add computational of integral values

README.md

@@ -11,6 +11,9 @@ A Python library for interpolating physical field data (electromagnetic forces,
   - Heat flux (scalar fields)
   - Heat generation (volumetric)
   - Heat Transfer Coefficient + bulk fluid temperature (convection BCs)
+- **Analysis tools**:
+  - Scalar field integration for computing total heat generation, flux, etc.
+  - EM force resultant computation for validating force/moment conservation
 - **Export to ANSYS APDL**: Direct export of interpolated results in APDL format
 - **Visualization**: Built-in VTK export for ParaView or PyVista visualization
 - **Efficient**: KDTree-based spatial queries for fast neighbor searches
@@ -60,6 +63,58 @@ interpolator.export_to_ansys("output_directory")
 interpolator.build_vtk_output(outdir="vtk_output")
 ```
 
+## Analysis Methods
+
+After interpolation, InterpCore provides methods to analyze and validate results:
+
+### Scalar Integrals
+
+For scalar fields (heat flux, heat generation), you can compute the total integral over the destination mesh:
+
+```python
+# Requires volume or area data in the destination mesh
+file_idx = {"ids": 0, "dest_x": 1, "src_x": 1, "val": 4, "vol": 4}  # or "area": 5
+
+interpolator = Interpolator(
+    path_to_src_folder="source_data",
+    path_to_dest_mesh="destination_mesh.txt",
+    config=config,
+    file_idx=file_idx
+)
+
+interpolator.interpolate_all()
+
+# Compute integrals (e.g., total heat generation in W)
+integrals = interpolator.compute_scalar_integrals()
+# Returns: {"data_001": array([total_value])}
+```
+
+**Note**: The destination mesh must include volume (for 3D elements) or area (for 2D elements) data. Use the APDL scripts in [`apdl-scripts/`](apdl-scripts/) to export element centroids with volumes and areas.
+
+### EM Force Resultants
+
+For EM force fields, you can compute force and moment resultants to verify conservation:
+
+```python
+# After interpolation with EM_FORCE load type
+resultants = interpolator.compute_EM_resultants(pole=np.array([0.0, 0.0, 0.0]))
+
+# Returns for each source file:
+# {
+#     "force_001": {
+#         "R_F_EM": [Fx, Fy, Fz],           # Total force from source data
+#         "R_F_Mech": [Fx, Fy, Fz],         # Total force from interpolated data
+#         "R_M_EM": [Mx, My, Mz],           # Total moment from source data
+#         "R_M_Mech": [Mx, My, Mz],         # Total moment from interpolated data
+#         "f_err_comp": [ex, ey, ez],       # Relative force error by component
+#         "m_err_comp": [ex, ey, ez],       # Relative moment error by component
+#         "Unmapped_EM_Force": float        # Norm of unmapped forces
+#     }
+# }
+```
+
+This is useful for validating that the interpolation preserves global force and moment equilibrium. Small errors indicate good interpolation quality.
+
 ## Examples
 
 Complete working examples with sample data are available in the [`doc/`](doc/) folder:

apdl-scripts/export_centroids.apdl

@@ -26,29 +26,40 @@ CMSEL,S,%named_selection%
 ! Allocate arrays
 *DIM, nGs, ARRAY, nE, 3		! element centroid coordinates
 *DIM, nTId,ARRAY, nE        ! element ids
+*DIM, nArea,ARRAY, nE       ! element area
+*DIM, nVol,ARRAY, nE        ! element volume
 
 ! Loop through selected elements and store centroids
 *DO,i,1,nE				    ! loop on selected elements
     nTId(i)  = iE		    ! element Id
     nGs(i,1) = CENTRX(iE)	! centroid X
     nGs(i,2) = CENTRY(iE)	! centroid Y
     nGs(i,3) = CENTRZ(iE)	! centroid Z
+
+    ! Get area and volume using *GET
+    *GET,area_val,ELEM,iE,AREA
+    *GET,vol_val,ELEM,iE,VOLU
+    nArea(i) = area_val		! element area
+    nVol(i)  = vol_val		! element volume
+
     iE       = ELNEXT(iE)
 *ENDDO
 
 ! Write results to CSV file
 *CFOPEN,%output_file%,csv
 ! Write header
-*VWRITE,'Element_ID','X','Y','Z'
-(A,',',A,',',A,',',A)
+*VWRITE,'Element_ID','X','Y','Z','Area','Volume'
+(A,',',A,',',A,',',A,',',A,',',A)
 ! Write data
-*VWRITE,nTId(1),nGs(1,1),nGs(1,2),nGs(1,3)
-(F10.0,',',E16.9,',',E16.9,',',E16.9)
+*VWRITE,nTId(1),nGs(1,1),nGs(1,2),nGs(1,3),nArea(1),nVol(1)
+(F10.0,',',E16.9,',',E16.9,',',E16.9,',',E16.9,',',E16.9)
 *CFCLOS
 
 ! Clean up arrays
 *DIM, nGs, DELETE
 *DIM, nTId, DELETE
+*DIM, nArea, DELETE
+*DIM, nVol, DELETE
 
 *MSG,INFO
 Read CDB file '%cdb_file%.cdb' and exported %nE% element centroids from '%named_selection%' to %output_file%.csv

doc/em_force/em_force.ipynb

@@ -12,10 +12,19 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 1,
    "id": "04f7aa2d",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "c:\\ProgramData\\anaconda3\\envs\\interpcore\\Lib\\site-packages\\tqdm\\auto.py:21: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html\n",
+      "  from .autonotebook import tqdm as notebook_tqdm\n"
+     ]
+    }
+   ],
    "source": [
     "from interpcore.interpolator import Interpolator\n",
     "from interpcore.config import InterpolationConfig, QUERY_TYPE, INTERPOLATED_LOAD_TYPE\n",
@@ -32,15 +41,15 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 2,
    "id": "42549f4f",
    "metadata": {},
    "outputs": [
     {
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "100%|██████████| 1/1 [00:00<00:00, 113.32it/s]"
+      "100%|██████████| 1/1 [00:00<00:00, 81.83it/s]"
      ]
     },
     {
@@ -96,7 +105,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 3,
    "id": "6dc76b31",
    "metadata": {},
    "outputs": [
@@ -146,7 +155,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 4,
    "id": "d23ec832",
    "metadata": {},
    "outputs": [],
@@ -167,7 +176,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 5,
    "id": "4adb006f",
    "metadata": {},
    "outputs": [
@@ -222,6 +231,63 @@
     "plt.show()"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "3b0d279d",
+   "metadata": {},
+   "source": [
+    "## Compute Force and Moment Resultants\n",
+    "\n",
+    "Verify that the interpolation preserves global force and moment equilibrium by computing resultants."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "eb46e90a",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "============================================================\n",
+      "Results for: em_force_data\n",
+      "============================================================\n",
+      "\n",
+      "Force Resultant (Source):        [797.1  373.7  136.35]\n",
+      "Force Resultant (Interpolated):  [797.1  373.7  136.35]\n",
+      "Force Error (relative):          [-2.85251130e-16  0.00000000e+00  4.16893428e-16]\n",
+      "\n",
+      "Moment Resultant (Source):       [  758.52  -181.42 -4007.15]\n",
+      "Moment Resultant (Interpolated): [  756.21485572  -179.12590679 -3990.31095618]\n",
+      "Moment Error (relative):         [0.003039   0.01264521 0.00420225]\n",
+      "\n",
+      "Unmapped EM Force (norm):        0.000000\n"
+     ]
+    }
+   ],
+   "source": [
+    "import numpy as np\n",
+    "\n",
+    "# Compute resultants with pole at origin\n",
+    "resultants = interpolator.compute_EM_resultants(pole=np.array([0.0, 0.0, 0.0]))\n",
+    "\n",
+    "# Display results for the first data file\n",
+    "for name, result in resultants.items():\n",
+    "    print(f\"\\n{'='*60}\")\n",
+    "    print(f\"Results for: {name}\")\n",
+    "    print(f\"{'='*60}\")\n",
+    "    print(f\"\\nForce Resultant (Source):        {result['R_F_EM']}\")\n",
+    "    print(f\"Force Resultant (Interpolated):  {result['R_F_Mech']}\")\n",
+    "    print(f\"Force Error (relative):          {result['f_err_comp']}\")\n",
+    "    print(f\"\\nMoment Resultant (Source):       {result['R_M_EM']}\")\n",
+    "    print(f\"Moment Resultant (Interpolated): {result['R_M_Mech']}\")\n",
+    "    print(f\"Moment Error (relative):         {result['m_err_comp']}\")\n",
+    "    print(f\"\\nUnmapped EM Force (norm):        {result['Unmapped_EM_Force']:.6f}\")"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,