From b90247a0c3b89db9a408f37dae3bddee74eff8eb Mon Sep 17 00:00:00 2001 From: lu-kas Date: Mon, 26 Apr 2021 18:38:50 +0200 Subject: [PATCH 1/3] initial version for the hpc section --- book/content/tools/02_hpc/02_hpc.md | 143 +++++++++++++++++- book/content/tools/02_hpc/figs/amdahl.pdf | Bin 0 -> 17443 bytes book/content/tools/02_hpc/figs/amdahl.png | Bin 0 -> 1377904 bytes book/content/tools/02_hpc/figs/cluster.pdf | Bin 0 -> 30525 bytes book/content/tools/02_hpc/figs/cluster.png | Bin 0 -> 511304 bytes book/content/tools/02_hpc/figs/decomp_mpi.pdf | Bin 0 -> 77253 bytes book/content/tools/02_hpc/figs/decomp_mpi.png | Bin 0 -> 422344 bytes .../tools/02_hpc/figs/decomp_openmp.pdf | Bin 0 -> 30574 bytes .../tools/02_hpc/figs/decomp_openmp.png | Bin 0 -> 150216 bytes book/content/tools/02_hpc/figs/fork.pdf | Bin 0 -> 29798 bytes book/content/tools/02_hpc/figs/fork.png | Bin 0 -> 658195 bytes .../tools/02_hpc/figs/load_balance.pdf | Bin 0 -> 33567 bytes .../tools/02_hpc/figs/load_balance.png | Bin 0 -> 452307 bytes 13 files changed, 142 insertions(+), 1 deletion(-) create mode 100644 book/content/tools/02_hpc/figs/amdahl.pdf create mode 100644 book/content/tools/02_hpc/figs/amdahl.png create mode 100644 book/content/tools/02_hpc/figs/cluster.pdf create mode 100644 book/content/tools/02_hpc/figs/cluster.png create mode 100644 book/content/tools/02_hpc/figs/decomp_mpi.pdf create mode 100644 book/content/tools/02_hpc/figs/decomp_mpi.png create mode 100644 book/content/tools/02_hpc/figs/decomp_openmp.pdf create mode 100644 book/content/tools/02_hpc/figs/decomp_openmp.png create mode 100644 book/content/tools/02_hpc/figs/fork.pdf create mode 100644 book/content/tools/02_hpc/figs/fork.png create mode 100644 book/content/tools/02_hpc/figs/load_balance.pdf create mode 100644 book/content/tools/02_hpc/figs/load_balance.png diff --git a/book/content/tools/02_hpc/02_hpc.md b/book/content/tools/02_hpc/02_hpc.md index 7aca4e9f..72e177c4 100644 --- a/book/content/tools/02_hpc/02_hpc.md +++ b/book/content/tools/02_hpc/02_hpc.md @@ -1 +1,142 @@ -# High Performace Computing \ No newline at end of file +# High Performace Computing + +## Parallel Execution + +### General Principle + +* independent tasks (execution sections) may be run in parallel +* fork and join produce overhead +* the task separation may introduce additional serial tasks +* load balancing is crucial for efficient usage + +:::{figure-md} fig-hpc-fork + + +Serial and parallel execution of a set of tasks. +::: + +### Speedup + +The maximal achievable speedup $\mf s$, w.r.t. a serial execution, on $\mf n$ computing units is limited by the fraction of the execution that runs in parallel $\mf p$. This is reflected by Amdahl's law, see equation {eq}`eq-amdahls-law` and . + +$$ +s(n, p) = \frac{1}{p+\frac{1}{n}(1-p)} +$$(eq-amdahls-law) + +:::{figure-md} fig-hpc-amdahl + + +Visualisation for Amdah's law. +::: + +The speedup may even decrease, as some operations become more expensive with increasing number of participating processes, e.g. barriers, global reductions or broadcasts. + +:::{figure-md} fig-hpc-load-balance + + +Visualisation for Amdah's law. +::: + +An unequal work load per process may become the main problem. The execution of one iteration is in general determined by the slowest participant. + +### Parallelisation + +In FDS: +* MPI +* OpenMP + +The message passing interface (MPI) is a language-independent communications protocol used to program parallel computers (mainly for distributed memory machines). + +MPI allows to explicitly exchange messages between processes. Therefore it is up to the programmer to design appropriate data structures and algorithms to decompose the application. + +In CFD, typically the computational domain is explicitly decomposed and distributed over all MPI processes. +For stencil operations only neighbour cells are needed, thus only a domain’s halo needs to be shared. + + +Typically the data exchange (compose, transfer, decompose) produces the most overhead. This overhead is purely due to the explicit problem decomposition. + +:::{figure-md} fig-hpc-domain-mpi + + +Domain decomposition with MPI. +::: + +As MPI is only a definition, there is not a single implementation of MPI. The most common MPI implementations are: +* Open MPI, used on UNIX-like systems, open source and free +* MPICH, used on UNIX-like systems, open source and free +* Intel MPI Library (MPICH derivate), Windows & Linux, commercial +The MPI implementations include C/C++/FORTRAN header, libraries, compiler wrapper and runtime environment. + +In contrast to MPI, OpenMP (or short OMP) is a standard to implicitly distribute the execution on a shared memory system. + +OMP is implemented as pragmas for C/C++/FORTRAN, and are therefore non intrusive. +The typical application is to decompose loops and advise the compiler / runtime to distribute the loop iterations. + +However, the compiler / runtime must detect independent tasks. Loop carried dependencies may prevent parallelisation and data races may produce unpredictable results. + +To run an OMP application, there are a few handy environment variables + +* OMP NUM THREADS, number of OMP threads +* OMP STACKSIZE, the size of the stack for each thread + +The execution command is basically equal to the serial execution. A combination with MPI is possible and the OMP environment variables should be passed to the MPI processes. +The hybrid approach (MPI+OMP) is used to reduce the number of MPI processes and therefore the overhead of non-scaling operations. + +:::{figure-md} fig-hpc-domain-omp + + +Domain decomposition with OpenMP. +::: + +## Parallel Computer + +Many scientific and engineering problems require a large amount of computing time and / or memory. This is generally only available on supercomputers / high performance computing (HPC) systems. +Typical applications are: + +* science: particle physics, climate research, molecular dynamics +* engineering: CFD, structural mechanics, computer science + +HPC with computing power thousands times larger than personal computer allows to significantly reduce computing time and allows to solve new challenges. +Example: An CFD application run for a week on thousand processors would need 20 years on a personal computer (assuming it provides enough memory). + +A list of common terms used in HPC +* CPU, GPGPU, SIMD, SMP, NUMA, SMT +* compute node: nodes that are used only for computation, no direct user access +* front/login node: users login here, do compilation and job submission +* batch/submission system: system to allocate resources to a scheduled job +* interconnect: network between components or computing nodes (e.g. Infiniband, 10GE) +* FLOP/s: floating point operations per second +* peak performance: theoretical number of FLOP per second +* linpack performance: floating point performance in the linpack test +* top500 list: supercomputer ranking based on the linpack performance + + +:::{figure-md} fig-hpc-cluster + + +A very generalistic representation of an element / node of a cluster. +::: + + + +:::{figure-md} fig-hpc-moore + + +The development of the transistor count in the last 5 decades, which is represented by Moore's law. Source: [Wikimedia Commons](https://commons.wikimedia.org/wiki/File:Moore%27s_Law_Transistor_Count_1970-2020.png). +::: + + +[Top500 List, performance development](https://www.top500.org/statistics/perfdevel/) + +[JURECA @ FZJ](https://fz-juelich.de/ias/jsc/EN/Expertise/Supercomputers/JURECA/JURECA_node.html) + + + +:::{figure-md} fig-hpc-jureca-dc + + +JURECA-DC cluster at the Forschungszentrum Jülich. 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