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## Authors
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This material is created by [Francesc Verdugo](https://github.com/fverdugo/) with the help of [Gelieza Kötterheinrich](https://www.linkedin.com/in/gelieza/). Part of the notebooks are based on the course slides by [Henri Bal](https://www.vuhpdc.net/henri-bal/).
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This material is created by [Francesc Verdugo](https://github.com/fverdugo/) with the help of [Gelieza Kötterheinrich](https://www.linkedin.com/in/gelieza-k/). Part of the notebooks are based on the course slides by [Henri Bal](https://www.vuhpdc.net/henri-bal/).
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## License
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+20
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@@ -271,7 +271,7 @@
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},
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{
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"cell_type": "markdown",
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"id": "c518f863",
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"id": "6b17aee4",
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"metadata": {},
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"source": [
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"The outer loop of the algorithm is not parallelizable, since the iterations depend on the results of the previous iterations. However, we can extract parallelism from the inner loops. Let's have a look at two different parallelization schemes. \n",
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@@ -282,22 +282,22 @@
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},
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{
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"attachments": {
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}
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},
|
||||
"cell_type": "markdown",
|
||||
"id": "f06f0869",
|
||||
"id": "c518f863",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"<div>\n",
|
||||
"<img src=\"attachment:g23933.png\" align=\"left\" width=\"400\"/>\n",
|
||||
"<img src=\"attachment:fig-asp-1d-partition.png\" align=\"left\" width=\"400\"/>\n",
|
||||
"</div>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "a67e0aad",
|
||||
"id": "102d6fa2",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## What is the work per process at iteration k?\n",
|
||||
@@ -307,22 +307,22 @@
|
||||
},
|
||||
{
|
||||
"attachments": {
|
||||
"g26595.png": {
|
||||
"image/png": 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truncated
|
||||
"fig-asp-data-updated.png": {
|
||||
"image/png": "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 truncated
|
||||
}
|
||||
},
|
||||
"cell_type": "markdown",
|
||||
"id": "53a94ed3",
|
||||
"id": "a67e0aad",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"<div>\n",
|
||||
"<img src=\"attachment:g26595.png\" align=\"left\" width=\"250\"/>\n",
|
||||
"<img src=\"attachment:fig-asp-data-updated.png\" align=\"left\" width=\"250\"/>\n",
|
||||
"</div>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "d083cd53",
|
||||
"id": "d9d29899",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"It is clear from the code that at a given iteration `k`, the matrix is updated from row `k` to `n` and from column `k` to `m`. If we look at how that reflects the distribution of work over the processes, we can see that CPU 1 does not have any work, whereas CPU 2 does a little work and CPU 3 and 4 do a lot of work. Thus, the work load is _imbalanced_ across the different processes. "
|
||||
@@ -330,16 +330,16 @@
|
||||
},
|
||||
{
|
||||
"attachments": {
|
||||
"g26786.png": {
|
||||
"image/png": 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truncated
|
||||
"fig-asp-data-updated-2.png": {
|
||||
"image/png": 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truncated
|
||||
}
|
||||
},
|
||||
"cell_type": "markdown",
|
||||
"id": "0d80cd72",
|
||||
"id": "d083cd53",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"<div>\n",
|
||||
"<img src=\"attachment:g26786.png\" align=\"left\" width=\"250\"/>\n",
|
||||
"<img src=\"attachment:fig-asp-data-updated-2.png\" align=\"left\" width=\"250\"/>\n",
|
||||
"</div>"
|
||||
]
|
||||
},
|
||||
@@ -379,7 +379,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "b90252f1",
|
||||
"id": "51498a44",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"### Cyclic partition\n",
|
||||
@@ -389,16 +389,16 @@
|
||||
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}
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},
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"cell_type": "markdown",
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"id": "6a4c4051",
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"id": "b90252f1",
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"metadata": {},
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"source": [
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||||
"<div>\n",
|
||||
"<img src=\"attachment:g27009.png\" align=\"left\" width=\"250\"/>\n",
|
||||
"<img src=\"attachment:fig-asp-data-updated-cyclic.png\" align=\"left\" width=\"250\"/>\n",
|
||||
"</div>"
|
||||
]
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},
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|
||||
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-9
@@ -5716,7 +5716,7 @@
|
||||
"id": "63c406e0",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"The number of iterations is now constant for different problem sizes. Thus, we have finally achieved to build an algorithmically scalable solver by combining the conjugate gradient method and the multi-grid method!"
|
||||
"The number of iterations is now constant for different problem sizes. Thus, we have finally achieved an algorithmically scalable solver by combining the conjugate gradient method and the multi-grid method!"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -5726,7 +5726,7 @@
|
||||
"source": [
|
||||
"### High-performance conjugate gradient (HPCG) benchmark\n",
|
||||
"\n",
|
||||
"- Alternative to HPL benchmark to rank the [top 500](https://www.top500.org/) computers\n"
|
||||
"The HPCG benchmark is an alternative to the HPL benchmark to rank the [top 500](https://www.top500.org/) computers. It is based on the CG + multigrid method, whereas the HPL benchmark is a Gaussian elimination type of algorithm. The HPCG was introduced because the CG + multigrid method is more commonly run on supercomputers than Gaussian elimination. While HPL gives a good indication of the peak performance, the HPCG benchmark is orders of magnitude below the peak performance. \n"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -5847,7 +5847,8 @@
|
||||
"id": "a8aa2ebd",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"### MPI implementation"
|
||||
"### MPI implementation\n",
|
||||
" TODO maybe question which MPI directive is used? (erase MPI.Allreduce from picture and put it into answer for the question"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -5961,28 +5962,28 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "a6433395",
|
||||
"id": "5e2926d0",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"<div class=\"alert alert-block alert-success\">\n",
|
||||
"<b>Question:</b> Which mesh partition does lead to less communication in the sparse matrix-vector product?\n",
|
||||
"</div>\n",
|
||||
"\n",
|
||||
"- Answer: 2d block (as for Jacobi method)\n"
|
||||
"- Answer: 2d block (as for Jacobi method)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"attachments": {
|
||||
"g20102.png": {
|
||||
"image/png": 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truncated
|
||||
"fig-pdes-2d-partition.png": {
|
||||
"image/png": "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 truncated
|
||||
}
|
||||
},
|
||||
"cell_type": "markdown",
|
||||
"id": "931e1fb6",
|
||||
"id": "a6433395",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"<div>\n",
|
||||
"<img src=\"attachment:g20102.png\" align=\"left\" width=\"400\"/>\n",
|
||||
"<img src=\"attachment:fig-pdes-2d-partition.png\" align=\"left\" width=\"400\"/>\n",
|
||||
"</div>"
|
||||
]
|
||||
},
|
||||
|
||||
Reference in new issue
Block a user