An approximate block factorization preconditioner for mixed-dimensional beam-solid interaction
Computer Methods in Applied Mechanics and Engineering,
Journal Year:
2024,
Volume and Issue:
431, P. 117256 - 117256
Published: July 30, 2024
This
paper
presents
a
scalable
approximate
block
factorization
preconditioner
for
mixed-dimensional
models
in
beam-solid
interaction
and
their
application
engineering.
In
particular,
it
studies
the
linear
systems
arising
from
regularized
mortar-type
approach
embedding
geometrically
exact
beams
into
solid
continua.
Due
to
lack
of
diagonal
dominance
2
×
system,
an
Block-LU
is
used.
It
exploits
sparsity
structure
beam
sub-block
construct
sparse
inverse,
which
then
not
only
used
explicitly
form
approximation
Schur
complement,
but
also
acts
as
smoother
within
prediction
correction
step
preconditioner.
The
complement
equation
tackled
with
algebraic
multigrid
method.
Although,
now,
by
one-level
method
only,
multi-level
nature
computationally
demanding
delivers
practice.
numerical
test
cases,
influence
different
algorithmic
parameters
on
quality
inverse
studied
weak
scaling
behavior
proposed
up
1000
MPI
ranks
demonstrated.
addition,
robustness
regarding
material
geometric
properties
shown,
before
finally
applied
analysis
steel-reinforced
concrete
structures
civil
Language: Английский
Mathematical and Numerical Analysis of Reduced Order Interface Conditions and Augmented Finite Elements for Mixed Dimensional Problems
Published: Jan. 1, 2024
In
this
paper,
we
are
interested
in
the
mathematical
properties
of
methods
based
on
a
fictitious
domain
approach
combined
with
reduced-order
interface
coupling
conditions,
which
have
been
recently
introduced
to
simulate
3D-1D
fluid-structure
or
structure-structure
coupled
problems.
To
give
insights
approximation
these
methods,
investigate
them
simplified
setting
by
considering
Poisson
problem
two-dimensional
non-homogeneous
Dirichlet
boundary
conditions
small
inclusions.
The
approximated
reduced
is
obtained
using
projection
Fourier
finite-dimensional
space
Lagrange
multiplier
associated
constraints,
obtaining
way
defective
conditions.
After
analyzing
existence
solution
problem,
prove
its
convergence
towards
original
full
when
size
holes
tends
zero,
rate
depends
number
modes
space.
particular,
our
estimates
highlight
fact
that
obtain
good
multiplier,
one
needs
consider
more
than
first
mode
(constant
mode).
This
key
issue
wants
deal
real
problems,
such
as
problems
for
instance.
Next,
numerical
discretization
finite
element
method
analyzed
case
where
computational
mesh
does
not
fit
inclusion
interface.
As
standard
types
optimal
due
lack
regularity
solution.
Moreover,
exhibits
well-known
locking
effect
and
same
order
magnitude.
apparent
increasing
affects
heavily.
resolve
issues,
propose
analyze
stabilized
an
enriched
additional
basis
functions
added
without
changing
multiplier.
Finally,
strategies
illustrated
experiments.
Language: Английский
Mathematical and numerical analysis of reduced order interface conditions and augmented finite elements for mixed dimensional problems
Computers & Mathematics with Applications,
Journal Year:
2024,
Volume and Issue:
175, P. 536 - 569
Published: Oct. 31, 2024
Language: Английский