Introduction

Writing a transformer

Here is an example transformer (identical to the DDM1 transformer implemented in this package):

from dune.ufl import Space, DirichletBC
import ufl

import ddfem

space = Space(2, dimRange=1)

domain = [[-1.25,-1.25],[1.25,1.25],[50,50]]
h = 2.5/50
epsilon = 4.5*h # !!!
print(f"h={h},epsilon={epsilon}")
ball = ddfem.geometry.Ball(radius=1, name="full", epsilon=epsilon)

D = lambda x: 0.1 - 0.05*ufl.dot(x,x) # !!!
b = lambda x: 3*ufl.as_vector([x[1],-x[0]]) # !!!
c = lambda x: 0.01 # !!!
f = lambda x: 0.1*ufl.as_vector([1 - ufl.dot(x,x)]) # !!!
g = lambda x: ufl.as_vector([ufl.sin(ufl.pi * x[0]) * ufl.sin(ufl.pi * x[1])]) # !!!
class Model:
    def S_i(t, x, U, DU):
        return f(x) - c(x) * U

    def F_c(t, x, U):
        return ufl.outer(U, b(x))

    def F_v(t, x, U, DU):
        return D(x) * DU

    boundary = {"full": ddfem.boundary.BndValue(g)}
    outFactor_i = 0.1
    outFactor_e = 3

h=0.05,epsilon=0.225

@ddfem.transformers.transformer
def DDM1(Model):
    class DDModel(Model):
        def S_e_source(t, x, U, DU):
            return DDModel.phi(x) * Model.S_e(t, x, U, DDModel.sigma(t, x, U, DU))

        def S_e_convection(t, x, U, DU):
            return -DDModel.BT.BndFlux_cExt(t, x, U)

        def S_outside(t, x, U, DU):
            return -(
                DDModel.BT.jumpV(t, x, U) * (1 - DDModel.phi(x)) / (DDModel.epsilon**3)
            )

        def S_i_source(t, x, U, DU):
            return DDModel.phi(x) * Model.S_i(t, x, U, DDModel.sigma(t, x, U, DU))

        def S_i_diffusion(t, x, U, DU):
            if DDModel.BT.BndFlux_vExt is not None:
                diffusion = DDModel.BT.BndFlux_vExt(t, x, U, DU)
            else:
                diffusion = ufl.zero(U.ufl_shape)
            return diffusion

        def F_c(t, x, U):
            return DDModel.phi(x) * Model.F_c(t, x, U)

        def F_v(t, x, U, DU):
            return DDModel.phi(x) * Model.F_v(t, x, U, DDModel.sigma(t, x, U, DU))

    return DDModel

ModelDDM1 = DDM1(Model, ball)

uh = ddfem.solve(ddfem.model2ufl(ModelDDM1, space, DirichletBC=DirichletBC), domain)
ddfem.plotSolution(ball,uh,figsize=[10,10])

TODO: add information on @ddfem.transformers.transformer decorator

This page was generated from the notebook transformers_nb.ipynb and is part of the tutorial for the ddfem package using the dune-fem python bindings