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zingalezingale
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update before talk
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‎presentations/pyro_intro.ipynb‎

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"source": [
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"## Design ideas:\n",
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"\n",
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" * _Clarity is emphasized over performance_\n",
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"\n",
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" * Single driver implements core evolution\n",
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" \n",
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" * Clarity is emphasized over performance\n",
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" \n",
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" \n",
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" * Object-oriented structure: each solver provides a simulation class to manage the different parts of the update\n",
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" \n",
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" * All solvers are 2-d: right balance of complexity and usefulness\n",
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" - _Nov 2018_: python + NumPy + Numba"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"slideshow": {
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"slide_type": "slide"
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}
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},
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"source": [
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"## Our usage\n",
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"\n",
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" * We start new undergraduate researchers out with pyro to learn about simulation workflows\n",
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" * Typically have UG add a new problem setup"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"</div>"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"slideshow": {
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"slide_type": "slide"
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}
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},
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"source": [
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"## Grids\n",
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"\n",
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"* ``patch`` module manages grids and data that lives on them\n",
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"\n",
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"* Fills boundaries, does prolongation/restriction for multigrid\n",
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"\n",
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"* Many convenience functions"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {
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"slideshow": {
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"slide_type": "skip"
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}
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},
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"outputs": [],
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"source": [
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"import mesh.patch as patch\n",
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"import mesh.boundary as bnd\n",
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"import numpy as np"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {
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"slideshow": {
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"slide_type": "fragment"
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}
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"2-d grid: nx = 16, ny = 16, ng = 2\n"
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]
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}
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],
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"source": [
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"g = patch.Grid2d(16, 16, ng=2)\n",
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"print(g)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {
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"slideshow": {
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"slide_type": "fragment"
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}
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"BCs: -x: periodic +x: periodic -y: reflect-even +y: outflow\n"
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]
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}
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],
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"source": [
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"bc = bnd.BC(xlb=\"periodic\", xrb=\"periodic\", ylb=\"reflect\", yrb=\"outflow\")\n",
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"print(bc)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {
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"slideshow": {
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"slide_type": "fragment"
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}
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"cc data: nx = 16, ny = 16, ng = 2\n",
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" nvars = 1\n",
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" variables:\n",
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" a: min: 0.0000000000 max: 0.0000000000\n",
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" BCs: -x: periodic +x: periodic -y: reflect-even +y: outflow \n",
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"\n"
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]
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}
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],
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"source": [
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"d = patch.CellCenterData2d(g)\n",
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"d.register_var(\"a\", bc)\n",
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"d.create()\n",
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"print(d)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"slideshow": {
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"slide_type": "slide"
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}
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},
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"source": [
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"## Grids"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {
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"slideshow": {
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"slide_type": "fragment"
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}
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},
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"outputs": [],
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"source": [
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"a = d.get_var(\"a\")"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Data is stored as an ``ArrayIndexer`` object, which makes it easy to implement differencing on the entire array.\n",
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"\n",
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"To implement:\n",
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"$$ b = \\frac{a_{i+1,j} - a_{i-1,j}}{2 \\Delta x}$$"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {},
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"outputs": [],
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"source": [
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"b = g.scratch_array()\n",
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"b.v()[:,:] = (a.ip(1) - a.ip(-1))/(2.0*a.g.dx)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"source": [
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"## Running\n",
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"\n",
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"* Each solver has a collection of problem setups (initial conditions) and inputs files\n",
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"\n",
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"* Commandline:\n",
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"\n",
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" ```\n",
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"execution_count": 7,
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"metadata": {
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"slideshow": {
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"slide_type": "fragment"
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"\u001b[33mparameter vis.store_images never used\u001b[0m\n",
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"\u001b[33mparameter particles.n_particles never used\u001b[0m\n",
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"\u001b[33mparameter particles.particle_generator never used\u001b[0m\n",
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"main: 0.08537530899047852\n"
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"main: 0.18631219863891602\n"
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]
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},
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{
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"data": {
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"text/plain": [
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"<advection.simulation.Simulation at 0x7f9c1829df10>"
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"<advection.simulation.Simulation at 0x7fc0a799b910>"
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]
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},
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"execution_count": 1,
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"execution_count": 7,
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"metadata": {},
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"output_type": "execute_result"
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}
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"execution_count": 8,
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"metadata": {
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"slideshow": {
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"slide_type": "fragment"
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"execution_count": 9,
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"metadata": {
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"slideshow": {
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"slide_type": "fragment"
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}
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},
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"source": [
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"## Grids"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {
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"slideshow": {
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"slide_type": "fragment"
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}
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"2-d grid: nx = 16, ny = 16, ng = 2\n"
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]
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}
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],
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"source": [
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"import mesh.patch as patch\n",
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"import mesh.boundary as bnd\n",
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"import numpy as np\n",
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"## Other solvers\n",
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"\n",
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"g = patch.Grid2d(16, 16, ng=2)\n",
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"print(g)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {
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"slideshow": {
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"slide_type": "fragment"
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}
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"BCs: -x: periodic +x: periodic -y: reflect-even +y: outflow\n"
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]
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}
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],
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"source": [
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"bc = bnd.BC(xlb=\"periodic\", xrb=\"periodic\", ylb=\"reflect\", yrb=\"outflow\")\n",
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"print(bc)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {
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"slideshow": {
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"slide_type": "fragment"
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}
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"cc data: nx = 16, ny = 16, ng = 2\n",
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" nvars = 1\n",
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" variables:\n",
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" a: min: 0.0000000000 max: 0.0000000000\n",
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" BCs: -x: periodic +x: periodic -y: reflect-even +y: outflow \n",
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"\n"
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]
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}
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],
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"source": [
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"d = patch.CellCenterData2d(g)\n",
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"d.register_var(\"a\", bc)\n",
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"d.create()\n",
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"print(d)"
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"![compressible](quad.png) \n"
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]
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},
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{
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}
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},
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"source": [
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"## Grids"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {
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"slideshow": {
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"slide_type": "fragment"
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}
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},
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"outputs": [],
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"source": [
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"a = d.get_var(\"a\")\n",
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"a.v()[:,:] = np.random.rand(g.nx, g.ny)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Data is stored as an ``ArrayIndexer`` object, which makes it easy to implement differencing on the entire array.\n",
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"## Other solvers\n",
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"\n",
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"To implement:\n",
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"$$ b = \\frac{a_{i+1,j} - a_{i-1,j}}{2 \\Delta x}$$"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"metadata": {},
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"outputs": [],
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"source": [
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"b = g.scratch_array()\n",
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"b.v()[:,:] = (a.ip(1) - a.ip(-1))/(2.0*a.g.dx)"
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"![incompressible](shear.png)"
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]
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},
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{

‎presentations/quad.png‎

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‎presentations/shear.png‎

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