Hi All, Thanks to David for the response, and looking through the code this does appear to be in principle what I am after. However, I have been unable to get a minimal example working to do this across two different meshes, which is ultimately what I need: from firedrake import UnitSquareMesh, FunctionSpace, TestFunction, Interpolator mesh1 = UnitSquareMesh(10, 10) V1 = FunctionSpace(mesh1, "CG", 1) mesh2 = UnitSquareMesh(4, 4) V2 = FunctionSpace(mesh2, "CG", 1) v = TestFunction(V2) interp_obj = Interpolator(v, V2) This gives me a RunTimeError when creating the PyOP2 Sparsity object, as the itersets of the two PyOP2 Map objects obtained from the cell_node_map method for the two function spaces are not the same. I was only able to get this to run when using identical meshes for the two different function spaces – is that the only type of interpolation that is supported in this manner? Any suggestions would be greatly appreciated. Cheers, Eric From: "Ham, David A" <david.ham@imperial.ac.uk> Date: Wednesday, 11 March 2020 at 19:19 To: Eric Daub <edaub@turing.ac.uk> Cc: firedrake <firedrake@imperial.ac.uk> Subject: Re: Firedrake in a project at ATI Dear Eric, Thanks for the email. Since you indicated that you tried to join the mailing list, I have taken the liberty of subscribing you to the list and copying the list in on my answer. We currently have what you want for the cases of point evaluation node elements (i.e. CG and DG elements). See: https://www.firedrakeproject.org/interpolation.html#interpolator-objects<https://eur01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.firedrakeproject.org%2Finterpolation.html%23interpolator-objects&data=02%7C01%7Cedaub%40turing.ac.uk%7C86343747734c45f1991008d7c5f119b1%7C4395f4a7e4554f958a9f1fbaef6384f9%7C0%7C0%7C637195511630974440&sdata=%2FCB0%2BHtD20oNbKZ%2BbGzwL35PK85ESIBSUCqpF%2BS1B9Q%3D&reserved=0> . The interpolator object contains the interpolation matrix in appropriate cases. There are people working on generalising this to all the elements we have, and making the differentiation work cleanly so that things like point forcing and point measurements work seamlessly. I hope we have more progress on this in the coming months. Cheers, David -- Dr David Ham Department of Mathematics Imperial College London https://www.imperial.ac.uk/people/david.ham From: Eric Daub <edaub@turing.ac.uk> Date: Wednesday, 11 March 2020 at 12:19 To: "Ham, David A" <david.ham@imperial.ac.uk> Subject: Firedrake in a project at ATI Dear David, I am an RSE at the Turing working with Mark Girolami (and Alastair Gregory before he moved to a new position) on implementing a probabilistic version of the Finite Element Method that he has developed over the past couple of years. The method provides a Bayesian framework for finding FEM solutions conditioned on sensor data, and Mark hopes that this tool will become a part of several research projects in the Turing Data-Centric Engineering Programme. Some other ICL researchers (Craig Buchanan and Leroy Gardner in Civil Engineering) are also involved with this research program. I am building our software on top of Firedrake as suggested by Alastair, as it nicely supports much of what we need to do straight out of the box (in particular, easily integrating with PETSc and ensemble parallelism have made my job relatively straightforward, as those have proven to be the difficult bits of the implementation thus far). However, one additional piece that is necessary for the FEM solves required by the method is the ability to access the matrix that interpolates between the FEM DOF nodes and arbitrary sensor locations where data has been collected. This involves evaluating the FEM basis functions at all of the sensor locations and collecting them in a sparse matrix. I did not see a simple way to do this using the existing interfaces, but it is highly likely that I missed something. I have a simplified version that works for linear CG elements on triangular/tetrahedral meshes that I have been using for testing purposes, but eventually want to implement this for the more general case. Any advice on how to proceed would be greatly appreciated. I attempted to join the Firedrake listserver, as I suspect that some of the discussions arising there may be relevant to my work, though it seems that my request never went through. If I can join the list I would be happy to re-pose my question there for the development team if you feel that would be more appropriate. Thanks for your help, and I hope that my work can help get more people using Firedrake in various research threads here at the Turing. 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While we take care to protect our systems from virus attacks and other harmful events, we give no warranty that this message (including attachments) is free of any virus or other harmful matter, and we accept no responsibility for any loss or damage resulting from the recipient receiving, opening or using it. E-mail transmission cannot be guaranteed to be secure or error-free as information could be intercepted, corrupted, lost, destroyed, arrive late or be incomplete. If you think someone may have interfered with this email, please contact the Alan Turing Institute by telephone only and speak to the person dealing with your matter or the Accounts Department. Fraudsters are increasingly targeting organisations and their affiliates, often requesting funds to be transferred to a different bank account. The Alan Turing’s bank details are contained within our terms of engagement. 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