Introduction to Computational Science (aka Scientific Computing)

Transcription

1 (aka Scientific Computing) Xianyi Zeng Department of Mathematical Sciences The University of Texas at El Paso. August 23, 2016.

2 Acknowledgement Dr. Shirley Moore for setting up a high standard of the quality of this course and sharing her previous course materials. Dr. Victor Eijkhout for sharing his excellent textbook online. Eli Etherton for his introction to Linux: https: // www. youtube. com/ watch? v= _gcwcohmcog

3 Definition Computational science is an interdisciplinary field in which realistic mathematical models combined with scientific computing methods are used to study systems of real-world scientific or societal interest. The 2005 Report to the President, Computational Science: Ensuring America s Competitiveness, states that: the most scientifically important and economically promising research frontiers in the 21st century will be conquered by those most skilled with advanced computing technologies and computational science applications.

4 Computation has established itself as the third facet of modern science. Computational science involves the appropriate use of a computational architecture to apply an algorithm, or method, to solve a scientific application, or problem. The combination of Application, Algorithm, and Architecture results in a Model.

5 Simulation: The third facet of science Traditional scientific and engineering paradigm: Do theory or paper design. Perform experiments or build system. Limitations: Too difficult e.g., building large wind tunnels. Too expensive e.g., building a throw-away passenger jet. Too slow e.g., wait for climate change or tectonic evolution. Too dangerous e.g., weapons, drug design, climate experimentation. Computational science paradigm: Use high performance computer systems to simulate the phenomenon. Base model on physical laws and efficient numerical methods.

6 What do computational scientists do? Combine scientific programming and mathematical skills with knowledge of application fields to computationally model systems of interest. Mathematical and programming skills: calculus, linear algebra, differential equations, statistics. simulation methods, parallel computing, scientific computing libraries and tools, visualization.

7 Introduction to Computational Science Example 1: Aircraft design F-117 (1981) F-35A (2006) Source: wikipedia.org Numerical simulations in the aviation industry: Shorten design cycle and reduce cost. Enable 3D full-aircraft design optimization. Move from an exploration tool to a full flight physics production capability.

8 Example 1: Aircraft design 2010 use of CFD at Airbus. Adel Abbas-Bayoumi and Klaus Becker, An industrial view on numerical simulation for aircraft aerodynamic design, Journal of Mathematics in Industry, (2011) 1:10.

9 Example 2: Movie industry Numerical simulation in the modern visual effects: Physics-based simulations. Geometric modeling and computer vision. Realize scientific fiction scenes. Reduce film-making budget. PhysBAM: Ron Fedkiw (two-time Academy Award winner). Lighthouse (coupled SPH and LSM fluid simulation). Burning solids into fluids. A collection of PhysBAM videos.

10 Example 3: Protein folding Source: wikipedia.org The physical process by which a protein chain acquires its native 3D structure. Very important application in non-conventional drug design. Experiments and numerical simulation greatly complement each other. Involve simple equations but very intense computations.

11 Supercomputers See a current list of the world s fastest at: Strategic importance of supercomputing Essential for scientific discovery. Critical for national security. Fundamental contributor to the economy and competitativeness through use in engineering and manufacturing. Supercomputers are tools for solving the most challenging scientific problems through large-scale simulations.

12 Units of measure High Performance Computing (HPC) units are: Flop: floating point operation, usually double precision unless noted. Flop/s: floating point operations per second. Bytes: size of data (a double precision floating point number is 8). Typical sizes are millions, billions, trillions... Mega Mflop/s = 10 6 flop/sec Mbyte = 2 20 = bytes Gega Gflop/s = 10 9 flop/sec Gbyte = bytes Tera Tflop/s = flop/sec Tbyte = bytes Pera Pflop/s = flop/sec Pbyte = bytes Exa Eflop/s = flop/sec Ebyte = bytes Zetta Zflop/s = flop/sec Zbyte = bytes Yotta Yflop/s = flop/sec Ybyte = bytes Current fastest (public) machine 93 Pflop/s. (As of November 2015, the fastest machine was 33.9 Pflop/s.)

13 Units of measure High Performance Computing (HPC) units are: Flop: floating point operation, usually double precision unless noted. Flop/s: floating point operations per second. Bytes: size of data (a double precision floating point number is 8). Typical sizes are millions, billions, trillions... Mega Mflop/s = 10 6 flop/sec Mbyte = 2 20 = bytes Gega Gflop/s = 10 9 flop/sec Gbyte = bytes Tera Tflop/s = flop/sec Tbyte = bytes Pera Pflop/s = flop/sec Pbyte = bytes Exa Eflop/s = flop/sec Ebyte = bytes Zetta Zflop/s = flop/sec Zbyte = bytes Yotta Yflop/s = flop/sec Ybyte = bytes Current fastest (public) machine 93 Pflop/s. (As of November 2015, the fastest machine was 33.9 Pflop/s.)

14 Introduction to Computational Science Moore s law Slide by Jack Dongarra

15 Clock frequency scaling replaced by scaling cores/chip Data from Kunle Olukotun, Lance Hammond, Herb Sutter, Burton Smith, Chris Batten, and Krste Asanoviç. Slide from Kathy Yelick

16 Performance has also slowed, along with power Data from Kunle Olukotun, Lance Hammond, Herb Sutter, Burton Smith, Chris Batten, and Krste Asanoviç. Slide from Kathy Yelick

17 Introduction to Computational Science Hierarchical heterogeneous architectures

18 Moore s law reinterpreted Number of cores per chip double every 2 year, while clock speed decreases (not increases). Need to deal with systems with millions of concurrent threads. Need to be able to easily replace inter-chip parallelism with intro-chip parallelism. Number of threads of execution doubles every 2 year.

19 Power efficiency For Exascale need to be around 50 Gflops/W, a factor of 20 needed.

20 High cost of data movement Flop/s or percentage of peak flop/s become much less relevant. Source: John Shalf, LBNL. Algorithms and software: Minimize data movement; perform more work per unit data movement.

21 Course Information Goals of this course: Acquire a broad range of skills and knowledge needed to use computationally intensive methods. Develop an awareness of the resources available to keep abreast of the rapidly changing field of computational science. Major course topics: Basic skills in Unix/Linux. Scientific programming languages. Parallel computing architectures. Parallel programming paradignms. Dense and sparse linear algebra libraries.

22 Course Information Website: Syllabus. Lecture material. Homework sets and lab assignments. Blackboard: Grades. Instructor: Xianyi Zeng Office: Bell Hall 202. Office hours: 10:00am 12:00pm Friday. Teaching assistant: Osei Tweneboah Office: Bell Hall 206. Office hours: 10:00am 12:00pm Monday. Course format: Two lectures with class activities, One hour lab/hands-on practice. Class preparation: Read materials prior to class.

23 Course Information Get access to a Linux machine: No action required if you already use a Linux operating system. Install Command Line Tools if you use Mac OS. Download and install Ubuntu Desktop from if you use Windows. If there are any questions, ask Google, the instructor, or the TA. XSEDE ( Extreme Science and Engineering Discovery Environment. Stampede at Texas Advanced Computing Center (TACC) Workshops held at UTEP MPI: September 7 8. OpenMP: October 4. More details about the XSEDE workshop will be announced.