Approaching the Challenge of GridEnabling Applications

1
Approaching the Challenge of Grid-Enabling
Applications

• Kieran Nolan
• May 15th, 2008

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Agenda

• Challenges to Consider
• About Grid Enabling
• Background on Level-Set Methods
• An Approach to Grid Enabling
• Summary
• Discussion Q/A

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Challenges to consider

• From the July 2007 final report to the NSF on
  Cyber Fluid Dynamics
• Although large-scale computing has brought many
  advances to the field, expertise for scaling
  codes effectively to possibly hundreds of
  thousands of processors is not widely available,
  especially for flows with multiphysics content
  where the mathematical foundations of the subject
  often cause difficulties often not widely
  appreciated by practitioners in other
  disciplines.
• most in the community do not see a clear path
  to mechanisms for open-source code development or
  efficient handling of large datasets which are
  essential for wide participation.

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About Grid Enabling

• What Does it Mean to Grid Enable?
• Why Consider Grid Enabling?
• What Makes This a Challenge?
• What Approaches Exist?

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What Does it Mean to Grid Enable?

• Grid Enabling refers to the adaptation or
  development of a program to provide the
  capability of interfacing with a grid middleware
  in order to schedule and utilize resources from a
  dynamic and distributed pool of grid resources
  in a manner that effectively meets the programs
  needs

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Why Consider Grid Enabling?

• Utilize resources available through the grid
  environment
• Avoid (or minimize) purchasing high-end computing
  hardware
• Leverage underutilized resources in an enterprise
• Optimize usage of expensive resources (hardware
  software)
• Most applications can be adapted to run in a grid
  environment with varying benefits
• i.e. some problems benefit from performance
  improvement, while others seek access to scarce
  resources
• The most ideal problems tend to possess these
  characteristics
• Highly parallelizable algorithms
• Highly cohesive, lightly coupled algorithms
• Computational extensive algorithms

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What Makes Grid Enabling a Challenge?

• Different challenges present themselves depending
  on whether the program to grid enable is a COTS
  or home-grown product
• COTS must design around program limitations
• Home-grown must design to a grid application
  programming interface
• Common Challenges
• Standards for grid technologies
• Software licensing issues
• Network bandwidth requirements
• Complications with horizontal business
  integration
• Security concerns

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How to Approach Grid Enabling?

• Considerations on approach taken
• Type of infrastructure being utilized
• Cluster based solutions (consider departmental
  grids)
• Enterprise grid solutions
• Global grid solutions
• Type of application
• COTS
• Custom development
• Profile of application
• Computationally demanding
• Data intensive
• Desired result
• Performance improvement
• Schedule to complete
• Usage of specialized resource(s)

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Background on Level-Set Methods

• Why Grid Enable Level-Set Methods?
• Background on Level-Set Methods
• Decomposition of Level-Set Methods
• Computational Challenges in Level-Set Methods
• Numerical Methods for PDEs
• Sample Problems

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Why Grid Enable Level-Set Methods?

• Problem Need to simulate dynamic implicit
  surfaces and time-dependent partial differential
  equations
• How this is accomplished Complex level-set based
  algorithms that require extensive computational
  power for even relatively simple scenarios
• Challenge How can level-set methods be adapted
  to effectively leverage the distributed nature of
  resources available through a grid environment?

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Background on Level-Set Methods

• What are level-set methods?
• Numerical methods used for solving a class of
  partial differential equations (PDEs)
  Hamilton-Jacobi (HJ) PDEs
• Implicitly represent surfaces using a level-set
  function
• A wide array of surface motions can be
  accommodated
• Allow evolution of interfaces as a zero level-set
  function of a time-dependent function
• Where are level-set methods used?
• Useful when front-capturing techniques are more
  suitable than front-tracking or when complex
  motion is being modeled
• Many applications exist for level-set methods,
  including
• Image processing
• Graphics
• Fluid dynamics

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Decomposition of Level-Set Methods

• Requires manipulation of 3-D grid spaces, similar
  to that shown on the right
• Extensive use of matrix operations
• High order accuracy requires high resolution (?x,
  ?y) grids and fine time steps (?t)

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Computational Challenges in Level-Set Methods

• Partial Derivative Calculations (PDEs)
• Laplacian Calculations
• Signed Distance Function (SDF)
• Fast Marching Methods, Re-Initialization
• Calculation of Normals, Gradients, Curvatures,
  and Directional Derivatives
• Velocity and External Flows

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Numerical Methods for PDEs

• Methods available for use in solving the
  advection problems include
• The Simple Upwind Method
• Essentially Non-Oscillatory Method (ENO)
• Based on Newtons divided differences method
• Offers up to third order spatial accuracy
• Weighted Essentially Non-Oscillatory Method
  (WENO)
• Enhances accuracy of the ENO method
• Offers up to fifth order spatial accuracy
• Total Variation Diminishing Runge-Kutta (TVD RK)
• Higher order accuracy through temporal
  discretization
• Offers up to third degree temporal accuracy

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Sample Level-Set Problems

• Following are two examples of level-set methods

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Level-Set Methods 1-D Advection Example

• Problem Statement (hat problem)
• One dimensional advection problem
• Domain -2 lt x lt 7, subject to the condition that

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1-D Advection Example Graphical Solution

• The following graphic is the output of the hat
  problem at final time T 5 using all TVD RK
  techniques and all ENOs/WENO

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Level-Set Methods 2-D Advection Example

• Implement a two-dimensional motion due to
  external flow fields as done in the Sun,
  Beckermann paper
• Using an initial level-set function as described
  by
• Started with a simple 2-D advection without the
  right-hand side to show that it can be moved
  effectively with

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2-D Advection Example Graphical Solution

• Implemented using the 5th order WENO with the
  right-hand side included over a 160x160 grid on x
  ? 0,1 and y ? 0,1.

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An Approach to Grid Enabling

• Characterization of Grid Enabling Level-Set
  Methods
• How to Approach this Problem?
• About the Grid Enabled Level-Set Solution
• Simulation of the Grid Environment

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Characterization of Grid Enabling Level-Set
Methods

• Type of infrastructure to utilize
• Enterprise grid solutions
• Type of application
• Custom application
• Profile of application
• Computationally demanding with data
  considerations
• Desired result
• Performance improvement

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How to Approach this Problem?

• Grid Environment
• Identify the necessary components of the grid
  environment
• Architect the experimental grid environment
• Identify and understand potential approaches for
  scheduling and executing on the grid environment
• Develop a method to simulate the described
  environment
• Level-Set Methods
• Understand detailed mechanics behind level-set
  methods
• Adapt algorithms to execute on grid environment
• Execute representative set of problems on grid
  simulation environment
• Identify best-fit approach from possible
  candidates
• Explanation of appropriateness of chosen
  scheduling approach to dynamics of the level-set
  mechanics

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About the Grid Enabled Level-Set Solution

• Three major components to consider
• How does the algorithm interface with the grid?
• How do we simulate the grid infrastructure?
• How do we effectively schedule across grid
  resources?

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Simulation of the Grid Environment

• A key element of the grid enabling approach used
  for level-set methods includes simulating the
  grid environment
• Multiple grid simulation tools exist
• GridSim
• http//www.gridbus.org/gridsim/
• MicroGrid
• http//www-csag.ucsd.edu/projects/grid/microgrid.h
  tml
• SimGrid
• http//simgrid.gforge.inria.fr/
• Bricks
• http//ninf.apgrid.org/bricks/

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Summary

• Grid enabling an application...
• allows it to leverage grid resources
• may depend on its type and profile
• presents many potential benefits
• The approach to grid enabling level-set methods
• seeks to leverage grid resources to reduce
  overall run-time
• seeks to identify the most suitable scheduling
  approach based on simulation of resources and
  application profile
• Grid Simulation
• allows for testing various grid configurations
• allows for testing various scheduling approaches
• allows for profiling the execution and
  communication overheads

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Discussion Q/A

• Questions?
• Comments?
• Discussion topics?