Initial Conditions and Function update on time in mixed Element

[dokken]

@VINICIUS_DANIEL_PERE

How to determine an initial concentration the of mobile ions c0= 2740 , in time t =0 for each subdomain ( hydrogel and elastomer) , for a mixed elements.

@VINICIUS_DANIEL_PERE

# Initial electro-chemical potentials
init_omgPos = Expression('abs(x[1])>=int2-tol?std::log((cPos0)):std::log((cNum))', int2=int2, tol = tol, cPos0 = cPos0, cNum=DOLFIN_EPS, degree=0)

omgPos_init = interpolate(init_omgPos,ME.sub(1).collapse())
assign(w_old.sub(1),omgPos_init)
assign(w.sub(1),omgPos_init)

I guess you are referring to this?

In the code below, you are mixing a whole lot of ufl and numpy

@VINICIUS_DANIEL_PERE

class init_Omg:
    def __init__(self):
        self.scaley= scaleY
        self.int2= int2
        self.tol= tol
        self.c= 0
        self.CNum= DOlfin_Eps
        
    def init_Omg_eval(self,x):
        if x[1]>= 700e-6 + tol:
            #return ufl.ln(self.c) #
            return np.log(self.c, dtype=np.int32)
        if x[1]<= 200e-6 - tol:
            return np.log(self.c, dtype=np.int32)
        else:
            return np.log(self.CNum, dtype=np.int32)

    def init_Omg_(self,x):
        return ufl.conditional(ufl.ge(x[1],200e+6 + tol), ufl.ln(self.c), ufl.ln(self.CNum))
    

Let us consider a simple MWE, on a unit square:

from IPython import embed
from mpi4py import MPI
from dolfinx import fem, io, nls, log, mesh, plot
import numpy as np
from petsc4py.PETSc import ScalarType
import ufl
from dolfinx.io import gmshio


domain = mesh.create_rectangle(MPI.COMM_WORLD, [[2, 2], [3, 3]], [10, 10])
"""Function Space"""
# Define function space, scalar
U2 = ufl.VectorElement("Lagrange", domain.ufl_cell(), 1)  # Displacent
# concentrações + - , electric potential
P1 = ufl.FiniteElement("Lagrange", domain.ufl_cell(), 1)
D0 = ufl.FiniteElement("DG", domain.ufl_cell(), 0)
D1 = ufl.FiniteElement("DG", domain.ufl_cell(), 1)

# DOFs
TH = ufl.MixedElement([U2, P1, P1, P1])
ME = fem.FunctionSpace(domain, TH)  # Total space for all DOFs
w = fem.Function(ME)

a = 2.5
cpos0 = 1.1
cNum = 2


def init_omega(x):
    condition = x[1] > a
    condition_inverse = np.invert(condition)
    return condition*np.log(cpos0) + condition_inverse * np.log(cNum)
w.sub(1).interpolate(init_omega)

Here I’ve created a simply numpy function with the same functionality as

@VINICIUS_DANIEL_PERE

init_omgPos = Expression('abs(x[1])>=int2-tol?std::log((cPos0)):std::log((cNum))', int2=int2, tol = tol, cPos0 = cPos0, cNum=DOLFIN_EPS, degree=0)

where you replace a with int2-tol etc.

As long as your example is kept as partial snippets, it is quite hard to give you any further guidance (and it is aso the reason why it has taken so long to write up a reply). I would strongly suggest you try to simplify your code, and have a look at: PETSc NonlinearProblem running slow - #4 by dokken
as it seems rather relevant for the second question.