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Tsunami Modeling with Accelerated Graphics Board (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

OutlineIntroduction to Tsunamis and Tsunami Modeling 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

David

Erik

Spring

Yaolin

OutlineBackground related to tsunamis Data Visualization_Amira applied in tsunami simulation Potential Tsunami Hazard along Chinese Coast

Background

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

Tsunami or Harbour Wave

A Japanese word represented by two characters: tsu & nami tsu means harbour & nami means wave

Tsunami Definition & Causes

Scientific term? Tsunami ? Seismic sea waves ? Tidal waves

Basic Concept

Wave in the OceanWaves are the undulatory motion of a water surface.

Parts of a wave are, Wave crest, Wave trough, Wave height (H), Wave Amplitude, Wave length (L),and Wave period (T). Wave period provides a basis for the wave classifications: Capillary waves, Chop, Swell, Tsunamis, Seiches.

Wave types

Wave in the Ocean

Most of the waves present on the oceans surface are wind-generated waves.

Size and type of wind-generated waves are controlled by: Wind velocity, Wind duration, Fetch, and Original state of sea surface.

Wave Properties

7-3

Wave in the Ocean

The shallower the water, the greater the interaction between the wave and the bottom alters the wave properties, eventually causing the wave to collapse.

SPEED decreases as depth decreases. Wave length decreases as depth decreases. Wave height increases as depth decreases. Refraction is the bending of a wave into an area where it travels more slowly.

Wave Properties

Wave in the Ocean

7-5

TsunamiTsunamis 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.

Tsunami Source (1)

Tsunami Source (2)

Tsunami Source (3)

Background

Numerical Tsunami Modeling

Tsunami Sources in the world (2180 events from 1628BC to 2005)

Background

Seismic Tsunami Modelling

Killer Tsunamis in Historical Times

Background

Numerical Tsunami Modelling Global Earthquakes Distribution

90% earthquakes happened along Pacific Ocean belt 80% earthquakes induced tsunami happened along arc-channel of the Pacific Ocean plate

General Tsunami ModellingPhysical Analysis Numerical Simulation Visualization Results Analysis

1 2 3

4

Displacement Field (initial Condition) Propagation (Linear and Nonlinear model) Run-up

Seismic Tsunami Modelling

Seismic Tsunami Modelling

1 Analyze the phenomenon 2 Choose Coordinates 3 Choose the equations

Navier-Stokes Equations System Boussinesq Equations Shallow Water Equations

(Local and Far-field)

4 solution of grid

Etopo1, Etopo2, Strm30, or local bathymetry data

5 Boundary and initial conditions

The initial wave( From earthquake)

6 Visualization 7Analysis results

Satellite data or tidal data

Generation, Propagation, and Run-up of Tsunamis

Generation

Propagation

Run-up/down

dispersion effect

nonlinear effect

Existing Tsunami Models

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

Data Visualization __ Amira

Load Topography Background

Movie Maker

Highlight of Visualization with Amira 3

This figure shows the height field with a scaled height.

Wave Propagation Visualization of Tsunami ModelingEastern China Sea

Wave Propagation Visualization of Tsunami ModelingSolomon Islands

Wave Propagation Comparison of Linear and Nonlinear Modeling

Different Bathymetry Resolution Comparison of Nonlinear Modeling on Shallow Part of the Ocean Part

Grids: 1201*1201

601*601

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

Linear

Linear Shallow Water Equations Applied in SCS

Nonlienar

Linear

Nonlinear

Linear and Nonlinear Model in Yellow Sea Area

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

Tsunami Simulation with GPU Programming

Jessica Schmidt Undergraduate summer intern

Overview

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

Viable set-up for real-time tsunami visualizationBy Jessica

Earthqua ke

Tsunami Simulation with GPU Programming Real Tsunami Visualization (Interface Window) Tsunami Warning

Seismology

Tsuna mi

Bathymetric Data

By Erik

GPUGraphics 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 CPUComputes many complex math problems Faster graphics processing speed Increased detailed and complexity without

CUDACompute Unified Device Architecture Developed by NVIDIA Based on CBenefits

Drawbacks

Takes load off CPU Easy to learn and implement

Difficult to find video card , MAC is cooler for this .

GPU Specs.GPU Core clock (MHz) Shader clock (MHz) Memory Amount (MB) Memory Interface Memory bandwidth (GB/s) GeForce 8600M GeForce 8800 GT Ultra 540 1190 256 128-bit 22.4 612 1500 1080 768 384-bit 103.7

Memory clock (MHz) 700

There Fill other Texture are Rate GPUs that work with CUDA as well. 8.64 39.2 - NVIDIA GeForce 8000 and above (billion/sec) - NVIDIA Quadro, DELUXE MODEL - NVIDIA Tesla

Jessicas Job This SummerCovert linear tsunami codesSpring Liu ----second Finite Difference Method Cecile Piret ---- Radial Basis Function (RBF)

Implement CUDA for Springs and Ceciles linear codes, then see if there is speedup

2-D Shallow Water EquationsLinear Non-Linearz M N + + =0 t x y M M 2 MN z x + ( )+ ( ) + gD + = 0 t x D y D x M MN N2 z y + ( ) + ( ) + gD + = 0 t x D y D y D = total water depth, D = z + h = density x, y = shear stress along x and y axis

z M N + =0 + x y t M z + gD =0 t x N z =0 + gD t y

M, N = mass fluxes in horizontal plane z = wave height t = time h = ocean water depth

athymetric Data: Etopo1

arameters of Rupture: rom HARVARD Database , Miyaki Ishii

isualization: Amira

An Introduction

Radial Basis Functions (RBF) Method

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.

Given scattered data The RBF Define the RBFinterpolant

method

Given scattered data The RBF Define the RBFinterpolant

method

Given scattered data The RBF Define the RBFinterpolant Find by solving the system

method

The RBF methodCoding the RBF method is fast and easyRBF part of the code

The RBF method

+

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 RBF