How to Compare Two COMSOL Solutions Using Join Dataset
You changed the mesh. Or you changed a parameter. The new result looks "about the same" as the old one. But how much is "about"? And where in the model is the change biggest?
Most users open two plots side by side and compare them by eye. This is slow, and it hides small but important differences. COMSOL has a better tool for this job: the Join dataset. It combines two solutions into one dataset, so you can plot the difference directly.
What the Join Dataset Does
The Join dataset takes two source datasets, called data1 and data2, and combines them. The default is simply data1 - data2. You can then use this new dataset in any plot, just like a normal Solution dataset.
Typical uses:
Mesh convergence - compare a coarse mesh and a fine mesh, and see where the mesh still matters.
Parameter studies - compare two load cases, two inlet velocities, or two material values.
Study variants - compare two studies with the same geometry and physics.
Step 1: Prepare Two Solutions
You need two solutions first. There are three common ways:
Two meshes. Add a second mesh (Mesh toolbar → Add Mesh). Create two studies. In each study step, use the Mesh Selection section to choose Mesh 1 for the first study and Mesh 2 for the second.
Two parameter values. Run a Parametric Sweep. You can compare two parameter values from the same sweep - you do not need two studies.
Two studies. For example, two different boundary conditions on the same geometry.
Compute both solutions before you continue. In our example, we use two identical models of heat transfer with two different meshes.
Step 2: Add the Join Dataset
In the Model Builder, go to Results, right-click Datasets, and choose Join. (In the ribbon, look under Results → More Datasets.)
The settings window has two sections: Data 1 and Data 2. In each one:
Choose the source dataset in the Data list.
In the Solutions list, choose All (default) or One.
Use One when your source is a parametric sweep or a time-dependent study. A second list appears, and you pick the exact parameter value or time. So for a sweep, you can point both Data 1 and Data 2 to the same dataset, but choose a different parameter value in each.
Step 3: Choose the Combination Method
Below, Data 2 is the Combination section with a Method list:
Difference (default) - data1 - data2
Norm of difference - abs(data1 - data2)
Product, Quotient, Sum
General - type your own formula in the Expression field, for example (data1-data2)^2
Explicit - no fixed formula. You write data1() and data2() directly in the plot expression.
For a quick check, Norm of difference is often the best choice. You see only the size of the change, and the color scale is easy to read.
Step 4: Plot the Difference
Create a new 2D or 3D Plot Group. Set Dataset to Join 1. Add a Surface plot and type the quantity, for example T. Like here
COMSOL now shows the difference of that quantity, not the quantity itself. Areas with high values are where the two solutions disagree. In a mesh study, this tells you exactly where to refine.
Tips and limits
The order matters. When the two meshes differ, COMSOL looks up points from one mesh in the other and interpolates. This is not symmetric. If you swap Data 1 and Data 2, the numbers can change slightly. Keep the same order in all your comparisons.
Geometry must match. Join works best when both solutions use the same geometry. If the geometries differ, some plot types are not available.
Selections are limited. You cannot always pick domains or boundaries for a Join dataset. Newer versions allow a Selection subnode if both source datasets use the same geometry. Otherwise, add the selection to the source Solution datasets and point Join to those.
Comparing only integrals? If you only need to compare one number, like total heat flux or drag force, use an Evaluation Group with Transformation type set to Difference instead. COMSOL says this gives better accuracy than integrating over a Join dataset.
Different variable names? With the method Explicit, you can compare two models with different variable names, for example data1(u1) - data2(u2).
Summary
The Join dataset replaces "looks the same to me" with a real number and a real map. Prepare two solutions, add a Join dataset, pick a method, and plot. In two minutes, you know where your model is sensitive to the mesh or to a parameter, and where it is not.
