finally the third paper relates to the domain of meteorology namely the analysis of singular vectors (SVs) of the Florida State University Global Spectral Model and its adjoint, which includes linearized full physics of the atmosphere. It is demonstrated that the physical processes, especially precipitation, fundamentally affect the leading SVs. When the SVs are coupled with the precipitation geographically, their growth rates increase substantially.

The impact of Professor Hussaini on these papers and the quality of their presentation is finally outlined.

F. Le Dimet, Joseph Fourier University
Title: Assimilation of Images

Since more than five decades the ocean and the atmosphere are observed by satellites. The prediction of the evolution of geophysical fluids has been largely improved by Eulerian data provided by satellites (e.g. vertical profile of temperature for the atmosphere or surface elevation for the ocean). But the dynamics of images is also an important information, of Lagrangian type, mainly used, at the present time, as a qualitative information. The purpose of this talk is to present a first exploration to combine images and numerical models.

A first answer will be given to the questions:
- Where is the information in the evolution of images?
- How to assimilate this information in numerical models?

Talks Session D

D.1. K. Taira, Florida State University/Florida A&M University
Title: The immersed boundary projection method and its applications

The immersed boundary method solves fluid flow around bodies with arbitrary geometry on a structured grid. The body is represented by introducing boundary force at Lagrangian points located along the body surface. The immersed boundary projection method solves for this boundary force through projection to enforce the no-slip condition, which is analogous to how incompressibility is imposed with the use of projection. The present implicit approach requires no ad-hoc relations for determining the boundary force and can be extended to fluid-structure interaction problems. Techniques for accelerating the computation (nullspace method) and satisfying other physical constraints will be presented. Some applications of the immersed boundary projection method to analyze three-dimensional vortex dynamics around low-aspect-ratio wings, flow control for airfoil lift enhancement, and fluid-structure interactions will be presented.

D.2. W. Oates, Florida State University/Florida A&M University
Title: Multiple Length and Time Scale Effects in Functional Materials

In this presentation, I will give an overview of some of the current developments and challenges in understanding electroactive materials at multiple length and time scales. In the first example, I will discuss a hard ferroelectric material and correlate length scales between sub-atomic quantum mechanics and macroscopic continuum mechanics. This will include how nonlinear mechanics and quadrupole density re- lations can be identified from density function theory and the Hellmann-Feynman theorem. In the second example, a soft dielectric elastomer is discussed. These ma- terials exhibit complex viscoelastic behavior that spans a broad range of time scales. Bayesian statistics are utilized to formulate a stochastic based homogenized viscoelas- tic model that significantly improves model estimates of rate dependent deformation in soft dielectric elastomers.

D.3. P. Rikvold, Florida State University
Title:Modeling Power Grids

Power grids are complex engineering systems of vital importance to modern industrialized societies, and it is important to understand how to improve their resistance to the spread of local malfunctions. However, because of security concerns it is difficult to obtain detailed data on the structures, generating capacities, and power demands for real power systems. In order to be able to test network-analysis algorithms under a variety of conditions, it is therefore desirable to develop artificial models that can be tuned to reflect properties of real grids, and also can be scaled to study effects of the grid size.

Here we present an study in which we use Monte Carlo methods to generate random grids that agree with the degree distribution for the vertices (power plants and consumers) and the length distribution for the transmission lines in the Florida high-voltage power grid. These model grids are used to test the performance of algorithms to partition the grid into semi-independent islands. We find that it is more difficult to partition these model grids than the real Florida grid, suggesting that the real grid contains correlations that are absent in our current generation of models.

D.4. A. Krothapalli, Florida State University/Florida A&M University
Title: Thermodynamic Modeling of the Multiple Parabolic Reflector Flat Panel Collector (MPFC)

The Multiple Parabolic Reflector Flat Panel Collector (MPFC) is composed of parabolic trough reflectors positioned in an enclosed frame, reflecting solar radiation towards tubular receivers. The frame remains stationary throughout the year while the receivers track the reflected solar rays. The goal of the design is to provide heat at 150 degrees Centigrade for a lower cost than current types of solar thermal panels. An analysis of the MPFC is segmented into geometric optics and thermal losses. Ray tracing is used to find the optimal position of the receiver as the angle of incident light on the aperture changes. The intercept factor on the receiver is used to determine the optical efficiency of the incident energy on the collector. Computational fluid dynamics (CFD) is used to determine the coefficient of convection within the two-dimensional cavity. Standard convection models could not be used due to the unique geometry. A first-law thermal analysis is used to determine the heat gain and heat loss of the system. Temperatures of surfaces within the MPFC are calculated numerically due to the nonlinear nature of the system. Overall system efficiency is calculated to estimate the effectiveness of the collector. Individual parameters can be changed to optimize the system without the need to build (or rebuild) prototypes