Use our own script to do documentation deployment

Because the default branch is called main in both AMReX-Codes.github.io and
amrex-tutorials, there is a name conflict in our previous setup using
JamesIves/github-pages-deploy-action. So we switch to our script.

.github/workflows/docs.yml

@@ -1,5 +1,10 @@
 name: Build and Deploy
 on: [push, pull_request]
+
+concurrency:
+  group: ${{ github.ref }}-${{ github.head_ref }}-docs
+  cancel-in-progress: true
+
 jobs:
   build-and-deploy:
     runs-on: ubuntu-latest
@@ -26,11 +31,39 @@ jobs:
 
       - name: Deploy
         if: github.event_name == 'push' && github.repository == 'AMReX-Codes/amrex-tutorials' && github.ref == 'refs/heads/main'
-        uses: JamesIves/github-pages-deploy-action@v4
-        with:
-          ssh-key: ${{ secrets.DEPLOY_KEY }}
-          repository-name: AMReX-Codes/AMReX-Codes.github.io
-          branch: main # The branch the action should deploy to.
-          folder: Docs/build/html # The folder the action should deploy.
-          target_folder: amrex/tutorials_html # The folder the action should deploy to.
-          clean: false # Do not remove existing files from the deploy target.
+        env:
+          SSH_KEY: ${{ secrets.DEPLOY_KEY }}
+        run: |
+          # https://blog.benoitblanchon.fr/github-action-run-ssh-commands/
+          echo "Configure SSH"
+          mkdir -p ~/.ssh/
+          echo "$SSH_KEY" > ~/.ssh/deploy_key
+          chmod 600 ~/.ssh/deploy_key
+          cat >>~/.ssh/config <<END
+          Host *
+            IdentityFile ~/.ssh/deploy_key
+            StrictHostKeyChecking no
+          END
+
+          echo "Configure git"
+          git config --global user.name "$(git log -1 --pretty=format:'%an')"
+          git config --global user.email $(git log -1 --pretty=format:'%ae')
+          git config --global core.ignorecase false
+
+          DEPLOY_SOURCE=${PWD}/Docs/build/html
+          DEPLOY_SOURCE_HEAD=$(git rev-parse --short HEAD)
+          cd ..
+          echo "git clone AMReX-Codes.github.io"
+          git clone --depth=1 -b main git@github.com:AMReX-Codes/AMReX-Codes.github.io
+          cd AMReX-Codes.github.io/amrex/tutorials_html/
+          rsync -q -av --checksum --progress ${DEPLOY_SOURCE}/. .
+          git add --all .
+          if [ -n "$(git status --porcelain)" ]; then
+            git commit -m "Deoploying from amrex-tutorials ${DEPLOY_SOURCE_HEAD}" --no-verify
+            echo "git push to AMReX-Codes.github.io"
+            git --no-pager show HEAD
+            echo "Successfully completed deployment"
+          else
+            git config -l
+            echo "No changes to deploy"
+          fi