diff --git a/fpie/core/openmp/grid.cc b/fpie/core/openmp/grid.cc
index 7862eb01..a0ed4122 100644
--- a/fpie/core/openmp/grid.cc
+++ b/fpie/core/openmp/grid.cc
@@ -32,13 +32,13 @@ inline void OpenMPGridSolver::update_equation(int id) {
   int id1 = off3 - 3;
   int id2 = off3 + 3;
   int id3 = off3 + m3;
-  tgt[off3 + 0] = (grad[off3 + 0] + tgt[id0 + 0] + tgt[id1 + 0] + tgt[id2 + 0] +
+  tmp[off3 + 0] = (grad[off3 + 0] + tgt[id0 + 0] + tgt[id1 + 0] + tgt[id2 + 0] +
                    tgt[id3 + 0]) /
                   4.0;
-  tgt[off3 + 1] = (grad[off3 + 1] + tgt[id0 + 1] + tgt[id1 + 1] + tgt[id2 + 1] +
+  tmp[off3 + 1] = (grad[off3 + 1] + tgt[id0 + 1] + tgt[id1 + 1] + tgt[id2 + 1] +
                    tgt[id3 + 1]) /
                   4.0;
-  tgt[off3 + 2] = (grad[off3 + 2] + tgt[id0 + 2] + tgt[id1 + 2] + tgt[id2 + 2] +
+  tmp[off3 + 2] = (grad[off3 + 2] + tgt[id0 + 2] + tgt[id1 + 2] + tgt[id2 + 2] +
                    tgt[id3 + 2]) /
                   4.0;
 }
@@ -91,6 +91,15 @@ OpenMPGridSolver::step(int iteration) {
         }
       }
     }
+#pragma omp parallel for schedule(static)
+    for (int id = 0; id < N * M; ++id) {
+      if (mask[id]) {
+        int off3 = id * 3;
+        tgt[off3 + 0] = tmp[off3 + 0];
+        tgt[off3 + 1] = tmp[off3 + 1];
+        tgt[off3 + 2] = tmp[off3 + 2];
+      }
+    }
   }
   calc_error();
 #pragma omp parallel for schedule(static)
diff --git a/fpie/process.py b/fpie/process.py
index a5c84401..bb8ca22b 100644
--- a/fpie/process.py
+++ b/fpie/process.py
@@ -8,7 +8,25 @@
 
 from fpie import np_solver
 
-CPU_COUNT = os.cpu_count() or 1
+DEFAULT_CPU_CAP = 8
+
+
+def _default_cpu_count() -> int:
+    """Pick a conservative default for CPU-backed solvers."""
+    candidates: list[int] = []
+    cpu_count = os.cpu_count()
+    if cpu_count is not None:
+        candidates.append(cpu_count)
+    try:
+        candidates.append(len(os.sched_getaffinity(0)))
+    except (AttributeError, OSError):
+        pass
+    if not candidates:
+        return 1
+    return max(1, min(min(candidates), DEFAULT_CPU_CAP))
+
+
+CPU_COUNT = _default_cpu_count()
 DEFAULT_BACKEND = "numpy"
 ALL_BACKEND = ["numpy"]
 MPI: Any | None = None
diff --git a/tests/test_smoke.py b/tests/test_smoke.py
index 49fed554..5fc9cf19 100644
--- a/tests/test_smoke.py
+++ b/tests/test_smoke.py
@@ -6,7 +6,11 @@
 
 import numpy as np
 
-from fpie.process import EquProcessor, GridProcessor
+from fpie.process import (
+    ALL_BACKEND,
+    EquProcessor,
+    GridProcessor,
+)
 
 
 class SmokeTest(unittest.TestCase):
@@ -41,6 +45,26 @@ def test_grid_processor_numpy_backend(self) -> None:
         self.assertEqual(out.dtype, np.uint8)
         self.assertEqual(err.shape, (3,))
 
+    @unittest.skipUnless("openmp" in ALL_BACKEND, "OpenMP backend unavailable")
+    def test_grid_processor_openmp_matches_numpy(self) -> None:
+        """OpenMP grid solver should match the NumPy Jacobi update."""
+        rng = np.random.default_rng(0)
+        src = rng.integers(0, 256, size=(24, 24, 3), dtype=np.uint8)
+        tgt = rng.integers(0, 256, size=(24, 24, 3), dtype=np.uint8)
+        mask = np.zeros((24, 24), dtype=np.uint8)
+        mask[2:-2, 2:-2] = (rng.random((20, 20)) > 0.35).astype(np.uint8) * 255
+
+        proc_np = GridProcessor(backend="numpy", grid_x=1, grid_y=1)
+        proc_omp = GridProcessor(backend="openmp", n_cpu=4, grid_x=1, grid_y=1)
+        proc_np.reset(src, mask, tgt.copy(), (0, 0), (0, 0))
+        proc_omp.reset(src, mask, tgt.copy(), (0, 0), (0, 0))
+
+        out_np, err_np = proc_np.step(5)
+        out_omp, err_omp = proc_omp.step(5)
+
+        np.testing.assert_array_equal(out_omp, out_np)
+        np.testing.assert_allclose(err_omp, err_np, rtol=1e-5, atol=1e-5)
+
     def test_cli_check_backend(self) -> None:
         """Verify the CLI can report available backends."""
         result = subprocess.run(