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Rectangular matrix assempling
6 years 3 months ago #327
by Karatza
Rectangular matrix assempling was created by Karatza
Hi,
I have the following FE spaces:
I would like to define BilinearForm with V1 as test space and V2 as trial space, resulting in a rectangular matrix when assembled. Is it possible to do so? thanks and best regards Makis
I have the following FE spaces:
Code:
V = H1(mesh, order=1)
V1 = FESpace([V, V])
V2 = FESpace([V])
I would like to define BilinearForm with V1 as test space and V2 as trial space, resulting in a rectangular matrix when assembled. Is it possible to do so? thanks and best regards Makis
- christopher
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6 years 3 months ago - 6 years 3 months ago #329
by christopher
Replied by christopher on topic Rectangular matrix assempling
Yes this is possible, but the definition of V2 is not necessary, you can use V here as well. Just give the BilinearForm a different test and trial space:
Best
Christopher
Code:
from netgen.geom2d import unit_square
from ngsolve import *
mesh = Mesh(unit_square.GenerateMesh(maxh=0.2))
V = H1(mesh,order=1,dirichlet="top")
V1 = FESpace([V,V])
u = V.TrialFunction()
v1,v2 = V1.TestFunction()
a = BilinearForm(trialspace=V,testspace=V1)
a += SymbolicBFI(u * (v1 + 2*v2))
a.Assemble()
print(a.mat)
Best
Christopher
Last edit: 6 years 3 months ago by christopher.
The following user(s) said Thank You: Karatza
6 years 3 months ago #331
by Karatza
Replied by Karatza on topic Rectangular matrix assempling
Dear Christopher, thank you for your quick and accurate response!
Furthermore, I would like to better understand if ngspy has capabilities to perform symbolic manipulation for what concerns coefficient functions, linear forms and bilinear forms.
Two typical cases that I would like to tackle are the definition of functions that:
* given as input a bilinear form a for a scalar elliptic problem: I would like to manipulate it to get (in a new bilinear form) its adjoint a* by swapping test and trial functions.
* given as input a linear form F, say F(v) = \int_{\Omega} f*v, where f is some coefficient function defined on \Omega: I would like to obtain a new bilinear form G(v) where f is replaced by a different coefficient function. I would like to have both F(v) and G(v) available, so I cannot simply re-assign in-place values in f.
Thanks,
best regards,
Makis
Furthermore, I would like to better understand if ngspy has capabilities to perform symbolic manipulation for what concerns coefficient functions, linear forms and bilinear forms.
Two typical cases that I would like to tackle are the definition of functions that:
* given as input a bilinear form a for a scalar elliptic problem: I would like to manipulate it to get (in a new bilinear form) its adjoint a* by swapping test and trial functions.
* given as input a linear form F, say F(v) = \int_{\Omega} f*v, where f is some coefficient function defined on \Omega: I would like to obtain a new bilinear form G(v) where f is replaced by a different coefficient function. I would like to have both F(v) and G(v) available, so I cannot simply re-assign in-place values in f.
Thanks,
best regards,
Makis
- christopher
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6 years 3 months ago #334
by christopher
Replied by christopher on topic Rectangular matrix assempling
For the first point:
Is it enough if you can apply the transpose of the matrix? The matrix obtained by a.mat has operations like MultTrans and MultTransAdd which do
mat.MultTrans(s,x,y) does y = s * trans(mat) * x
mat.MultTransAdd(s,x,y) does y += s * trans(mat) * x
with s being a scalar.
Second question:
You can just use 2 linearforms for that.
Best
Christopher
Is it enough if you can apply the transpose of the matrix? The matrix obtained by a.mat has operations like MultTrans and MultTransAdd which do
mat.MultTrans(s,x,y) does y = s * trans(mat) * x
mat.MultTransAdd(s,x,y) does y += s * trans(mat) * x
with s being a scalar.
Second question:
You can just use 2 linearforms for that.
Best
Christopher
The following user(s) said Thank You: Karatza
6 years 3 months ago #336
by Karatza
Replied by Karatza on topic Rectangular matrix assempling
Dear Christopher,
thank you very much for your response. Let me rephrase my questions: I am inquiring if it possible to generate a new form on the fly. For instance, in the case of the second question, ideally I would like to have the following function
Of course I can define two linear forms (one with f and one with g), but I would be grateful to understand if capabilities like the one sketched in generate_on_the_fly() are available.
Thanks,
Makis
thank you very much for your response. Let me rephrase my questions: I am inquiring if it possible to generate a new form on the fly. For instance, in the case of the second question, ideally I would like to have the following function
Code:
def generate_on_the_fly(original_linear_form):
# create a copy of of original_linear_form into a new variable, say modified_linear_form
# replace f with some other forcing term (say g) inside modified_linear_form (but not in original_linear_form)
return modified_linear_form
Of course I can define two linear forms (one with f and one with g), but I would be grateful to understand if capabilities like the one sketched in generate_on_the_fly() are available.
Thanks,
Makis
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