62,048 research outputs found
Multibody Multipole Methods
A three-body potential function can account for interactions among triples of
particles which are uncaptured by pairwise interaction functions such as
Coulombic or Lennard-Jones potentials. Likewise, a multibody potential of order
can account for interactions among -tuples of particles uncaptured by
interaction functions of lower orders. To date, the computation of multibody
potential functions for a large number of particles has not been possible due
to its scaling cost. In this paper we describe a fast tree-code for
efficiently approximating multibody potentials that can be factorized as
products of functions of pairwise distances. For the first time, we show how to
derive a Barnes-Hut type algorithm for handling interactions among more than
two particles. Our algorithm uses two approximation schemes: 1) a deterministic
series expansion-based method; 2) a Monte Carlo-based approximation based on
the central limit theorem. Our approach guarantees a user-specified bound on
the absolute or relative error in the computed potential with an asymptotic
probability guarantee. We provide speedup results on a three-body dispersion
potential, the Axilrod-Teller potential.Comment: To appear in Journal of Computational Physic
Recursive regularization step for high-order lattice Boltzmann methods
A lattice Boltzmann method (LBM) with enhanced stability and accuracy is
presented for various Hermite tensor-based lattice structures. The collision
operator relies on a regularization step, which is here improved through a
recursive computation of non-equilibrium Hermite polynomial coefficients. In
addition to the reduced computational cost of this procedure with respect to
the standard one, the recursive step allows to considerably enhance the
stability and accuracy of the numerical scheme by properly filtering out second
(and higher) order non-hydrodynamic contributions in under-resolved conditions.
This is first shown in the isothermal case where the simulation of the doubly
periodic shear layer is performed with a Reynolds number ranging from to
, and where a thorough analysis of the case at is
conducted. In the latter, results obtained using both regularization steps are
compared against the BGK-LBM for standard (D2Q9) and high-order (D2V17 and
D2V37) lattice structures, confirming the tremendous increase of stability
range of the proposed approach. Further comparisons on thermal and fully
compressible flows, using the general extension of this procedure, are then
conducted through the numerical simulation of Sod shock tubes with the D2V37
lattice. They confirm the stability increase induced by the recursive approach
as compared with the standard one.Comment: Accepted for publication as a Regular Article in Physical Review
Asymptotic constant-factor approximation algorithm for the Traveling Salesperson Problem for Dubins' vehicle
This article proposes the first known algorithm that achieves a
constant-factor approximation of the minimum length tour for a Dubins' vehicle
through points on the plane. By Dubins' vehicle, we mean a vehicle
constrained to move at constant speed along paths with bounded curvature
without reversing direction. For this version of the classic Traveling
Salesperson Problem, our algorithm closes the gap between previously
established lower and upper bounds; the achievable performance is of order
Phase-field boundary conditions for the voxel finite cell method: surface-free stress analysis of CT-based bone structures
The voxel finite cell method employs unfitted finite element meshes and voxel quadrature rules to seamlessly
transfer CT data into patient-specific bone discretizations. The method, however, still requires the explicit
parametrization of boundary surfaces to impose traction and displacement boundary conditions, which
constitutes a potential roadblock to automation. We explore a phase-field based formulation for imposing
traction and displacement constraints in a diffuse sense. Its essential component is a diffuse geometry model
generated from metastable phase-field solutions of the Allen-Cahn problem that assumes the imaging data as
initial condition. Phase-field approximations of the boundary and its gradient are then employed to transfer
all boundary terms in the variational formulation into volumetric terms. We show that in the context of the
voxel finite cell method, diffuse boundary conditions achieve the same accuracy as boundary conditions
defined over explicit sharp surfaces, if the inherent length scales, i.e., the interface width of the phase-field,
the voxel spacing and the mesh size, are properly related. We demonstrate the flexibility of the new method
by analyzing stresses in a human femur and a vertebral body
A Step-indexed Semantics of Imperative Objects
Step-indexed semantic interpretations of types were proposed as an
alternative to purely syntactic proofs of type safety using subject reduction.
The types are interpreted as sets of values indexed by the number of
computation steps for which these values are guaranteed to behave like proper
elements of the type. Building on work by Ahmed, Appel and others, we introduce
a step-indexed semantics for the imperative object calculus of Abadi and
Cardelli. Providing a semantic account of this calculus using more
`traditional', domain-theoretic approaches has proved challenging due to the
combination of dynamically allocated objects, higher-order store, and an
expressive type system. Here we show that, using step-indexing, one can
interpret a rich type discipline with object types, subtyping, recursive and
bounded quantified types in the presence of state
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