1,948 research outputs found
A semi-Lagrangian Vlasov solver in tensor train format
In this article, we derive a semi-Lagrangian scheme for the solution of the
Vlasov equation represented as a low-parametric tensor. Grid-based methods for
the Vlasov equation have been shown to give accurate results but their use has
mostly been limited to simulations in two dimensional phase space due to
extensive memory requirements in higher dimensions. Compression of the solution
via high-order singular value decomposition can help in reducing the storage
requirements and the tensor train (TT) format provides efficient basic linear
algebra routines for low-rank representations of tensors. In this paper, we
develop interpolation formulas for a semi-Lagrangian solver in TT format. In
order to efficiently implement the method, we propose a compression of the
matrix representing the interpolation step and an efficient implementation of
the Hadamard product. We show numerical simulations for standard test cases in
two, four and six dimensional phase space. Depending on the test case, the
memory requirements reduce by a factor in four and a factor
in six dimensions compared to the full-grid method
Direct Mapping of Massive Compact Objects in Extragalactic Dark Halos
A significant fraction of non-baryonic or baryonic dark matter in galactic
halos may consist of MASsive Compact Objects (MASCOs) with mass
M=10^{1-4}M_{sun}. Possible candidates for such compact objects include
primordial black holes or remnants of primordial (Population III) stars. We
propose a method for directly detecting MASCOs in extragalactic halos, using
the VLBI techniques with extremely high resolution. If a galactic halo
comprising a large number of MASCOs produces multiple images of a background
radio-loud QSO by gravitational lensing, then a high-resolution radio map of
each macro-lensed image should reveal microlensing effects by MASCOs. To assess
their observational feasibility, we simulate microlensing of the radio-loud,
four-image lensed QSO, B1422+231, assuming angular resolution of ~0.01 mas.
MASCOs are represented by point masses. For comparison, we also simulate
microlensing of B1422+231 by singular isothermal spheres. We find that the
surface brightness of the macro-lensed images shows distinct spatial patterns
on the scale of the Einstein radius of the perturbers. In the case of
point-mass perturbers, many tiny dark spots also appear in the macro-lensed
images associated with a decrease in the surface brightness toward the fringe
of the original QSO image, whereas no such spots are available in the SIS
models. Based on the size, position and magnified or demagnified patterns of
images, we shall be able to determine the mass and density profile of a MASCO
as well as its spatial distribution and abundance in a galactic halo.Comment: 4 pages, 3 figure
Efficient Explicit Time Stepping of High Order Discontinuous Galerkin Schemes for Waves
This work presents algorithms for the efficient implementation of
discontinuous Galerkin methods with explicit time stepping for acoustic wave
propagation on unstructured meshes of quadrilaterals or hexahedra. A crucial
step towards efficiency is to evaluate operators in a matrix-free way with
sum-factorization kernels. The method allows for general curved geometries and
variable coefficients. Temporal discretization is carried out by low-storage
explicit Runge-Kutta schemes and the arbitrary derivative (ADER) method. For
ADER, we propose a flexible basis change approach that combines cheap face
integrals with cell evaluation using collocated nodes and quadrature points.
Additionally, a degree reduction for the optimized cell evaluation is presented
to decrease the computational cost when evaluating higher order spatial
derivatives as required in ADER time stepping. We analyze and compare the
performance of state-of-the-art Runge-Kutta schemes and ADER time stepping with
the proposed optimizations. ADER involves fewer operations and additionally
reaches higher throughput by higher arithmetic intensities and hence decreases
the required computational time significantly. Comparison of Runge-Kutta and
ADER at their respective CFL stability limit renders ADER especially beneficial
for higher orders when the Butcher barrier implies an overproportional amount
of stages. Moreover, vector updates in explicit Runge--Kutta schemes are shown
to take a substantial amount of the computational time due to their memory
intensity
An intelligent real time 3D vision system for robotic welding tasks
MARWIN is a top-level robot control system that has been designed for automatic robot welding tasks. It extracts welding parameters and calculates robot trajectories directly from CAD models which are then verified by real-time 3D scanning and registration. MARWIN's 3D computer vision provides a user-centred robot environment in which a task is specified by the user by simply confirming and/or adjusting suggested parameters and welding sequences. The focus of this paper is on describing a mathematical formulation for fast 3D reconstruction using structured light together with the mechanical design and testing of the 3D vision system and show how such technologies can be exploited in robot welding tasks
Robot trajectory planning using OLP and structured light 3D machine vision
This paper proposes a new methodology for robotic offline programming (OLP) addressing the issue of automatic program generation directly from 3D CAD models and verification through online 3D reconstruction. Limitations of current OLP include manufacturing tolerances between CAD and workpieces and inaccuracies in workpiece placement and modelled work cell. These issues are addressed and demonstrated through surface scanning, registration, and global and local error estimation. The method allows the robot to adjust the welding path designed from the CAD model to the actual workpiece. Alternatively, for non-repetitive tasks and where a CAD model is not available, it is possible to interactively define the path online over the scanned surface
GEMPIC: Geometric ElectroMagnetic Particle-In-Cell Methods
We present a novel framework for Finite Element Particle-in-Cell methods
based on the discretization of the underlying Hamiltonian structure of the
Vlasov-Maxwell system. We derive a semi-discrete Poisson bracket, which retains
the defining properties of a bracket, anti-symmetry and the Jacobi identity, as
well as conservation of its Casimir invariants, implying that the semi-discrete
system is still a Hamiltonian system. In order to obtain a fully discrete
Poisson integrator, the semi-discrete bracket is used in conjunction with
Hamiltonian splitting methods for integration in time. Techniques from Finite
Element Exterior Calculus ensure conservation of the divergence of the magnetic
field and Gauss' law as well as stability of the field solver. The resulting
methods are gauge invariant, feature exact charge conservation and show
excellent long-time energy and momentum behaviour. Due to the generality of our
framework, these conservation properties are guaranteed independently of a
particular choice of the Finite Element basis, as long as the corresponding
Finite Element spaces satisfy certain compatibility conditions.Comment: 57 Page
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