AMSC 663-664 Projects, 2003-2004

Below are the links to each student's AMSC 663-664 project webpage.

• Chris Danforth, danforth@math.umd.edu
  Project Title: 3-Level Quasi-Geostrophic Global Weather Model
  Project Supervisors: James Yorke, Eugenia Kalnay and Bob Cahalan
  

  Abstract: The well respected Quasi-Geostrophic global weather model of Marshall and Molteni will be modified to measure model error through nudging. The original code will be documented and altered to generate both forecasts and climatological averages on a time scale relevant to model error. Data structures and library dependencies will be changed so that the model will run on both workstations and clusters, and output to the GRADS software.

  Context: Numerical weather forecasting errors grow as a result of two inherent difficulties, inaccurate initial conditions and model deficiencies. Most current atmospheric chaos research focusses on generating ensembles of initial conditions, assuming a perfect model. My code will enable us to evaluate the effect of this assumption, using shadowing experiments to estimate model error.

• Kate Despain, despain@glue.umd.edu
  Project Title: Simulating Kinetic Alfven Wave Turbulence
  Project Supervisor: Jim Drake (Physics)
  

  Abstract: Using Gryffin or an appropriate derivative as a starting point, I hope to create a parallelized 3-D code to simulate kinetic Alfven wave turbulence. I will be working in cylindrical coordinates and matching boundary conditions specified by an experiment at the Large Plasma Devise (LAPD) at UCLA run by Troy Carter. I will compare my initial 2-D work to that done by Biskamp and Drake for validation purposes.

Context: Our hope is to use this new code to find the relationship between wave number and energy for perturbations in a regime between the ideal MHD limit and the gyrokinetic limit. We also hope to provide theoretical support to the Troy Carter experiment and ultimately include more physics so that this regime can be more rigoriously studied.

• Dongwook Lee, dwlee@glue.umd.edu
  Project Title: A Numerical Implementation of a Magnetohydrodynamics Scheme Using A Staggered Mesh Algorithm With High Order Godunov Fluxes
  Project Supervisor: Anil Deane (IPST)
  

  Abstract: The modeling of computational magnetohydrodynamics (MHD) plays a very important role currently. The proper use of numerical scheme and their simulations contribute to better understanding of physics. In particular, computer simulations are one of the most efficient ways to understand many complicated phenomena in MHD. The recent development of the computer industry has made it possible to perform large scale computing such as massive parallel computation, yet, the full three dimensional MHD implementations are still great challege. In MHD, many efforts have been made to maintain the solenoidal magnetic constraint in many shock-capturing codes. The physical meaning of the word "solenoidal" refers to the fact that the absence of magnetic monopoles (or sources), i.e., there are no counterparts such as electric charges in magnetic fields. Numerically, however, this divergence-free phenomenon acts as a severe constraint. The goal for this project is to implement the "constrained transport" type of algorithm, which was suggested by Balsara and Spicer (see Ref. in project proposal report). The method will use the high order Godunov scheme combined with a staggered mesh algorithm on the Cartesian coordinates. Examples of classical MHD problems are "1D MHD Brio-Wu's shock tube problem" and "2D Orszag-Tang vortex problem" (see project proposal report).

  Context: This project will include numerical implementations based on the scheme by Balsara and Spicer (J. Comp. Phys., 149 (1999), pp.270-292). The method uses the staggered mesh algorithm. This can provide different collocations of the electric fields and the upwinded fluxes, which are favored by high order Godunov method. The algorithm is robust to maintain the divergence-free solenoidal magnetic field constraint, which is one of the severe constraints in terms of code implementation. The scientific validation studies will be available by comparing the project solutions with several famous 1D and 2D examples; "1D MHD Brio-Wu's shock tube problem" and "2D Orszag-Tang vortex problem". Visualization will be done using VizFlow, which is a visualization pacakage developed by Drs. G. Stanchev and A. Deane (Laboratory for Computation and Visualization, IPST, Univ. of Maryland). It allows for 2D and 3D visualization for fluid dynamics and MHD data that is adaptively refined (AMR), multi-blocked, and multi-processor.

• Aaron Lott, palott@math.umd.edu
  Project Title: 2D Spectral Element Scheme for Viscous Burgers' Equation
  Project Supervisor: Anil Deane (IPST)
  

  Abstract: I will be implementing an adaptive spectral element method using p-type refinement to solve the 1D and 2D Burgers equation. This will involve building the discretized model using spectral elements, a non-linear PDE solver, and an a posteriori error estimator to form a refinement criteria. By implementing an this algorithm, we will be able to use p-refinement of the elements to gain exponential convergence to the solution.

  Context: The Navier Stokes equations govern incompressible fluid flow. Scientists use variations of these equations to model many fluids, including the movements of the Earth's Mantle. My PhD. science application is to build a 3D adaptive spectral element method to solve the mantle convection problem. Burger's Equation contains the same nonlinearity, as the Navier Stokes equations and also is advanced in time the same way. Thus implementing an adaptive spectral element method using p-refinement to solve 2D Burgers equations can be used as a foundation to solve the 3D Navier Stokes equations.

• Scott Olsson, olsson@math.umd.edu
  Project Title: Hiearchical Probabilistic Latent Categorization for MALACH
  Project Supervisor: Doug Oard
  

  Abstract: A hierarchical probabilistic latent categorizer for co-occurrence data in the MALACH project is proposed. Assuming a probabilistic generative model for word-document co-occurrences, we may estimate the conditional probability of a document given a class by iterative maximization of its probability function; this may be done using a tempered Expectation-Maximization (EM) algorithm. Bayes' theorem then gives the posterior class probability for each class, where we expect the largest to be the document category. Such a categorizer, as well as a non-hierarchical categorizer using the k nearest neighbor algorithm (as a basis for comparison), will be developed and applied to the MALACH data set.

  Context: The MALACH (Multilingual Access to Large spoken ArCHives) is a joint collaboration between researchers at UMD, JHU, IBM and the Survivors of the Shoah Visual History Foundation (VHF), whose purpose is to "dramatically improve access to large multilingual collections of recorded speech in oral history archives."

  Transcriptions of survivor testimonies' are being produced using automatic speech recognition which must then be categorized for efficient information retrieval. This project seeks to leverage hierarchical properties of these categories (eg, Berlin is in Germany which is a location) to improve categorization.

• Achim Nonnenmacher, Anonnenmacher@gmx.de
  Project Title: MHD Applications in Aerospace
  Project Supervisor: Anil Deane (IPST)
  

  Abstract: Application of an electromagnetic field on a weakly ionized plasma flow past a blunt body and in a scramjet inlet moving at high velocity can reduce supersonic drag. These concepts will be evaluated by numerical simulation using compressible 2-D viscous electroMHD equations.

  Context: Efficient development and design of high-speed vehicles depends on the ability to reduce drag and heat transfer, and to achieve flow control in engines.

• Gustavo Rohde, rohdeg@math.umd.edu
  Project Title: Nonrigid Registration of 3D Multi-Channel Medical Images
  Project Supervisors: C. Berenstein and D. Healy
  

  Abstract: A program capable of performing automatic alignment of a series 3D of multi-channel images to a common template image is proposed. The proposed program takes as input a series of multi-channel images as well as a specified target image. On output the program shall produce a series of images that represents the series of input images properly aligned to the target image, as well as the files containing the transformations necessary to align each image.

  Context: Image registration refers to the process of identifying the spatial correspondence between different images. Registration of medical images is an important procedure in many aspects of biomedical research and clinical practice. It is a necessary step in studying the variation of biological tissue properties, such as shape and composition, described in images across a given population, among numerous other applications. Although the problem of registering a single channel (scalar) image to another single channel image has been extensively studied, the problem of registering a multi-channel (multispectral) image to another multi-channel image has been seldom considered in the biomedical engineering literature. Recently, we have proposed a methodology for performing automatic registration of multi-channel images using similarity measures based on multivariate statistics. At this time, however, the lack of an efficient implementation of these methods significantly hinders further research in the area.

• Robert Shuttleworth, rshuttle@cscamm.umd.edu
  Project Title: Block Preconditioners for the Navier-Stokes Equations
  Project Supervisor: Howard Elman (Computer Science)
  

  Abstract: The goal of this project is to implement a suite of block preconditioners for the Navier-Stokes equations. These preconditioners are based upon classical pressure correction methods, those developed by Kay, Loghin, Elman, Silvester, and Wathen (KLESW), and blends of the pressure project and KLESW methods. In turn, massively parallel preconditioners will increase the solution accuracy and the convergence rate of the iterative solvers. Therefore, this set of codes will allow scientists and engineers to pose and solve more challenging and realistic problems.

  Context: At the heart of many science and engineering problems are the solution of incompressible flows. Complex flow simulations are of great importance to many technology and national security entities. These include representatives of federal agencies such as DOE, DOD, and ARPA, and to industry. Flow simulations, which are governed by the Navier-Stokes equations, can be applied to modeling diverse areas such as combustion, pollution, chemical reactions, manufacturing, and energy research.

• Andy Tillotson, tillotwa@glue.umd.edu
  Project Title: Magnetorotational Instability in Nearly Inviscid Systems
  Project Supervisors: Dan Lathrop (Physics) and Bill Dorland (CSCAMM)
  

  Abstract: This computational project focuses on analyzing the Magnetorotational Instability (MRI) in nearly inviscid plasma flows. Through the modernizing of existing code and the generation of original code, the goal of this project is to reproduce the fundamental aspects of MRI in the linear 2D regime, validate the code by comparing with the results of popular astrophysical software, and extend the code to the full nonlinear 3D regime.

  Context: A question of considerable interest in the astrophysical community involves the mechanism of orbital energy dissipation in accretion disks. Accretion disks, like many astrophysical flows, are nearly inviscid, and consequently, it is unlikely that purely hydrodynamic turbulence could cause the dissipation required for the gas to flow onto the central object. However, when the gas is warm enough to become partially ionized, accretion disks become magnetohydrodynamic fluids. The mechanism now widely believed to be the source of the necessary turbulence and orbital decay is magnetorotational instability.

• Weigang Zhong, wzhong@math.umd.edu
  Project Title: Numerical Simulation in 2-D Martensitic Phase Transition and Microstructure
  Project Supervisor: Bo Li (CSCAMM)
  

  Abstract: Crystal is the solid whose atomic structures are determined by lattices. One type of special crystal is Martensitic crystal, which can undergo reversible, diffusionless, structural phase transformations. We call this kind of transformations are martensitic transformations. It is observed in various metals, alloys, ceramics and even biological systems. For instance, it has the role in strengthening steel. The martensitic microstructure is the fine-scale mixtures of coherent phases of martensitic crystals. A very good example of martensitic crystal is some shape-memory alloys.

  Context: I am interested in the martensitic microstructure produced in the continuum transformation, in which the high temperature austenite phase transforms to the low-temperature martensite phase. Specifically I will investigate the 2-D vectorial problem with surface energy, in which the situation along the interface will be considered. The well-known two-well problem with different choices of energy density functions will be simulated in my project. My program will be open to other properly defined energy density functions by simply changing the function definition. Both numerical solutions and graphs will be given as results.

  In mathematics, it is an energy minimization problem. I will use finite element deformations of the domain, and use conjugate gradient method to do the minimization. Some improvements will be done in the computation like preconditioning. Parallelism will be applied in my project.