diff --git a/crates/specialized/rtx-cfd/src/kernels/cuda/e3_cg.cu b/crates/specialized/rtx-cfd/src/kernels/cuda/e3_cg.cu
index f92ea06..78f7a8a 100644
--- a/crates/specialized/rtx-cfd/src/kernels/cuda/e3_cg.cu
+++ b/crates/specialized/rtx-cfd/src/kernels/cuda/e3_cg.cu
@@ -198,3 +198,27 @@ extern "C" __global__ void e3_cg_scatter_f64(
     int g = cells[t];
     z[g] = (double) x0[g];
 }
+
+
+
+/* P1-5 (c): scatter compact (index, value) lists into persistent buffers. */
+extern "C" __global__ void e3_scat_f64(int n, const unsigned int* __restrict__ idx, const double* __restrict__ val, double* __restrict__ dst)
+{
+    int t = blockIdx.x * blockDim.x + threadIdx.x;
+    if (t < n) dst[idx[t]] = val[t];
+}
+extern "C" __global__ void e3_scat_f32(int n, const unsigned int* __restrict__ idx, const float* __restrict__ val, float* __restrict__ dst)
+{
+    int t = blockIdx.x * blockDim.x + threadIdx.x;
+    if (t < n) dst[idx[t]] = val[t];
+}
+extern "C" __global__ void e3_scat_u32(int n, const unsigned int* __restrict__ idx, const unsigned int* __restrict__ val, unsigned int* __restrict__ dst)
+{
+    int t = blockIdx.x * blockDim.x + threadIdx.x;
+    if (t < n) dst[idx[t]] = val[t];
+}
+extern "C" __global__ void e3_scat_i32(int n, const unsigned int* __restrict__ idx, const int* __restrict__ val, int* __restrict__ dst)
+{
+    int t = blockIdx.x * blockDim.x + threadIdx.x;
+    if (t < n) dst[idx[t]] = val[t];
+}
diff --git a/crates/specialized/rtx-cfd/src/solvers/incompressible/embedded3/poisson/device.rs b/crates/specialized/rtx-cfd/src/solvers/incompressible/embedded3/poisson/device.rs
index afb956e..9eafae2 100644
--- a/crates/specialized/rtx-cfd/src/solvers/incompressible/embedded3/poisson/device.rs
+++ b/crates/specialized/rtx-cfd/src/solvers/incompressible/embedded3/poisson/device.rs
@@ -203,6 +203,43 @@ impl DeviceVcycle {
         self.fine_cells = level0.cells.clone();
     }
 
+    /// P1-5 (c): as [`Self::refresh_fine`] with only the rows of `rows`
+    /// scattered into the persistent coefficient and neighbour buffers; the
+    /// index lists that change length are uploaded whole.
+    pub fn refresh_fine_rows(&mut self, level0: &LevelExport, rows: &[u32]) {
+        let rt = runtime();
+        let up_u = |v: &[u32]| -> CudaSlice<u32> {
+            rt.stream
+                .memcpy_stod(if v.is_empty() { &[0u32][..] } else { v })
+                .expect("upload")
+        };
+        let lv = &mut self.levels[0];
+        if lv.ae.len() != level0.ae.len() {
+            drop(lv);
+            self.refresh_fine(level0);
+            return;
+        }
+        lv.n_cells = level0.cells.len();
+        lv.n_red = level0.red.len();
+        lv.n_black = level0.black.len();
+        lv.cells = up_u(&level0.cells);
+        lv.red = up_u(&level0.red);
+        lv.black = up_u(&level0.black);
+        let pick_u = |v: &[u32]| rows.iter().map(|&i| v[i as usize]).collect::<Vec<u32>>();
+        let pick_f = |v: &[f32]| rows.iter().map(|&i| v[i as usize]).collect::<Vec<f32>>();
+        super::device_cg::scatter_u32(rows, &pick_u(&level0.top), &mut lv.top);
+        super::device_cg::scatter_u32(rows, &pick_u(&level0.bot), &mut lv.bot);
+        super::device_cg::scatter_u32(rows, &pick_u(&level0.coarse_of), &mut lv.coarse_of);
+        super::device_cg::scatter_f32(rows, &pick_f(&level0.ae), &mut lv.ae);
+        super::device_cg::scatter_f32(rows, &pick_f(&level0.aw), &mut lv.aw);
+        super::device_cg::scatter_f32(rows, &pick_f(&level0.an), &mut lv.an);
+        super::device_cg::scatter_f32(rows, &pick_f(&level0.as_), &mut lv.as_);
+        super::device_cg::scatter_f32(rows, &pick_f(&level0.at), &mut lv.at);
+        super::device_cg::scatter_f32(rows, &pick_f(&level0.ab), &mut lv.ab);
+        super::device_cg::scatter_f32(rows, &pick_f(&level0.ap), &mut lv.ap);
+        self.fine_cells = level0.cells.clone();
+    }
+
     /// Zero the finest level's right-hand side (a gather writes only the
     /// current cells; stale entries elsewhere would restrict into the
     /// coarse levels).
diff --git a/crates/specialized/rtx-cfd/src/solvers/incompressible/embedded3/poisson/device_cg.rs b/crates/specialized/rtx-cfd/src/solvers/incompressible/embedded3/poisson/device_cg.rs
index 6a4f4fb..e2377fb 100644
--- a/crates/specialized/rtx-cfd/src/solvers/incompressible/embedded3/poisson/device_cg.rs
+++ b/crates/specialized/rtx-cfd/src/solvers/incompressible/embedded3/poisson/device_cg.rs
@@ -15,6 +15,10 @@ const KERNELS: &str = include_str!("../../../../kernels/cuda/e3_cg.cu");
 
 struct CgKernels {
     _module: Arc<CudaModule>,
+    scat_f64: CudaFunction,
+    scat_f32: CudaFunction,
+    scat_u32: CudaFunction,
+    scat_i32: CudaFunction,
     spmv: CudaFunction,
     residual: CudaFunction,
     dot_partial: CudaFunction,
@@ -32,11 +36,101 @@ struct CgKernels {
 
 static CG: OnceLock<CgKernels> = OnceLock::new();
 
+/// P1-5 (c): write `val[t]` to `dst[idx[t]]` on the device (the compact
+/// lists uploaded, one launch). Empty lists are a no-op.
+pub(crate) fn scatter_f64(idx: &[u32], val: &[f64], dst: &mut CudaSlice<f64>) {
+    if idx.is_empty() {
+        return;
+    }
+    let rt = runtime();
+    let k = kernels();
+    let d_idx = rt.stream.memcpy_stod(idx).expect("scatter idx");
+    let d_val = rt.stream.memcpy_stod(val).expect("scatter val");
+    let n = idx.len() as i32;
+    unsafe {
+        rt.stream
+            .launch_builder(&k.scat_f64)
+            .arg(&n)
+            .arg(&d_idx)
+            .arg(&d_val)
+            .arg(dst)
+            .launch(cfg(idx.len()))
+            .expect("scatter f64");
+    }
+}
+
+pub(crate) fn scatter_f32(idx: &[u32], val: &[f32], dst: &mut CudaSlice<f32>) {
+    if idx.is_empty() {
+        return;
+    }
+    let rt = runtime();
+    let k = kernels();
+    let d_idx = rt.stream.memcpy_stod(idx).expect("scatter idx");
+    let d_val = rt.stream.memcpy_stod(val).expect("scatter val");
+    let n = idx.len() as i32;
+    unsafe {
+        rt.stream
+            .launch_builder(&k.scat_f32)
+            .arg(&n)
+            .arg(&d_idx)
+            .arg(&d_val)
+            .arg(dst)
+            .launch(cfg(idx.len()))
+            .expect("scatter f32");
+    }
+}
+
+pub(crate) fn scatter_u32(idx: &[u32], val: &[u32], dst: &mut CudaSlice<u32>) {
+    if idx.is_empty() {
+        return;
+    }
+    let rt = runtime();
+    let k = kernels();
+    let d_idx = rt.stream.memcpy_stod(idx).expect("scatter idx");
+    let d_val = rt.stream.memcpy_stod(val).expect("scatter val");
+    let n = idx.len() as i32;
+    unsafe {
+        rt.stream
+            .launch_builder(&k.scat_u32)
+            .arg(&n)
+            .arg(&d_idx)
+            .arg(&d_val)
+            .arg(dst)
+            .launch(cfg(idx.len()))
+            .expect("scatter u32");
+    }
+}
+
+pub(crate) fn scatter_i32(idx: &[u32], val: &[i32], dst: &mut CudaSlice<i32>) {
+    if idx.is_empty() {
+        return;
+    }
+    let rt = runtime();
+    let k = kernels();
+    let d_idx = rt.stream.memcpy_stod(idx).expect("scatter idx");
+    let d_val = rt.stream.memcpy_stod(val).expect("scatter val");
+    let n = idx.len() as i32;
+    unsafe {
+        rt.stream
+            .launch_builder(&k.scat_i32)
+            .arg(&n)
+            .arg(&d_idx)
+            .arg(&d_val)
+            .arg(dst)
+            .launch(cfg(idx.len()))
+            .expect("scatter i32");
+    }
+}
+
 fn kernels() -> &'static CgKernels {
     CG.get_or_init(|| {
         let module = load_module(KERNELS, "e3_cg.cu", true);
         let f = |name: &str| module.load_function(name).expect(name);
         CgKernels {
+            scat_f64: f("e3_scat_f64"),
+            scat_f32: f("e3_scat_f32"),
+            scat_u32: f("e3_scat_u32"),
+            scat_i32: f("e3_scat_i32"),
             spmv: f("e3_cg_spmv"),
             residual: f("e3_cg_residual"),
             dot_partial: f("e3_cg_dot_partial"),
@@ -293,15 +387,35 @@ impl DeviceCg {
             self.partial = rt.stream.alloc_zeros::<f64>(self.n_blocks).expect("alloc");
         }
         self.cells = up_u(&to_u32(&fine.cells));
-        self.top = up_u(&to_u32(&fine.top));
-        self.bot = up_u(&to_u32(&fine.bot));
-        self.ae = up_f(&fine.ae);
-        self.aw = up_f(&fine.aw);
-        self.an = up_f(&fine.an);
-        self.as_ = up_f(&fine.as_);
-        self.at = up_f(&fine.at);
-        self.ab = up_f(&fine.ab);
-        self.ap = up_f(&fine.ap);
+        // P1-5 (c): with a patched level the changed rows are scattered into
+        // the persistent buffers (the same values everywhere else).
+        let rows_u32: Option<Vec<u32>> = match (patched, changed) {
+            (true, Some(rows)) if self.ae.len() == fine.ae.len() => Some(rows.iter().map(|&i| i as u32).collect()),
+            _ => None,
+        };
+        if let Some(rows) = rows_u32.as_deref() {
+            let pick_f = |v: &[f64]| rows.iter().map(|&i| v[i as usize]).collect::<Vec<f64>>();
+            let pick_u = |v: &[usize]| rows.iter().map(|&i| if v[i as usize] == usize::MAX { u32::MAX } else { v[i as usize] as u32 }).collect::<Vec<u32>>();
+            scatter_u32(rows, &pick_u(&fine.top), &mut self.top);
+            scatter_u32(rows, &pick_u(&fine.bot), &mut self.bot);
+            scatter_f64(rows, &pick_f(&fine.ae), &mut self.ae);
+            scatter_f64(rows, &pick_f(&fine.aw), &mut self.aw);
+            scatter_f64(rows, &pick_f(&fine.an), &mut self.an);
+            scatter_f64(rows, &pick_f(&fine.as_), &mut self.as_);
+            scatter_f64(rows, &pick_f(&fine.at), &mut self.at);
+            scatter_f64(rows, &pick_f(&fine.ab), &mut self.ab);
+            scatter_f64(rows, &pick_f(&fine.ap), &mut self.ap);
+        } else {
+            self.top = up_u(&to_u32(&fine.top));
+            self.bot = up_u(&to_u32(&fine.bot));
+            self.ae = up_f(&fine.ae);
+            self.aw = up_f(&fine.aw);
+            self.an = up_f(&fine.an);
+            self.as_ = up_f(&fine.as_);
+            self.at = up_f(&fine.at);
+            self.ab = up_f(&fine.ab);
+            self.ap = up_f(&fine.ap);
+        }
         self.link_ptr = up_u(&link_ptr);
         self.link_idx = up_u(&link_idx);
         self.link_coef = up_f(if link_coef.is_empty() {
@@ -332,7 +446,10 @@ impl DeviceCg {
             assert!(same(&fine_level.ae, &full.ae) && same(&fine_level.aw, &full.aw) && same(&fine_level.an, &full.an) && same(&fine_level.as_, &full.as_) && same(&fine_level.at, &full.at) && same(&fine_level.ab, &full.ab) && same(&fine_level.ap, &full.ap), "band export: coefficients differ");
         }
         let l_export = lap.elapsed();
-        self.vcycle.refresh_fine(&fine_level);
+        match rows_u32.as_deref() {
+            Some(rows) if self.fine_export.is_some() => self.vcycle.refresh_fine_rows(&fine_level, rows),
+            _ => self.vcycle.refresh_fine(&fine_level),
+        }
         self.fine_export = Some(fine_level);
         self.fine = Some(fine);
         if profile {