# Problem with variational derivative

I am solving a coupled problem: Nonlinear advection-diffusion and hyperelasticity

#Function spaces are:

Q = FunctionSpace(mesh, "CG", 1);

V = VectorFunctionS

U = VectorFunctionS

#Functions for advection-diff

u1c = Function(Q) #Solution from current time step

u10 = Function(Q) #Initial condition

#Functions for hyperelasticity

v2 = TestFunction(U) # Test function

du2 = TrialFunction(U) # Incremental displacement

u2c = Function(U) # Displacement in current time step

#Concentration field influencing the stress. Strain energy function psi(C), where C is the right Cauchy-Green tensor.

psi = ((u10/u1c)

P = 2*((u1c/

#Variational form

L2 = inner(P, grad(v2))*dx(1) - inner(B, v2)*dx(1) - inner(T2, v2)*ds(1)

a2 = derivative(L2, u2c, du2)

# Solve nonlinear variational problem

problem = VariationalProb

This code takes inordinately long to form the matrices, but appears to converge quadratically to the correct solution. If instead I move the multiplication by (u10/u1c) from

P = 2*((u1c/

psi = ((u10/u1c)

P = 2*F*diff(psi, C) #Stress

the matrices are assembled faster by a factor of 30 or 40, but the starting residual is different and I lose quadratic convergence of the residual.

Is there something obviously wrong? It is unexpected that rewriting the stress without changing its mathematical form causes such a difference in the assembly and solution procedures.

----Krishna

## Question information

- Language:
- English Edit question

- Status:
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- DOLFIN Edit question

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- Last query:
- 2010-06-08

- Last reply:
- 2010-06-08

Garth Wells (garth-wells) said : | #1 |

On 08/06/10 16:19, Krishna Garikipati wrote:

> New question #113926 on DOLFIN:

> https:/

>

> I am solving a coupled problem: Nonlinear advection-diffusion and hyperelasticity

>

> #Function spaces are:

> Q = FunctionSpace(mesh, "CG", 1);

> V = VectorFunctionS

> U = VectorFunctionS

>

> #Functions for advection-diff

> u1c = Function(Q) #Solution from current time step

> u10 = Function(Q) #Initial condition

>

> #Functions for hyperelasticity

> v2 = TestFunction(U) # Test function

> du2 = TrialFunction(U) # Incremental displacement

> u2c = Function(U) # Displacement in current time step

>

> #Concentration field influencing the stress. Strain energy function psi(C), where C is the right Cauchy-Green tensor.

> psi = ((u10/u1c)

> P = 2*((u1c/

>

> #Variational form

> L2 = inner(P, grad(v2))*dx(1) - inner(B, v2)*dx(1) - inner(T2, v2)*ds(1)

> a2 = derivative(L2, u2c, du2)

> # Solve nonlinear variational problem

> problem = VariationalProb

> cell_domains=

> exterior_

> nonlinear=True)

>

>

> This code takes inordinately long to form the matrices, but appears to converge quadratically to the correct solution.

Try putting

parameters

parameters

somewhere near the top of your file. It will take longer to compile the

code the first time through, but the assembly should be much faster

(likely orders of magnitude faster).

> If instead I move the multiplication by (u10/u1c) from

> P = 2*((u1c/

>

> psi = ((u10/u1c)

> P = 2*F*diff(psi, C) #Stress

>

> psi = ((u10/u1c)

> P = 2*((u1c/

> the matrices are assembled faster by a factor of 30 or 40, but the starting residual is different and I lose quadratic convergence of the residual.

>

> Is there something obviously wrong? It is unexpected that rewriting the stress without changing its mathematical form causes such a difference in the assembly and solution procedures.

>

It should of course give the same result if the expressions are the

same, but if may affect the runtime, particularly when optimisations are

switched off (Kristian could comment in more details).

Garth

> ----Krishna

>

>

>

On 8 June 2010 17:19, Krishna Garikipati

<email address hidden> wrote:

> New question #113926 on DOLFIN:

> https:/

>

> I am solving a coupled problem: Nonlinear advection-diffusion and hyperelasticity

>

> #Function spaces are:

> Q = FunctionSpace(mesh, "CG", 1);

> V = VectorFunctionS

> U = VectorFunctionS

>

> #Functions for advection-diff

> u1c = Function(Q) #Solution from current time step

> u10 = Function(Q) #Initial condition

>

> #Functions for hyperelasticity

> v2 = TestFunction(U) # Test function

> du2 = TrialFunction(U) # Incremental displacement

> u2c = Function(U) # Displacement in current time step

>

> #Concentration field influencing the stress. Strain energy function psi(C), where C is the right Cauchy-Green tensor.

> psi = ((u10/u1c)

> P = 2*((u1c/

>

> #Variational form

> L2 = inner(P, grad(v2))*dx(1) - inner(B, v2)*dx(1) - inner(T2, v2)*ds(1)

> a2 = derivative(L2, u2c, du2)

Could you send the entire definition of the variational form? Some

variables like const1, const2, const3, B, T2, C (did I miss any?) are

not defined, I can't get FFC to compile without.

> # Solve nonlinear variational problem

> problem = VariationalProb

> cell_domains=

> exterior_

> nonlinear=True)

>

>

> This code takes inordinately long to form the matrices, but appears to converge quadratically to the correct solution. If instead I move the multiplication by (u10/u1c) from

> P = 2*((u1c/

>

> psi = ((u10/u1c)

> P = 2*F*diff(psi, C) #Stress

>

> the matrices are assembled faster by a factor of 30 or 40, but the starting residual is different and I lose quadratic convergence of the residual.

The expressions for psi and P have been simplified since only one

power (**0.3333) remains. These kind of reductions are not done in UFL

or FFC so that might explain the difference in runtime.

The results should of course be the same, but as they are not this can

of course be another reason why the runtime differs (because you

assemble something different).

To get to the bottom of this I guess we need to compare the UFL

expressions or look at the generated code.

Kristian

> Is there something obviously wrong? It is unexpected that rewriting the stress without changing its mathematical form causes such a difference in the assembly and solution procedures.

>

> ----Krishna

>

>

>

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## Can you help with this problem?

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