Hello again,

Managed I managed to figure it out. Below is an example where I have a domain with 5 boundaries and I am trying to set the Physical Line like someone suggested. Does this look right?

If yes, then I think I'm in good shape. One problem is that the boundary layer is very narrow for my choice of parameters so it's hard to know whether the boundary value is really zero. I don't suppose there is an easy way to find out the maximum of the boundary value in the numerical solution?

element_size = 0.05;

// Printing points from 1 to 6.

Point(1) = {-0.000000, -0.000000, 0, element_size};

Point(2) = {4.27, 0.54, 0, element_size};

Point(3) = {2.98, 4.00, 0, element_size};

Point(4) = {0.50, 3.58, 0, element_size};

Point(5) = {-1.70, 1.33, 0, element_size};

// Printing Spline points 1 to 6.

Line(1) = {1,2};

Line(2) = {2,3};

Line(3) = {3,4};

Line(4) = {4,5};

Line(5) = {5,1};

// Printing line loop from spline 1 to 2

Line Loops(1) = {1,2,3,4,5};

Plane Surface(6) = {1};

Physical Surface(7) = {6};

Physical Line(8) = {1};

------------------
Francis Poulin

Associate Dean, Undergraduate Studies
Associate Professor
Department of Applied Mathematics
University of Waterloo

email:           fpoulin@uwaterloo.ca
Web:            https://uwaterloo.ca/poulin-research-group/
Telephone: +1 519 888 4567 x32637

Sorry, I thought I had upgraded to the latest version of firedrake but I had not. I have since fixed that and am now using the version of firedrake based on python3, which is using 3.5.2.

I am happy to say that when I try using this example in my script it seems to work very nicely. It does inf act solve the weak form and imposes the correct BCS.

Now for my oceanic basin case, below are the last two lines in my code. From this I gather that the name for the physical surface is [2], and that consists of the entire domain.

Plane Surface(1) = {1};

Physical Surface(2) = {1};

If I want to impose Dirichlet BCs everywhere then should I do the following?

#bc = DirichletBC(Z.sub(0), 0.0, "on_boundary")

bc = DirichletBC(Z.sub(0), 0.0, [2])

I commented out what I had before, which I thought would impose the BCs everywhere but it didn't seem to do that.

------------------
Francis Poulin

From: firedrake-bounces@imperial.ac.uk <firedrake-bounces@imperial.ac.uk> on behalf of Homolya, Miklós <m.homolya14@imperial.ac.uk>
Sent: Friday, November 3, 2017 11:39:23 AM
To: G. D. McBain; firedrake
Subject: Re: [firedrake] problems with importing a mesh

These look like the optional type annotations. I think they were introduced in Python 3.6, while Firedrake requires Python 3.5+

You are probably running Python 3.5.x then. Just remove those colon types, or alternatively try Python 3.6.

From: firedrake-bounces@imperial.ac.uk <firedrake-bounces@imperial.ac.uk> on behalf of Francis Poulin <fpoulin@uwaterloo.ca>
Sent: 03 November 2017 15:11:34
To: G. D. McBain
Cc: firedrake
Subject: Re: [firedrake] problems with importing a mesh

Thanks for all the helpful information. I am starting to understand but not quiet there yet.

I was able to generate the mesh but when I try running your script I get the following problem. Is there a different syntax we should be using?

(firedrake) fpoulin@domlt32:~/Dropbox/Research_Christine/Notebooks/TestGeometry$ python membrane.py quadrant.msh

File "membrane.py", line 11

def main(meshfile: str) -> None:

^

SyntaxError: invalid syntax

What I understand is I should be specifying a label to the boundary and use this label to impose the BC's. I tried importing your geometry into my notebook and that seemed to go okay but when I try plotting I get the Assertion error.

Any more help would be greatly appreciated.

------------------
Francis Poulin

From: G. D. McBain <gdmcbain@protonmail.com>
Sent: Friday, November 3, 2017 2:09 AM
To: Francis Poulin
Cc: firedrake@imperial.ac.uk
Subject: Re: [firedrake] problems with importing a mesh

I am curious to see what you find does the trick.

It seems that my warning was obsolete. Whereas, I find from my old notes, that failure label each part of the boundary in Gmsh raised:

AssertionError: Every marker has to be contained in unique_markers

and in Feb. 2016, L. M. wrote: ‘If you provide a marker for one of the external boundaries of your mesh, you need to do so for all of them.’

https://mailman.ic.ac.uk/mailman/htdig/firedrake/2016-February/001809.html

I find today that this isn't the case. I hadn't noticed this being fixed as I'd simply complied by labelling everything. Anyway thank you to whoever fixed that, in Firedrake or upstream.

As for my coastline problem, the good news is that I can now import the geometry. The bad news is that when I solve the weak for of the PDE it does not impose the Dirichlet BCs.

So to satisfy myself of the above, I prepared a simple example with a Dirichlet condition on part of the boundary and natural conditions on the rest. The same technique might work for your problem.

Consider the plane Poisson equation with constant unit forcing on a circle with homogeneous Dirichlet conditions, but exploiting two lines of symmetry using just a quadrant with natural conditions on the two radii. The exact answer on the circle is that the integral of the solution divided by the square of the area should be 1/8 pi, or four times on the quarter-model, so 1/2pi.

%<---quadrant.geo

Point(1) = {1, 0, 0, 1.0};

Point(2) = {0, 0, 0, 1.0};

Point(3) = {0, 1, 0, 1.0};

Circle(1) = {1, 2, 3};

Line(2) = {3, 2};

Line(3) = {2, 1};

Line Loop(1) = {1, 2, 3};

Plane Surface(1) = {1};

Physical Surface("membrane", 2) = {1};

Physical Line("rim", 1) = {1};

--->%

Note that the last line specifies the quarter-circle perimeter from "Circle(1)" but not the radii of symmetry "Line(2)" or "Line(3)".

The Dirichlet boundary condition is imposed on the perimeter of the circle using "[1]" for the 1 of the Physical Line:

bc = DirichletBC(V, 0.0, [1])

Running this with

$ gmsh -2 -clscale 6.25e-2 quadrant.geo

$ python membrane.py quadrant.msh

I get 0.15905285125 which is 1/2 pi to four decimal places.