86,441 research outputs found
An Integral geometry based method for fast form-factor computation
Monte Carlo techniques have been widely used in rendering algorithms for local integration. For example, to
compute the contribution of a patch to the luminance of another. In the present paper we propose an
algorithm based on Integral geometry where Monte Carlo is applied globally. We give some results of the
implementation to validate the proposition and we study the error of the technique, as well as its complexity.Postprint (published version
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 Isogeometric Boundary Element Method based on Independent Field Approximation
An isogeometric boundary element method for problems in elasticity is
presented, which is based on an independent approximation for the geometry,
traction and displacement field. This enables a flexible choice of refinement
strategies, permits an efficient evaluation of geometry related information, a
mixed collocation scheme which deals with discontinuous tractions along
non-smooth boundaries and a significant reduction of the right hand side of the
system of equations for common boundary conditions. All these benefits are
achieved without any loss of accuracy compared to conventional isogeometric
formulations. The system matrices are approximated by means of hierarchical
matrices to reduce the computational complexity for large scale analysis. For
the required geometrical bisection of the domain, a strategy for the evaluation
of bounding boxes containing the supports of NURBS basis functions is
presented. The versatility and accuracy of the proposed methodology is
demonstrated by convergence studies showing optimal rates and real world
examples in two and three dimensions.Comment: 32 pages, 27 figure
Numerical methods for computing Casimir interactions
We review several different approaches for computing Casimir forces and
related fluctuation-induced interactions between bodies of arbitrary shapes and
materials. The relationships between this problem and well known computational
techniques from classical electromagnetism are emphasized. We also review the
basic principles of standard computational methods, categorizing them according
to three criteria---choice of problem, basis, and solution technique---that can
be used to classify proposals for the Casimir problem as well. In this way,
mature classical methods can be exploited to model Casimir physics, with a few
important modifications.Comment: 46 pages, 142 references, 5 figures. To appear in upcoming Lecture
Notes in Physics book on Casimir Physic
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