A few basics

[rhaynes74]

Hi folks, I have a few basic questions about obtaining solution traces and enforcing boundary conditions.
Suppose I have solved a 2d problem with the solution stored in function U.

I would like to obtain a (Dirichlet) trace of the solution in the domain and use it as a Dirichlet boundary condition for another PDE solve. What is the best way of doing this? Can assume (if it makes a difference) that the PDEs are on compatible meshes (same number and orientation of elements).

Related - suppose I want to provide the boundary data pointwise in an array, maybe loaded from a datafile , how is this best achieved.

Sorry for the basic questions!

[colinjcotter]

On the same mesh, you can just provide U as the value to DirichletBC. On different meshes, you will need to interpolate from one mesh to the other. From: rhaynes74 ***@***.***> Date: Friday, 19 April 2024 at 15:12 To: firedrakeproject/firedrake ***@***.***> Cc: Subscribed ***@***.***> Subject: [firedrakeproject/firedrake] A few basics (Discussion #3513) Hi folks, I have a few basic questions about obtaining solution traces and enforcing boundary conditions. Suppose I have solved a 2d problem with the solution stored in function U. I would like to obtain a (Dirichlet) trace of the solution in the domain and use it as a Dirichlet boundary condition for another PDE solve. What is the best way of doing this? Can assume (if it makes a difference) that the PDEs are on compatible meshes (same number and orientation of elements). Related - suppose I want to provide the boundary data pointwise in an array, maybe loaded from a datafile , how is this best achieved. Sorry for the basic questions! — Reply to this email directly, view it on GitHub<#3513>, or unsubscribe<https://github.com/notifications/unsubscribe-auth/ABOSV4UANPVN6CQAJQ5FD3LY6EQ23AVCNFSM6AAAAABGPIPC7SVHI2DSMVQWIX3LMV43ERDJONRXK43TNFXW4OZWGUZDQOJUGM>. You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>

[rhaynes74]

I am not sure what is happening on the hood of interpolate, but is it necessary to interpolate onto the whole of the mesh for the second problem? In some instances I could imagine that the mesh for the second problem may extend past the mesh for the first problem.

[colinjcotter]

No it isn’t. This is all described here: https://www.firedrakeproject.org/interpolation.html#id5 From: rhaynes74 ***@***.***> Date: Friday, 19 April 2024 at 15:38 To: firedrakeproject/firedrake ***@***.***> Cc: Cotter, Colin J ***@***.***>, Comment ***@***.***> Subject: Re: [firedrakeproject/firedrake] A few basics (Discussion #3513) I am not sure what is happening on the hood of interpolate, but is it necessary to interpolate onto the whole of the mesh for the second problem? In some instances I could imagine that the mesh for the second problem may extend past the mesh for the first problem. — Reply to this email directly, view it on GitHub<#3513 (reply in thread)>, or unsubscribe<https://github.com/notifications/unsubscribe-auth/ABOSV4RLCG6NWGSFFSYZYRDY6ET6LAVCNFSM6AAAAABGPIPC7SVHI2DSMVQWIX3LMV43SRDJONRXK43TNFXW4Q3PNVWWK3TUHM4TCNRXGU2DQ>. You are receiving this because you commented.Message ID: ***@***.***>