140 research outputs found
Highly accurate special quadrature methods for Stokesian particle suspensions in confined geometries
Boundary integral methods are highly suited for problems with complicated
geometries, but require special quadrature methods to accurately compute the
singular and nearly singular layer potentials that appear in them. This paper
presents a boundary integral method that can be used to study the motion of
rigid particles in three-dimensional periodic Stokes flow with confining walls.
A centrepiece of our method is the highly accurate special quadrature method,
which is based on a combination of upsampled quadrature and quadrature by
expansion (QBX), accelerated using a precomputation scheme. The method is
demonstrated for rodlike and spheroidal particles, with the confining geometry
given by a pipe or a pair of flat walls. A parameter selection strategy for the
special quadrature method is presented and tested. Periodic interactions are
computed using the Spectral Ewald (SE) fast summation method, which allows our
method to run in O(n log n) time for n grid points, assuming the number of
geometrical objects grows while the grid point concentration is kept fixed.Comment: 46 pages, 41 figure
Fast and spectrally accurate summation of 2-periodic Stokes potentials
We derive a Ewald decomposition for the Stokeslet in planar periodicity and a
novel PME-type O(N log N) method for the fast evaluation of the resulting sums.
The decomposition is the natural 2P counterpart to the classical 3P
decomposition by Hasimoto, and is given in an explicit form not found in the
literature. Truncation error estimates are provided to aid in selecting
parameters. The fast, PME-type, method appears to be the first fast method for
computing Stokeslet Ewald sums in planar periodicity, and has three attractive
properties: it is spectrally accurate; it uses the minimal amount of memory
that a gridded Ewald method can use; and provides clarity regarding numerical
errors and how to choose parameters. Analytical and numerical results are give
to support this. We explore the practicalities of the proposed method, and
survey the computational issues involved in applying it to 2-periodic boundary
integral Stokes problems
A fast integral equation method for solid particles in viscous flow using quadrature by expansion
Boundary integral methods are advantageous when simulating viscous flow
around rigid particles, due to the reduction in number of unknowns and
straightforward handling of the geometry. In this work we present a fast and
accurate framework for simulating spheroids in periodic Stokes flow, which is
based on the completed double layer boundary integral formulation. The
framework implements a new method known as quadrature by expansion (QBX), which
uses surrogate local expansions of the layer potential to evaluate it to very
high accuracy both on and off the particle surfaces. This quadrature method is
accelerated through a newly developed precomputation scheme. The long range
interactions are computed using the spectral Ewald (SE) fast summation method,
which after integration with QBX allows the resulting system to be solved in M
log M time, where M is the number of particles. This framework is suitable for
simulations of large particle systems, and can be used for studying e.g. porous
media models
Adaptive quadrature by expansion for layer potential evaluation in two dimensions
When solving partial differential equations using boundary integral equation
methods, accurate evaluation of singular and nearly singular integrals in layer
potentials is crucial. A recent scheme for this is quadrature by expansion
(QBX), which solves the problem by locally approximating the potential using a
local expansion centered at some distance from the source boundary. In this
paper we introduce an extension of the QBX scheme in 2D denoted AQBX - adaptive
quadrature by expansion - which combines QBX with an algorithm for automated
selection of parameters, based on a target error tolerance. A key component in
this algorithm is the ability to accurately estimate the numerical errors in
the coefficients of the expansion. Combining previous results for flat panels
with a procedure for taking the panel shape into account, we derive such error
estimates for arbitrarily shaped boundaries in 2D that are discretized using
panel-based Gauss-Legendre quadrature. Applying our scheme to numerical
solutions of Dirichlet problems for the Laplace and Helmholtz equations, and
also for solving these equations, we find that the scheme is able to satisfy a
given target tolerance to within an order of magnitude, making it useful for
practical applications. This represents a significant simplification over the
original QBX algorithm, in which choosing a good set of parameters can be hard
A tale of the tall : A short report on stature in Late Neolithic–Early Bronze Age southern Scandinavia
Human stature as a measurement for evaluating physical status is used by the World Health Organiza-tion (WHO) as well as bioarchaeologists. The reason for this is that only about 80% depends on genetic factors, while 20% depend on the environment. Bad living conditions decrease stature in a population. This paper aims to make a short review of earlier reports on stature in Late Neolithic–Early Bronze Age Southern Scandinavia and to provide some new data. It is clear that stature in Late Neolithic–Early Bronze Age Scandinavia was very high, equal to modern statures
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