Mathematical and Computer Sciences and Engineering Division
Seminars
Spring 2010
May 15:
Dr. George Turkiyyah – American University of Beirut
Real Time Finite Modeling for High Fidelity Surgical Simulation
Nonlinear multigrid algorithms are discussed in the context of fully implicit compressible resistive magnetohydrodynamics (MHD) simulations. F-cycle multigrid methods can reduce the algebraic error
of the (non)linear equations of discretized PDEs to the order of the discretization error in one iteration, thereby allowing for minimal work per time step (the equivalent of about 10 residual calculations).
May 8:
Dr. Mark Adams – Columbia University
Nonlinear multigrid methods for fully implicit resistive magnetohydrodynamics simulations
As part of this seminar, Dr. Mark Adams presents a haptic simulator that allows users to interact with a virtual model of a 3D anatomy to practice and rehearse surgical procedures. Multi-handed control allows the user to operate on the model, feel the forces involved in performing a procedure, and see 3D stereoscopic deformations superposed on the stresses induced by the operations. The simulator allows cutting through skin and tissue, undermining skin to separate it from the subcutaneous soft tissue, addition of sutures to close wounds, and manipulation using multiple surgical instruments.
In this seminar, Dr. Mark Adams will describe scalable methods for representing and computing, at haptic rates, the general deformation of a nonlinear finite element model whose topology and geometry are being dynamically modified. Cuts, closures, reconnections can be introduced dynamically, in general position, without preprocessing, nor local remeshing. The methods rely on progressively updating the finite element solution space with discontinuous basis functions evolving with the cuts, and on corresponding fast incremental methods specialized to the structure of the basis update to handle the computations involved. A hierarchical representation of the stiffness matrix allows us to tame model complexity and consciously trade performance and accuracy even at run-time.
May 2:
Dr. Jack J. Dongarra - University of Tennessee, Knoxville
Five Important Concepts to Consider When Using High Performance Systems at Scale
In this talk, Dr. Jack Dongarra examines how high performance computing has changed over the last decade and look toward the future in terms of trends. These changes have had and will continue to have a major impact on our software. Some of the software and algorithm challenges have already been encountered, such as management of communication and memory hierarchies through a combination of compile-time and run-time techniques, but the increased scale of computation, depth of memory hierarchies, range of latencies, and increased run-time environment variability will make these problems much harder. Dr. Dongarra will examine five areas of research that will have an importance impact in the development of software.
April 27:
Dr. Liangjun Zhang – Stanford University
Efficient Motion Planning Algorithms and Their Applications
The current generation of petascale machines has allowed high-fidelity simulations in many application domains. However, as we refine the resolution in a single physics domain, the error introduced in the input parameters or boundary conditions by neglecting the multiphysics coupling becomes significant. The future petacscale and exascale platforms will allow coupled multiphysics simulations in high fidelity. This talk will describe a motivating application in neutron transport and present the architectural and algorithmic challenges encountered in these simulations on the fastest machines available today. When the seven-dimensional neutron transport equation is discretized, several large-scale linear systems need to be solved. The presentation will discuss a scalable solution methodology (using PETSc library) for the discrete ordinates, even-parity form of the neutron transport equation for complex geometric configurations.
April 24:
Dinesh Kaushik - KAUST,
Computational Challenges in Coupled High-fidelity Multiphysics Simulations of Particle Transport
The current generation of petascale machines has allowed high-fidelity simulations in many application domains. However, as we refine the resolution in a single physics domain, the error introduced in the input parameters or boundary conditions by neglecting the multiphysics coupling becomes significant. The future petacscale and exascale platforms will allow coupled multiphysics simulations in high fidelity. This talk will describe a motivating application in neutron transport and present the architectural and algorithmic challenges encountered in these simulations on the fastest machines available today. When the seven-dimensional neutron transport equation is discretized, several large-scale linear systems need to be solved. The presentation will discuss a scalable solution methodology (using PETSc library) for the discrete ordinates, even-parity form of the neutron transport equation for complex geometric configurations.
April 10:
Dr. Aslan Kasimov - KAUST
Problems in shock dynamics: from traffic jams to black holes
The talk is an overview of several phenomena in shock dynamics that can be described by a special class of hyperbolic systems with source terms. They range from continuum models of traffic flow, to hydraulic jumps, to detonation waves. In all cases, a phenomenon involves a shock wave followed by a transonic flow where both the shock path and the location of the sonic point are unknown thus making it a free-boundary problem with two free boundaries. Mathematically, the similarity of the phenomena is reflected in the singular structure of the underlying hyperbolic systems and the existence of a sonic locus which plays a role similar to that of a black-hole event horizon. Dr. Kasimov will highlight common issues in understanding them from experimental, mathematical, and computational points of view.
March 21
Dr. Gilbert Strang, MIT
Teaching and Learning Computational Science and Engineering
In this seminar, Dr. Gilbert Strang will discuss the future of computational science and engineering. Each lecture discusses a model problem and a code to solve it. This MIT course is popular with engineering students and their departments, who want exposure to ideas and also to software (especially MATLAB).
The main sections of the course are Applied Linear Algebra, Differential Equations, Finite Differences and Finite Elements, Fourier Methods, Analytical Methods, Large Sparse Systems, and Optimization. The starting point is to understand the second difference matrices (entries 1, -2, 1) that appear everywhere in scientific computing and simulation. Linear algebra is crucial!
The need to move beyond the older courses in engineering mathematics, and connect directly to computing, is widely recognized. A pure software course misses the foundations for understanding new problems. The combination of analysis with computational science and engineering is powerful.
March 13:
Dr. Ibrahim Hoteit - KAUST
Kalman-Based Filters for Analyzing and Predicting the State of Large Dimensional Nonlinear Systems
This talk will give an overview of the Bayesian-based filtering methods that combine model outputs with data in order to determine the best possible estimate of the state of the system under study. This is an active area of research with many applications in weather, ocean and climate sciences, and more recently in reservoir engineering. The derivation of these methods from the Kalman filter approach and the nonlinear filtering theory will be presented. New directions and applications will be also discussed. An example of application of filtering methods for predicting the evolution of the loop current in the Gulf of Mexico to support oil industry operations will be presented.
March 6:
Dr. Marco Di Francesco - University of L'Aquila
Transport PDE's in social and biological aggregation phenomena
Partial differential equations of transport type arise very often in the study of social and biological aggregation phenomena. I will present models featuring a certain number of interacting "individuals", the movement of which is driven by diffusion (of linear and nonlinear type), transport due to external forces, transport due to "nonlocal" binary interaction with all the other individuals, possible interactions with a surrounding environment (e.g. an incompressible fluid). Our study is mostly related with the mathematical (analytical) theory of (systems of) partial differential equations obtained in the limit as the number of individuals is very large. In many of these situations, a rigorous proof of the existence of a global solution is non trivial. In some of them, solutions may become "unbounded" as a consequence of the density of a certain family of individuals "concentrating" to a Dirac's delta measure. I will describe my studies on the qualitative and asymptotic (large time) behaviour of solutions as well. The presented work is in collaboration with the applied PDE group at DAMTP in Cambridge. Dr. Di Francesco will also give an overview of previous results in this field.
February 27:
Jed Pitera – IBM
Smart computers, smarter molecules
Many of the challenges facing the world today (energy, transportation, water, environment, and heath) require new materials with novel or tailored properties (solar cells, batteries, membranes, catalysts, and pharmaceuticals). To address these challenges, physical scientists and engineers will need to design and control the properties of materials at the nanoscale (~10^-9 meters, the size of a few atoms). While the physical forces that act at this scale are well understood, they are often complex and counter-intuitive. Computer simulations provide an essential tool to help us interpret experiments and develop insights into this new world. These simulations rely on advances in high performance computing (HPC) systems to enable faster, more realistic, and more predictive results. At present, however, the HPC field is in flux, with a wealth of new architectures (embedded systems, hardware accelerators, custom systems, clouds) promising significant performance or power-efficiency improvements for specific classes of problems. In this talk, Jed Pitera will discuss how these changes in HPC systems may impact the practice of computational science, illustrated with examples from computational biology and materials research at IBM
February 23:
Dr. Alyn Rockwood
Geometric Algebra and the Conformal Space
An introduction to Geometric Algebra (GA) is presented, including its unifying nature in mathematics. GA subsumes, for examples: complex analysis, vector algebra, quaternions, crystallographic space groups, exterior and simplectic algebras into one algebraic system. By so doing, it minimizes the need for translations and redundant learning. Many useful applications have been developed, such as in inverse kinematics, motion capture, animation, elastic bending and cosmology. It is becoming an increasingly popular system for computer graphics, CV, robotics, astrophysics and mechanics, to name a few. One elucidated example within in the structure of GA is a 5 dimensional space, called the Conformal Space, because it linearizes the conformal group. A quadratic map from 3D GA is defined by translating both the origin and the point of infinity into a 5D space, much as affine space translates the origin into 4D space and linearizes affine transformations. Possible applications in Geophysics will be discussed.
February 15:
Dr. Jean-Claude Latombe – Stanford University
Motion planning for multi-limbed robots on uneven terrain (Host: Moshkov)
In this talk, Jean-Claude Latombe will describe the problem of planning the trajectory of a multi-limbed robot over a given terrain and I will present a planner that first selects a sequence of contacts (hence, a sequence of feasible spaces) and then searches for a sub-trajectory in each space using a Probabilistic Road Map (PRM) planning method. One key issue faced by this planner is to assess the existence of a feasible sub-trajectory very quickly in order to avoid wasting time on infeasible sequences of contacts. Dr. Latombe will show experimental results on two 4-limbed rock-climbing robots, and simulation results on a humanoid robot (that can use its hands to achieve equilibrium) and a 6-legged lunar vehicle. Our tests have revealed that the connectivity of the feasible spaces may vary greatly between robots. This surprising observation has major impact on the heuristics that may be used to speedup planning.