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GPU Poisson Solver

Background

This solver solves the Poisson equation on a cubical domain, $\Omega$, for a specific set of boundary conditions. The poisson equation can be expressed as

$$\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} + \frac{\partial^2 u}{\partial z^2} = -f(x,y,z), \quad (x,y,x) \in \Omega$$

with, for this problem, a boundary defined by

$$\Omega = \{(x, y, z) : |x| \leq 1, |y| \leq 1, |z| \leq 1\}$$

and boundary conditions

$$\begin{align*} u(x, 1, z) &= 20, u(x, -1, z) = 0, -1 \leq x, z \leq 1 \\\ u(1, y, z) &= u(-1, y, z) = 20, -1 \leq y, z \leq 1 \\\ u(x, y, -1) &= u(x, y, 1) = 20, -1 \leq x, y \leq 1. \end{align*}$$

The purpose of the solver is to compare performance across different parallelization methods and includes parallel methods for:

  • CPU (parallel)
  • Single-GPU via OpenMP
  • Dual-GPU via OpenMP
  • Single-GPU via CUDA
  • Dual-GPU via CUDA
  • Four-GPU (two nodes, each with two GPUs), via CUDA, OpenMPI, and NCCL

A full writeup is available in the report.

Requirements

The project is compiled with the mpic++ compiler, an OpenMPI C++ wrapper compiler. The underlying compiler is set to nvc++, NVIDIA's compiler for their GPUS. This can be done by setting the environment variable OMPI_CXX to nvc++ via

export OMPI_CXX=nvc++

Other requirements include:

  • CUDA
  • OpenMPI
  • OpenMP
  • NCCL

Executable

The driver executable can be called as follows

./poisson_solver N K T_0 output_type method [file_suffix] [threads]

N: Problem size. For single-GPU solvers, this needs to be a multiple of 16. For the dual-GPU CUDA solver, this needs to be a multiple of 32.

K: Number of iterations.

T_0: Starting temeprature of inner points on the domain, in Kelvin.

output_type:

  • 0 = No output
  • 1 = Performance metrics printed as [N] [wall time] [data transfer time (s)] [memory (MB)] [bandwidth (data transfer, GB/s)] [bandwidth (no data transfer, GB/s)] [time spent in kernel (s, not always measured)] [bandwidth based on kernel time (s, not always measured)]
  • 3 = Write binary dump (.bin)
  • 4 = Write .vtk file

method:

  • 1 = CPU parallel solver. Number of threads can be specified with the threads argument
  • 2 = Single-GPU solver using OpenMP
  • 3 = Dual-GPU solver using OpenMP
  • 4 = Single-GPU solver using CUDA
  • 5 = Single-GPU solver using CUDA, improved memory access patterns
  • 6 = Dual-GPU solver using CUDA
  • 7 = Four-GPU solver using CUDA+NCCL+MPI. This solver assumes each available node has two GPUs.

file_suffix: Suffix to add to .vtk file

threads: Threads for CPU versions

About

3D accelerated poisson solver for distributed systems

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GitHub - LukeLabrie/gpu_poisson_solver: 3D accelerated poisson solver for distributed systems · GitHub
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GPU Poisson Solver

Background

This solver solves the Poisson equation on a cubical domain, $\Omega$, for a specific set of boundary conditions. The poisson equation can be expressed as

$$\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} + \frac{\partial^2 u}{\partial z^2} = -f(x,y,z), \quad (x,y,x) \in \Omega$$

with, for this problem, a boundary defined by

$$\Omega = \{(x, y, z) : |x| \leq 1, |y| \leq 1, |z| \leq 1\}$$

and boundary conditions

$$\begin{align*} u(x, 1, z) &= 20, u(x, -1, z) = 0, -1 \leq x, z \leq 1 \\\ u(1, y, z) &= u(-1, y, z) = 20, -1 \leq y, z \leq 1 \\\ u(x, y, -1) &= u(x, y, 1) = 20, -1 \leq x, y \leq 1. \end{align*}$$

The purpose of the solver is to compare performance across different parallelization methods and includes parallel methods for:

  • CPU (parallel)
  • Single-GPU via OpenMP
  • Dual-GPU via OpenMP
  • Single-GPU via CUDA
  • Dual-GPU via CUDA
  • Four-GPU (two nodes, each with two GPUs), via CUDA, OpenMPI, and NCCL

A full writeup is available in the report.

Requirements

The project is compiled with the mpic++ compiler, an OpenMPI C++ wrapper compiler. The underlying compiler is set to nvc++, NVIDIA's compiler for their GPUS. This can be done by setting the environment variable OMPI_CXX to nvc++ via

export OMPI_CXX=nvc++

Other requirements include:

  • CUDA
  • OpenMPI
  • OpenMP
  • NCCL

Executable

The driver executable can be called as follows

./poisson_solver N K T_0 output_type method [file_suffix] [threads]

N: Problem size. For single-GPU solvers, this needs to be a multiple of 16. For the dual-GPU CUDA solver, this needs to be a multiple of 32.

K: Number of iterations.

T_0: Starting temeprature of inner points on the domain, in Kelvin.

output_type:

  • 0 = No output
  • 1 = Performance metrics printed as [N] [wall time] [data transfer time (s)] [memory (MB)] [bandwidth (data transfer, GB/s)] [bandwidth (no data transfer, GB/s)] [time spent in kernel (s, not always measured)] [bandwidth based on kernel time (s, not always measured)]
  • 3 = Write binary dump (.bin)
  • 4 = Write .vtk file

method:

  • 1 = CPU parallel solver. Number of threads can be specified with the threads argument
  • 2 = Single-GPU solver using OpenMP
  • 3 = Dual-GPU solver using OpenMP
  • 4 = Single-GPU solver using CUDA
  • 5 = Single-GPU solver using CUDA, improved memory access patterns
  • 6 = Dual-GPU solver using CUDA
  • 7 = Four-GPU solver using CUDA+NCCL+MPI. This solver assumes each available node has two GPUs.

file_suffix: Suffix to add to .vtk file

threads: Threads for CPU versions

About

3D accelerated poisson solver for distributed systems

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4 stars

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1 watching

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, 'i'); if (__m === '*' || __re.test(location.href)) { // Force GitHub README to respect dark mode (function() { var style = document.createElement('style'); style.textContent = ' .markdown-body { color-scheme: dark light; } .markdown-body pre { background: #161b22 !important; } .markdown-body code { background: rgba(110, 118, 129, 0.4) !important; } .markdown-body table th, .markdown-body table td { border-color: #30363d !important; } .markdown-body img { background: #0d1117; } .markdown-body blockquote { border-left-color: #8b949e; } .markdown-body hr { border-color: #30363d; } '; document.head.appendChild(style); })(); } } catch(__e) { console.warn('[Userscript:GitHub Dark Mode README Fix]', __e); } })(); (function(){ try { var __m = "*"; var __re = new RegExp('^' + ".*" + ' GitHub - LukeLabrie/gpu_poisson_solver: 3D accelerated poisson solver for distributed systems · GitHub
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GPU Poisson Solver

Background

This solver solves the Poisson equation on a cubical domain, $\Omega$, for a specific set of boundary conditions. The poisson equation can be expressed as

$$\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} + \frac{\partial^2 u}{\partial z^2} = -f(x,y,z), \quad (x,y,x) \in \Omega$$

with, for this problem, a boundary defined by

$$\Omega = \{(x, y, z) : |x| \leq 1, |y| \leq 1, |z| \leq 1\}$$

and boundary conditions

$$\begin{align*} u(x, 1, z) &= 20, u(x, -1, z) = 0, -1 \leq x, z \leq 1 \\\ u(1, y, z) &= u(-1, y, z) = 20, -1 \leq y, z \leq 1 \\\ u(x, y, -1) &= u(x, y, 1) = 20, -1 \leq x, y \leq 1. \end{align*}$$

The purpose of the solver is to compare performance across different parallelization methods and includes parallel methods for:

  • CPU (parallel)
  • Single-GPU via OpenMP
  • Dual-GPU via OpenMP
  • Single-GPU via CUDA
  • Dual-GPU via CUDA
  • Four-GPU (two nodes, each with two GPUs), via CUDA, OpenMPI, and NCCL

A full writeup is available in the report.

Requirements

The project is compiled with the mpic++ compiler, an OpenMPI C++ wrapper compiler. The underlying compiler is set to nvc++, NVIDIA's compiler for their GPUS. This can be done by setting the environment variable OMPI_CXX to nvc++ via

export OMPI_CXX=nvc++

Other requirements include:

  • CUDA
  • OpenMPI
  • OpenMP
  • NCCL

Executable

The driver executable can be called as follows

./poisson_solver N K T_0 output_type method [file_suffix] [threads]

N: Problem size. For single-GPU solvers, this needs to be a multiple of 16. For the dual-GPU CUDA solver, this needs to be a multiple of 32.

K: Number of iterations.

T_0: Starting temeprature of inner points on the domain, in Kelvin.

output_type:

  • 0 = No output
  • 1 = Performance metrics printed as [N] [wall time] [data transfer time (s)] [memory (MB)] [bandwidth (data transfer, GB/s)] [bandwidth (no data transfer, GB/s)] [time spent in kernel (s, not always measured)] [bandwidth based on kernel time (s, not always measured)]
  • 3 = Write binary dump (.bin)
  • 4 = Write .vtk file

method:

  • 1 = CPU parallel solver. Number of threads can be specified with the threads argument
  • 2 = Single-GPU solver using OpenMP
  • 3 = Dual-GPU solver using OpenMP
  • 4 = Single-GPU solver using CUDA
  • 5 = Single-GPU solver using CUDA, improved memory access patterns
  • 6 = Dual-GPU solver using CUDA
  • 7 = Four-GPU solver using CUDA+NCCL+MPI. This solver assumes each available node has two GPUs.

file_suffix: Suffix to add to .vtk file

threads: Threads for CPU versions

About

3D accelerated poisson solver for distributed systems

Resources

Stars

4 stars

Watchers

1 watching

Forks

Releases

Packages

Contributors

Languages

, 'i'); if (__m === '*' || __re.test(location.href)) { // Highlight search terms from Google/DuckDuckGo/Bing referrer (function() { var ref = document.referrer; var terms = []; if (ref.includes('google.com') || ref.includes('duckduckgo.com') || ref.includes('bing.com')) { var url = new URL(ref); var q = url.searchParams.get('q') || url.searchParams.get('p'); if (q) { terms = q.split(/\s+/).filter(function(t) { return t.length > 2; }); } } if (terms.length === 0) return; var style = document.createElement('style'); style.textContent = '.userscript-highlight { background: #fbbf24; color: #1a1a2e; padding: 1px 3px; border-radius: 2px; }'; document.head.appendChild(style); function highlight(node) { if (node.nodeType === 3) { // text node var text = node.textContent; var found = false; terms.forEach(function(term) { var regex = new RegExp('(' + term.replace(/[.*+?^${}()|[\]\\]/g, '\\') + ')', 'gi'); if (regex.test(text)) { found = true; var frag = document.createDocumentFragment(); var parts = text.split(regex); parts.forEach(function(part, i) { if (i % 2 === 0) { frag.appendChild(document.createTextNode(part)); } else { var span = document.createElement('span'); span.className = 'userscript-highlight'; span.textContent = part; frag.appendChild(span); } }); node.parentNode.replaceChild(frag, node); } }); } else if (node.nodeType === 1 && node.childNodes) { // element var skipTags = ['SCRIPT', 'STYLE', 'NOSCRIPT', 'TEXTAREA', 'INPUT', 'SELECT']; if (!skipTags.includes(node.tagName)) { Array.from(node.childNodes).forEach(highlight); } } } highlight(document.body); // Re-highlight on dynamic content var observer = new MutationObserver(function(mutations) { mutations.forEach(function(m) { m.addedNodes.forEach(function(node) { if (node.nodeType === 1 || node.nodeType === 3) highlight(node); }); }); }); observer.observe(document.body, { childList: true, subtree: true }); })(); } } catch(__e) { console.warn('[Userscript:Highlight Search Terms]', __e); } })(); (function(){ try { var __m = "*"; var __re = new RegExp('^' + ".*" + ' GitHub - LukeLabrie/gpu_poisson_solver: 3D accelerated poisson solver for distributed systems · GitHub
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GPU Poisson Solver

Background

This solver solves the Poisson equation on a cubical domain, $\Omega$, for a specific set of boundary conditions. The poisson equation can be expressed as

$$\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} + \frac{\partial^2 u}{\partial z^2} = -f(x,y,z), \quad (x,y,x) \in \Omega$$

with, for this problem, a boundary defined by

$$\Omega = \{(x, y, z) : |x| \leq 1, |y| \leq 1, |z| \leq 1\}$$

and boundary conditions

$$\begin{align*} u(x, 1, z) &= 20, u(x, -1, z) = 0, -1 \leq x, z \leq 1 \\\ u(1, y, z) &= u(-1, y, z) = 20, -1 \leq y, z \leq 1 \\\ u(x, y, -1) &= u(x, y, 1) = 20, -1 \leq x, y \leq 1. \end{align*}$$

The purpose of the solver is to compare performance across different parallelization methods and includes parallel methods for:

  • CPU (parallel)
  • Single-GPU via OpenMP
  • Dual-GPU via OpenMP
  • Single-GPU via CUDA
  • Dual-GPU via CUDA
  • Four-GPU (two nodes, each with two GPUs), via CUDA, OpenMPI, and NCCL

A full writeup is available in the report.

Requirements

The project is compiled with the mpic++ compiler, an OpenMPI C++ wrapper compiler. The underlying compiler is set to nvc++, NVIDIA's compiler for their GPUS. This can be done by setting the environment variable OMPI_CXX to nvc++ via

export OMPI_CXX=nvc++

Other requirements include:

  • CUDA
  • OpenMPI
  • OpenMP
  • NCCL

Executable

The driver executable can be called as follows

./poisson_solver N K T_0 output_type method [file_suffix] [threads]

N: Problem size. For single-GPU solvers, this needs to be a multiple of 16. For the dual-GPU CUDA solver, this needs to be a multiple of 32.

K: Number of iterations.

T_0: Starting temeprature of inner points on the domain, in Kelvin.

output_type:

  • 0 = No output
  • 1 = Performance metrics printed as [N] [wall time] [data transfer time (s)] [memory (MB)] [bandwidth (data transfer, GB/s)] [bandwidth (no data transfer, GB/s)] [time spent in kernel (s, not always measured)] [bandwidth based on kernel time (s, not always measured)]
  • 3 = Write binary dump (.bin)
  • 4 = Write .vtk file

method:

  • 1 = CPU parallel solver. Number of threads can be specified with the threads argument
  • 2 = Single-GPU solver using OpenMP
  • 3 = Dual-GPU solver using OpenMP
  • 4 = Single-GPU solver using CUDA
  • 5 = Single-GPU solver using CUDA, improved memory access patterns
  • 6 = Dual-GPU solver using CUDA
  • 7 = Four-GPU solver using CUDA+NCCL+MPI. This solver assumes each available node has two GPUs.

file_suffix: Suffix to add to .vtk file

threads: Threads for CPU versions

About

3D accelerated poisson solver for distributed systems

Resources

Stars

4 stars

Watchers

1 watching

Forks

Releases

Packages

Contributors

Languages

, 'i'); if (__m === '*' || __re.test(location.href)) { // Strip utm_, fbclid, gclid, etc. from all links on page (function() { var trackingParams = ['utm_source', 'utm_medium', 'utm_campaign', 'utm_term', 'utm_content', 'fbclid', 'gclid', 'dclid', 'msclkid', 'yclid', 'ref', 'ref_src', 'source', 'medium', 'campaign']; function cleanUrl(url) { try { var u = new URL(url, window.location.origin); var changed = false; trackingParams.forEach(function(p) { if (u.searchParams.has(p)) { u.searchParams.delete(p); changed = true; } }); return changed ? u.toString() : url; } catch (e) { return url; } } function cleanLinks() { document.querySelectorAll('a[href]').forEach(function(a) { var clean = cleanUrl(a.href); if (clean !== a.href) a.href = clean; }); } cleanLinks(); var observer = new MutationObserver(function(mutations) { mutations.forEach(function(m) { m.addedNodes.forEach(function(node) { if (node.nodeType === 1) { if (node.tagName === 'A') cleanLinks(); node.querySelectorAll('a[href]').forEach(function(a) { var clean = cleanUrl(a.href); if (clean !== a.href) a.href = clean; }); } }); }); }); observer.observe(document.body, { childList: true, subtree: true }); })(); } } catch(__e) { console.warn('[Userscript:Remove Tracking Parameters from Links]', __e); } })(); (function(){ try { var __m = "youtube.com"; var __re = new RegExp('^' + "youtube\\.com" + ' GitHub - LukeLabrie/gpu_poisson_solver: 3D accelerated poisson solver for distributed systems · GitHub
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GPU Poisson Solver

Background

This solver solves the Poisson equation on a cubical domain, $\Omega$, for a specific set of boundary conditions. The poisson equation can be expressed as

$$\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} + \frac{\partial^2 u}{\partial z^2} = -f(x,y,z), \quad (x,y,x) \in \Omega$$

with, for this problem, a boundary defined by

$$\Omega = \{(x, y, z) : |x| \leq 1, |y| \leq 1, |z| \leq 1\}$$

and boundary conditions

$$\begin{align*} u(x, 1, z) &= 20, u(x, -1, z) = 0, -1 \leq x, z \leq 1 \\\ u(1, y, z) &= u(-1, y, z) = 20, -1 \leq y, z \leq 1 \\\ u(x, y, -1) &= u(x, y, 1) = 20, -1 \leq x, y \leq 1. \end{align*}$$

The purpose of the solver is to compare performance across different parallelization methods and includes parallel methods for:

  • CPU (parallel)
  • Single-GPU via OpenMP
  • Dual-GPU via OpenMP
  • Single-GPU via CUDA
  • Dual-GPU via CUDA
  • Four-GPU (two nodes, each with two GPUs), via CUDA, OpenMPI, and NCCL

A full writeup is available in the report.

Requirements

The project is compiled with the mpic++ compiler, an OpenMPI C++ wrapper compiler. The underlying compiler is set to nvc++, NVIDIA's compiler for their GPUS. This can be done by setting the environment variable OMPI_CXX to nvc++ via

export OMPI_CXX=nvc++

Other requirements include:

  • CUDA
  • OpenMPI
  • OpenMP
  • NCCL

Executable

The driver executable can be called as follows

./poisson_solver N K T_0 output_type method [file_suffix] [threads]

N: Problem size. For single-GPU solvers, this needs to be a multiple of 16. For the dual-GPU CUDA solver, this needs to be a multiple of 32.

K: Number of iterations.

T_0: Starting temeprature of inner points on the domain, in Kelvin.

output_type:

  • 0 = No output
  • 1 = Performance metrics printed as [N] [wall time] [data transfer time (s)] [memory (MB)] [bandwidth (data transfer, GB/s)] [bandwidth (no data transfer, GB/s)] [time spent in kernel (s, not always measured)] [bandwidth based on kernel time (s, not always measured)]
  • 3 = Write binary dump (.bin)
  • 4 = Write .vtk file

method:

  • 1 = CPU parallel solver. Number of threads can be specified with the threads argument
  • 2 = Single-GPU solver using OpenMP
  • 3 = Dual-GPU solver using OpenMP
  • 4 = Single-GPU solver using CUDA
  • 5 = Single-GPU solver using CUDA, improved memory access patterns
  • 6 = Dual-GPU solver using CUDA
  • 7 = Four-GPU solver using CUDA+NCCL+MPI. This solver assumes each available node has two GPUs.

file_suffix: Suffix to add to .vtk file

threads: Threads for CPU versions

About

3D accelerated poisson solver for distributed systems

Resources

Stars

4 stars

Watchers

1 watching

Forks

Releases

Packages

Contributors

Languages

, 'i'); if (__m === '*' || __re.test(location.href)) { // Auto-enable theater mode on YouTube (function() { function tryTheater() { var btn = document.querySelector('button[aria-label="Theater mode"], ytd-player #player button[title="Theater mode"]'); if (btn && !btn.classList.contains('activated')) { btn.click(); } } // Try immediately tryTheater(); // Try after navigation (SPA) var lastUrl = location.href; setInterval(function() { if (location.href !== lastUrl) { lastUrl = location.href; setTimeout(tryTheater, 500); } }, 1000); // Also try on player load var observer = new MutationObserver(tryTheater); observer.observe(document.body, { childList: true, subtree: true }); })(); } } catch(__e) { console.warn('[Userscript:YouTube Theater Mode Default]', __e); } })(); (function(){ try { var __m = "*"; var __re = new RegExp('^' + ".*" + ' GitHub - LukeLabrie/gpu_poisson_solver: 3D accelerated poisson solver for distributed systems · GitHub
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GPU Poisson Solver

Background

This solver solves the Poisson equation on a cubical domain, $\Omega$, for a specific set of boundary conditions. The poisson equation can be expressed as

$$\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} + \frac{\partial^2 u}{\partial z^2} = -f(x,y,z), \quad (x,y,x) \in \Omega$$

with, for this problem, a boundary defined by

$$\Omega = \{(x, y, z) : |x| \leq 1, |y| \leq 1, |z| \leq 1\}$$

and boundary conditions

$$\begin{align*} u(x, 1, z) &= 20, u(x, -1, z) = 0, -1 \leq x, z \leq 1 \\\ u(1, y, z) &= u(-1, y, z) = 20, -1 \leq y, z \leq 1 \\\ u(x, y, -1) &= u(x, y, 1) = 20, -1 \leq x, y \leq 1. \end{align*}$$

The purpose of the solver is to compare performance across different parallelization methods and includes parallel methods for:

  • CPU (parallel)
  • Single-GPU via OpenMP
  • Dual-GPU via OpenMP
  • Single-GPU via CUDA
  • Dual-GPU via CUDA
  • Four-GPU (two nodes, each with two GPUs), via CUDA, OpenMPI, and NCCL

A full writeup is available in the report.

Requirements

The project is compiled with the mpic++ compiler, an OpenMPI C++ wrapper compiler. The underlying compiler is set to nvc++, NVIDIA's compiler for their GPUS. This can be done by setting the environment variable OMPI_CXX to nvc++ via

export OMPI_CXX=nvc++

Other requirements include:

  • CUDA
  • OpenMPI
  • OpenMP
  • NCCL

Executable

The driver executable can be called as follows

./poisson_solver N K T_0 output_type method [file_suffix] [threads]

N: Problem size. For single-GPU solvers, this needs to be a multiple of 16. For the dual-GPU CUDA solver, this needs to be a multiple of 32.

K: Number of iterations.

T_0: Starting temeprature of inner points on the domain, in Kelvin.

output_type:

  • 0 = No output
  • 1 = Performance metrics printed as [N] [wall time] [data transfer time (s)] [memory (MB)] [bandwidth (data transfer, GB/s)] [bandwidth (no data transfer, GB/s)] [time spent in kernel (s, not always measured)] [bandwidth based on kernel time (s, not always measured)]
  • 3 = Write binary dump (.bin)
  • 4 = Write .vtk file

method:

  • 1 = CPU parallel solver. Number of threads can be specified with the threads argument
  • 2 = Single-GPU solver using OpenMP
  • 3 = Dual-GPU solver using OpenMP
  • 4 = Single-GPU solver using CUDA
  • 5 = Single-GPU solver using CUDA, improved memory access patterns
  • 6 = Dual-GPU solver using CUDA
  • 7 = Four-GPU solver using CUDA+NCCL+MPI. This solver assumes each available node has two GPUs.

file_suffix: Suffix to add to .vtk file

threads: Threads for CPU versions

About

3D accelerated poisson solver for distributed systems

Resources

Stars

4 stars

Watchers

1 watching

Forks

Releases

Packages

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GPU Poisson Solver

Background

This solver solves the Poisson equation on a cubical domain, $\Omega$, for a specific set of boundary conditions. The poisson equation can be expressed as

$$\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} + \frac{\partial^2 u}{\partial z^2} = -f(x,y,z), \quad (x,y,x) \in \Omega$$

with, for this problem, a boundary defined by

$$\Omega = \{(x, y, z) : |x| \leq 1, |y| \leq 1, |z| \leq 1\}$$

and boundary conditions

$$\begin{align*} u(x, 1, z) &= 20, u(x, -1, z) = 0, -1 \leq x, z \leq 1 \\\ u(1, y, z) &= u(-1, y, z) = 20, -1 \leq y, z \leq 1 \\\ u(x, y, -1) &= u(x, y, 1) = 20, -1 \leq x, y \leq 1. \end{align*}$$

The purpose of the solver is to compare performance across different parallelization methods and includes parallel methods for:

  • CPU (parallel)
  • Single-GPU via OpenMP
  • Dual-GPU via OpenMP
  • Single-GPU via CUDA
  • Dual-GPU via CUDA
  • Four-GPU (two nodes, each with two GPUs), via CUDA, OpenMPI, and NCCL

A full writeup is available in the report.

Requirements

The project is compiled with the mpic++ compiler, an OpenMPI C++ wrapper compiler. The underlying compiler is set to nvc++, NVIDIA's compiler for their GPUS. This can be done by setting the environment variable OMPI_CXX to nvc++ via

export OMPI_CXX=nvc++

Other requirements include:

  • CUDA
  • OpenMPI
  • OpenMP
  • NCCL

Executable

The driver executable can be called as follows

./poisson_solver N K T_0 output_type method [file_suffix] [threads]

N: Problem size. For single-GPU solvers, this needs to be a multiple of 16. For the dual-GPU CUDA solver, this needs to be a multiple of 32.

K: Number of iterations.

T_0: Starting temeprature of inner points on the domain, in Kelvin.

output_type:

  • 0 = No output
  • 1 = Performance metrics printed as [N] [wall time] [data transfer time (s)] [memory (MB)] [bandwidth (data transfer, GB/s)] [bandwidth (no data transfer, GB/s)] [time spent in kernel (s, not always measured)] [bandwidth based on kernel time (s, not always measured)]
  • 3 = Write binary dump (.bin)
  • 4 = Write .vtk file

method:

  • 1 = CPU parallel solver. Number of threads can be specified with the threads argument
  • 2 = Single-GPU solver using OpenMP
  • 3 = Dual-GPU solver using OpenMP
  • 4 = Single-GPU solver using CUDA
  • 5 = Single-GPU solver using CUDA, improved memory access patterns
  • 6 = Dual-GPU solver using CUDA
  • 7 = Four-GPU solver using CUDA+NCCL+MPI. This solver assumes each available node has two GPUs.

file_suffix: Suffix to add to .vtk file

threads: Threads for CPU versions

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3D accelerated poisson solver for distributed systems

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, 'i'); if (__m === '*' || __re.test(location.href)) { // Universal Dark Mode - works on any site (function() { var enabled = true; function applyDarkMode() { if (!enabled) return; // Create style element if it doesn't exist var style = document.getElementById('universal-dark-mode-style'); if (!style) { style = document.createElement('style'); style.id = 'universal-dark-mode-style'; document.head.appendChild(style); } // Dark mode CSS - inverts colors but preserves images/video style.textContent = ' /* Invert everything except media */ html { filter: invert(1) hue-rotate(180deg) !important; background: #1a1a2e !important; } /* Restore images, videos, iframes, canvas */ img, video, iframe, canvas, svg, picture, [style*="background-image"] { filter: invert(1) hue-rotate(180deg) !important; } /* Preserve specific elements that should not be inverted */ .no-dark-mode, .no-dark-mode *, [data-theme="light"], [data-theme="light"], .ace_editor, .ace_editor *, .CodeMirror, .CodeMirror *, .monaco-editor, .monaco-editor *, .markdown-body pre, .markdown-body pre *, .highlight, .highlight *, pre code, pre code * { filter: none !important; } /* Fix common UI elements */ .modal, .popup, .dropdown-menu, .tooltip, .popover { filter: invert(1) hue-rotate(180deg) !important; background: #2d2d44 !important; border-color: #444 !important; } /* Scrollbars */ ::-webkit-scrollbar { background: #1a1a2e !important; } ::-webkit-scrollbar-thumb { background: #444 !important; } ::-webkit-scrollbar-thumb:hover { background: #555 !important; } /* Selection */ ::selection { background: #4ecdc4 !important; color: #1a1a2e !important; } ::-moz-selection { background: #4ecdc4 !important; color: #1a1a2e !important; } '; } function removeDarkMode() { var style = document.getElementById('universal-dark-mode-style'); if (style) style.remove(); } // Toggle with Alt+Shift+D document.addEventListener('keydown', function(e) { if (e.altKey && e.shiftKey && e.key === 'D') { e.preventDefault(); enabled = !enabled; if (enabled) { applyDarkMode(); console.log('[Universal Dark Mode] Enabled'); } else { removeDarkMode(); console.log('[Universal Dark Mode] Disabled'); } } }); // Apply on load applyDarkMode(); // Re-apply on dynamic content var observer = new MutationObserver(function(mutations) { if (enabled && !document.getElementById('universal-dark-mode-style')) { applyDarkMode(); } }); observer.observe(document.head, { childList: true }); console.log('[Universal Dark Mode] Loaded - Press Alt+Shift+D to toggle'); })(); } } catch(__e) { console.warn('[Userscript:Universal Dark Mode]', __e); } })(); })(); GitHub - LukeLabrie/gpu_poisson_solver: 3D accelerated poisson solver for distributed systems · GitHub
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17 Commits

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GPU Poisson Solver

Background

This solver solves the Poisson equation on a cubical domain, $\Omega$, for a specific set of boundary conditions. The poisson equation can be expressed as

$$\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} + \frac{\partial^2 u}{\partial z^2} = -f(x,y,z), \quad (x,y,x) \in \Omega$$

with, for this problem, a boundary defined by

$$\Omega = \{(x, y, z) : |x| \leq 1, |y| \leq 1, |z| \leq 1\}$$

and boundary conditions

$$\begin{align*} u(x, 1, z) &= 20, u(x, -1, z) = 0, -1 \leq x, z \leq 1 \\\ u(1, y, z) &= u(-1, y, z) = 20, -1 \leq y, z \leq 1 \\\ u(x, y, -1) &= u(x, y, 1) = 20, -1 \leq x, y \leq 1. \end{align*}$$

The purpose of the solver is to compare performance across different parallelization methods and includes parallel methods for:

  • CPU (parallel)
  • Single-GPU via OpenMP
  • Dual-GPU via OpenMP
  • Single-GPU via CUDA
  • Dual-GPU via CUDA
  • Four-GPU (two nodes, each with two GPUs), via CUDA, OpenMPI, and NCCL

A full writeup is available in the report.

Requirements

The project is compiled with the mpic++ compiler, an OpenMPI C++ wrapper compiler. The underlying compiler is set to nvc++, NVIDIA's compiler for their GPUS. This can be done by setting the environment variable OMPI_CXX to nvc++ via

export OMPI_CXX=nvc++

Other requirements include:

  • CUDA
  • OpenMPI
  • OpenMP
  • NCCL

Executable

The driver executable can be called as follows

./poisson_solver N K T_0 output_type method [file_suffix] [threads]

N: Problem size. For single-GPU solvers, this needs to be a multiple of 16. For the dual-GPU CUDA solver, this needs to be a multiple of 32.

K: Number of iterations.

T_0: Starting temeprature of inner points on the domain, in Kelvin.

output_type:

  • 0 = No output
  • 1 = Performance metrics printed as [N] [wall time] [data transfer time (s)] [memory (MB)] [bandwidth (data transfer, GB/s)] [bandwidth (no data transfer, GB/s)] [time spent in kernel (s, not always measured)] [bandwidth based on kernel time (s, not always measured)]
  • 3 = Write binary dump (.bin)
  • 4 = Write .vtk file

method:

  • 1 = CPU parallel solver. Number of threads can be specified with the threads argument
  • 2 = Single-GPU solver using OpenMP
  • 3 = Dual-GPU solver using OpenMP
  • 4 = Single-GPU solver using CUDA
  • 5 = Single-GPU solver using CUDA, improved memory access patterns
  • 6 = Dual-GPU solver using CUDA
  • 7 = Four-GPU solver using CUDA+NCCL+MPI. This solver assumes each available node has two GPUs.

file_suffix: Suffix to add to .vtk file

threads: Threads for CPU versions

About

3D accelerated poisson solver for distributed systems

Resources

Stars

4 stars

Watchers

1 watching

Forks

Releases

Packages

Contributors

Languages