diff --git a/applications/test/HashTable4/Test-HashTable4.cxx b/applications/test/HashTable4/Test-HashTable4.cxx
index e474436870..12b63ae291 100644
--- a/applications/test/HashTable4/Test-HashTable4.cxx
+++ b/applications/test/HashTable4/Test-HashTable4.cxx
@@ -206,7 +206,7 @@ int main(int argc, char *argv[])
             #endif
 
             loopInsert(map, nElem);
-            (void)timer.cpuTimeIncrement();
+            timer.resetCpuTimeIncrement();
 
             unsigned long sum = 0;
             for (label loopi = 0; loopi < nFind*nLoops; ++loopi)
@@ -268,7 +268,7 @@ int main(int argc, char *argv[])
             HashSet<label, Hash<label>> map(32);
 
             loopInsert(map, nElem);
-            (void)timer.cpuTimeIncrement();
+            timer.resetCpuTimeIncrement();
 
             unsigned long sum = 0;
             for (label loopi = 0; loopi < nFind*nLoops; ++loopi)
diff --git a/applications/test/nullObject/Make/files b/applications/test/nullObject/Make/files
index dffa06d747..fdd71c155e 100644
--- a/applications/test/nullObject/Make/files
+++ b/applications/test/nullObject/Make/files
@@ -1,3 +1,3 @@
-Test-nullObject.C
+Test-nullObject.cxx
 
 EXE = $(FOAM_USER_APPBIN)/Test-nullObject
diff --git a/applications/test/nullObject/Test-nullObject.C b/applications/test/nullObject/Test-nullObject.cxx
similarity index 92%
rename from applications/test/nullObject/Test-nullObject.C
rename to applications/test/nullObject/Test-nullObject.cxx
index 0f7cd10dad..475a4e55b0 100644
--- a/applications/test/nullObject/Test-nullObject.C
+++ b/applications/test/nullObject/Test-nullObject.cxx
@@ -37,6 +37,7 @@ Description
 #include "HashSet.H"
 #include "faceList.H"
 #include "pointField.H"
+#include "globalIndex.H"
 #include "IOstreams.H"
 
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
@@ -150,6 +151,18 @@ int main()
     NullObject::nullObject = "hello world";
     NullObject::nullObject = Foam::identity(5);
 
+
+    {
+        const auto& gi = globalIndex::null();
+        Info<< "globalIndex::null() => "
+            << " empty: " << gi.empty()
+            << " nProcs: " << gi.nProcs()
+            << " total-size: " << gi.totalSize() << nl;
+
+        // Even this works
+        Info<< "   offsets: " << gi.offsets() << nl;
+    }
+
     Info<< nl;
 
     return 0;
diff --git a/applications/utilities/mesh/manipulation/renumberMesh/renumberMesh.C b/applications/utilities/mesh/manipulation/renumberMesh/renumberMesh.C
index 7c08c679a5..64011258c6 100644
--- a/applications/utilities/mesh/manipulation/renumberMesh/renumberMesh.C
+++ b/applications/utilities/mesh/manipulation/renumberMesh/renumberMesh.C
@@ -123,6 +123,7 @@ Usage
 \*---------------------------------------------------------------------------*/
 
 #include "argList.H"
+#include "clockTime.H"
 #include "timeSelector.H"
 #include "IOobjectList.H"
 #include "fvMesh.H"
@@ -147,6 +148,24 @@ Usage
 
 using namespace Foam;
 
+// Slightly messy way of handling timing, but since the timing points
+// are scattered between 'main()' and other local functions...
+
+clockTime timer;
+
+// Timing categories
+enum TimingType
+{
+    READ_MESH,    // Reading mesh
+    READ_FIELDS,  // Reading fields
+    DECOMPOSE,    // Domain decomposition (if any)
+    CELL_CELLS,   // globalMeshData::calcCellCells
+    RENUMBER,     // The renumberMethod
+    REORDER,      // Mesh reordering (topoChange)
+    WRITING,      // Writing mesh/fields
+};
+FixedList<double, 8> timings;
+
 
 // Create named field from labelList for post-processing
 tmp<volScalarField> createScalarField
@@ -205,8 +224,8 @@ void getBand
     scalar& sumSqrIntersect     // scalar to avoid overflow
 )
 {
-    labelList cellBandwidth(nCells, Zero);
-    scalarField nIntersect(nCells, Zero);
+    labelList cellBandwidth(nCells, Foam::zero{});
+    scalarField nIntersect(nCells, Foam::zero{});
 
     forAll(neighbour, facei)
     {
@@ -627,8 +646,33 @@ CompactListList<label> regionRenumber
         invertOneToManyCompact(nRegions, cellToRegion)
     );
 
-    if (method.needs_mesh())
+    if (method.no_topology())
     {
+        // Special case when renumberMesh is only used for decomposition.
+        // - can skip generating the connectivity
+        // - nonetheless calculate the order in case it is non-identity
+
+        timer.resetTimeIncrement();
+
+        forAll(regionCellOrder, regioni)
+        {
+            // Note: cellMap is identical to regionToCells[regioni]
+            // since it is already sorted
+
+            labelList subCellOrder =
+                method.renumber(regionCellOrder[regioni].size());
+
+            // Per region reordering (inplace but with SubList)
+            regionCellOrder[regioni] =
+                labelUIndList(regionCellOrder[regioni], subCellOrder)();
+        }
+
+        timings[TimingType::RENUMBER] += timer.timeIncrement();
+    }
+    else if (method.needs_mesh())
+    {
+        timer.resetTimeIncrement();
+
         forAll(regionCellOrder, regioni)
         {
             // Info<< "    region " << regioni
@@ -645,20 +689,20 @@ CompactListList<label> regionRenumber
             // (assuming they are properly sorted!)
             const labelList& cellMap = subsetter.cellMap();
 
-            labelList subCellOrder = method.renumber
-            (
-                subsetter.subMesh(),
-                subsetter.subMesh().cellCentres()
-            );
+            labelList subCellOrder = method.renumber(subsetter.subMesh());
 
             UPstream::parRun(oldParRun);  // Restore parallel state
 
             // Per region reordering
             regionCellOrder[regioni] = labelUIndList(cellMap, subCellOrder);
         }
+
+        timings[TimingType::RENUMBER] += timer.timeIncrement();
     }
     else
     {
+        timer.resetTimeIncrement();
+
         forAll(regionCellOrder, regioni)
         {
             // Info<< "    region " << regioni
@@ -677,17 +721,16 @@ CompactListList<label> regionRenumber
                 cellCells
             );
 
-            // Note: cellCentres not needed by every renumber method
-            labelList subCellOrder = method.renumber
-            (
-                cellCells,
-                pointField(mesh.cellCentres(), cellMap)
-            );
+            timings[TimingType::CELL_CELLS] += timer.timeIncrement();
+
+            labelList subCellOrder = method.renumber(cellCells);
 
             UPstream::parRun(oldParRun);  // Restore parallel state
 
             // Per region reordering
             regionCellOrder[regioni] = labelUIndList(cellMap, subCellOrder);
+
+            timings[TimingType::RENUMBER] += timer.timeIncrement();
         }
     }
     // Info<< endl;
@@ -832,8 +875,15 @@ int main(int argc, char *argv[])
 
     runTime.setTime(Times[startTime], startTime);
 
+
+    // Start/reset all timings
+    timer.resetTime();
+    timings = Foam::zero{};
+
     #include "createNamedMeshes.H"
 
+    timings[TimingType::READ_MESH] += timer.timeIncrement();
+
 
     for (fvMesh& mesh : meshes)
     {
@@ -881,6 +931,7 @@ int main(int argc, char *argv[])
         bool sortCoupledFaceCells = false;
         bool writeMaps = args.found("write-maps");
         bool orderPoints = false;
+        bool useRegionFaceOrder = false;
         label blockSize = 0;
 
         // Construct renumberMethod
@@ -920,6 +971,12 @@ int main(int argc, char *argv[])
                         << " and region-external."
                         << nl << endl;
                 }
+
+                if (blockSize > 0)
+                {
+                    useRegionFaceOrder =
+                        renumberDict.getOrDefault("regionFaceOrder", false);
+                }
             }
 
             orderPoints = renumberDict.getOrDefault("orderPoints", false);
@@ -969,12 +1026,12 @@ int main(int argc, char *argv[])
         {
             renumberPtr.reset(new CuthillMcKeeRenumber(renumberDict));
             Info<< "Using renumber-method: " << renumberPtr().type()
-                << " [default]" << nl << endl;
+                << " [default]" << endl;
         }
         else
         {
             Info<< "Using renumber-method: " << renumberPtr().type()
-                << nl << endl;
+                << endl;
         }
 
 
@@ -1042,6 +1099,10 @@ int main(int argc, char *argv[])
 
         if (!dryrun && doFields)
         {
+            Info<< nl << "Reading fields" << nl;
+
+            timer.resetTimeIncrement();
+
             objects = IOobjectList(mesh, runTime.timeName());
             storedObjects.reserve(objects.size());
 
@@ -1089,6 +1150,8 @@ int main(int argc, char *argv[])
 
             #undef ReadFields
             #undef ReadPointFields
+
+            timings[TimingType::READ_FIELDS] += timer.timeIncrement();
         }
 
 
@@ -1116,6 +1179,8 @@ int main(int argc, char *argv[])
 
         if (blockSize > 0 && !doDecompose)
         {
+            timer.resetTimeIncrement();
+
             // Renumbering in two phases. Should be done in one so mapping of
             // fields is done correctly!
 
@@ -1143,6 +1208,7 @@ int main(int argc, char *argv[])
 
             UPstream::parRun(oldParRun);  // Restore parallel state
 
+            timings[TimingType::DECOMPOSE] += timer.timeIncrement();
 
             // For debugging: write out region
             createScalarField
@@ -1163,12 +1229,14 @@ int main(int argc, char *argv[])
             cellOrder = regionCellOrder.values();
 
             // Determine new to old face order with new cell numbering
-            faceOrder = getRegionFaceOrder
-            (
-                mesh,
-                cellOrder,
-                cellToRegion
-            );
+            if (useRegionFaceOrder)
+            {
+                faceOrder = getRegionFaceOrder(mesh, cellOrder, cellToRegion);
+            }
+            else
+            {
+                faceOrder = getFaceOrder(mesh, cellOrder);
+            }
         }
         else
         {
@@ -1178,6 +1246,8 @@ int main(int argc, char *argv[])
                 // 1. decompose into regions (like decomposePar)
                 // 2. renumber each sub-region
 
+                timer.resetTimeIncrement();
+
                 // Read decompositionMethod dictionary
                 IOdictionary decomposeDict
                 (
@@ -1212,6 +1282,8 @@ int main(int argc, char *argv[])
                     )
                 );
 
+                timings[TimingType::DECOMPOSE] += timer.timeIncrement();
+
                 UPstream::parRun(oldParRun);  // Restore parallel state
 
                 CompactListList<label> regionCellOrder =
@@ -1236,11 +1308,21 @@ int main(int argc, char *argv[])
             else
             {
                 // Determines sorted back to original cell ordering
-                cellOrder = renumberPtr().renumber
-                (
-                    mesh,
-                    mesh.cellCentres()
-                );
+
+                const auto& method = renumberPtr();
+
+                timer.resetTimeIncrement();
+
+                if (method.no_topology())
+                {
+                    cellOrder = method.renumber(mesh.nCells());
+                }
+                else
+                {
+                    cellOrder = method.renumber(mesh);
+                }
+
+                timings[TimingType::RENUMBER] += timer.timeIncrement();
             }
 
 
@@ -1321,11 +1403,7 @@ int main(int argc, char *argv[])
 
 
             // Determine new to old face order with new cell numbering
-            faceOrder = getFaceOrder
-            (
-                mesh,
-                cellOrder      // New to old cell
-            );
+            faceOrder = getFaceOrder(mesh, cellOrder);
         }
 
 
@@ -1681,6 +1759,8 @@ int main(int argc, char *argv[])
         }
         else
         {
+            timer.resetTimeIncrement();
+
             if (overwrite)
             {
                 mesh.setInstance(oldInstance);
@@ -1720,6 +1800,8 @@ int main(int argc, char *argv[])
 
             mesh.write();
 
+            timings[TimingType::WRITING] += timer.timeIncrement();
+
             if (writeMaps)
             {
                 // For debugging: write out region
@@ -1771,6 +1853,19 @@ int main(int argc, char *argv[])
         }
     }
 
+    Info<< nl
+        << "Timings:" << nl
+        << "    read mesh   : " << timings[TimingType::READ_MESH] << nl
+        << "    read fields : " << timings[TimingType::READ_FIELDS] << nl
+        << "    decompose   : " << timings[TimingType::DECOMPOSE] << nl
+        << "    cell-cells  : " << timings[TimingType::CELL_CELLS] << nl
+        << "    renumber    : " << timings[TimingType::RENUMBER] << nl
+        << "    write       : " << timings[TimingType::WRITING] << nl
+        << "TotalTime = " << timer.elapsedTime() << " s" << nl
+        << nl;
+
+    runTime.printExecutionTime(Info);
+
     Info<< "End\n" << endl;
 
     return 0;
diff --git a/etc/caseDicts/annotated/renumberMeshDict b/etc/caseDicts/annotated/renumberMeshDict
index 80f960d014..1bf012a57e 100644
--- a/etc/caseDicts/annotated/renumberMeshDict
+++ b/etc/caseDicts/annotated/renumberMeshDict
@@ -38,6 +38,11 @@ sortCoupledFaceCells false;
 // Optional entry: sort points into internal and boundary points
 //orderPoints false;
 
+// Optional entry (experimental) - for block-by-block (blockSize > 0) option:
+// - sort intra-region and iter-region faces separately.
+//   This will likely lead to non-upper triangular ordering between regions.
+//regionFaceOrder false;
+
 
 method          CuthillMcKee;
 //method          RCM;  // == reverseCuthillMcKee;
diff --git a/src/OSspecific/POSIX/cpuTime/cpuTimePosix.C b/src/OSspecific/POSIX/cpuTime/cpuTimePosix.C
index 47af1c635c..027b29b41a 100644
--- a/src/OSspecific/POSIX/cpuTime/cpuTimePosix.C
+++ b/src/OSspecific/POSIX/cpuTime/cpuTimePosix.C
@@ -77,6 +77,12 @@ void Foam::cpuTimePosix::resetCpuTime()
 }
 
 
+void Foam::cpuTimePosix::resetCpuTimeIncrement() const
+{
+    last_.update();
+}
+
+
 double Foam::cpuTimePosix::elapsedCpuTime() const
 {
     last_.update();
diff --git a/src/OSspecific/POSIX/cpuTime/cpuTimePosix.H b/src/OSspecific/POSIX/cpuTime/cpuTimePosix.H
index f657d232f1..efb6ada7f1 100644
--- a/src/OSspecific/POSIX/cpuTime/cpuTimePosix.H
+++ b/src/OSspecific/POSIX/cpuTime/cpuTimePosix.H
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2014 OpenFOAM Foundation
-    Copyright (C) 2018 OpenCFD Ltd.
+    Copyright (C) 2018-2024 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -72,7 +72,8 @@ class cpuTimePosix
         //- Start time, at the time of construction
         value_type start_;
 
-        //- Last time when elapsedTime or timeIncrement was called
+        //- Last time when elapsedCpuTime or cpuTimeIncrement was called.
+        //- Also affected by resetCpuTime and resetCpuTimeIncrement.
         mutable value_type last_;
 
 
@@ -95,10 +96,14 @@ public:
         //- Reset to use the current time for the start time
         void resetCpuTime();
 
-        //- Return CPU time (in seconds) from the start
+        //- Reset to use the current time for the increment point
+        void resetCpuTimeIncrement() const;
+
+        //- Return CPU time [seconds] from the start
         double elapsedCpuTime() const;
 
-        //- Return CPU time (in seconds) since last call to cpuTimeIncrement()
+        //- Return CPU time [seconds] since last call to cpuTimeIncrement(),
+        //- resetCpuTimeIncrement().
         double cpuTimeIncrement() const;
 };
 
diff --git a/src/OpenFOAM/fields/Fields/fieldTypes.C b/src/OpenFOAM/fields/Fields/fieldTypes.C
index 943ecdd46f..79ff2e60d9 100644
--- a/src/OpenFOAM/fields/Fields/fieldTypes.C
+++ b/src/OpenFOAM/fields/Fields/fieldTypes.C
@@ -5,7 +5,7 @@
     \\  /    A nd           | www.openfoam.com
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
-    Copyright (C) 2018-2023 OpenCFD Ltd.
+    Copyright (C) 2018-2024 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -59,6 +59,11 @@ const Foam::word Foam::fieldTypes::extrapolatedCalculatedType
     Foam::fieldTypes::extrapolatedCalculatedTypeName_()
 );
 
+const Foam::word Foam::fieldTypes::processorType
+(
+    Foam::fieldTypes::processorTypeName_()
+);
+
 const Foam::word Foam::fieldTypes::zeroGradientType
 (
     Foam::fieldTypes::zeroGradientTypeName_()
diff --git a/src/OpenFOAM/fields/Fields/fieldTypes.H b/src/OpenFOAM/fields/Fields/fieldTypes.H
index 9f279730a1..55d8e62942 100644
--- a/src/OpenFOAM/fields/Fields/fieldTypes.H
+++ b/src/OpenFOAM/fields/Fields/fieldTypes.H
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2016 OpenFOAM Foundation
-    Copyright (C) 2018-2023 OpenCFD Ltd.
+    Copyright (C) 2018-2024 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -105,6 +105,12 @@ inline const char* extrapolatedCalculatedTypeName_() noexcept
 //- A combined \c zero-gradient and \c calculated patch field type
 extern const word extrapolatedCalculatedType;
 
+//- A \c processor patch field type
+inline const char* processorTypeName_() noexcept { return "processor"; }
+
+//- A \c processor patch field type
+extern const word processorType;
+
 //- A \c zeroGradient patch field type
 inline const char* zeroGradientTypeName_() noexcept { return "zeroGradient"; }
 
diff --git a/src/OpenFOAM/global/clockTime/clockTime.H b/src/OpenFOAM/global/clockTime/clockTime.H
index 5a82387dc6..e3e1a15518 100644
--- a/src/OpenFOAM/global/clockTime/clockTime.H
+++ b/src/OpenFOAM/global/clockTime/clockTime.H
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011 OpenFOAM Foundation
-    Copyright (C) 2018-2020 OpenCFD Ltd.
+    Copyright (C) 2018-2024 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -46,8 +46,8 @@ SourceFiles
 
 \*---------------------------------------------------------------------------*/
 
-#ifndef clockTime_H
-#define clockTime_H
+#ifndef Foam_clockTime_H
+#define Foam_clockTime_H
 
 #include "clockValue.H"
 
@@ -67,7 +67,8 @@ class clockTime
         //- Time point at start, or after resetTime
         clockValue start_;
 
-        //- Time point when elapsedTime or timeIncrement was called
+        //- Time point when elapsedTime or timeIncrement was called.
+        //- Also updated by resetTime and resetTimeIncrement.
         mutable clockValue last_;
 
 
@@ -84,13 +85,18 @@ public:
 
     // Member Functions
 
-        //- Reset to use the current clock value for the start point
+        //- Reset to use the current clock value for the start
+        //- and increment points
         inline void resetTime();
 
+        //- Reset to use the current clock value for the increment point
+        inline void resetTimeIncrement() const;
+
         //- The time [seconds] since the start point
         inline double elapsedTime() const;
 
-        //- The time [seconds] since the last call to timeIncrement()
+        //- The time [seconds] since the last call to elapsedTime(),
+        //- timeIncrement() or resetTime(), resetTimeIncrement()
         inline double timeIncrement() const;
 };
 
diff --git a/src/OpenFOAM/global/clockTime/clockTimeI.H b/src/OpenFOAM/global/clockTime/clockTimeI.H
index 6ec10f4d25..92d86af60c 100644
--- a/src/OpenFOAM/global/clockTime/clockTimeI.H
+++ b/src/OpenFOAM/global/clockTime/clockTimeI.H
@@ -5,7 +5,7 @@
     \\  /    A nd           | www.openfoam.com
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
-    Copyright (C) 2018-2020 OpenCFD Ltd.
+    Copyright (C) 2018-2024 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -50,6 +50,12 @@ inline void Foam::clockTime::resetTime()
 }
 
 
+inline void Foam::clockTime::resetTimeIncrement() const
+{
+    last_.update();
+}
+
+
 inline double Foam::clockTime::elapsedTime() const
 {
     last_.update();
diff --git a/src/OpenFOAM/global/clockValue/clockValue.H b/src/OpenFOAM/global/clockValue/clockValue.H
index 6d402abd8c..5dfe3303c7 100644
--- a/src/OpenFOAM/global/clockValue/clockValue.H
+++ b/src/OpenFOAM/global/clockValue/clockValue.H
@@ -36,8 +36,8 @@ SourceFiles
 
 \*---------------------------------------------------------------------------*/
 
-#ifndef clockValue_H
-#define clockValue_H
+#ifndef Foam_clockValue_H
+#define Foam_clockValue_H
 
 #include <chrono>
 #include <string>
@@ -93,10 +93,7 @@ public:
     // Member Functions
 
         //- The time duration
-        inline const value_type& value() const
-        {
-            return value_;
-        }
+        const value_type& value() const noexcept { return value_; }
 
         //- Reset to zero
         inline void clear();
diff --git a/src/OpenFOAM/global/cpuTime/cpuTimeCxx.C b/src/OpenFOAM/global/cpuTime/cpuTimeCxx.C
index fbb8277975..d762851bf8 100644
--- a/src/OpenFOAM/global/cpuTime/cpuTimeCxx.C
+++ b/src/OpenFOAM/global/cpuTime/cpuTimeCxx.C
@@ -65,6 +65,12 @@ void Foam::cpuTimeCxx::resetCpuTime()
 }
 
 
+void Foam::cpuTimeCxx::resetCpuTimeIncrement() const
+{
+    last_.update();
+}
+
+
 double Foam::cpuTimeCxx::elapsedCpuTime() const
 {
     last_.update();
diff --git a/src/OpenFOAM/global/cpuTime/cpuTimeCxx.H b/src/OpenFOAM/global/cpuTime/cpuTimeCxx.H
index 91e5c939c0..4f0476fa30 100644
--- a/src/OpenFOAM/global/cpuTime/cpuTimeCxx.H
+++ b/src/OpenFOAM/global/cpuTime/cpuTimeCxx.H
@@ -5,7 +5,7 @@
     \\  /    A nd           | www.openfoam.com
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
-    Copyright (C) 2018-2019 OpenCFD Ltd.
+    Copyright (C) 2018-2024 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -37,8 +37,8 @@ SourceFiles
 
 \*---------------------------------------------------------------------------*/
 
-#ifndef cpuTimeCxx_H
-#define cpuTimeCxx_H
+#ifndef Foam_cpuTimeCxx_H
+#define Foam_cpuTimeCxx_H
 
 #include <ctime>
 
@@ -71,7 +71,8 @@ class cpuTimeCxx
         //- Start time, at the time of construction
         value_type start_;
 
-        //- Last time when elapsedTime or timeIncrement was called
+        //- Last time when elapsedCpuTime or cpuTimeIncrement was called.
+        //- Also affected by resetCpuTime and resetCpuTimeIncrement.
         mutable value_type last_;
 
 
@@ -91,13 +92,17 @@ public:
 
     // Member Functions
 
-        //- Reset to use the current time for the start time
+        //- Reset to use the current time for the start and increment points
         void resetCpuTime();
 
+        //- Reset to use the current time for the increment point
+        void resetCpuTimeIncrement() const;
+
         //- Return CPU time (in seconds) from the start
         double elapsedCpuTime() const;
 
-        //- Return CPU time (in seconds) since last call to cpuTimeIncrement()
+        //- Return CPU time [seconds] since last call to cpuTimeIncrement(),
+        //- resetCpuTimeIncrement().
         double cpuTimeIncrement() const;
 };
 
diff --git a/src/OpenFOAM/global/profiling/profilingPstream.H b/src/OpenFOAM/global/profiling/profilingPstream.H
index 8256fb1418..37284223af 100644
--- a/src/OpenFOAM/global/profiling/profilingPstream.H
+++ b/src/OpenFOAM/global/profiling/profilingPstream.H
@@ -158,7 +158,7 @@ public:
         {
             if (!suspend_ && timer_)
             {
-                (void) timer_->cpuTimeIncrement();
+                timer_->resetCpuTimeIncrement();
             }
         }
 
diff --git a/src/OpenFOAM/meshes/bandCompression/bandCompression.C b/src/OpenFOAM/meshes/bandCompression/bandCompression.C
index b2f1a977ad..b03596db79 100644
--- a/src/OpenFOAM/meshes/bandCompression/bandCompression.C
+++ b/src/OpenFOAM/meshes/bandCompression/bandCompression.C
@@ -159,6 +159,13 @@ Foam::labelList cuthill_mckee_algorithm
         }
     }
 
+    // Debug:
+    // - the peak capacity of queuedCells approximates the
+    //   maximum intermediate bandwidth
+    #if 0
+    Pout<< "bandCompression: peak-capacity=" << queuedCells.capacity() << nl;
+    #endif
+
     // Now we have new-to-old in newOrder.
     return newOrder;
 }
@@ -306,8 +313,14 @@ Foam::labelList Foam::meshTools::bandCompression
         }
     }
 
-    // Now we have new-to-old in newOrder.
+    // Debug:
+    // - the peak capacity of queuedCells approximates the
+    //   maximum intermediate bandwidth
+    #if 0
+    Pout<< "bandCompression: peak-capacity=" << queuedCells.capacity() << nl;
+    #endif
 
+    // Now we have new-to-old in newOrder.
     return newOrder;
 }
 
diff --git a/src/OpenFOAM/meshes/bandCompression/bandCompression.H b/src/OpenFOAM/meshes/bandCompression/bandCompression.H
index d90cca8e58..00553c7a22 100644
--- a/src/OpenFOAM/meshes/bandCompression/bandCompression.H
+++ b/src/OpenFOAM/meshes/bandCompression/bandCompression.H
@@ -103,15 +103,17 @@ labelList bandCompression
 namespace Foam
 {
 
-//- Forward to meshTools::bandCompression
+//- Deprecated - prefer meshTools::bandCompression()
 //  \deprecated(2022-03) prefer meshTools::bandCompression()
+FOAM_DEPRECATED_FOR(2022-03, "meshTools::bandCompression()")
 inline labelList bandCompression(const labelListList& cellCellAddressing)
 {
     return meshTools::bandCompression(cellCellAddressing);
 }
 
-//- Forward to meshTools::bandCompression
+//- Deprecated - prefer meshTools::bandCompression()
 //  \deprecated(2022-03) prefer meshTools::bandCompression()
+FOAM_DEPRECATED_FOR(2022-03, "meshTools::bandCompression()")
 inline labelList bandCompression
 (
     const labelUList& cellCells,
diff --git a/src/OpenFOAM/parallel/globalIndex/globalIndex.H b/src/OpenFOAM/parallel/globalIndex/globalIndex.H
index f5b82a44cf..598c82e552 100644
--- a/src/OpenFOAM/parallel/globalIndex/globalIndex.H
+++ b/src/OpenFOAM/parallel/globalIndex/globalIndex.H
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2017 OpenFOAM Foundation
-    Copyright (C) 2018-2023 OpenCFD Ltd.
+    Copyright (C) 2018-2024 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -118,6 +118,16 @@ public:
         struct gatherNonLocal{};
 
 
+    // Static Member Functions
+
+        //- Return a null globalIndex (reference to a nullObject).
+        //- Behaves like an empty globalIndex
+        static const globalIndex& null() noexcept
+        {
+            return NullObjectRef<globalIndex>();
+        }
+
+
     // Constructors
 
         //- Default construct (empty)
diff --git a/src/renumber/SloanRenumber/SloanRenumber.C b/src/renumber/SloanRenumber/SloanRenumber.C
index 9ef6ca08ed..df5c3f624d 100644
--- a/src/renumber/SloanRenumber/SloanRenumber.C
+++ b/src/renumber/SloanRenumber/SloanRenumber.C
@@ -30,7 +30,6 @@ License
 
 #include "SloanRenumber.H"
 #include "addToRunTimeSelectionTable.H"
-#include "globalMeshData.H"
 #include "processorPolyPatch.H"
 #include "syncTools.H"
 
@@ -165,8 +164,7 @@ Foam::labelList renumberImpl(Graph& G, const bool useReverse)
 
 Foam::labelList Foam::SloanRenumber::renumber
 (
-    const polyMesh& mesh,
-    const pointField& points
+    const polyMesh& mesh
 ) const
 {
     // Construct graph : faceOwner + connections across cyclics.
@@ -186,7 +184,7 @@ Foam::labelList Foam::SloanRenumber::renumber
     Graph G(mesh.nCells());
 
     // Add internal faces
-    forAll(mesh.faceNeighbour(), facei)
+    for (label facei = 0; facei < mesh.nInternalFaces(); ++facei)
     {
         add_edge(mesh.faceOwner()[facei], mesh.faceNeighbour()[facei], G);
     }
@@ -226,8 +224,7 @@ Foam::labelList Foam::SloanRenumber::renumber
 
 Foam::labelList Foam::SloanRenumber::renumber
 (
-    const CompactListList<label>& cellCells,
-    const pointField&
+    const CompactListList<label>& cellCells
 ) const
 {
     Graph G(cellCells.size());
@@ -251,8 +248,7 @@ Foam::labelList Foam::SloanRenumber::renumber
 
 Foam::labelList Foam::SloanRenumber::renumber
 (
-    const labelListList& cellCells,
-    const pointField&
+    const labelListList& cellCells
 ) const
 {
     Graph G(cellCells.size());
diff --git a/src/renumber/SloanRenumber/SloanRenumber.H b/src/renumber/SloanRenumber/SloanRenumber.H
index 46aa185356..a2c42c5cc3 100644
--- a/src/renumber/SloanRenumber/SloanRenumber.H
+++ b/src/renumber/SloanRenumber/SloanRenumber.H
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2012-2015 OpenFOAM Foundation
-    Copyright (C) 2022 OpenCFD Ltd.
+    Copyright (C) 2022-2024 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -83,44 +83,26 @@ public:
         //- Toggle reverse on/off
         void reverse(bool on) noexcept { reverse_ = on; }
 
-        //- The renumbering method does not require a polyMesh
-        virtual bool needs_mesh() const { return false; }
+
+    // With mesh topology
+
+        //- Return the cell visit order (from ordered back to original cell id)
+        //- using the mesh to determine the connectivity.
+        virtual labelList renumber(const polyMesh& mesh) const;
 
 
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
-        //  This is only defined for geometric renumberMethods.
-        virtual labelList renumber(const pointField&) const
-        {
-            NotImplemented;
-            return labelList();
-        }
+    // With explicit topology
 
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
-        //  Use the mesh connectivity (if needed)
+        //- Return the cell visit order (from ordered back to original cell id)
         virtual labelList renumber
         (
-            const polyMesh& mesh,
-            const pointField& cc
+            const CompactListList<label>& cellCells
         ) const;
 
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
+        //- Return the cell visit order (from ordered back to original cell id)
         virtual labelList renumber
         (
-            const CompactListList<label>& cellCells,
-            const pointField& cellCentres
-        ) const;
-
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
-        //  The connectivity is equal to mesh.cellCells() except
-        //  - the connections are across coupled patches
-        virtual labelList renumber
-        (
-            const labelListList& cellCells,
-            const pointField& cc
+            const labelListList& cellCells
         ) const;
 };
 
diff --git a/src/renumber/renumberMethods/CuthillMcKeeRenumber/CuthillMcKeeRenumber.C b/src/renumber/renumberMethods/CuthillMcKeeRenumber/CuthillMcKeeRenumber.C
index 241be2cbe3..4e7827d503 100644
--- a/src/renumber/renumberMethods/CuthillMcKeeRenumber/CuthillMcKeeRenumber.C
+++ b/src/renumber/renumberMethods/CuthillMcKeeRenumber/CuthillMcKeeRenumber.C
@@ -112,8 +112,7 @@ Foam::reverseCuthillMcKeeRenumber::reverseCuthillMcKeeRenumber
 
 Foam::labelList Foam::CuthillMcKeeRenumber::renumber
 (
-    const polyMesh& mesh,
-    const pointField&
+    const polyMesh& mesh
 ) const
 {
     labelList orderedToOld = meshTools::bandCompression(mesh);
@@ -129,26 +128,7 @@ Foam::labelList Foam::CuthillMcKeeRenumber::renumber
 
 Foam::labelList Foam::CuthillMcKeeRenumber::renumber
 (
-    const labelList& cellCells,
-    const labelList& offsets,
-    const pointField& cc
-) const
-{
-    labelList orderedToOld = meshTools::bandCompression(cellCells, offsets);
-
-    if (reverse_)
-    {
-        Foam::reverse(orderedToOld);
-    }
-
-    return orderedToOld;
-}
-
-
-Foam::labelList Foam::CuthillMcKeeRenumber::renumber
-(
-    const CompactListList<label>& cellCells,
-    const pointField&
+    const CompactListList<label>& cellCells
 ) const
 {
     labelList orderedToOld = meshTools::bandCompression(cellCells);
@@ -164,8 +144,7 @@ Foam::labelList Foam::CuthillMcKeeRenumber::renumber
 
 Foam::labelList Foam::CuthillMcKeeRenumber::renumber
 (
-    const labelListList& cellCells,
-    const pointField&
+    const labelListList& cellCells
 ) const
 {
     labelList orderedToOld = meshTools::bandCompression(cellCells);
@@ -179,4 +158,21 @@ Foam::labelList Foam::CuthillMcKeeRenumber::renumber
 }
 
 
+// Foam::labelList Foam::CuthillMcKeeRenumber::renumber
+// (
+//     const labelUList& cellCells,
+//     const labelUList& offsets
+// ) const
+// {
+//     labelList orderedToOld = meshTools::bandCompression(cellCells, offsets);
+//
+//     if (reverse_)
+//     {
+//         Foam::reverse(orderedToOld);
+//     }
+//
+//     return orderedToOld;
+// }
+
+
 // ************************************************************************* //
diff --git a/src/renumber/renumberMethods/CuthillMcKeeRenumber/CuthillMcKeeRenumber.H b/src/renumber/renumberMethods/CuthillMcKeeRenumber/CuthillMcKeeRenumber.H
index 45a07be355..506deef95d 100644
--- a/src/renumber/renumberMethods/CuthillMcKeeRenumber/CuthillMcKeeRenumber.H
+++ b/src/renumber/renumberMethods/CuthillMcKeeRenumber/CuthillMcKeeRenumber.H
@@ -30,6 +30,9 @@ Class
 Description
     Cuthill-McKee renumbering (CM or RCM)
 
+SeeAlso
+    Foam::meshTools::bandCompression
+
 SourceFiles
     CuthillMcKeeRenumber.C
 
@@ -85,62 +88,32 @@ public:
         //- Toggle reverse on/off
         void reverse(bool on) noexcept { reverse_ = on; }
 
-        //- The renumbering method does not require a polyMesh
-        virtual bool needs_mesh() const { return false; }
 
+    // With mesh topology
 
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
-        //  This is only defined for geometric renumberMethods.
-        virtual labelList renumber(const pointField&) const
-        {
-            NotImplemented;
-            return labelList();
-        }
-
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
-        //  Use the mesh connectivity (if needed)
+        //- Return the cell visit order (from ordered back to original cell id)
+        //- using the mesh to determine the connectivity.
         virtual labelList renumber
         (
             //! Mesh connectivity (see globalMeshData::calcCellCells)
-            const polyMesh& mesh,
-            //! \em ignored
-            const pointField& cellCentres
+            const polyMesh& mesh
         ) const;
 
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
-        //  Connectivity in losort addressing (= neighbour + offsets into
-        //  neighbour)
-        virtual labelList renumber
-        (
-            const labelList& cellCells,
-            const labelList& offsets,
-            //! \em ignored
-            const pointField& cellCentres
-        ) const;
 
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
+    // With explicit topology
+
+        //- Return the cell visit order (from ordered back to original cell id).
         virtual labelList renumber
         (
             //! Mesh connectivity
-            const CompactListList<label>& cellCells,
-            //! \em ignored
-            const pointField& cellCentres
+            const CompactListList<label>& cellCells
         ) const;
 
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
-        //  The connectivity is equal to mesh.cellCells() except
-        //  - the connections are across coupled patches
+        //- Return the cell visit order (from ordered back to original cell id).
         virtual labelList renumber
         (
             //! Mesh connectivity
-            const labelListList& cellCells,
-            //! \em ignored
-            const pointField& cellCentres
+            const labelListList& cellCells
         ) const;
 };
 
diff --git a/src/renumber/renumberMethods/manualRenumber/manualRenumber.C b/src/renumber/renumberMethods/manualRenumber/manualRenumber.C
index 61dc497239..875ced3af0 100644
--- a/src/renumber/renumberMethods/manualRenumber/manualRenumber.C
+++ b/src/renumber/renumberMethods/manualRenumber/manualRenumber.C
@@ -68,10 +68,11 @@ Foam::manualRenumber::manualRenumber(const dictionary& dict)
 
 Foam::labelList Foam::manualRenumber::renumber
 (
-    const polyMesh& mesh,
-    const pointField& points
+    const polyMesh& mesh
 ) const
 {
+    const label nCells = mesh.nCells();
+
     labelList newToOld
     (
         labelIOList::readContents
@@ -87,31 +88,27 @@ Foam::labelList Foam::manualRenumber::renumber
     );
 
     // Check if the final renumbering is OK
-    if (newToOld.size() != points.size())
+    if (newToOld.size() != nCells)
     {
         FatalErrorInFunction
-            << "Size of renumber list does not correspond "
-            << "to the number of points.  Size: "
-            << newToOld.size() << " Number of points: "
-            << points.size()
-            << ".\n" << "Manual renumbering data read from file "
-            << dataFile_ << "." << endl
+            << "Size of renumber list: "
+            << newToOld.size() << " != number of cells: " << nCells << nl
+            << "Renumbering data read from file " << dataFile_ << endl
             << exit(FatalError);
     }
 
     // Invert to see if one to one
-    labelList oldToNew(points.size(), -1);
+    labelList oldToNew(nCells, -1);
     forAll(newToOld, i)
     {
         const label origCelli = newToOld[i];
 
-        if (origCelli < 0 || origCelli >= points.size())
+        if (origCelli < 0 || origCelli >= nCells)
         {
             FatalErrorInFunction
-                << "Renumbering is not one-to-one. Index "
-                << i << " maps onto original cell " << origCelli
-                << ".\n" << "Manual renumbering data read from file "
-                << dataFile_ << nl
+                << "Renumbering range error. Index " << i
+                << " maps to cell " << origCelli << " from " << nCells << nl
+                << "Renumbering data read from file " << dataFile_ << endl
                 << exit(FatalError);
         }
 
@@ -124,8 +121,7 @@ Foam::labelList Foam::manualRenumber::renumber
             FatalErrorInFunction
                 << "Renumbering is not one-to-one. Index " << i << " and "
                 << oldToNew[origCelli] << " map onto " << origCelli << nl
-                << "Manual renumbering data read from file "
-                << dataFile_ << nl
+                << "Renumbering data read from file " << dataFile_ << endl
                 << exit(FatalError);
         }
     }
diff --git a/src/renumber/renumberMethods/manualRenumber/manualRenumber.H b/src/renumber/renumberMethods/manualRenumber/manualRenumber.H
index 208a6d959b..42cfded204 100644
--- a/src/renumber/renumberMethods/manualRenumber/manualRenumber.H
+++ b/src/renumber/renumberMethods/manualRenumber/manualRenumber.H
@@ -80,41 +80,31 @@ public:
         virtual bool needs_mesh() const { return true; }
 
 
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
-        virtual labelList renumber(const pointField&) const
-        {
-            NotImplemented;
-            return labelList();
-        }
+    // With mesh topology
 
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
-        //  Uses mesh for regIOobject
+        //- Return the cell visit order (from ordered back to original cell id)
+        //- using the mesh for its IOobject and instance.
+        virtual labelList renumber(const polyMesh& mesh) const;
+
+
+    // With explicit topology - Not implemented!
+
+        //- Return the cell visit order (from ordered back to original cell id)
+        //- Not implemented!
         virtual labelList renumber
         (
-            const polyMesh& mesh,
-            const pointField& cc
-        ) const;
-
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
-        virtual labelList renumber
-        (
-            const CompactListList<label>& cellCells,
-            const pointField& cellCentres
+            const CompactListList<label>& cellCells
         ) const
         {
             NotImplemented;
             return labelList();
         }
 
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
+        //- Return the cell visit order (from ordered back to original cell id)
+        //- Not implemented!
         virtual labelList renumber
         (
-            const labelListList& cellCells,
-            const pointField& cellCentres
+            const labelListList& cellCells
         ) const
         {
             NotImplemented;
diff --git a/src/renumber/renumberMethods/noRenumber/noRenumber.C b/src/renumber/renumberMethods/noRenumber/noRenumber.C
index 6387830399..2e647b0004 100644
--- a/src/renumber/renumberMethods/noRenumber/noRenumber.C
+++ b/src/renumber/renumberMethods/noRenumber/noRenumber.C
@@ -60,6 +60,15 @@ Foam::noRenumber::noRenumber(const dictionary& dict)
 
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
+Foam::labelList Foam::noRenumber::renumber
+(
+    const label nCells
+) const
+{
+    return Foam::identity(nCells);
+}
+
+
 Foam::labelList Foam::noRenumber::renumber
 (
     const pointField& cellCentres
@@ -71,8 +80,7 @@ Foam::labelList Foam::noRenumber::renumber
 
 Foam::labelList Foam::noRenumber::renumber
 (
-    const polyMesh& mesh,
-    const pointField&
+    const polyMesh& mesh
 ) const
 {
     return Foam::identity(mesh.nCells());
@@ -81,8 +89,7 @@ Foam::labelList Foam::noRenumber::renumber
 
 Foam::labelList Foam::noRenumber::renumber
 (
-    const CompactListList<label>& cellCells,
-    const pointField&
+    const CompactListList<label>& cellCells
 ) const
 {
     return Foam::identity(cellCells.size());
@@ -91,8 +98,7 @@ Foam::labelList Foam::noRenumber::renumber
 
 Foam::labelList Foam::noRenumber::renumber
 (
-    const labelListList& cellCells,
-    const pointField&
+    const labelListList& cellCells
 ) const
 {
     return Foam::identity(cellCells.size());
diff --git a/src/renumber/renumberMethods/noRenumber/noRenumber.H b/src/renumber/renumberMethods/noRenumber/noRenumber.H
index 98273362da..03a5c37018 100644
--- a/src/renumber/renumberMethods/noRenumber/noRenumber.H
+++ b/src/renumber/renumberMethods/noRenumber/noRenumber.H
@@ -73,42 +73,48 @@ public:
 
     // Member Functions
 
-        //- The renumbering method does not require a polyMesh
-        virtual bool needs_mesh() const { return false; }
+        //- Renumbering method without mesh or cell-cell topology!
+        virtual bool no_topology() const { return true; }
 
 
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
+    // No topology
+
+        //- Return the cell visit order (from ordered back to original cell id)
+        //- based solely on the number of cells.
+        virtual labelList renumber(const label nCells) const;
+
+        //- Return the cell visit order (from ordered back to original cell id).
+        //- based solely on pointField size
         virtual labelList renumber(const pointField&) const;
 
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
+
+    // With mesh topology
+
+        //- Return the cell visit order (from ordered back to original cell id)
+        //- using the mesh only for the number of cells
         virtual labelList renumber
         (
-            //! Mesh number of cells
-            const polyMesh& mesh,
-            //! \em ignored
-            const pointField& cellCentres
+            //! Mesh provides the number of cells
+            const polyMesh& mesh
         ) const;
 
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
+
+    // With explicit topology
+
+        //- Return the cell visit order (from ordered back to original cell id)
+        //- using the topology only for the number of cells
         virtual labelList renumber
         (
-            //! Mesh connectivity for number of cells
-            const CompactListList<label>& cellCells,
-            //! \em ignored
-            const pointField& cellCentres
+            //! Connectivity provides the number of cells
+            const CompactListList<label>& cellCells
         ) const;
 
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
+        //- Return the cell visit order (from ordered back to original cell id)
+        //- using the topology only for the number of cells
         virtual labelList renumber
         (
-            //! Mesh connectivity for number of cells
-            const labelListList& cellCells,
-            //! \em ignored
-            const pointField& cellCentres
+            //! Connectivity provides the number of cells
+            const labelListList& cellCells
         ) const;
 };
 
diff --git a/src/renumber/renumberMethods/randomRenumber/randomRenumber.C b/src/renumber/renumberMethods/randomRenumber/randomRenumber.C
index 4ae111352d..2a79a544cb 100644
--- a/src/renumber/renumberMethods/randomRenumber/randomRenumber.C
+++ b/src/renumber/renumberMethods/randomRenumber/randomRenumber.C
@@ -86,6 +86,15 @@ Foam::randomRenumber::randomRenumber(const dictionary& dict)
 
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
+Foam::labelList Foam::randomRenumber::renumber
+(
+    const label nCells
+) const
+{
+    return randomMap(nCells);
+}
+
+
 Foam::labelList Foam::randomRenumber::renumber
 (
     const pointField& cellCentres
@@ -97,8 +106,7 @@ Foam::labelList Foam::randomRenumber::renumber
 
 Foam::labelList Foam::randomRenumber::renumber
 (
-    const polyMesh& mesh,
-    const pointField&
+    const polyMesh& mesh
 ) const
 {
     return randomMap(mesh.nCells());
@@ -107,8 +115,7 @@ Foam::labelList Foam::randomRenumber::renumber
 
 Foam::labelList Foam::randomRenumber::renumber
 (
-    const CompactListList<label>& cellCells,
-    const pointField&
+    const CompactListList<label>& cellCells
 ) const
 {
     return randomMap(cellCells.size());
@@ -117,8 +124,7 @@ Foam::labelList Foam::randomRenumber::renumber
 
 Foam::labelList Foam::randomRenumber::renumber
 (
-    const labelListList& cellCells,
-    const pointField&
+    const labelListList& cellCells
 ) const
 {
     return randomMap(cellCells.size());
diff --git a/src/renumber/renumberMethods/randomRenumber/randomRenumber.H b/src/renumber/renumberMethods/randomRenumber/randomRenumber.H
index 5769be0ce7..8637f2e977 100644
--- a/src/renumber/renumberMethods/randomRenumber/randomRenumber.H
+++ b/src/renumber/renumberMethods/randomRenumber/randomRenumber.H
@@ -72,42 +72,48 @@ public:
 
     // Member Functions
 
-        //- The renumbering method does not require a polyMesh
-        virtual bool needs_mesh() const { return false; }
+        //- Renumbering method without mesh or cell-cell topology!
+        virtual bool no_topology() const { return true; }
 
 
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
+    // No topology
+
+        //- Return the cell visit order (from ordered back to original cell id)
+        //- based solely on the number of cells.
+        virtual labelList renumber(const label nCells) const;
+
+        //- Return the cell visit order (from ordered back to original cell id).
+        //- based solely on pointField size
         virtual labelList renumber(const pointField&) const;
 
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
+
+    // With mesh topology
+
+        //- Return the cell visit order (from ordered back to original cell id)
+        //- using the mesh only for the number of cells
         virtual labelList renumber
         (
-            //! Mesh number of cells
-            const polyMesh& mesh,
-            //! \em ignored
-            const pointField& cellCentres
+            //! Mesh provides the number of cells
+            const polyMesh& mesh
         ) const;
 
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
+
+    // With explicit topology
+
+        //- Return the cell visit order (from ordered back to original cell id)
+        //- using the topology only for the number of cells
         virtual labelList renumber
         (
-            //! Mesh connectivity for number of cells
-            const CompactListList<label>& cellCells,
-            //! \em ignored
-            const pointField& cellCentres
+            //! Connectivity provides the number of cells
+            const CompactListList<label>& cellCells
         ) const;
 
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
+        //- Return the cell visit order (from ordered back to original cell id)
+        //- using the topology only for the number of cells
         virtual labelList renumber
         (
-            //! Mesh connectivity for number of cells
-            const labelListList& cellCells,
-            //! \em ignored
-            const pointField& cellCentres
+            //! Connectivity provides the number of cells
+            const labelListList& cellCells
         ) const;
 };
 
diff --git a/src/renumber/renumberMethods/renumberMethod/renumberMethod.C b/src/renumber/renumberMethods/renumberMethod/renumberMethod.C
index 7cb556bd8f..cd31aac832 100644
--- a/src/renumber/renumberMethods/renumberMethod/renumberMethod.C
+++ b/src/renumber/renumberMethods/renumberMethod/renumberMethod.C
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2015 OpenFOAM Foundation
-    Copyright (C) 2019-2023 OpenCFD Ltd.
+    Copyright (C) 2019-2024 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -82,10 +82,14 @@ Foam::autoPtr<Foam::renumberMethod> Foam::renumberMethod::New
 
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
-Foam::labelList Foam::renumberMethod::renumber
-(
-    const pointField&
-) const
+Foam::labelList Foam::renumberMethod::renumber(const label nCells) const
+{
+    NotImplemented;
+    return labelList();
+}
+
+
+Foam::labelList Foam::renumberMethod::renumber(const pointField& cc) const
 {
     NotImplemented;
     return labelList();
@@ -94,44 +98,21 @@ Foam::labelList Foam::renumberMethod::renumber
 
 Foam::labelList Foam::renumberMethod::renumber
 (
-    const polyMesh& mesh,
-    const pointField& points
+    const polyMesh& mesh
 ) const
 {
     // Local mesh connectivity
     CompactListList<label> cellCells;
     globalMeshData::calcCellCells(mesh, cellCells);
 
-    return renumber(cellCells, points);
-}
-
-
-Foam::labelList Foam::renumberMethod::renumber
-(
-    const CompactListList<label>& cellCells,
-    const pointField& points
-) const
-{
-    return renumber(cellCells.unpack(), points);
-}
-
-
-Foam::labelList Foam::renumberMethod::renumber
-(
-    const labelList& cellCells,
-    const labelList& offsets,
-    const pointField& cc
-) const
-{
-    NotImplemented;
-    return labelList();
+    return renumber(cellCells);
 }
 
 
 Foam::labelList Foam::renumberMethod::renumber
 (
     const polyMesh& mesh,
-    const labelList& fineToCoarse,
+    const labelUList& fineToCoarse,
     const pointField& coarsePoints
 ) const
 {
@@ -140,16 +121,13 @@ Foam::labelList Foam::renumberMethod::renumber
     (
         mesh,
         fineToCoarse,
-        coarsePoints.size(),
+        coarsePoints.size(),   // nLocalCoarse
         false,  // local only (parallel = false)
         coarseCellCells
     );
 
     // Renumber based on agglomerated points
-    labelList coarseDistribution
-    (
-        renumber(coarseCellCells, coarsePoints)
-    );
+    labelList coarseDistribution = renumber(coarseCellCells);
 
     // From coarse back to fine for original mesh
     return labelList(coarseDistribution, fineToCoarse);
diff --git a/src/renumber/renumberMethods/renumberMethod/renumberMethod.H b/src/renumber/renumberMethods/renumberMethod/renumberMethod.H
index 9bfa6dd6c5..ec751c5eeb 100644
--- a/src/renumber/renumberMethods/renumberMethod/renumberMethod.H
+++ b/src/renumber/renumberMethods/renumberMethod/renumberMethod.H
@@ -98,72 +98,99 @@ public:
 
     // Member Functions
 
-        //- Does renumbering method require a polyMesh?
+        //- Renumbering method without mesh or cell-cell topology
+        //- (very special case)
+        virtual bool no_topology() const { return false; }
+
+        //- Renumbering method requires a polyMesh for its topology
         virtual bool needs_mesh() const { return false; }
 
 
     // No topology
 
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
-        //  This is only defined for geometric renumber methods.
+        //- Return the cell visit order (from ordered back to original cell id)
+        //- based solely on the number of cells.
+        //  Only applicable for no_topology() methods.
+        virtual labelList renumber(const label nCells) const;
+
+        //- Return the cell visit order (from ordered back to original cell id)
+        //- based solely on the cell centres (or number of cell centres).
+        //  Only applicable for no_topology() methods.
         virtual labelList renumber(const pointField&) const;
 
 
-    // Topology provided by mesh
+    // With mesh topology
 
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
-        //  Use the mesh connectivity (if needed)
-        virtual labelList renumber(const polyMesh&, const pointField&) const;
+        //- Return the cell visit order (from ordered back to original cell id)
+        //- using the mesh to determine the connectivity.
+        virtual labelList renumber(const polyMesh& mesh) const;
 
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
-        //  Gets passed agglomeration map (from fine to coarse cells) and coarse
-        //  cell
-        //  location. Can be overridden by renumberMethods that provide this
-        //  functionality natively. Coarse cells are local to the processor
-        //  (if in parallel). If you want to have coarse cells spanning
-        //  processors use the globalCellCells instead.
+
+    // With explicit topology
+
+        //- Return the cell visit order (from ordered back to original cell id),
+        virtual labelList renumber
+        (
+            //! Mesh connectivity
+            const CompactListList<label>& cellCells
+        ) const = 0;
+
+        //- Return the cell visit order (from ordered back to original cell id),
+        virtual labelList renumber
+        (
+            //! Mesh connectivity
+            const labelListList& cellCells
+        ) const = 0;
+
+
+    // Housekeeping
+
+        //- Deprecated - the pointField is unused
+        //  \deprecated(2024-03) the pointField is unused
+        FOAM_DEPRECATED_FOR(2024-03, "renumber(const polyMesh&)")
         virtual labelList renumber
         (
             const polyMesh& mesh,
-            const labelList& fineToCoarse,
-            const pointField& coarsePoints
-        ) const;
-
-
-    // Topology provided explicitly
-
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
-        //  Addressing in losort addressing (= neighbour + offsets into
-        //  neighbour)
-        virtual labelList renumber
-        (
-            const labelList& cellCells,
-            const labelList& offsets,
             const pointField&
-        ) const;
+        ) const
+        {
+            return renumber(mesh);
+        }
 
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
-        //  Uses 'unpack' internally, so should be overloaded when possible
+        //- Deprecated - the pointField is unused
+        //  \deprecated(2024-03) the pointField is unused
+        FOAM_DEPRECATED_FOR(2024-03, "renumber(const CompactListList<label>&)")
         virtual labelList renumber
         (
             const CompactListList<label>& cellCells,
-            const pointField& cellCentres
-        ) const;
+            const pointField&
+        ) const
+        {
+            return renumber(cellCells);
+        }
 
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
-        //  The connectivity is equal to mesh.cellCells() except
-        //  - the connections are across coupled patches
+        //- Deprecated - the pointField is unused
+        //  \deprecated(2024-03) the pointField is unused
+        FOAM_DEPRECATED_FOR(2024-03, "renumber(const labelListList&)")
         virtual labelList renumber
         (
             const labelListList& cellCells,
-            const pointField& cellCentres
-        ) const = 0;
+            const pointField&
+        ) const
+        {
+            return renumber(cellCells);
+        }
+
+        //- Deprecated - renumbering with agglomeration map.
+        //- Calculate globalCellCells directly
+        //  \deprecated(2024-03) calculate globalCellCells directly
+        FOAM_DEPRECATED_FOR(2024-03, "calcCellCells and renumber separately")
+        virtual labelList renumber
+        (
+            const polyMesh& mesh,
+            const labelUList& fineToCoarse,
+            const pointField& coarsePoints
+        ) const;
 };
 
 
diff --git a/src/renumber/renumberMethods/springRenumber/springRenumber.C b/src/renumber/renumberMethods/springRenumber/springRenumber.C
index b0063d6b59..c46a8ef5f4 100644
--- a/src/renumber/renumberMethods/springRenumber/springRenumber.C
+++ b/src/renumber/renumberMethods/springRenumber/springRenumber.C
@@ -159,8 +159,7 @@ Foam::labelList Foam::springRenumber::renumberImpl
 
 Foam::labelList Foam::springRenumber::renumber
 (
-    const polyMesh& mesh,
-    const pointField&
+    const polyMesh& mesh
 ) const
 {
     // Local mesh connectivity
@@ -173,8 +172,7 @@ Foam::labelList Foam::springRenumber::renumber
 
 Foam::labelList Foam::springRenumber::renumber
 (
-    const CompactListList<label>& cellCells,
-    const pointField&
+    const CompactListList<label>& cellCells
 ) const
 {
     return renumberImpl(cellCells);
@@ -183,8 +181,7 @@ Foam::labelList Foam::springRenumber::renumber
 
 Foam::labelList Foam::springRenumber::renumber
 (
-    const labelListList& cellCells,
-    const pointField&
+    const labelListList& cellCells
 ) const
 {
     return renumberImpl(cellCells);
diff --git a/src/renumber/renumberMethods/springRenumber/springRenumber.H b/src/renumber/renumberMethods/springRenumber/springRenumber.H
index bf0d8ac8b5..5d95ca1469 100644
--- a/src/renumber/renumberMethods/springRenumber/springRenumber.H
+++ b/src/renumber/renumberMethods/springRenumber/springRenumber.H
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2015 OpenFOAM Foundation
-    Copyright (C) 2022 OpenCFD Ltd.
+    Copyright (C) 2022-2024 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -111,40 +111,31 @@ public:
 
     // Member Functions
 
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
-        //  This is only defined for geometric renumberMethods.
-        virtual labelList renumber(const pointField&) const
-        {
-            NotImplemented;
-            return labelList();
-        }
+    // With mesh topology
 
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
-        //  Use the mesh connectivity (if needed)
+        //- Return the cell visit order (from ordered back to original cell id)
+        //- using the mesh to determine the connectivity.
         virtual labelList renumber
         (
-            const polyMesh& mesh,
-            const pointField&
+            //! Mesh connectivity (see globalMeshData::calcCellCells)
+            const polyMesh& mesh
         ) const;
 
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
+
+    // With explicit topology
+
+        //- Return the cell visit order (from ordered back to original cell id)
         virtual labelList renumber
         (
-            const CompactListList<label>& cellCells,
-            const pointField& cellCentres
+            //! Mesh connectivity
+            const CompactListList<label>& cellCells
         ) const;
 
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
-        //  The connectivity is equal to mesh.cellCells() except
-        //  - the connections are across coupled patches
+        //- Return the cell visit order (from ordered back to original cell id)
         virtual labelList renumber
         (
-            const labelListList& cellCells,
-            const pointField& cellCentres
+            //! Mesh connectivity
+            const labelListList& cellCells
         ) const;
 };
 
diff --git a/src/renumber/renumberMethods/structuredRenumber/structuredRenumber.C b/src/renumber/renumberMethods/structuredRenumber/structuredRenumber.C
index f5a13168a9..7f25008337 100644
--- a/src/renumber/renumberMethods/structuredRenumber/structuredRenumber.C
+++ b/src/renumber/renumberMethods/structuredRenumber/structuredRenumber.C
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2012-2017 OpenFOAM Foundation
-    Copyright (C) 2018-2020 OpenCFD Ltd.
+    Copyright (C) 2018-2024 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -137,18 +137,9 @@ bool Foam::structuredRenumber::layerLess::operator()
 
 Foam::labelList Foam::structuredRenumber::renumber
 (
-    const polyMesh& mesh,
-    const pointField& points
+    const polyMesh& mesh
 ) const
 {
-    if (points.size() != mesh.nCells())
-    {
-        FatalErrorInFunction
-            << "Number of points " << points.size()
-            << " should equal the number of cells " << mesh.nCells()
-            << exit(FatalError);
-    }
-
     const polyBoundaryMesh& pbm = mesh.boundaryMesh();
     const labelHashSet patchIDs(pbm.patchSet(patches_));
 
@@ -187,21 +178,20 @@ Foam::labelList Foam::structuredRenumber::renumber
             dynamic_cast<const fvMesh&>(mesh),
             patchCells
         );
-        const fvMesh& subMesh = subsetter.subMesh();
 
-        pointField subPoints(points, subsetter.cellMap());
+        const labelList& cellMap = subsetter.cellMap();
 
         // Locally renumber the layer of cells
-        labelList subOrder(method_().renumber(subMesh, subPoints));
+        labelList subOrder = method_().renumber(subsetter.subMesh());
 
         labelList subOrigToOrdered(invert(subOrder.size(), subOrder));
 
-        globalIndex globalSubCells(subOrder.size());
+        const globalIndex globalSubCells(subOrder.size());
 
         // Transfer to final decomposition and convert into global numbering
         forAll(subOrder, i)
         {
-            orderedToOld[subsetter.cellMap()[i]] =
+            orderedToOld[cellMap[i]] =
                 globalSubCells.toGlobal(subOrigToOrdered[i]);
         }
     }
@@ -253,11 +243,7 @@ Foam::labelList Foam::structuredRenumber::renumber
     // by any visited cell so are used only if the number of nLayers is limited.
     labelList oldToOrdered
     (
-        invert
-        (
-            mesh.nCells(),
-            method_().renumber(mesh, points)
-        )
+        invert(mesh.nCells(), method_().renumber(mesh))
     );
 
     // Use specialised sorting to sorted either layers or columns first
diff --git a/src/renumber/renumberMethods/structuredRenumber/structuredRenumber.H b/src/renumber/renumberMethods/structuredRenumber/structuredRenumber.H
index f436862832..37477cfe15 100644
--- a/src/renumber/renumberMethods/structuredRenumber/structuredRenumber.H
+++ b/src/renumber/renumberMethods/structuredRenumber/structuredRenumber.H
@@ -132,46 +132,38 @@ public:
 
     // Member Functions
 
-        //- Renumbering method requires a polyMesh
+        //- Renumbering method requires a polyMesh!
         virtual bool needs_mesh() const { return true; }
 
 
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
-        //  This is only defined for geometric renumberMethods.
-        virtual labelList renumber(const pointField&) const
-        {
-            NotImplemented;
-            return labelList();
-        }
+    // With mesh topology
 
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
-        //  Use the mesh connectivity (if needed)
+        //- Return the cell visit order (from ordered back to original cell id)
+        //  using the mesh.
         virtual labelList renumber
         (
-            const polyMesh& mesh,
-            const pointField& cc
+            const polyMesh& mesh
         ) const;
 
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
+
+    // With explicit topology - Not implemented!
+
+        //- Return the cell visit order (from ordered back to original cell id).
+        //- Not implemented!
         virtual labelList renumber
         (
-            const CompactListList<label>& cellCells,
-            const pointField& cellCentres
+            const CompactListList<label>& cellCells
         ) const
         {
             NotImplemented;
             return labelList();
         }
 
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
+        //- Return the cell visit order (from ordered back to original cell id).
+        //- Not implemented!
         virtual labelList renumber
         (
-            const labelListList& cellCells,
-            const pointField& cellCentres
+            const labelListList& cellCells
         ) const
         {
             NotImplemented;
diff --git a/src/renumber/zoltanRenumber/zoltanRenumber.C b/src/renumber/zoltanRenumber/zoltanRenumber.C
index 5cd44e1193..58348e8dc9 100644
--- a/src/renumber/zoltanRenumber/zoltanRenumber.C
+++ b/src/renumber/zoltanRenumber/zoltanRenumber.C
@@ -24,10 +24,7 @@ License
     You should have received a copy of the GNU General Public License
     along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
 
-Class
-    Foam::zoltanRenumber
-
-Description
+Notes
     Renumber using Zoltan
 
     Zoltan install:
@@ -46,9 +43,6 @@ Description
         --prefix=$ZOLTAN_ARCH_DIR \
         --with-ccflags=-fPIC --with-cxxflags=-fPIC --with-ldflags=-shared
 
-SourceFiles
-    zoltanRenumber.C
-
 \*---------------------------------------------------------------------------*/
 
 #include "zoltanRenumber.H"
@@ -365,8 +359,7 @@ Foam::zoltanRenumber::zoltanRenumber(const dictionary& dict)
 
 Foam::labelList Foam::zoltanRenumber::renumber
 (
-    const polyMesh& pMesh,
-    const pointField& points
+    const polyMesh& pMesh
 ) const
 {
     // Zoltan_Initialize will trigger MPI_Init() if not already done.
diff --git a/src/renumber/zoltanRenumber/zoltanRenumber.H b/src/renumber/zoltanRenumber/zoltanRenumber.H
index b6f7c625ef..c7446ec297 100644
--- a/src/renumber/zoltanRenumber/zoltanRenumber.H
+++ b/src/renumber/zoltanRenumber/zoltanRenumber.H
@@ -83,46 +83,38 @@ public:
 
     // Member Functions
 
-        //- Renumbering method requires a polyMesh
+        //- Renumbering method requires a polyMesh for its topology
         virtual bool needs_mesh() const { return true; }
 
 
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
-        //  This is only defined for geometric renumberMethods.
-        virtual labelList renumber(const pointField&) const
-        {
-            NotImplemented;
-            return labelList();
-        }
+    // With mesh topology
 
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
-        //  Use the mesh connectivity (if needed)
+        //- Return the cell visit order (from ordered back to original cell id)
+        //- uses the mesh for connectivity and global exchanges
         virtual labelList renumber
         (
-            const polyMesh& mesh,
-            const pointField& cc
+            const polyMesh& mesh
         ) const;
 
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
+
+    // With explicit topology - Not implemented!
+
+        //- Return the cell visit order (from ordered back to original cell id).
+        //- Not implemented!
         virtual labelList renumber
         (
-            const CompactListList<label>& cellCells,
-            const pointField& cellCentres
+            const CompactListList<label>& cellCells
         ) const
         {
             NotImplemented;
             return labelList();
         }
 
-        //- Return the order in which cells need to be visited
-        //- (ie. from ordered back to original cell label).
+        //- Return the cell visit order (from ordered back to original cell id).
+        //- Not implemented!
         virtual labelList renumber
         (
-            const labelListList& cellCells,
-            const pointField& cellCentres
+            const labelListList& cellCells
         ) const
         {
             NotImplemented;