Approaching the Challenge of Grid- Enabling Applications Kieran Nolan May 15 th, 2008

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

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.

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

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 program’s needs

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

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

How to Approach Grid Enabling? Considerations on approach taken… 1. Type of infrastructure being utilized Cluster based solutions (consider departmental grids) Enterprise grid solutions Global grid solutions 2. Type of application COTS Custom development 3. Profile of application Computationally demanding Data intensive 4. Desired result Performance improvement Schedule to complete Usage of specialized resource(s)

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

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?

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

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) Level-Set Problem GradientLaplacian Derivatives Signed Distance Function

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

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 Newton’s 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

Sample Level-Set Problems Following are two examples of level-set methods

Level-Set Methods: 1-D Advection Example Problem Statement (“hat” problem): One dimensional advection problem: Domain -2 < x < 7, subject to the condition that:

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:

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:

2-D Advection Example: Graphical Solution Implemented using the 5 th order WENO with the right-hand side included over a 160x160 grid on x  [0,1] and y  [0,1].

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

Characterization of Grid Enabling Level-Set Methods 1. Type of infrastructure to utilize Enterprise grid solutions 2. Type of application Custom application 3. Profile of application Computationally demanding with data considerations 4. Desired result Performance improvement

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

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? Computational Resources Grid Application Interface Interface to grid Scheduling Simulation Level-Set Problem GradientLaplacian Derivatives Signed Distance Function

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 MicroGrid SimGrid Bricks

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

Discussion & Q/A Questions? Comments? Discussion topics?