[ff3d-users] Basic Question on Fictitious Domain method

[Juzar Thingna]

Hello Everyone,
I'm quite new to the fictitious domain method of solving PDE. I wanted to
know how is this method better than the Finite element method? while doing
some basic research one advantage I see is that the number of iterations for
convergence in CG is quite small in complex geometries because of the
pre-conditioner used. But I'm still not able to figure out how the geometry
can make the matrix ill-conditioned?

Any help or basic reading would be really helpful.

Regards,
Juzar Thingna
Center for Computation Science and Engineering
National University of Singapore

[Stephane Del Pino]

Hello.

Post by Juzar Thingna
Hello Everyone,
I'm quite new to the fictitious domain method of solving PDE. I wanted to
know how is this method better than the Finite element method?

It is not better. FDM relies usually on finite element method.

Post by Juzar Thingna
while doing
some basic research one advantage I see is that the number of iterations
for convergence in CG is quite small in complex geometries because of the
pre-conditioner used.

This can be the case for some methods but in ff3d, FDM are used to avoid the
complexity of 3D mesh generation. It is not a performance issue.

Post by Juzar Thingna
But I'm still not able to figure out how the
geometry can make the matrix ill-conditioned?

You should have a look to finite element method analysis.

Best regards,
S.