Scientific Computing I

Transcription

1 Scientific Computing I Module 1: Introduction Michael Bader Lehrstuhl Informatik V Winter 2016/2017

2 Scientific Computing = Science + Computing? Science on Computers?? Computational Science??? Michael Bader Scientific Computing I Module 1: Introduction Winter 2016/2017 2

3 What is Computational Science and Engineering? Computational science and engineering (CSE) is a multidisciplinary field of research and education lying at the intersection of applied mathematics, statistics, computer science, and core disciplines of science and engineering. CSE is devoted to the development and use of computational methods and for scientific discovery in all branches of the sciences, for the advancement of innovation in engineering and technology, and for the support of decision-making across a spectrum of societally important application areas. U. Rüde et al.: Research and Education in Computational Science and Engineering, Michael Bader Scientific Computing I Module 1: Introduction Winter 2016/2017 3

4 Part I: An Interdisciplinary Discipline Gaining Scientific Knowledge The classical scientific process Approaches to science Where Simulation is Needed Drawbacks of Theory and Experiment Two Large Examples Molecular Dynamics and Blood Flow Michael Bader Scientific Computing I Module 1: Introduction Winter 2016/2017 4

5 Part II: Tasks of Scientific Computing The Simulation Pipeline Stages of the Simulation Pipeline Michael Bader Scientific Computing I Module 1: Introduction Winter 2016/2017 5

6 Part I An Interdisciplinary Discipline Michael Bader Scientific Computing I Module 1: Introduction Winter 2016/2017 6

7 Gaining Scientific Knowledge The Classical Scientific Process 1. characterization observation quantification/measurement 2. hypothesis theory model 3. prediction consequences/logical deducation from hypothesis/model? 4. experiment verification/falsification discrepancies might lead to improved model Michael Bader Scientific Computing I Module 1: Introduction Winter 2016/2017 7

8 Gaining Scientific Knowledge (2) Approaches to Science: 1. theoretical investigation hypothesis / models analytical calculations Gedankenexperiments Science 2. experimentation build model scenarios predict theoretical results and compare with outcome 3. simulation Why would we need that? Experiments Simulation Theory Michael Bader Scientific Computing I Module 1: Introduction Winter 2016/2017 8

9 The Scientific Process Revisited Scientific/Engineering Tasks: Reality Theory Solution Experiment Validation understand processes (model) elaborate theory and derive solution/hypothesis verify/validate hypotheses/models (experiment) design and optimize (model or theory or experiment) Michael Bader Scientific Computing I Module 1: Introduction Winter 2016/2017 9

10 Where Simulation is Needed Replacing Analytical Solutions: Reality Theory Simulation Experiment Validation analytical solution impossible or hard to compute use numerical approximation instead application: validate a complex model understand processes validate assumptions Michael Bader Scientific Computing I Module 1: Introduction Winter 2016/

11 Where Simulation is Needed (2) Replacing Experiments: Reality Theory Solution Simulation Validation analytical theoretical solution available replace experiments by simulation of a more detailed model application: develop a simple model neglecting non-relevant effects with reduced dimensionality reduced-order models Michael Bader Scientific Computing I Module 1: Introduction Winter 2016/

12 Where Simulation is Needed (3) Replacing Analytical Solvers and Experiments: Reality Simulation Prediction detailed and accurate mathematical model given use simulation only requires real world scenario description application: predict reality (weather/climate/earthquake/...) forecasts design and optimization uncertainty quantification Michael Bader Scientific Computing I Module 1: Introduction Winter 2016/

13 Drawbacks of Theory and Experiment Theoretical Investigation: analytical solutions for simple scenarios, only models usually very complicated or even impossible to solve Experiments: might be impossible to do might be dangerous or unwelcome might be very expensive (in time/money) Michael Bader Scientific Computing I Module 1: Introduction Winter 2016/

14 Where Experiments are Impossible Astrophysics: life cycle of stars, galaxies,... motion of planets, asteroids, comets,... Geophysics: displacement of the earth s magnetic field continental drift Image sources: Top: High-resolution simulations of clusters of galaxies using Gadget; Bottom: Magnetic field lines after a hypermassive star collapses to a black hole (simulation by L. Rezzolla et al., Univ. Frankfurt; Michael Bader Scientific Computing I Module 1: Introduction Winter 2016/

15 Where Experiments are Impossible Meteorology: weather forecasts simulation of hurricanes and storm surges Climate and Ocean Modelling: greenhouse effect ocean currents (gulf stream, etc.) tsunami simulation Image source: Cooperative Institute for Meteorological Satellite Studies, Space Science and Engineering Center, University of Wisconsin-Madison; Michael Bader Scientific Computing I Module 1: Introduction Winter 2016/

16 When There is No Second Try Stability of Buildings: large span bridges or skyscrapers consider wind loads, earthquakes,... Astronautics flight path of space crafts or satellites re-entry of space crafts Michael Bader Scientific Computing I Module 1: Introduction Winter 2016/

17 Where Experiments have Harmful Side-effects Propagation of Pollutants: pollutants in air, water, or soil predict long-term behaviour Nuclear Research: security of nuclear power plants nuclear weapons Michael Bader Scientific Computing I Module 1: Introduction Winter 2016/

18 Where Experiments are Expensive Car Industry: aerodynamics crash tests assembly of parts build prototypes or rather simulate? also combustion processes, vehicle dynamics,... Michael Bader Scientific Computing I Module 1: Introduction Winter 2016/

19 Example PRACE Award 2013 World-record simulation with molecules as performance study anticipating large-scale experiments to investigate nano-fluids: size dependence of inter-facial quantities such as surface tension behavior of droplets, interactions between droplets, nucleation 6.3 µm Drop of acetone in its vapor phase, used as model for fuel Simulated a cube of liquid Krypton of edge length l = 6.3µm Michael Bader Scientific Computing I Module 1: Introduction Winter 2016/

20 Example PRACE Award 2013 (2) Simulation HPC-Related Data: N-body simulation with N = molecules 100 TB RAM required only to store particles positions and velocities (single precision), 200 TB memory in total Simulation on SuperMUC (LRZ, Munich): 9126 nodes (each 2x eight-core Intel SandyBridge, i.e cores total) leight-weight hybrid parallelisation: MPI plus OpenMP Runtime: 40 s per iteration; terminated after 10 time steps parallel efficiency: 86 % and 9.4 % peak performance Further info: Video! Michael Bader Scientific Computing I Module 1: Introduction Winter 2016/

21 Example Gordon Bell Prize 2010 direct simulation of blood flow particulate flow simulation (coupled problem) Stokes flow for blood plasma red blood cells as immersed, deformable particles (Rahimian,..., Biros, 2010) Michael Bader Scientific Computing I Module 1: Introduction Winter 2016/

22 Example Gordon Bell Prize 2010 (2) Simulation HPC-Related Data: up to 260 Mio blood cells, up to unknowns fast multipole method to compute Stokes flow (octree-based; octree-level 4 24) scalability: 327 CPU-GPU nodes on Keeneland cluster, 200,000 AMD cores on Jaguar (ORNL) 0.7 Petaflops/s sustained performance on Jaguar extensive use of GEMM routine (matrix multiplication) runtime: 1 minute per time step Article for Supercomputing conference: Michael Bader Scientific Computing I Module 1: Introduction Winter 2016/

23 Example Dynamic Rupture Simulation (Heinecke, Breuer, et al., 2014) earthquake simulation: dynamic rupture and seismic wave propagation high-order discontinuous Galerkin method on an adaptive unstructured tetrahedral mesh Michael Bader Scientific Computing I Module 1: Introduction Winter 2016/

24 Example Dynamic Rupture Simulation (2) Simulation HPC-Related Data: 191 Mio grid cells, close to unknowns 234,456 time steps production run: 7h on SuperMUC (147,456 cores), 1.25 PetaFlop/s scalability: 6,144 nodes (2 CPU + MIC) on Stampede, 8,000 nodes (2 CPUs + 3 MICs) on Tianhe Petaflops/s on Stamped; 3.3 Petaflops/s on Tianhe-2 seismic wave propagation: 8.6 Petaflops/s on Tianhe-2 hardware-optimized dense and sparse matrix multiplications Video: Michael Bader Scientific Computing I Module 1: Introduction Winter 2016/

25 Part II Components of Scientific Computing Michael Bader Scientific Computing I Module 1: Introduction Winter 2016/

26 The Simulation Pipeline v a l i d a t i o n phenomenon, process etc. modelling mathematical model numerical treatment numerical algorithm simulation code implementation visualization results to interpret embedding statement tool Michael Bader Scientific Computing I Module 1: Introduction Winter 2016/

27 The Simulation Technische Universität München Pipeline II The Simulation Pipeline Basis of Computational Engineering Mathematical model Discretization & solver Parallel implementation, HPC Validation Insight, Design Software Exploration H.-J. Bungartz: Introduction to the BGCE image courtesy: H.-J. Bungartz 1 BGCE 2014 Opening Weekend and Annual Meeting, Bernried, April 11 13, 2014 Michael Bader Scientific Computing I Module 1: Introduction Winter 2016/

28 1 CSE: DRIVING SCIENTIFIC AND ENGINEERING PROGRESS The Simulation Pipeline III Problem description Idealization Mathematical model Quantification Conceptual model New Insight Design, Control, Optimization Experiment Discretization Model validation Parameter identification Developing a CSE model Model verification Comparison Algorithmic model Data Simulation Software HPC model Parallelization image from: U. Rüde et al.: Research and Education in Computational Science and Engineering, Figure 2: CSE pipeline, from physical problem to model and algorithms to efficient implementation in simulation software with verification and validation driven by data. The pipeline is actually a loop that requires multiple Michael feedbacks. Bader Scientific Computing I Module 1: Introduction Winter 2016/

29 Steps in the Simulation Pipeline Mathematical Modelling classification, types of models differential equations population models heat equations Numerical Treatment discretization grid generation, time stepping numerical integration of ODE/PDE continuous vs. discretized model Michael Bader Scientific Computing I Module 1: Introduction Winter 2016/

30 Steps in the Simulation Pipeline (2) Implementation data structures and algorithms platform-aware programming parallel programming embedding Visualization visualization techniques computational steering images first? = Verification & Validation, Uncertainty Quantification Michael Bader Scientific Computing I Module 1: Introduction Winter 2016/

31 Part III Organisation Michael Bader Scientific Computing I Module 1: Introduction Winter 2016/

32 Relation: SciComp1 other CSE courses Scientific Computing I Numerical Analysis ODEs, PDEs,... Scientific Computing Lab Advanced Programming Matlab/tools hands on C++ Michael Bader Scientific Computing I Module 1: Introduction Winter 2016/

33 Roadmap of the Lecture 1. Introduction: Discipline 2. Population Modelling Discrete Models 3. Population Modelling Continuous Models 4. Numerical Methods for ODEs 5. Heat Transfer Discrete and Continuous Models 6. Analytical and Numerical Solutions of the 1D Heat Equation 7. Introduction to Finite Element Methods 8. Case Study Computational Fluid Dynamics Michael Bader Scientific Computing I Module 1: Introduction Winter 2016/

34 Color Code for Headers Black Headers: for all slides with regular topics Green Headers: summarized details: will be explained in the lecture, but usually not as an explicit slide; green slides will only appear in the handout versions Red Headers: advanced topics or outlook: will not be part of the exam topics Blue Headers: background information or fundamental concepts that are probably already known, but are important throughout the lecture topics that will be discussed in detail in other lectures (Numerical Programming, e.g.) Michael Bader Scientific Computing I Module 1: Introduction Winter 2016/

35 ECTS, Modules, Tutorials ECTS, Modules: 5 ECTS (2+2 lectures/tutorials per week) CSE: compulsory course Biomed. Computing/Computer Science: elective/master catalogue others? Tutorials: to be updated! 2 groups; started/starts Oct 24/26 Mon, Wed, TUMonline course closed register for waiting list Michael Bader Scientific Computing I Module 1: Introduction Winter 2016/