Dear all, I'm trying to use adaptive algorithm in Firedrake. Because it's essential in my thesis. I have problem with marking cell and locally refining step. The following is my test code for one iteration: REFINE_RATIO = 0.50 # Refine 50 % of the cells in each iteration mesh = UnitSquareMesh(4, 4) BDM = FunctionSpace(mesh, "BDM", 1) DG = FunctionSpace(mesh, "DG", 0) W = BDM * DG sigma, u = TrialFunctions(W) tau, v = TestFunctions(W) x, y = SpatialCoordinate(mesh) f = Function(DG).interpolate( 10*exp(-(pow(x - 0.5, 2) + pow(y - 0.5, 2)) / 0.02)) a = (dot(sigma, tau) + div(tau)*u + div(sigma)*v)*dx L = - f*v*dx bc0 = DirichletBC(W.sub(0), as_vector([0.0, -sin(5*x)]), 1) bc1 = DirichletBC(W.sub(0), as_vector([0.0, sin(5*y)]), 2) w = Function(W) solve(a == L, w, bcs=[bc0, bc1]) sigma, u = w.split() expr = (div(sigma)+f)*(div(sigma)+f) P0 = FunctionSpace(mesh, "DG", 0) Re = project(expr, P0) coeffs = Re.dat.data ss = sorted(coeffs, reverse=True)[int(len(coeffs)*REFINE_RATIO)] #-------------------------The followin are marking and refining which work in Dolfin --------------------------- cell_markers = MeshFunction("bool", mesh, mesh.topology().dim()) for c in cells(mesh): cell_markers[c] = coeffs[c.index()] > ss mesh = refine(mesh, cell_markers) 1) How can I use the loop over the cells in Firedrake? ( for c in ?) 2) Is there a way to refine some marked cell in Firedrake? Your answer will be greatly appreciated. All the best, Amireh
Dear Amireh, Some effort to do mesh adaptation has been done in Firedrake, notably in: https://arxiv.org/pdf/1610.09874.pdf and https://arxiv.org/pdf/1612.08077.pdf I know this does not answer your specific questions, however, it might be worth looking at what's already there before trying to do complicated stuff, as neither of your questions has a trivial answer (as far as I'm aware). Best wishes, -- Nicolas On 03/08/2018 10:03, Amireh Mousavi wrote:
Dear all,
I'm trying to use adaptive algorithm in Firedrake. Because it's essential in my thesis. I have problem with /marking cell/ and /locally refining/ step. The following is my test code for one iteration:
REFINE_RATIO = 0.50 # Refine 50 % of the cells in each iteration mesh = UnitSquareMesh(4, 4) BDM = FunctionSpace(mesh, "BDM", 1) DG = FunctionSpace(mesh, "DG", 0) W = BDM * DG sigma, u = TrialFunctions(W) tau, v = TestFunctions(W) x, y = SpatialCoordinate(mesh) f = Function(DG).interpolate( 10*exp(-(pow(x - 0.5, 2) + pow(y - 0.5, 2)) / 0.02)) a = (dot(sigma, tau) + div(tau)*u + div(sigma)*v)*dx L = - f*v*dx bc0 = DirichletBC(W.sub(0), as_vector([0.0, -sin(5*x)]), 1) bc1 = DirichletBC(W.sub(0), as_vector([0.0, sin(5*y)]), 2) w = Function(W) solve(a == L, w, bcs=[bc0, bc1]) sigma, u = w.split() expr = (div(sigma)+f)*(div(sigma)+f) P0 = FunctionSpace(mesh, "DG", 0) Re = project(expr, P0) coeffs = Re.dat.data ss = sorted(coeffs, reverse=True)[int(len(coeffs)*REFINE_RATIO)] #-------------------------The followin are marking and refining which work in Dolfin --------------------------- cell_markers = MeshFunction("bool", mesh, mesh.topology().dim()) for c in cells(mesh): cell_markers[c] = coeffs[c.index()] > ss mesh = refine(mesh, cell_markers)
1) How can I use the loop over the cells in Firedrake? ( *for c in ?*) 2) Is there a way to refine some marked cell in Firedrake?
Your answer will be greatly appreciated.
All the best, Amireh
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-- Nicolas Barral Dept. of Earth Science and Engineering Imperial College London Royal School of Mines - Office 4.88 London SW7 2AZ
participants (2)
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Amireh Mousavi
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Nicolas Barral