Biology Reference
In-Depth Information
5. Introduction to Continuum Particle Methods
Particle methods are point-based spatiotemporal simulation methods
that exhibit a number of favorable properties, which help address the
complications of spatiotemporal biological systems (cf. Sec. 2):
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They are the most universal simulation method. Particle methods
can be used for all types of models in Fig. 2, whereas most other
numerical methods are limited to one or two types of models.
•
They are intimately linked to the physical or biological process they
represent, since particles correspond to real-world entities (in dis-
crete models) or approximate field quantities (in continuous models).
The interactions between the particles can mostly be intuitively
understood as forces or exchange of mass. This prevents spurious,
unphysical modes from showing up in the simulation results, a capa-
bility that has recently also been developed for FE methods.
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They are well suited for simulations in complex geometries, such as
the ER shown in Fig. 1,
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and for simulations on complex curved
surfaces such as intracellular membranes.
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No computational
mesh needs to be generated and no connectivity constraints satis-
fied. This effectively avoids the increased algorithmic complexity
of mesh-based methods in complex geometries due to loss of the
“nice” structure of the matrix.
•
Due to their inherent regularity (particles have a finite size that
defines the resolution of the method; cf. Sec. 5.1), particle meth-
ods can easily handle topological changes such as fusion and fission
in the simulated geometry. Mesh-based methods need special reg-
ularization so as not to become unstable when two fusing or sep-
arating objects touch in exactly one point.
•
They are inherently adaptive, as particles are only required where
the represented quantity is present, and the motion of the particles
automatically tracks these regions. This constitutes an important
computational advantage compared to mesh-based methods,
where a mesh is required throughout the computational domain.
