An efficient and energy-stable scheme for the modified phase-field crystal equation with a strong nonlinear vacancy potential
AIMS Mathematics,
Год журнала:
2025,
Номер
10(3), С. 5568 - 5582
Опубликована: Янв. 1, 2025
Язык: Английский
Phase field modeling of melting and solidification dynamics in metallic powders during the bed fusion process
Communications in Nonlinear Science and Numerical Simulation,
Год журнала:
2025,
Номер
unknown, С. 108762 - 108762
Опубликована: Март 1, 2025
Язык: Английский
Maximum Principle-Preserving Computational Algorithm for the 3D High-Order Allen–Cahn Equation
Mathematics,
Год журнала:
2025,
Номер
13(7), С. 1085 - 1085
Опубликована: Март 26, 2025
We
propose
an
unconditionally
stable
computational
algorithm
that
preserves
the
maximum
principle
for
three-dimensional
(3D)
high-order
Allen–Cahn
(AC)
equation.
The
presented
applies
operator-splitting
technique
decomposes
original
equation
into
nonlinear
and
linear
diffusion
equations.
To
guarantee
unconditional
stability
of
numerical
solution,
we
solve
using
frozen
coefficient
technique,
which
simplifies
computations
by
approximating
variable
coefficients
constants
within
small
regions.
For
equation,
use
implicit
finite
difference
scheme
under
method.
validate
efficiency
proposed
algorithm,
conducted
several
tests.
results
confirm
achieves
even
large
time
step
sizes
polynomial
potential.
In
addition,
analyze
motion
mean
curvature
in
space
show
solutions
closely
match
analytical
solutions.
Finally,
robustness
method
is
evaluated
noisy
data
conditions,
its
ability
to
accurately
classify
complex
structures
demonstrated.
These
reliability
simulating
phase-field
models
with
a
Язык: Английский
Benchmark problems for physics-informed neural networks: The Allen–Cahn equation
AIMS Mathematics,
Год журнала:
2025,
Номер
10(3), С. 7319 - 7338
Опубликована: Янв. 1, 2025
Язык: Английский
Phase-field computation for 3D shell reconstruction with an energy-stable and uniquely solvable BDF2 method
Computers & Mathematics with Applications,
Год журнала:
2025,
Номер
189, С. 1 - 23
Опубликована: Апрель 2, 2025
Язык: Английский
Highly efficient and accurate numerical schemes for the anisotropic phase field crystal models by using the improved scalar auxiliary variable (iSAV) approach
Communications in Nonlinear Science and Numerical Simulation,
Год журнала:
2025,
Номер
unknown, С. 108875 - 108875
Опубликована: Апрель 1, 2025
Язык: Английский
Fast numerical study on spatial nonuniform grids for two-dimensional fractional coupled equations with fractional Neumann boundary conditions
Joon Hyuk Kang,
Wenping Fan,
Zhenhao Lu
и другие.
Applied Mathematics Letters,
Год журнала:
2025,
Номер
169, С. 109609 - 109609
Опубликована: Май 17, 2025
Язык: Английский
A Unified Algorithm Framework for Phase‐Field Based Multimaterial Topology Optimization With Various Graded Interfaces
International Journal for Numerical Methods in Engineering,
Год журнала:
2025,
Номер
126(10)
Опубликована: Май 20, 2025
ABSTRACT
In
this
work,
we
present
a
unified
algorithm
framework
for
multimaterial
topology
optimization
with
various
graded
interfaces
based
on
the
phase
field
method.
framework,
problem
is
transformed
into
solving
set
of
linear
partial
differential
equations
(PDEs).
We
then
introduce
scalar
variable
to
grade
material
property,
resulting
in
complex
nonlinear
interpolation
operator
effective
elastic
tensor.
Following
that,
define
an
auxiliary
substitute
all
transformations
elliptic
equation
system.
A
second‐order
accurate
Crank–Nicolson
scheme
applied
reformulated
system,
which
high‐order
terms
are
treated
semi‐explicit
fashion.
prove
that
proposed
unconditionally
energy
stable
and
demonstrate
its
stability
as
well
accuracy
by
numerical
examples.
series
benchmark
problems
different
interfacial
behaviors
topological
design
investigated
verify
effectiveness
our
The
sensitivity
parameters
model
analyzed
evaluate
their
effects
structure.
Язык: Английский