From 06efd62402e6fced8b82820ea9b360a20af1244b Mon Sep 17 00:00:00 2001
From: Martin Bauer <martin.bauer@fau.de>
Date: Fri, 22 Mar 2019 14:43:41 +0100
Subject: [PATCH] Extended data handling tutorial
---
...g.ipynb => 03_tutorial_datahandling.ipynb} | 297 +++++++++++++++---
... => 04_tutorial_advection_diffusion.ipynb} | 0
...l_phasefield_spinodal_decomposition.ipynb} | 0
...utorial_phasefield_dentritic_growth.ipynb} | 0
4 files changed, 261 insertions(+), 36 deletions(-)
rename doc/notebooks/{06_tutorial_datahandling.ipynb => 03_tutorial_datahandling.ipynb} (50%)
rename doc/notebooks/{03_tutorial_advection_diffusion.ipynb => 04_tutorial_advection_diffusion.ipynb} (100%)
rename doc/notebooks/{04_tutorial_phasefield_spinodal_decomposition.ipynb => 05_tutorial_phasefield_spinodal_decomposition.ipynb} (100%)
rename doc/notebooks/{05_tutorial_phasefield_dentritic_growth.ipynb => 06_tutorial_phasefield_dentritic_growth.ipynb} (100%)
diff --git a/doc/notebooks/06_tutorial_datahandling.ipynb b/doc/notebooks/03_tutorial_datahandling.ipynb
similarity index 50%
rename from doc/notebooks/06_tutorial_datahandling.ipynb
rename to doc/notebooks/03_tutorial_datahandling.ipynb
index b24a667..75a7209 100644
--- a/doc/notebooks/06_tutorial_datahandling.ipynb
+++ b/doc/notebooks/03_tutorial_datahandling.ipynb
@@ -70,7 +70,7 @@
"\n",
"One concept of *pystencils* that may be confusing at first, is the differences between pystencils fields and numpy arrays. Fields are used to describe the computation *symbolically* with sympy, while numpy arrays hold the actual values where the computation is executed on. \n",
"\n",
- "One option to create and execute a *pystencils* kernel is listed below. For reason that become clear later we call this the **variable-field-size workflow**:\n",
+ "One option to create and execute a *pystencils* kernel is listed below. For reasons that become clear later we call this the **variable-field-size workflow**:\n",
"\n",
"1. define pystencils fields\n",
"2. use sympy and the pystencils fields to define an update rule, that describes what should be done on *every cell* \n",
@@ -92,7 +92,8 @@
"\n",
"# 2. define update rule\n",
"update_rule = [ps.Assignment(lhs=dst_field[0, 0],\n",
- " rhs=(src_field[1, 0] + src_field[-1, 0] + src_field[0, 1] + src_field[0, -1]) / 4)]\n",
+ " rhs=(src_field[1, 0] + src_field[-1, 0] + \n",
+ " src_field[0, 1] + src_field[0, -1]) / 4)]\n",
"\n",
"# 3. compile update rule to function\n",
"kernel_function = ps.create_kernel(update_rule).compile()\n",
@@ -245,9 +246,9 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "Even if it looks very ugly and low-level :) lets look at this code in a bit more detail. The code is generated in a way that is works for different array sizes. The size of the array is passed in the `_size_dst_` variables that specifiy the shape of the array for each dimension. Also, the memory layout (linearization) of the array can be different. That means the array could be stored in row-major or column-major order - if we pass in the array strides correctly the kernel does the right thing. If you're not familiar with the concept of strides check out [this stackoverflow post](https://stackoverflow.com/questions/53097952/how-to-understand-numpy-strides-for-layman) or search in the numpy documentation for strides - C vs Fortran order.\n",
+ "Even if it looks very ugly and low-level :) lets look at this code in a bit more detail. The code is generated in a way that it works for different array sizes. The size of the array is passed in the `_size_dst_` variables that specifiy the shape of the array for each dimension. Also, the memory layout (linearization) of the array can be different. That means the array could be stored in row-major or column-major order - if we pass in the array strides correctly the kernel does the right thing. If you're not familiar with the concept of strides check out [this stackoverflow post](https://stackoverflow.com/questions/53097952/how-to-understand-numpy-strides-for-layman) or search in the numpy documentation for strides - C vs Fortran order.\n",
"\n",
- "The goal of *pystencils* is to produce the fastest possible code. On technique to do this is to use all available information already on compile time and generate code that is highly adapted to the specific problem. In our case we already know the shape and strides of the arrays we want to apply the kernel on, so we can make use of this information. This idea leads to the **fixed-field-size workflow**. The main difference there is that we define the arrays first and therefore let *pystencils* know about the array shapes and strides, so that is can generate more specific code:\n",
+ "The goal of *pystencils* is to produce the fastest possible code. One technique to do this is to use all available information already on compile time and generate code that is highly adapted to the specific problem. In our case we already know the shape and strides of the arrays we want to apply the kernel to, so we can make use of this information. This idea leads to the **fixed-field-size workflow**. The main difference there is that we define the arrays first and therefore let *pystencils* know about the array shapes and strides, so that it can generate more specific code:\n",
"\n",
"1. create numpy arrays that hold your data\n",
"2. define pystencils fields, this time telling pystencils already which arrays they correspond to, so that it knows about the size and strides\n",
@@ -273,7 +274,8 @@
"\n",
"# 3. define update rule\n",
"update_rule = [ps.Assignment(lhs=dst_field[0, 0],\n",
- " rhs=(src_field[1, 0] + src_field[-1, 0] + src_field[0, 1] + src_field[0, -1]) / 4)]\n",
+ " rhs=(src_field[1, 0] + src_field[-1, 0] + \n",
+ " src_field[0, 1] + src_field[0, -1]) / 4)]\n",
"\n",
"# 4. compile it\n",
"kernel_function = ps.create_kernel(update_rule).compile()\n",
@@ -425,7 +427,7 @@
"source": [
"Compare this to the code above! It looks much simpler. The reason is that all index computations are already simplified since the exact field sizes and strides are known. This kernel now only works on arrays of the previously specified size. \n",
"\n",
- "Lets try what happens if we try to use a different array:"
+ "Lets try what happens if we use a different array:"
]
},
{
@@ -456,7 +458,7 @@
"### 1.2. GPU simulations\n",
"\n",
"Let's now jump to a seemingly unrelated topic: running kernels on the GPU. \n",
- "To run on GPU not many changes are required: When creating the kernel an additional parameter `target='gpu'` has to be passed. Also, the compiled kernel cannot be called with numpy arrays, but has to be called with `pycuda.gpuarray`s instead. That means, we have to transfer our numpy array to GPU first. From this step we obtain a gpuarray, then we can run the kernel, hopefully multiple times so that the data transfer was worth the time. Finally we transfer the finished result back to CPU. In code this looks like this:"
+ "When creating the kernel, an additional parameter `target='gpu'` has to be passed. Also, the compiled kernel cannot be called with numpy arrays directly, but has to be called with `pycuda.gpuarray`s instead. That means, we have to transfer our numpy array to GPU first. From this step we obtain a gpuarray, then we can run the kernel, hopefully multiple times so that the data transfer was worth the time. Finally we transfer the finished result back to CPU:"
]
},
{
@@ -554,7 +556,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "This method is nice and easy, but you should not use it if you want your simulation to run on distributed-memory clusters. We'll see why in the next section about distributed memory parallelization. So it is good habit to not access the arrays directly but use the data handling to do so. We can, for example, initialize the array also with the following code:"
+ "This method is nice and easy, but you should not use it if you want your simulation to run on distributed-memory clusters. We'll see why in the last section. So it is good habit to not access the arrays directly but use the data handling to do so. We can, for example, initialize the array also with the following code:"
]
},
{
@@ -600,6 +602,25 @@
"dh.run_kernel(kernel_function)"
]
},
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "To access the data read-only instead of using `cpu_arrays` the gather function should be used.\n",
+ "This function gives you a read-only copy of the domain or part of the domain. \n",
+ "We will discuss this function later in more detail when we look at MPI parallel simulations.\n",
+ "For serial simulations keep in mind that modifying the resulting array does not change your original data!"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "read_only_copy = dh.gather_array('src', ps.make_slice[:, :], ghost_layers=False)"
+ ]
+ },
{
"cell_type": "markdown",
"metadata": {},
@@ -614,7 +635,7 @@
},
{
"cell_type": "code",
- "execution_count": 14,
+ "execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
@@ -641,7 +662,7 @@
},
{
"cell_type": "code",
- "execution_count": 15,
+ "execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
@@ -659,7 +680,7 @@
},
{
"cell_type": "code",
- "execution_count": 16,
+ "execution_count": 17,
"metadata": {},
"outputs": [],
"source": [
@@ -679,47 +700,105 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "### 2.2 Ghost Layers and periodicity"
+ "### 2.2 Ghost Layers and periodicity\n",
+ "\n",
+ "The data handling can also provide periodic boundary conditions. Therefor the domain is extended by one layer of cells, the so-called ghost layer or halo layer."
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 18,
"metadata": {},
- "outputs": [],
- "source": []
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Shape of domain (30, 30)\n",
+ "Direct access to arrays (32, 32)\n",
+ "Gather (32, 32)\n"
+ ]
+ }
+ ],
+ "source": [
+ "print(\"Shape of domain \", dh.shape)\n",
+ "print(\"Direct access to arrays \", dh.cpu_arrays['src'].shape)\n",
+ "print(\"Gather \", dh.gather_array('src', ghost_layers=True).shape)"
+ ]
},
{
- "cell_type": "code",
- "execution_count": null,
+ "cell_type": "markdown",
"metadata": {},
- "outputs": [],
- "source": []
+ "source": [
+ " So the actual arrays are 2 cells larger than what you asked for. This additional layer is used to copy over the data from the other end of the array, such that for the stencil algorithm effectively the domain is periodic. This copying operation has to be started manually though:"
+ ]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 19,
"metadata": {},
- "outputs": [],
- "source": []
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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vb1MPCwDcTnYzANvmKrUAAACMEJwAAACMWOefRXldkj9I8vCquqGqfmF+LADgVOxmAJbiyJlu0N3POh+DAADrsZsBWAqn1AIAADBCcAIAADBCcAIAADBCcAIAADBCcAIAADBCcAIAADBCcAIAADBCcAIAADBCcAIAADBCcAIAADBCcAIAADBCcAIAADBCcAIAADBCcAIAADBCcAIAADBCcAIAADBCcAIAADBCcAIAADBCcAIAADBCcAIAADBCcAIAADBCcAIAADDiyLYHYDOe+IBLtz0CANwudhjA97r6lm1PsBme4QQAAGCE4AQAAGCE4AQAAGCE4AQAAGCE4AQAAGCE4AQAAGCE4AQAAGCE4AQAAGCE4AQAAGCE4AQAAGCE4AQAAGCE4AQAAGCE4AQAAGCE4AQAAGCE4AQAAGCE4AQAAGCE4AQAAGCE4AQAAGCE4AQAAGCE4AQAAGCE4AQAAGCE4AQAAGDEWsFZVZdX1aeq6tNV9cvTQwEAp2c3A7AEZwzOqrogyW8meVKSRyR5VlU9YnowAOBgdjMAS7HOM5yPTvLp7v5Md387yeuTPG12LADgNOxmABZhneC8KMn1J318w+pzAMB22M0ALMI6wVkHfK6/50ZVV1TVsao6duLEiXOfDAA4FbsZgEVYJzhvSPLAkz6+OMmNt71Rd1/Z3Ue7++je3t6m5gMAvpfdDMAirBOcH0nyQ1X1g1V15yTPTPJ7s2MBAKdhNwOwCEfOdIPuvrmqfjHJO5NckORV3X3t+GQAwIHsZgCW4ozBmSTd/fYkbx+eBQBYk90MwBKsc0otAAAAnDXBCQAAwAjBCQAAwAjBCQAAwAjBCQAAwAjBCQAAwAjBCQAAwAjBCQAAwAjBCQAAwAjBCQAAwAjBCQAAwAjBCQAAwAjBCQAAwAjBCQAAwAjBCQAAwAjBCQAAwAjBCQAAwAjBCQAAwAjBCQAAwAjBCQAAwAjBCQAAwAjBCQAAwIjq7s0/aNWJJJ87i7vcN8mXNj7I4bCrx+a4lmdXj81xLc/ZHtuDu3tvapg7Crv5u+zqsTmu5dnVY3NcyzO2m0eC82xV1bHuPrrtOSbs6rE5ruXZ1WNzXMuzy8e2S3b592lXj81xLc+uHpvjWp7JY3NKLQAAACMEJwAAACMOS3Beue0BBu3qsTmu5dnVY3Ncy7PLx7ZLdvn3aVePzXEtz64em+NanrFjOxSv4QQAAGD3HJZnOAEAANgxhyY4q+rpVXVtVd1SVYu/+lNVXV5Vn6qqT1fVL297nk2pqldV1U1V9fFtz7JJVfXAqnpvVV23+nP4gm3PtAlVddeq+nBVfWx1XC/d9kybVFUXVNUfVtVbtz3LJlXVZ6vqv1fVNVV1bNvzbEpV3buq3lRVn1x9rz122zNxenbzMtjNy2I3L5PdfPsdmuBM8vEkfzvJ+7c9yLmqqguS/GaSJyV5RJJnVdUjtjvVxlyV5PJtDzHg5iQv6u4fTvKYJM/fkd+zbyV5XHc/MsmlSS6vqsdseaZNekGS67Y9xJCf6u5Ld+zy6/86yTu6+68keWR29/dul9jNy3BV7OYlsZuXy26+HQ5NcHb3dd39qW3PsSGPTvLp7v5Md387yeuTPG3LM21Ed78/yZe3Pcemdffnu/ujq/e/lv1vtou2O9W5631fX3144eptJ164XVUXJ3lykldsexbOrKruleQnk7wySbr72939le1OxZnYzctgNy+L3cxhcb5286EJzh1zUZLrT/r4huzA/yDvKKrqkiSPSvKh7U6yGatTW65JclOSq7t7J44ryW8keXGSW7Y9yIBO8q6qOl5VV2x7mA15SJITSV69OtXqFVV1920PxR2K3bxgdvNi2M3Lcl5283kNzqp6d1V9/IC3nfgJ40nqgM/txE+udl1V3SPJ7yZ5YXd/ddvzbEJ3f6e7L01ycZJHV9WPbnumc1VVT0lyU3cf3/YsQy7r7h/L/ql/z6+qn9z2QBtwJMmPJfl33f2oJN9IsjOvoVsyu5nDzm5eBrt5kc7Lbj6y6Qc8ne5+/Pn89bbohiQPPOnji5PcuKVZWFNVXZj9hfaa7n7ztufZtO7+SlW9L/uv81n6hSUuS/LUqvqZJHdNcq+q+p3ufvaW59qI7r5x9d+bquot2T8VcOmvobshyQ0n/RT/TRGch4LdzGFmNy+K3bw852U3O6V2xkeS/FBV/WBV3TnJM5P83pZn4jSqqrJ//vp13f2ybc+zKVW1V1X3Xr1/tySPT/LJ7U517rr7Jd19cXdfkv3vr/fsykKrqrtX1T1vfT/JE7L8v4Sku7+Q5PqqevjqU38zySe2OBJ3PHbzwtjNy2I3L8/52s2HJjir6m9V1Q1JHpvkbVX1zm3PdHt1981JfjHJO7P/Avc3dPe1251qM6rqdUn+IMnDq+qGqvqFbc+0IZcleU6Sx60ud33N6id0S3f/JO+tqj/K/l+2ru7unbpM+Q66X5IPVNXHknw4ydu6+x1bnmlT/nGS16z+PF6a5Ne3PA9nYDcvg928OHbz8tjN56C6vXwBAACAzTs0z3ACAACwWwQnAAAAIwQnAAAAIwQnAAAAIwQnAAAAIwQnAAAAIwQnAAAAIwQnAAAAI/4/V7RA5XxySx0AAAAASUVORK5CYII=\n",
+ "text/plain": [
+ "<Figure size 1152x432 with 2 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "dh = ps.create_data_handling((4, 4), periodicity=(True, False))\n",
+ "dh.add_array(\"src\")\n",
+ "\n",
+ "# get copy function\n",
+ "copy_fct = dh.synchronization_function(['src'])\n",
+ "\n",
+ "dh.fill('src', 0.0, ghost_layers=True)\n",
+ "dh.fill('src', 3.0, ghost_layers=False)\n",
+ "before_sync = dh.gather_array('src', ghost_layers=True).copy()\n",
+ "\n",
+ "copy_fct() # copy over to get periodicity in x direction\n",
+ "\n",
+ "after_sync = dh.gather_array('src', ghost_layers=True).copy()\n",
+ "plt.subplot(1,2,1)\n",
+ "plt.scalar_field(before_sync);\n",
+ "plt.title(\"Before\")\n",
+ "plt.subplot(1,2,2)\n",
+ "plt.scalar_field(after_sync);\n",
+ "plt.title(\"After\");"
+ ]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
- "## 3. Going (MPI) parallel - the parallel data handling"
+ "## 3. Going (MPI) parallel - the parallel data handling\n",
+ "\n",
+ "### 3.1. Conceptual overview\n",
+ "To run MPI parallel simulations the waLBerla framework is used. waLBerla has to be compiled against your local MPI library and thus is a bit hard to install. We suggest to use the version shipped with conda for testing. For production, when you want to run on a cluster the best option is to build waLBerla yourself against the MPI library that is installed on your cluster.\n",
+ "\n",
+ "Now lets have a look on how to write code that runs MPI parallel.\n",
+ "Since the data is distributed, we don't have access to the full array any more but only to the part that is stored locally. The domain is split into so called blocks, where one process might get one (or sometimes multiple) blocks. To do anything with the local part of the data we iterate over the **local** blocks to get the contents as numpy arrays. The blocks returned in the loop differ from process to process.\n",
+ "\n",
+ "Copy the following snippet to a python file and run with multiple processes e.g.:\n",
+ "``mpirun -np 4 myscript.py`` you will see that there are as many blocks as processes."
]
},
{
"cell_type": "code",
- "execution_count": 17,
+ "execution_count": 20,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
- "(-1, -1)\n"
+ "(-1, -1) (32, 32)\n"
]
}
],
@@ -727,39 +806,185 @@
"dh = ps.create_data_handling(domain_size=(30, 30), parallel=True)\n",
"field = dh.add_array('field')\n",
"for block in dh.iterate():\n",
- " print(block.offset) # offset is in global coordinates, where first inner cell has coordiante (0,0) and ghost layers have negative coordinates\n",
+ " # offset is in global coordinates, where first inner cell has coordiante (0,0) \n",
+ " # and ghost layers have negative coordinates\n",
+ " print(block.offset, block['field'].shape) \n",
" \n",
" # use offset to create a local array 'my_data' for the part of the domain\n",
" #np.copyto(block[field.name], my_data)"
]
},
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "To get some more interesting results here in the notebook we put multiple blocks onto our single notebook process. This makes not much sense for real simulations, but for testing and demonstration purposes this is useful."
+ ]
+ },
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 21,
"metadata": {},
- "outputs": [],
- "source": []
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "(-1, -1, -1) (22, 12, 22)\n",
+ "(19, -1, -1) (22, 12, 22)\n",
+ "(-1, -1, 19) (22, 12, 22)\n",
+ "(19, -1, 19) (22, 12, 22)\n"
+ ]
+ }
+ ],
+ "source": [
+ "from waLBerla import createUniformBlockGrid\n",
+ "from pystencils.datahandling import ParallelDataHandling\n",
+ "\n",
+ "blocks = createUniformBlockGrid(blocks=(2,1,2), cellsPerBlock=(20, 10, 20), \n",
+ " oneBlockPerProcess=False, periodic=(1, 0, 0))\n",
+ "dh = ParallelDataHandling(blocks)\n",
+ "field = dh.add_array('field')\n",
+ "for block in dh.iterate():\n",
+ " print(block.offset, block['field'].shape)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now we see that we have four blocks with (20, 10, 20) block each, and the global domain is (40, 10, 40) big.\n",
+ "All subblock also have a ghost layer around them, which is used to synchronize with their neighboring blocks (over the network). For ghost layer synchronization the same `synchronization_function` is used that we used above for periodic boundaries, because copying between blocks and copying the ghost layer for periodicity uses the same mechanism."
+ ]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 22,
"metadata": {},
- "outputs": [],
- "source": []
+ "outputs": [
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/latex": [
+ "$$\\left ( 40, \\quad 10, \\quad 40\\right )$$"
+ ],
+ "text/plain": [
+ "(40, 10, 40)"
+ ]
+ },
+ "execution_count": 22,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "dh.gather_array('field').shape"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### 3.2. Parallel example \n",
+ "\n",
+ "To illustrate this in more detail, lets run a simple kernel on a parallel domain. waLBerla can handle 3D domains only, so we choose a z-size of 1."
+ ]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 23,
"metadata": {},
"outputs": [],
- "source": []
+ "source": [
+ "blocks = createUniformBlockGrid(blocks=(2,4,1), cellsPerBlock=(20, 10, 1), \n",
+ " oneBlockPerProcess=False, periodic=(1, 1, 0))\n",
+ "dh = ParallelDataHandling(blocks, dim=2)\n",
+ "src_field = dh.add_array('src')\n",
+ "dst_field = dh.add_array('dst')\n",
+ "\n",
+ "update_rule = [ps.Assignment(lhs=dst_field[0, 0 ],\n",
+ " rhs=(src_field[1, 0] + src_field[-1, 0] + \n",
+ " src_field[0, 1] + src_field[0, -1]) / 4)]\n",
+ "\n",
+ "# 3. compile update rule to function\n",
+ "kernel_function = ps.create_kernel(update_rule).compile()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now lets initialize the arrays. To do this we can get arrays (meshgrids) from the block with the coordinates of the local cells. We use this to initialize a circular shape."
+ ]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 24,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ "<Figure size 1152x432 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "dh.fill('src', 0.0)\n",
+ "for block in dh.iterate(ghost_layers=False, inner_ghost_layers=False):\n",
+ " x, y = block.midpoint_arrays\n",
+ " inside_sphere = (x -20)**2 + (y-25)**2 < 8 ** 2\n",
+ " block['src'][inside_sphere] = 1.0\n",
+ "plt.scalar_field( dh.gather_array('src') );"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now we can run our compute kernel on this data as usual. We just have to make sure that the field is synchronized after every step, i.e. that the ghost layers are correctly updated."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 25,
"metadata": {},
"outputs": [],
- "source": []
+ "source": [
+ "sync = dh.synchronization_function(['src'])\n",
+ "for i in range(40):\n",
+ " sync()\n",
+ " dh.run_kernel(kernel_function)\n",
+ " dh.swap('src', 'dst')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 26,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 1152x432 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.scalar_field( dh.gather_array('src') );"
+ ]
}
],
"metadata": {
diff --git a/doc/notebooks/03_tutorial_advection_diffusion.ipynb b/doc/notebooks/04_tutorial_advection_diffusion.ipynb
similarity index 100%
rename from doc/notebooks/03_tutorial_advection_diffusion.ipynb
rename to doc/notebooks/04_tutorial_advection_diffusion.ipynb
diff --git a/doc/notebooks/04_tutorial_phasefield_spinodal_decomposition.ipynb b/doc/notebooks/05_tutorial_phasefield_spinodal_decomposition.ipynb
similarity index 100%
rename from doc/notebooks/04_tutorial_phasefield_spinodal_decomposition.ipynb
rename to doc/notebooks/05_tutorial_phasefield_spinodal_decomposition.ipynb
diff --git a/doc/notebooks/05_tutorial_phasefield_dentritic_growth.ipynb b/doc/notebooks/06_tutorial_phasefield_dentritic_growth.ipynb
similarity index 100%
rename from doc/notebooks/05_tutorial_phasefield_dentritic_growth.ipynb
rename to doc/notebooks/06_tutorial_phasefield_dentritic_growth.ipynb
--
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