Hi John,

Here is an attempt to answer your questions.

Generally, one has some variable of interest (e.g., temperature) that DEPENDS on INDEPENDENT variables of space (x, y, z) and time (t). The equations to describe this dependence usually derive from conservation laws (e.g., energy balance, momentum balance, species balance, etc) that are only valid for differential elements of space and time. If your system depends on more than one independent variable or if you are unsure of how many independent variables it depends on, then you are in the realm of PDEs.

As to your second question, if the problem could be represented as an ODE, then the numerical solution would have revealed it in the plots (e.g., families of characteristic contour curves would be identifiable). So, the answer is no, this system can not be represented by an ODE. For an example where I was able to convert a PDE into a simpler ODE based on characteristic lines I observed in the numerical solution of the fully coupled PDE, look here.

Almost all ODEs, PDEs, or systems thereof, cannot be solved analytically. In contrast, with the advent of fast computers and improved algorithms, a much larger class of ODE/PDE can be solved at reasonable speeds. Further, if you start off with the numerical solution, it can give insights on reasonable assumptions for a potential analytical solution.

The strength of MMA is ______.

packages often don't share their math code and the code isn't "good" it does the job.

you can publish you mm code so mm have it, or keep it private for use in a pro product :)

Thank you for the github link. I will investigate when I have free moment.

In the StackExchange link provided by Kuba above, Alexi does provide a procedure to export COMSOL data so that it can be can be read into Mathematica. I used it successfully to compare Mathematica to COMSOL from my very first answer to an adsorption problem to the Wolfram Community here.

tbl = Import[
   "C:\\Users\\Tim\\Dropbox\\WolframCommunity\\BreakThrough\\comsol_\
data_export.csv"];
conc = tbl[[All, Range[2, 302, 2]]];
ListPlot3D[Transpose@conc, DataRange -> {{0, 2}, {0, 1.5}}, 
 PlotRange -> {{0, 1}, {0, 1.5}}, 
 ColorFunction -> (ColorData["DarkBands"][#3] &), 
 MeshFunctions -> {#2 &}, Mesh -> 20, AxesLabel -> Automatic, 
 MeshStyle -> {Black, Thick}, ImageSize -> Large]

Perhaps, one could try to automate the workflow in java on the COMSOL end to facilitate the transfer.

With regard to the mesh, it looks like one might be able to use pyNastran to help bridge the gap between COMSOL and Mathematica. I have used pyNastran in the past to extract nodes and connectivity from an optiStruct model (Nastran format) and it looks as though COMSOL will export a Nastran mesh. GUIs do help facilitate meshing operations.

Parsing a parameter file should be easy, but parsing how all the parameters are used throughout the model would be difficult and prone to errors.

Thanks for the reply. I am aware of MMA capabilities of manually track solutions with code. But I still wish they could make it simpler by adding a simple built-in function like TrackSolving[NDSolve[...]] instead of having us to implement it.

Just like in the past we have to write our own neural network but now we have NetTrain. Why not improve more fundamental functions like NDSolve?

Take a look at the extensive documentation “Advanced Solutions to Numerical Differential Equations“ and for NDSolve. There are methods to track solutions (combinations of EvaluationMonitor, StepMonitor, and Dynamic.

There are also good examples of doing solid mechanics.

@TimLaska, It is perfectly reasonable to mention use of other languages/programs in any of several situations.

(1) Validation of results.

(2) Asking about discrepancies in behavior between the two. (If the Wolfram Language is showing obviously buggy behavior, it is good also to report that directly. Also we do not take well to having the same issue reported repeatedly. But that tends to be an uncommon problem in any forum.)

(3) Discussion about linking to/from other programs.

(4) Speed comparison, when we are faster (just kidding-- if it is an apples-to-apples comparison and WL falls short, that's good for us and others to know about).

(5) Questions to the effect "Does the Wolfram Language have something similar or equivalent to the built-in function XXX from program YYY?"

I'm probably missing a few other valid reasons. In any case, it would be fine for you to add discussion of othe rprograms in this setting.

You may find this thread interesting: https://mathematica.stackexchange.com/q/154254/5478

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Yes, I did model in both COMSOL and MMA. I generally don't mention other codes because I don't want to appear as though I am promoting possible competition. I am, however, a firm believer in validation versus other standards whenever possible.

Thank you for the comment!