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Tsunami Modeling with Graphics Processing Unit (GPU) and Radial Basis Functions (RDF)

Tsunami Modeling with Graphics Processing Unit (GPU) and Radial Basis Functions (RDF). DAVID A. YUEN  Minnesota Supercomputing Institute,University of Minnesota, Minnesota JESSICA SCHMIDT Saint Scholastica College, Duluth, Minnesota ERIK O.D. SEVRE

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Tsunami Modeling with Graphics Processing Unit (GPU) and Radial Basis Functions (RDF)

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  1. Tsunami Modeling with Graphics Processing Unit (GPU) and Radial Basis Functions (RDF) DAVID A. YUEN  Minnesota Supercomputing Institute,University of Minnesota, Minnesota JESSICA SCHMIDT Saint Scholastica College, Duluth, Minnesota ERIK O.D. SEVRE Minnesota Supercomputing Institute University of Minnesota, Minnesota NAN ZHANG Medical School, University of Minnesota Minnesota GRADY B. WRIGHT Dept. of Mathematics , Boise State University, Boise, Idaho JESSICA SCHMIDT Saint Scholastica College, Duluth, Minnesota CECIL PIRET Institute of Applied Mathematics for Geosciences, National Center of Atmospheric Research, Boulder, Colorado SPRING LIU Minnesota Supercomputing Institute University of Minnesota, Minnesota NATASHA FLYER Institute of Applied Mathematics for Geosciences, National Center for Atmospheric Research, Boulder, Colorado

  2. Outline • Introduction to Tsunamis and Tsunami Modeling • Visualization of tsunamis with Amira visualization package • Virtues of  Graphics Accelerated Board (GPU) • Applications of GPU to Shallow-Water equations • Radial Basis Functions (RBF) Swirling Flows • Applications of GPU to RBF equations • Concluding Remarks

  3. Background

  4. What is a Tsunami? (soo-NAH-mee)

  5. Tsunami Definition & Causes

  6. Most of the waves present on the ocean’s surface are wind-generated waves. Wave types Wave in the Ocean Size and type of wind-generated waves are controlled by: Wind velocity, Wind duration, Fetch, and Original state of sea surface.

  7. Tsunamis consist of a series of long-period waves characterized by very long wave length (up to 100 km) and high speed (up to 760 km/hr) in the deep ocean. Because of their large wave length, tsunamis are shallow-water to intermediate-water waves as they travel across the ocean basin. They only become DANGEROUS, when reaching coastal areas where wave height can reach 10 m. Tsunamis originate from earthquakes, volcanic explosions, or submarine landslides. 7-5 Tsunami

  8. Tsunami Source (1)

  9. Tsunami Source (2)

  10. Tsunami Source (3)

  11. Background Numerical Tsunami Modeling Tsunami Sources in the world (2180 events from 1628BC to 2005)

  12. Background Seismic Tsunami Modelling Killer Tsunamis in Historical Times

  13. General Tsunami Modelling Displacement Field (initial Condition) Propagation (Linear and Nonlinear model) Run-up 1 Physical Analysis 2Numerical Simulation 3 Visualization 4 Result Analysis and Digestion

  14. Seismic Tsunami Modelling Navier-Stokes Equations System Boussinesq Equations Shallow Water Equations Seismic Tsunami Modelling 1 Analyze the phenomenon (Local and Far-field) 2 Choose Coordinates 3 Choose the equations 4 solution of grid Etopo1, Etopo2, Strm30, or local bathymetry data The initial wave( From earthquake) 5 Boundary and initial conditions 6 Visualization Satellite data or tidal data 7Analysis results

  15. Generation, Propagation, and Run-up of Tsunamis

  16. Existing Tsunami Models

  17. Introduction of Amira Amira is a powerful, multifaceted software platform for visualizing, manipulating, and understanding scientific data coming from a all types of sources and modalities. Multi purpose - One tool for interdisciplinary work Flexible - Option packages to configure amira to your needs Efficient - Exploits latest graphics cards and processors Easy to use - Intuitive user interface and great documentation Cost effective - Multiple options and flexible license models Handling large data - Very large data sets are easily accessible with specific readers Extensible - C++ coding wizard for technical extension and customization Support - Customer direct support with high level of interaction Innovative - Technology always up dated to the latest innovation

  18. Data Visualization __ Amira

  19. Load Topography Background

  20. Movie Maker

  21. Highlight of Visualization with Amira 3 This figure shows the height field with a scaled height.

  22. Wave Propagation Visualization of Tsunami Modeling- Eastern China Sea

  23. Wave Propagation Visualization of Tsunami Modeling- Solomon Islands

  24. Wave Propagation Comparison of Linear and Nonlinear Modeling

  25. Different Bathymetry Resolution Comparison of Nonlinear Modeling on Shallow Part of the Ocean Part Grids: 1201*1201 601*601

  26. Conclusion (1)   Visualization promotes a rapid understanding of the waves'  paths from initial stages ; influences from the initial surroundings(2)   Visualization Allows us to understand better the subsequent events when the waves are interacting with the coastline and off-shore islands(3)   Visualization  Helps to teach people about wave propagation for local and regional scenarios

  27. Linear and Nonlinear Model in Yellow Sea Area

  28. TSUNAMI SIMULATION WITH GPU PROGRAMMING JESSICA SCHMIDT from computer science and mathematics UNDERGRADUATE SUMMER INTERN

  29. Jessica Schmidt Undergraduate summer intern Tsunami Simulation with GPU Programming

  30. Overview • Why we do this project? • GPU with CUDA programming • Tsunami Simulation with CUDA • RBF ( RADIAL BASIS FUNCTIONS ) Summary • What does the future hold?

  31. Viable set-up for real-time tsunami visualization By Jessica Seismology Tsunami Simulation with GPU Programming Earthquake Real Tsunami Visualization (Interface Window) Bathymetric Data Tsunami By Erik Tsunami Warning

  32. GPU • Graphics Processing Unit • Much faster than CPU now • Getting more expensive, can easily now • Outstrip the cost of a laptop itself • Takes the load off of the CPU • Computes many complex math problems • Faster graphics processing speed • Increased detailed and complexity without compromising performance

  33. CUDA Benefits Drawbacks • Compute Unified Device Architecture • Developed by NVIDIA • Based on C Takes load off CPU Easy to learn and implement Difficult to find video card , MAC is cooler for this .

  34. GPU Specs. • There are other GPUs that work with CUDA as well. • NVIDIA GeForce 8000 and above • NVIDIA Quadro, DELUXE MODEL • NVIDIA Tesla

  35. Jessica’s Job This Summer • Covert linear tsunami codes • Spring Liu ----second Finite Difference Method • Cecile Piret ---- Radial Basis Function (RBF) • Implement CUDA for Spring’s and Cecile’s linear codes, then see if there is speedup

  36. 2-DShallowWaterEquations Linear Non-Linear M, N = mass fluxes in horizontal plane z = wave height t = time h = ocean water depth D = total water depth, D = z + h ρ = density τx, τy = shear stress along x and y axis

  37. Flow Chart: Bathymetric Data: Etopo1 Parameters of Rupture: From HARVARD Database , Miyaki Ishii Visualization: Amira

  38. Radial Basis Functions (RBF) Method An Introduction

  39. The RBF method 70s Rolland Hardy introduces a new method for scattered data interpolation for geological data, the MQ method, so named for its use as basis of the multi-quadric function. First published in JGR 70s-80s The method is generalized to more radial functions. It is renamed the “Radial Basis Functions (or RBF) method”. 90s Ed Kansa from UC Davis uses the RBF method to solve partial differential equations.

  40. The RBF method • Given scattered data • Define the RBF interpolant

  41. The RBF method • Given scattered data • Define the RBF interpolant

  42. The RBF method • Given scattered data • Define the RBF interpolant • Find by solving the system

  43. The RBF method Coding the RBF method is fast and easy RBF part of the code

  44. + Interpolation on scattered data. No grid necessary. Very easy implementation in N-dimensions. The basis functions are not orthogonal with each other, but we are guaranteed a non-singular system for most types of RBFs. Spectral accuracy for infinitely smooth radial functions - High complexity. No fast algorithm. The RBF method

  45. Radial Basis Functions (RBF)--- Cecile • Interpolating data takes the form: • Use RBFs to model 2-D linear waves • Cecile Piret wrote simulations using Matlab • Convert to GPU using Jacket – developed by Accelereyes

  46. The comparison of GPU and CPU ------- Linear Tsunami Codes Spring’s linear tsunami code (21600 time steps) Cecile’s linear tsunami code (400 time steps) Lilli – an opteron-based system with 4 CPUs GPU – nVIDIA 8600M GT graphics card Laptop – standard MacBook Pro

  47. Results for Tsunami Simulation beginning of simulation middle of simulation Simulation Movie

  48. Comparison

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