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@@ -35,21 +35,10 @@
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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": null,
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"id": "1dc78750",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"jacobi_4_check (generic function with 1 method)"
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]
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},
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"execution_count": 2,
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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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"outputs": [],
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"source": [
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"using Printf\n",
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"\n",
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@@ -75,7 +64,7 @@
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"## The Jacobi method for the Laplace equation\n",
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"\n",
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"\n",
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"The [Jacobi method](https://en.wikipedia.org/wiki/Jacobi_method) is a numerical tool to solve systems of linear algebraic equations. One of the main applications of the method is to solve boundary value problems (BVPs). I.e., given the values at the boundary (of a grid), the Jacobi method will find the interior values that fulfill a certain equation.\n",
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"The [Jacobi method](https://en.wikipedia.org/wiki/Jacobi_method) is a numerical tool to solve systems of linear algebraic equations. One of the main applications of the Jacobi method is to solve the equations resulting from boundary value problems (BVPs). I.e., given the values at the boundary (of a grid), we are interested in finding the interior values that fulfill a certain equation.\n",
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"\n"
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]
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},
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@@ -94,7 +83,7 @@
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"id": "93e84ff8",
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"metadata": {},
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"source": [
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"When solving a Laplace equation in 1D, the Jacobi method leads to this iterative scheme. The entry $i$ of vector $u$ at iteration $t+1$ is computed as:\n",
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"When solving a Laplace equation in 1D, the Jacobi method leads to the following iterative scheme: The entry $i$ of vector $u$ at iteration $t+1$ is computed as:\n",
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"\n",
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"$u^{t+1}_i = \\dfrac{u^t_{i-1}+u^t_{i+1}}{2}$"
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]
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@@ -106,26 +95,15 @@
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"source": [
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"### Serial implementation\n",
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"\n",
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"The following code implements the iterative scheme above for boundary conditions -1 and 1."
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"The following code implements the iterative scheme above for boundary conditions -1 and 1 on a grid with $n$ interior points."
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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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"execution_count": null,
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"id": "14a58308",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"jacobi (generic function with 1 method)"
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]
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},
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"execution_count": 6,
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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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"outputs": [],
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"source": [
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"function jacobi(n,niters)\n",
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" u = zeros(n+2)\n",
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@@ -144,28 +122,10 @@
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},
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{
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"cell_type": "code",
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"execution_count": 14,
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"execution_count": null,
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"id": "76e1eba1",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"7-element Vector{Float64}:\n",
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" -1.0\n",
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" 0.0\n",
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" 0.0\n",
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" 0.0\n",
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" 0.0\n",
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" 0.0\n",
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" 1.0"
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]
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},
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"execution_count": 14,
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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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"outputs": [],
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"source": [
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"jacobi(5,0)"
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]
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@@ -295,7 +255,8 @@
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"metadata": {},
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"source": [
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"## Parallelization of the Jacobi method\n",
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"\n"
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"\n",
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"Now, let us parallelize the Jacobi method."
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]
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},
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{
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@@ -305,8 +266,53 @@
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"source": [
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"### Parallelization strategy\n",
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"\n",
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"We saw in the previous notebook that a sufficiently large grain size is needed to achieve performance in a distributed algorithm. For Jacobi, one could update each entry of vector `u_new` in a different worker, but this would not be efficient. Instead, we use a parallelization strategy with a larger grain size that is analogous to the algorithm 3 we studied for the matrix-matrix multiplication:\n",
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"\n",
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"- Each worker updates a consecutive section of the array `u_new` \n",
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"\n"
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"\n",
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"The following figure displays the data distribution over 3 processes."
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]
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},
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{
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"attachments": {
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"fig09.png": {
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"image/png": 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}
|
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},
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"cell_type": "markdown",
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"id": "a9667c42",
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"metadata": {},
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"source": [
|
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"<div>\n",
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||||
"<img src=\"data:image/png;base64,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 truncated
|
||||
"</div>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "3f90d701",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"### Data dependencies\n",
|
||||
"\n",
|
||||
"Recall the Jacobi update:\n",
|
||||
"\n",
|
||||
"`u_new[i] = 0.5*(u[i-1]+u[i+1])`"
|
||||
]
|
||||
},
|
||||
{
|
||||
"attachments": {
|
||||
"fg10.png": {
|
||||
"image/png": 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truncated
|
||||
}
|
||||
},
|
||||
"cell_type": "markdown",
|
||||
"id": "210e80e7",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"<div>\n",
|
||||
"<img src=\"data:image/png;base64,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 truncated
|
||||
"</div>"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -314,24 +320,21 @@
|
||||
"id": "c4e2d000",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"### Data dependencies\n",
|
||||
"<div class=\"alert alert-block alert-success\">\n",
|
||||
"<b>Question:</b> In order to update the entries u_new[r:s], which data from other process will be needed by the process that owns the entries u[r:s]? Note: r and s are integers indicating the first and last index owned by this process (see picture above). \n",
|
||||
"</div>\n",
|
||||
"\n",
|
||||
"Recall:\n",
|
||||
"\n",
|
||||
"`u_new[i] = 0.5*(u[i-1]+u[i+1])`\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"Thus, each process will need values from the neighboring processes to perform the update of its boundary values."
|
||||
" b) Data at positions r-1 and s+1 "
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "428bce86",
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "3c437326",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"<div>\n",
|
||||
"<img src=\"data:image/png;base64,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 truncated
|
||||
"</div>"
|
||||
"# TODO"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -341,19 +344,58 @@
|
||||
"source": [
|
||||
"### Ghost (aka halo) cells\n",
|
||||
"\n",
|
||||
"A usual way of handling this type of data dependencies is using so-called ghost cells. Ghost cells represent the missing data dependencies in the data owned by each process. After importing the appropriate values from the neighbor processes one can perform the usual sequential Jacobi update locally in the processes."
|
||||
"A usual way of implementing the Jacobi method and related algorithms is using so-called ghost cells. Ghost cells represent the missing data dependencies in the data owned by each process. After importing the appropriate values from the neighbor processes one can perform the usual sequential Jacobi update locally in the processes."
|
||||
]
|
||||
},
|
||||
{
|
||||
"attachments": {
|
||||
"fig13.png": {
|
||||
"image/png": "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 truncated
|
||||
}
|
||||
},
|
||||
"cell_type": "markdown",
|
||||
"id": "98e0eb71",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"<div>\n",
|
||||
"<img src=\"data:image/png;base64,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 truncated
|
||||
"</div>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "cd1e3760",
|
||||
"id": "0148f9b3",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Thus, the algorithm is usually implemented following two main phases at each iteration Jacobi:\n",
|
||||
"\n",
|
||||
"1. Fill the ghost entries with communications\n",
|
||||
"2. Do the Jacobi update sequentially at each process"
|
||||
]
|
||||
},
|
||||
{
|
||||
"attachments": {
|
||||
"fig15.png": {
|
||||
"image/png": "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 truncated
|
||||
}
|
||||
},
|
||||
"cell_type": "markdown",
|
||||
"id": "baccd833",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"<div>\n",
|
||||
"<img src=\"data:image/png;base64,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 truncated
|
||||
"<img src=\"data:image/png;base64,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 truncated
|
||||
"</div>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "8b436c73",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Efficiency"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "5c397005",
|
||||
@@ -593,24 +635,24 @@
|
||||
"source": [
|
||||
"### Latency hiding\n",
|
||||
"\n",
|
||||
"Note that we only need communications to update the values at the boundary of the portion owned by each process. The other values (the one in green in the figure below) can be updated without communications. This provides the opportunity of overlapping the computation of the interior values (green cells in the figure) with the communication of the ghost values. This technique is called latency hiding, since we are hiding communication latency by overlapping it with communications that we need to do anyway.\n",
|
||||
"Can our implementation above be improved? Note that we only need communications to update the values at the boundary of the portion owned by each process. The other values (the one in green in the figure below) can be updated without communications. This provides the opportunity of overlapping the computation of the interior values (green cells in the figure) with the communication of the ghost values. This technique is called latency hiding, since we are hiding communication latency by overlapping it with communications that we need to do anyway.\n",
|
||||
"\n",
|
||||
"The modification of the implementation above to include latency hiding is leaved as an exercise (see below).\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"attachments": {
|
||||
"fig.png": {
|
||||
"image/png": 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truncated
|
||||
"fig16.png": {
|
||||
"image/png": 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truncated
|
||||
}
|
||||
},
|
||||
"cell_type": "markdown",
|
||||
"id": "5ae8701f",
|
||||
"id": "7d66b1a2",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"<div>\n",
|
||||
"<img src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAA6gAAADyCAYAAABAvOgkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAAewgAAHsIBbtB1PgAAABl0RVh0U29mdHdhcmUAd3d3Lmlua3NjYXBlLm9yZ5vuPBoAACAASURBVHic7d17fFxlgf/xz0nTO71ZKKWFUrByKbctlB+2ogJVi0q5rCCLrhVd7bqC6y6yK+yq4OruqoDu/lxXWryh+/uhFERIqSDIRS2lVKwCcoe2SIG29ELb9Jpk9o9n0pxMZ5I0JPM8ST7v12tePU/mzMy3STrNN+ec58nmzp1bQJIkSZKkyGpiB5AkSZIkCSyokiRJkqRE1JaMZ2ZZtiJGEEmSJElS31IoFCYCdzaPWxXULMtWzJkz5+lqh5IkSZIk9T3z5s2jUGiZFslTfCVJkiRJSbCgSpIkSZKSYEGVJEmSJCXBgipJkiRJSoIFVZIkSZKUBAuqJEmSJCkJFlRJkiRJUhIsqJIkSZKkJFhQJUmSJElJsKBKkiRJkpJgQZUkSZIkJcGCKkmSJElKggVVkiRJkpQEC6okSZIkKQkWVEmSJElSEiyokiRJkqQkWFAlSZIkSUmwoEqSJEmSkmBBlSRJkiQlwYIqSZIkSUqCBVWSJEmSlAQLqiRJkiQpCRZUSZIkSVISLKiSJEmSpCRYUCVJkiRJSbCgSpIkSZKSYEGVJEmSJCXBgipJkiRJSkJt7ACSJCk5Q4D3FrcXAvURs1TboOJtF33r7y1JSbCgSpKkUqOBG4vbbwSe7+Tz1ABvAqYCU4BhxY9fQrrl75+AzwP3ADMiZ5GkPseCKkmSusN/Ax8Ehpe573LSLagxvBc4E3gGuDpyFkmKyoIqSZJKbQQuK26v7+RzTKalnK4qPudRrzNXNfwJeBD4YxVf83hgDvArqldQDwJOyN0OAzLgJuCzVcogSXuwoEqSpFKbga++zue4DrgKeBh4Bfgw8IPX+ZzVcF3x1ptNBZZWuG+/agaRpFIWVEmS1B3+X+wAPch3CJNRbdnLxx0GHEe4RvjhTrzuBuC3xcd+CBjfieeQpC7lMjOSJKnUQUCheDs0cpZquxC4F7imiq/5MqEkPrWXj5tFmMxqzl4+7mnC5FdvAN5FuCZ43V4+hyR1C4+gSpIktTgUOAVoquJrTiZcn7sWuK8Kr7epeJOk5HgEVZIkKa73EY6EfjF2EEmKzYIqSZIkSUqCBVWSJEmSlASvQZUkSR01AphU4b5n8LpGSdLrZEGVJEkd9Tbgtgr3nQ7cWcUsfcWhVJ6l98TinycBX6mwzy3Akq4OJUndxYIqSZI6aiOV19v06Gn3mAB8tp19jiveylmOBVVSD2JBlSRJHfVrYGrsEH3MC8BXK9x3InAa8Afgjgr7/L47QklSd7GgSpIkpet54LIK932GUFCXtLGPJPUozuIrSZIkSUqCR1AlSVJ3OI4wcVKz43Pbnwa25sbfArZUI5QkKW0WVEmS1B3amln2CyXjH2JBlSRhQZUkSXvaAswrbnd2dt4ncs/Rnq3t71I1W4C1wIbYQbrZ94EDc+NDi3/OBO7Kffxe4N+qFUqSLKiSJKnUBuCvX+dz/Lp462m+Vrz1dtOAw8t8fFzx1mxtdeJIUmBBlSRJiutm4En2vgzWEZaheb4Tr/l3wLAO7PdCJ55bkjrNgipJkhTX48Xb3nq6eOuMSuumSlJULjMjSZIkSUqCBVWSJEmSlAQLqiRJkiQpCRZUSZIkSVISLKiSJEmSpCRYUCVJkiRJSXCZGSWvUChkdXV1D8XO0ZZrrrnm4OXLlw8B2Lx586sbNmxIbWHzfYH9itvbgBXxopQ1GJiYGz8FNMWJUt6ECRMOp/hLvQsvvPDFqVOnbo4cqaIsy26cNWvWVdV4rbq6uh8UCoWjqvFanTF//vwx999//2iAHTt21K9evTq1NR2HAhNy4ydiBWnDkbntF4D6WEEqmED4PAKsA9ZEzLKHkSNHjh4+fPgYgPHjx2+//PLLl8fO1JaBAweeMnPmzG7/Gt9+++1va2xsvKa7X6eztm/fXnPppZce3jxevXr1ih07dmyLmamMiYT/PyGsoftqvChl7Uf4+QNgK7AyYpY9DBo0aMiYMWMObh5/85vffCLLspiR2vOpM88888HYIarBgqrkffGLX8xOOOGEqbFztGX9+vW88MLun3uHAge3sXtsQ2n5DyNVx8cOUCr39aWxsfHwxP8TW1KtFyoUCkdlWZbsv89t27aV/tscEzFORyT7uSw6sv1doiot/NFt3LiRjRs3AjBgwIChWZaNjhypTTU1NVX52bCxsXFUyu8dWZa1et8Hkv1FXNFQWv+iNzVDaflFeRK2b99e+jWemvL/7VmWjYidoVo8xVeSJEmSlASPoKonui7Lsudih8jbtWvXFRRPsxk/fvzKVatWfTtypFJ/BbypuL0T+ELELOVMBc7Njb8MbImUpaza2tqvNDQ0ALB+/fp7syy7M3KkUrMLhcLkmAEKhcIdNTU198XMUGrz5s2fpHhEbfTo0dvWrVv3xciRSr0NeE9ufFmsIG34Ssvm+Adg/2XxopTz+49B08CwPeIVeOPNcfO0NmZM/aw1a56aANDYWGh4/vmRc2NnyhsyZOeYsWO3nhc5xq4syz4fOUMrO3bs2Af4XPN47NixN73yyiu/jRipnH8BBhS3nwW+EzFLOZ+g5ajuduDKaEnKGDdu3MkvvfTSGc3jhoaGfx44cGBjzEylCoXCvwPpHtbtJhZU9TiFQuHHs2bNuid2jrxJkyZdRrGgTpgwYdWqVau+GjlSqXfQUlB3Aanl+xitC+p/AasjZSmrX79+uwvq8uXLl5xxxhlJfQ4XLFgwDYhaULMs+1Vqn5fp06efTbGgjho1avu6deuSyke41jpfUL8GFCJlqSRXUCf/Dn7xo3hRyun/oVxBfRUe/mHcPK3tv//7TmgpqI0Nn/70yUnl++hHH598zjnPRy+oqb13XHDBBfuTK6gnnnjinXV1dakVwM/RUlBXkt7/7bNoXVCTynfCCSfszBfUH//4x1fPnz9/Z8xMperq6v6NPlhQPcVXkiRJkpQEC6okSZIkKQkWVEmSJElSEiyokiRJkqQkWFAlSZIkSUmwoEqSJEmSkmBBlSRJkiQlwYIqSZIkSUqCBVWSJEmSlAQLqiRJkiQpCRZUSZIkSVISLKiSJEmSpCRYUCVJkiRJSbCgSpIkSZKSYEGVJEmSJCXBgipJkiRJSoIFVZIkSZKUhNrYAdRtBgOTc+NlQFM7j6kBpuTGjwPbujiXJEmSJJVlQe29DgV+mxsPof2yOaDkMccAj3VxLkmSJEkqy1N8JUmSJElJsKBKkiRJkpJgQZUkSZIkJcGCKkmSJElKggVVkiRJkpQEC6okSZIkKQkWVEmSJElSEiyokiRJkqQkWFAlSZIkSUmwoEqSJEmSkmBB7b0KJeOsA4/ZpzuCSJIkSVJHWFB7ry0l446Uz4O7I4gkSZIkdYQFtfdaT+ujqJM68Jh3dFMWSZIkSWqXBbX32gIsz41Pb2f/YcBF3RdHkiRJktpmQe3d7s5tXwyMr7DfQOB64KBuTyRJkiRJFVhQe7d5QFNxexTwa+BcWq5H3Rc4H3gIOAf4fbUDSpIkSVKz2tgB1K0eBr4JfLo4PgSYX9xuovUvKF4ilNdnq5au8y6qq6s7K3aIvH/8x38c3Lz97LPPHgL8Z8Q45RyW2x5AevmOKhl/GdgaI0glDQ0Nu7cnTZr0jrq6uiER4+yhUCgcEzsDcEZdXd3Y2CHyvv3tb09s3l67du1g0vveP75k/B9RUnTY798Kk/aLnaK1pkEt2+sPgEmXxMuypxdfbJjYvN2vX03/6667N6l8/fs3vCF2BmBAXV1dUv82N23aNOSGG27YPV60aNFfACm8z+YNzG0fRnrvb4fktpN7/128ePGU/PgDH/jANbNnz26qtH8kHVmFo9exoPZ+nyn++SlaF9L89m+AvwDWVSvU65Fl2Z/HzlCqtrbln9LatWsPAP42Xpp29SftfAAfix2gVGNj4+7tESNGTAWmxkuTrOnFWzKGDGn5PcJrr702iPS/9xPPt/a4cEvVltGw5fzYKfI2bGjZ7tevpt/YsfVJ5UtELYl97w8YMKDVeP369TOAGXHSdMhBJPY5LDGQxPK9+uqrrcY1NTUXR4qiEhbU3q8R+Dvgu4QSejywH2GW3+cIR1TvIxxR7Qe8P/fYP1UzqCRJkqS+zYLadzxavLWlkZZTgJNxxRVXFBYsWHBb7BxtGTdu3BGNjY3DATZs2PDSyy+//GLsTCXGAQcWt7cAj0fMUs4+wOTc+Le0XD+dhCOOOOKEmpqafgD9+/d/BtjQzkOiybLskSq+1v2ESwSSNHz48AMnT548DmDbtm2bli9f/mTsTCWGA0fkxg/FCtKG/5PbfhLYFCtIBYcDI4rbL5PYL1f333//A0aPHn1Qcbse+GPkSG3avn37rmq8TpZlLwMp/99eM3ny5N1nyqxcufLx+vr60jXmY5tMy7wiL5Lee/GBhJ8/ILxvJPX+u88++wybMGHCkc3jQqGwlNZLNCalsbFxTewM1ZLNnTt39xciy7LD58yZ83TMQJIkSZKkvmHevHmHFQqFp5rHzuIrSZIkSUqCBVWSJCl9A9rfRZJ6PguqJElS+j5PmHV/39hBJKk7WVAlSZLS9xvgBOAR4LTIWSSp21hQJUmS0rcYeA04ALidsHxc/6iJJKkbWFAlSZLStwloKG4PAj4ALAMOjZZInTUodgApZRZUSZKknuGe3PYgwjqYi4G/jBNHnTCIcLr2XJz4SirLgipJktQz3AbU58YZMAb4r+J9Q2KE0l65lnAt8dnAfpGzSEmyoEqSJPUM9wNbynx8BDATeAI4tqqJtDc+CXwYaCQc9V4VN46UJguqJElSz7AW2FnhvgHABMJpwJdVLZE6ahrwjeL2Z4G7ILine truncated
|
||||
"</div>"
|
||||
"<img 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truncated
|
||||
"</div>\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -626,17 +668,17 @@
|
||||
},
|
||||
{
|
||||
"attachments": {
|
||||
"fig_jacobi_07.png": {
|
||||
"image/png": 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truncated
|
||||
"fig17.png": {
|
||||
"image/png": 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truncated
|
||||
}
|
||||
},
|
||||
"cell_type": "markdown",
|
||||
"id": "df867b3d",
|
||||
"id": "f14142ea",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"<div>\n",
|
||||
"<img src=\"data:image/png;base64,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 truncated
|
||||
"</div>\n"
|
||||
"<img src=\"data:image/png;base64,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 truncated
|
||||
"</div>"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -647,7 +689,9 @@
|
||||
"For the Laplace equation in 2D, the interior values in the computational grid (represented by a matrix $u$) are computed with this iterative scheme. The entry $(i,j)$ of matrix $u$ at iteration $t+1$ is computed as:\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"$u^{t+1}_{(i,j)} = \\dfrac{u^t_{(i-1,j)}+u^t_{(i+1,j)}+u^t_{(i,j-1)}+u^t_{(i,j+1)}}{4}$"
|
||||
"$u^{t+1}_{(i,j)} = \\dfrac{u^t_{(i-1,j)}+u^t_{(i+1,j)}+u^t_{(i,j-1)}+u^t_{(i,j+1)}}{4}$\n",
|
||||
"\n",
|
||||
"Note that each entry is updated as the average of the four neighbors (top,bottom,left,right) of that entry in the previous iteration. "
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -662,21 +706,10 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 26,
|
||||
"execution_count": null,
|
||||
"id": "4ab59b2f",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"jacobi_2d (generic function with 1 method)"
|
||||
]
|
||||
},
|
||||
"execution_count": 26,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"function jacobi_2d(n,niters)\n",
|
||||
" u = zeros(n+2,n+2)\n",
|
||||
@@ -700,33 +733,10 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 25,
|
||||
"execution_count": null,
|
||||
"id": "6da0aa54",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"12×12 Matrix{Float64}:\n",
|
||||
" 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0\n",
|
||||
" 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0\n",
|
||||
" 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0\n",
|
||||
" 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0\n",
|
||||
" 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0\n",
|
||||
" 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0\n",
|
||||
" 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0\n",
|
||||
" 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0\n",
|
||||
" 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0\n",
|
||||
" 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0\n",
|
||||
" 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0\n",
|
||||
" 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0"
|
||||
]
|
||||
},
|
||||
"execution_count": 25,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"u = jacobi_2d(10,0)"
|
||||
]
|
||||
@@ -736,7 +746,7 @@
|
||||
"id": "45d786dd",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"### Where do we can exploit parallelism?\n",
|
||||
"### Where can we exploit parallelism?\n",
|
||||
"\n",
|
||||
"```julia\n",
|
||||
"for t in 1:niters\n",
|
||||
@@ -762,68 +772,140 @@
|
||||
"id": "267ecd2a",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"### Parallelization strategies"
|
||||
"### Parallelization strategies\n",
|
||||
"\n",
|
||||
"In 2d one has more flexibility in order to distribute the data over the processes. We consider these three alternatives:\n",
|
||||
"\n",
|
||||
"- 1D block partition (each worker handles a subset of consecutive rows and all columns)\n",
|
||||
"- 2D block partition (each worker handles a subset of consecutive rows and columns)\n",
|
||||
"- 2D cyclic partition (each workers handles a subset of alternating rows ans columns)\n",
|
||||
"\n",
|
||||
"The three partition types are depicted in the following figure for 4 processes.\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"attachments": {
|
||||
"fig_jacobi_07.png": {
|
||||
"image/png": "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 truncated
|
||||
"fig18.png": {
|
||||
"image/png": "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 truncated
|
||||
}
|
||||
},
|
||||
"cell_type": "markdown",
|
||||
"id": "7445dc4a",
|
||||
"id": "e52959a5",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"<div>\n",
|
||||
"<img src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUUAAAFFCAYAAAB7dP9dAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAAewgAAHsIBbtB1PgAAABl0RVh0U29mdHdhcmUAd3d3Lmlua3NjYXBlLm9yZ5vuPBoAACAASURBVHic7J13nBxl/cffz+yVQAISShpFrChiQUGwgYJItWOkQ8rt7CUQkSKiIgvShYAhyd3sccQCCkHFgiggAnYEREUEpUpLgpqjhUtub+f7++PZyT47N7u3M7u3M/qb9+t1r+zMPjPzyczud5/yLQoQUlJSUlIAsOIWkJKSkpIkUqOYkpKSYtDh2z4Z+FMcQupwA7BJ+fXdwGkxagnCAV5bfj0EHBqjliBOAD5Wfi3AB2PUEsSbgcuM7ROB+2LSUoufA6r8+gfA5TFqCeK7wNTy64cBO0YtQVwI7FZ+PQwcEqOWIN4GXGLuEONvnzgUjcOLVPTdHLOWIO6lom91zFqCuJyKvlLMWoLYi+rP4F7xygmkREVf0gwi6M+dp+/emLUEcTMVfS/GrCWIfTA+g+nwOSUlJcUgNYopKSkpBqlRTElJSTFIjWJKSkqKgX/1uR4K2MK372VgQ4hzdAJTfPteBEZDnKMeFvAK374kacwAm/v2rQNGQpyjC5js2/cCrVlEmYL+/3uMEn5ifAsqK7Wg7/3LTeqC4OcS9v+9CTDJt2+oGVE+WvFsUo36O2x22EbQ35NGCbJVw8D6Rk/Q6OqzAr7va3830B1C7NW+4++j4m5TizCrzwq43neNu9AfhEb5tu/4v4yjMczqswXc4jv/7Whj2QgW8DPf8b+n2pD5CbP6/CnfuUeAPRvUBtrVwjWOLwLvHueYRlefNwP+7mvbF0LbFOAB3/GDDR7b6OrzFsAjvmssa1LjQAPHhVl93gJ41HeNMCvqU4AHfcc74xwTdvX5877zrwV2DKHxJN/xzwGvrtN+H1/7UC45QTf0srpHVOj1HfcS8MYGjgvrkjMVeMx3rcUNalzoO+5F4A3jHBPWJWc68IzvOvkG9X2B8B+WsC45fb5rPMzY3ncQ2wP/9h17SgPHhXHJeQf6195sf0QD1wD4pu+4+4FNGzw2jEvObujesXmtwxu8zrd8x/21QY1hXXJ2D9D4iQY1XuU77r4GNIY1igr4ke86d1L/x98j6P823v1vyigGXdQFPj7OMW9GD6HMax3dwLUgmp/iOwM0fqzuEcEaj2rgWlH8FD+AHpqaxmo8p+o90T038//00QauFdYodgN/pPo+rBznmA7gN75jbqR6GF2LsH6Kn/G1fxHYaZxj5vmOGQbe2oA2j7B+iif6rjdeTwVgfoDGtzSoL4qfor83NQS8apxjsr5jGu3YRPFT3AZ4yne9C8Y5JqjTtrSBazVtFEH3ABq9oZOJPmyB6M7bn/Nds16vKuqwBaI7b5/ru95qYEaNtlOBx33tL6nR1k8U5+3XAs/7rper0/6rvrZPAVs3eK2wRjHsNM6b0PNRZvt5DWrzCGsUw07jBGmcE0JfFKMYpPEPdTTuEqDx2AavFdV5ey+qOw8u8OE67b/j0zfe1JdHS4yiQoc7mcfeSfAN9Q9b/o6eH2qUqEZRAT9sUGPUYQtEN4oZ4FbfdX/B2PnFoHtd78PrJ2pEy6d91xwGdg1odyDV84glwkVGRYloaXQaZxLwZ1+7a0Jo84gS0dLoNM5k9FC+GY1RI1qCNF5cQ+PffO2+E+I6zUS0nOG77rPAtgHtjve1a2Tqy6MlRhGCey8X+do0O2yB5sL8tgzQeKGvTTPDFmguzG9b4F++63/B1+Zk3/uNDHNMmgnzu8J37X9QvXq+XYD+L4W8RtQwv0amca70nfshxq7+N0LUML9GpnG+3gKNzYT5BWn0T8t8g7GfgzAdm2aMouU7XoA7qO48vIVoU18eLTOKAHswdp7rI+X3goYE80OeH5qPfX4fehW0UY1zQ56/2dhnf09rlMpziDJp7KcZozgJnSAkqBfTAfzK995tNL6S7tFM7HO9aRx/T3c9wT3dRmgm9vlUnw5zGuewFmlsNvb5tACNryy/N8f33jA6gUIYmo19nsbYxcmzyu8FrYY3OvXl0VKjCHC67xz/QU98+4ct10Y4N7QmIcQXAzS+keaHLdCahBAX+XQ8iZ7XizJp7KfZhBCvR/uxmTrmAOf59q0BZkY4fzNGsdY0zpsYOye6III2j2aMYj2N/vtab962Hs0axaCppt/X0JiNcP5WJIR4P2MXJ/ejuakvj5YbxSDfOX/vK2x326QVRtECbhpH44OMdQ5uhFYYxU7gt+Pou5exDrON0IosOcf5tAxTbSgaWT2vRbNZcrYCnqD+vbsuojaPZrPkbI3+oauncbwV/nq0IkvO1oxd7fVrjNJpgNZlyTlrHH3rgJ0jnLflRhGCl8+9v/XA2yOeF1qXOmwa8HQdjVGHVq1KHRbk52d+kBqdNPbTqtRhX6+hTYCzmzhvK1KH+adxzL9/oueWm6EVqcP8LlXm3yM05gtai1alDvNPNZl/jfqrBtEqo2ihc1vW+hyGWbE3mRCjCGOXz72/hU2cE1qbT3FvgjX2NnHOVuZTPJjq+UXvL8yksZ9WGcWgFUgBfkm4cFE/rcqn6J/GEbQRelcT2jxalU/R73zvaQwTNRREK/MpfomxGtejHeej0sp8itOBVQEao/ZiYQLzKa5jbHzwerQvVFJYx1jDMIye80kC69BG0eQ5tCN03BQJjj9dSeti15shKPb2QbR/YFII0vgA2s8yKdTS+Od2C6lBkeBcAd9s5UVa0VMMWgHy/m4n/IqkSat6ilMYGzvbCo2t6inWm4K4gcaiQ4JoVU/x0hraGo1qqEUreoq7MNYlw/s7twltHq3oKQZFTHl/5zSpr1U9xXoam5kiaVVPMcjh3Pzu1Qp+GI8JGT774yH9f2dGPC+0zij6k1H4/86IeN5WGMWgWE//36KI526FUaw1rPf+GknsUYtmjWKtYb35f/5QRG0ezRrFoKguv8b9mtDXCqMYFNXVKo2tMor+8En/30+J1nlouVH0x0O+iC6WZH6QRtFL6lFohVHM+TS+UNbo9w/cO8K5W2EU/X5i/2ZsbGrUeZ1mjeIOaBcmU8tZ6Il3c1+YjDUmzRpFv2PxfYx1cWqmFwHNG0W/28h9jA2NbEZjK4yiv2PzZ3R0i7lvFXpOLyytMIpBiTZORPtUmvtOjXDulhrFIOdnL9HDBbTmoTdrFIOGVt7Chf/LEyZm16NZo1gvosDx6XuY8NEOzRjFDuDXPg1eoodmssGYNGMUj/Md60UjWYwNobyN6FMkzRjFuT4dL6HdRlqpsVmj6I8886ZEghz0g0JRx6NZoxg09eU9hyjp6vy0zCgGxWyaiR6CvlA/JXy272aMYtDQyvR2bya7i0czRnG82NNJvvML4Z3gmzGK/h82/4/GZ33vN5INxk9UoxjkVG5GIwWFUEadIolqFGs5vtfT+MUI+poxikEdm2ON94NCOU8PeY1mjaJ/6suf6GGJ7/0n0P6rjdIyo/h137FBiR6CfO8+F+Ia0JxR9A+tgnLobc/Y4WEjeQA9ohrFRjOpvI6xX6yeENeJahQPYKyDtv/zERStETapbxSjGBR+GPRj0WyyCo8oRrFeiGQ9jWaYZ6NENYpBCTOCEj0cxNje2HtDXKcZo+jPwxrks9sN3ONr92Ma79y0xCj6YzbrJXpotnsb1SgGxWyG0diof1tUoxgm516Y/4ufKEYxyBesVi+rmbRmEM0oFnzH1Eui0ExaM48oRnEghEb/3N2TITVGNYqDvuvWizxbHKCx0d5YVKMYNPVVKw9rULq74xu8TtNGMUrP5Wu+9mG6t1GMYtCwZbwceqbxEBqPhIhiFIMySI83H+fv9Taagi2sUQyKGriN+vNIQYlBGkmAC+GN4mxf+/EiploxRRLWKAZprBcxFRTm+ZMQGqMYxUZTw9XT2KirWBSjGDT1NV4e1rCfDY+mjGLQHFcjMZvNdG/DGsVGh1aNaPxuA8eFNYpBk8bLGzguarLesEYx77vGGmBWA8cFlUp4ZQPHhTGKryFabyBoiuTkBo7zCGMUg3osjSSjCFrlP6lBfWGNYtgkwqZG/2rviQ0cF8UoRu0E+NPdNZKKrSmj2O9rHyYeMuoHOqxRDDO08hPlAx3WKEYp3uURpaxDGKO4N2MzkTTq4xeUdKOREMBGjWKz80af9B0bJgSwUaMY9Ye1WY1hjGJQuYkwCTMODdA4XphiWKPYzHRRlE5RZKMYVOltjwaFekTp3oYxilG7z+Odo96wIoxR9PtLRokGWeA7x3jJIho1itswNmFG2GiQoLx3XxnnmEaNYrMrjKBTr5nnaHSKpFGjGPX8JssjnCOMUVzWAo1hi5uFMYpBU19hFhYhfAmKKqMYJpD/PrRvmscL6F5YGFaiwwHNqlz/CXmOevyFidG4tkldHr+iWt8QOmdiGJYDv6PatemlJnWB7nF9xLcvbLzrs2i/S9PB1x/LHQWF9nb4hrHvGcJ/dk4GVgScuxVY5XOb53+G8J+dzzJ2WqSVGq8s/3lE1XiFb18zSUFMhtGF3TxcwrsZ3Y/2VzVrPzdc8znMf+TBEG3r8ZcWnSeIpGu8v0XnaTYTShDPlv+a5anyXysR9JCvWTagh7cTgduic/83aFzfovME8WT5r1keiXpgK7PkpKSkpPzXkxrFlJSUFIPUKKakpKQYpEYxJSUlxSA1iikpKSkGirKzYhmvSluSMCvsuWjn5SQxmWqXiVa4x7SSSVR7GSRNXwfVVQrXk4zyBibmZ3CUEO4dbcLUJwSXjYiTTWm9C1kryWAEUPiNYkpKSsr/a9Lhc0pKSoqB33n7boKrecXJvlSM9/PAH2LUEsR7qORoHEVnlEkSuwAzje1b4hJSg62oDsX8I62NcmoFZm2SVcBf4xJSgw9Q+S6/jM4KlCTeSSUM0EVnHE8SU6mONLine truncated
|
||||
"<img src=\"data:image/png;base64,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 truncated
|
||||
"</div>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "e0cee28b",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Which of the thee alternatives is more efficient? To answer this question we need to quantify how much data is processed and communicated in each case. The following analysis assumes that the grid is of $N$ by $N$ cells and that the number of processes is $P$."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "f6ea16f5",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"### 1D block partition\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"attachments": {
|
||||
"g26521.png": {
|
||||
"image/png": 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truncated
|
||||
}
|
||||
},
|
||||
"cell_type": "markdown",
|
||||
"id": "0cfeca62",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"<div>\n",
|
||||
"<img src=\"data:image/png;base64,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 truncated
|
||||
"</div>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "4600c94a",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"- We update $N^2/P$ items per iteration\n",
|
||||
"- We need data from 2 neighbors (2 messages per iteration)\n",
|
||||
"- We communicate $N$ items per message\n",
|
||||
"- Communication/computation ratio is $O(P/N)$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "969c42ee",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"### Data dependencies"
|
||||
"### 2D block partition"
|
||||
]
|
||||
},
|
||||
{
|
||||
"attachments": {
|
||||
"fig_jacobi_07.png": {
|
||||
"image/png": 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||||
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|
||||
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truncated
|
||||
}
|
||||
},
|
||||
"cell_type": "markdown",
|
||||
"id": "b343f4c1",
|
||||
"id": "e5142fa1",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"\n",
|
||||
"<div>\n",
|
||||
"<img 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truncated
|
||||
"<img src=\"data:image/png;base64,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 truncated
|
||||
"</div>\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "df861921",
|
||||
"id": "091b0310",
|
||||
"metadata": {},
|
||||
"source": []
|
||||
"source": [
|
||||
"- We update $N^2/P$ items per iteration\n",
|
||||
"- We need data from 4 neighbors (4 messages per iteration)\n",
|
||||
"- We communicate $N/\\sqrt{P}$ items per message\n",
|
||||
"- Communication/computation ratio is $O(\\sqrt{P}/N)$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "a8fb49a3",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"### 2D cyclic partition"
|
||||
]
|
||||
},
|
||||
{
|
||||
"attachments": {
|
||||
"fig_jacobi_07.png": {
|
||||
"image/png": 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|
||||
}
|
||||
},
|
||||
"cell_type": "markdown",
|
||||
"id": "6f97781b",
|
||||
"id": "1bc30b74",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"\n",
|
||||
"<div>\n",
|
||||
"<img 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truncated
|
||||
"</div>\n"
|
||||
"<img src=\"data:image/png;base64,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 truncated
|
||||
"</div>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "c45f4e44",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"- We update $N^2/P$ items\n",
|
||||
"- We need data from 4 neighbors (4 messages per iteration)\n",
|
||||
"- We communicate $N^2/P$ items per message (the full data owned by the neighbor)\n",
|
||||
"- Communication/computation ratio is $O(1)$"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -831,9 +913,14 @@
|
||||
"id": "850b1848",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"### Complexity analysis\n",
|
||||
"### Which partition is the best one?\n",
|
||||
"\n",
|
||||
"The complexity analysis is let as an exercise (see below).\n"
|
||||
"- Both 1d and 2d block partitions are potentially scalable if $P<<N$\n",
|
||||
"- The 2d block partition is with the lowest communication complexity\n",
|
||||
"- The 1d block partition requires to send less messages (It can be useful if the fixed cost of sending a message is high)\n",
|
||||
"- The best strategy for a given problem size will thus depend on the machine, but the 2d block partition is the one used in practice since it has the lowest communication complexity.\n",
|
||||
"- Cyclic partitions are impractical for this application (but they are useful in others) \n",
|
||||
"\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -962,7 +1049,7 @@
|
||||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
||||
"display_name": "Julia 1.9.1",
|
||||
"display_name": "Julia 1.9.0",
|
||||
"language": "julia",
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Reference in new issue
Block a user