Apparently working BDMCF/E elements by dham · Pull Request #18 · firedrakeproject/fiat

dham · 2019-08-08T16:29:54Z

PR for review only. Don't merge as we need to PR into upstream.

This is linked to the Firedrake PR: firedrakeproject/firedrake#1488

wence- · 2020-05-01T11:36:52Z

+                    for j, f in enumerate(polynomials[:, 0]):
+                        T[j, 0, i] = f.evalf(subs=subs)
+                    for j, f in enumerate(polynomials[:, 1]):
+                        T[j, 1, i] = f.evalf(subs=subs)


This should use sympy.lambdify so it's not horribly slow like the existing serendipity stuff.

wence- · 2020-05-01T11:38:09Z

+        entity_ids[2][0] = list(range(cur, cur + 2*triangular_number(degree - 1)))
+        cur += 2*triangular_number(degree - 1)
+
+        formdegree = 1


Only used in the call to the superclass constructor.

wence- · 2020-05-01T11:39:16Z

+        return self._degree
+
+    def get_nodal_basis(self):
+        raise NotImplementedError("get_nodal_basis not implemented for bdmce")


BDMCE/F ?

wence- · 2020-05-01T11:40:03Z

+        raise NotImplementedError("get_dual_set is not implemented for bdmce")
+
+    def get_coeffs(self):
+        raise NotImplementedError("get_coeffs not implemented for bdmce")


Even though the construction is done on the prime basis directly (for tabulation), it would be good to implement a dual basis given that these elements are interpolatory.

wence- · 2020-05-01T11:40:55Z

+        return self.entity_closure_ids
+
+    def value_shape(self):
+        return (2,)


This should be ref_el.get_dimension() dependent or something, right?

wence- · 2020-05-01T11:42:02Z

+        return int(len(self.basis[(0, 0)])/2)
+
+
+def e_lambda_1_2d(deg, dx, dy, x_mid, y_mid):


docstrings. Maybe make a reference to the paper that introduces these elements?

wence- · 2020-05-01T11:42:29Z

+        flat_el = flatten_reference_cube(ref_el)
+        dim = flat_el.get_spatial_dimension()
+        if dim != 2:
+            raise Exception("BDMcf_k elements only valid for dimension 2")


Seems strange to call something a cube element when it's only valid for squares.

wence- · 2020-05-01T11:42:42Z

+        flat_el = flatten_reference_cube(ref_el)
+        dim = flat_el.get_spatial_dimension()
+        if dim != 2:
+            raise Exception("BDMcf_k elements only valid for dimension 2")


wence- · 2020-07-24T09:51:58Z

Can we add fiat level tests for these elements? It appears they don't produce the right results at lowest order.

wence- · 2020-07-24T12:18:30Z

I am confused by the association of basis functions to topological entities (at least for BDMce) at degree 1.

The FIAT quad is numbered:

     3    
  1-----3
  |     |
0 |     | 1
  |     |
  0-----2
     2

import FIAT
cell = FIAT.reference_element.UFCQuadrilateral()
element = FIAT.brezzi_douglas_marini_cube.BrezziDouglasMariniCubeEdge(cell, 1)
element.entity_dofs()
=> {0: {0: [], 1: [], 2: [], 3: []},
 1: {0: [0, 1], 1: [2, 3], 2: [4, 5], 3: [6, 7]},
 2: {0: []}}

So let's look at the first two basis functions which lie on the edge x = 0.

print(element.basis[0, 0][:2])
=> [[0, 1.0*x - 1.0], [0.5*y*(1.0*y - 1.0), (1.0 - 1.0*x)*(1.0 - 2*y)]]

I don't know exactly what these should be, but I was expecting things that have a x component that varies linearly in y, and are constant in x. Is this wrong?

In any case, if I look at the next two basis functions

print(element.basis[0,0][2:4])                                         
=> [[0, -1.0*x], [0.5*y*(1.0 - 1.0*y), 1.0*x*(1.0 - 2*y)]]

It seems these pair up "nicely?" with the corresponding basis functions 0 and 1. What am I missing?

Given this, it would be good if the implementation pointed to a reference for the basis functions. If they're the standard ones described in the Brezzi Boffi and Fortin book, it seems odd that they're defined in this primal way, rather than by using a dual basis (which is explicitly described there).

tommbendall · 2021-01-25T13:34:54Z

+               [(-leg(deg, x_mid)*dy[0], -leg(deg-1, x_mid)*dx[0]*dx[1]/(deg+1))] +
+               [(-leg(j, x_mid)*dy[1], 0) for j in range(deg)] +
+               [(-leg(deg, x_mid)*dy[1], leg(deg-1, x_mid)*dx[0]*dx[1]/(deg+1))])
+


My understanding of the issues @pefarrell was reporting with the lowest-order spaces is that these basis functions aren't quite right.

When taking the 2D curl of each basis function (or the divergence for BDMCF) it should return a polynomial of deg-1.

Inspection of these basis functions shows that this is correct for the functions such as
[(0, -leg(j, y_mid)*dx[0]) for j in range(deg)]
but not quite for those like
[(-leg(deg-1, y_mid)*dy[0]*dy[1], -leg(deg, y_mid)*dx[0])].

I did a bit of maths and I think that one component of these needs modifying by a coefficient. Running the bdmc_riesz test in the bdmc branch of Firedrake, I got a convergence rate of deg+1 when using the following functions (which ensure that the curl/div of the basis functions is of the correct polynomial order):

from sympy import binomial coeff = binomial(2*deg,deg) / ((deg+1)*binomial(2*(deg-1), deg-1)) EL = tuple([(0, -leg(j, y_mid)*dx[0]) for j in range(deg)] + [(coeff*-leg(deg-1, y_mid)*dy[0]*dy[1], -leg(deg, y_mid)*dx[0])] + [(0, -leg(j, y_mid)*dx[1]) for j in range(deg)] + [(coeff*leg(deg-1, y_mid)*dy[0]*dy[1], -leg(deg, y_mid)*dx[1])] + [(-leg(j, x_mid)*dy[0], 0) for j in range(deg)] + [(-leg(deg, x_mid)*dy[0], coeff*-leg(deg-1, x_mid)*dx[0]*dx[1])] + [(-leg(j, x_mid)*dy[1], 0) for j in range(deg)] + [(-leg(deg, x_mid)*dy[1], coeff*leg(deg-1, x_mid)*dx[0]*dx[1])])

tommbendall · 2021-01-28T11:39:27Z

I think I've addressed most of @wence- 's comments -- I have not changed the name cube (even though these are elements on quads), and I have not yet implemented a dual basis.

jmv2009 · 2021-06-06T15:52:41Z

FYI: Just is in #22, this will not work in Fenics without dual basis.

wence- · 2022-06-29T10:06:06Z

This was superseded by #22 and can be closed, yes? Ping @rckirby

rckirby · 2022-06-29T18:56:14Z

My understanding is that BDMCE/F implement the S elements, while trimmed serendipity implement the S- elements so that they are a bit different. Maybe @dham recalls what was going on there?

Done

cyruscycheng21 and others added 16 commits June 25, 2019 23:30

started bdmc element

1d8589e

started implementing entity_dofs

1492475

first draft bdmc

6658ada

minor fixes

a7c5ede

change name poly to polynomials

aff450f

minor updates

276512c

flake8 complaint

de2976c

minor edits

7ebba5a

minor changes

13b6abb

minor changes

ab2848c

new docstring for flatten_reference_cube

78d9395

fix docstring

cd03c26

changed basis function order

87841f9

working for degree 1 and 2

2c42a0c

Merge branch 'master' into bdmc

7c55630

Flake8

c84d83d

dham mentioned this pull request Aug 8, 2019

Bdmc FInAT/FInAT#55

Merged

cyruscycheng21 and others added 4 commits August 9, 2019 03:03

working bdmcf

d33bac1

Andrew's basis functions

48b59d2

add mappings

a4f88e4

Merge remote-tracking branch 'origin/master' into bdmc

eb67c5e

wence- previously requested changes May 1, 2020

View reviewed changes

Merge branch 'master' into bdmc

b4d7e39

tommbendall reviewed Jan 25, 2021

View reviewed changes

tommbendall added 4 commits January 26, 2021 17:25

Merge branch 'master' into bdmc

dca55b6

fix BDMCE/F elements by correcting coefficients for basis

758ef37

Tidy up BDMCE/F elements

d10132a

Lint fixes

c8bc383

fix doc string text

03edbe9

allow tabulation on edges

5040d42

Merge branch 'master' into bdmc

b2843bc

tommbendall mentioned this pull request Jul 25, 2023

Bdmc firedrakeproject/firedrake#1488

Merged

dham merged commit e440a06 into master Sep 20, 2023

dham deleted the bdmc branch September 20, 2023 15:15

		return int(len(self.basis[(0, 0)])/2)


		def e_lambda_1_2d(deg, dx, dy, x_mid, y_mid):

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wence- commented Jul 24, 2020

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dham commented Aug 8, 2019 •

edited by tommbendall

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wence- commented Jul 24, 2020 •

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