98 research outputs found
Stochastic Bundle Adjustment for Efficient and Scalable 3D Reconstruction
Current bundle adjustment solvers such as the Levenberg-Marquardt (LM)
algorithm are limited by the bottleneck in solving the Reduced Camera System
(RCS) whose dimension is proportional to the camera number. When the problem is
scaled up, this step is neither efficient in computation nor manageable for a
single compute node. In this work, we propose a stochastic bundle adjustment
algorithm which seeks to decompose the RCS approximately inside the LM
iterations to improve the efficiency and scalability. It first reformulates the
quadratic programming problem of an LM iteration based on the clustering of the
visibility graph by introducing the equality constraints across clusters. Then,
we propose to relax it into a chance constrained problem and solve it through
sampled convex program. The relaxation is intended to eliminate the
interdependence between clusters embodied by the constraints, so that a large
RCS can be decomposed into independent linear sub-problems. Numerical
experiments on unordered Internet image sets and sequential SLAM image sets, as
well as distributed experiments on large-scale datasets, have demonstrated the
high efficiency and scalability of the proposed approach. Codes are released at
https://github.com/zlthinker/STBA.Comment: Accepted by ECCV 202
A stabilized finite element method for finite-strain three-field poroelasticity
We construct a stabilized finite-element method to compute flow and finitestrain
deformations in an incompressible poroelastic medium. We employ a three-
field mixed formulation to calculate displacement, fluid flux and pressure directly
and introduce a Lagrange multiplier to enforce flux boundary conditions. We use
a low order approximation, namely, continuous piecewise-linear approximation
for the displacements and fluid flux, and piecewise-constant approximation for
the pressure. This results in a simple matrix structure with low bandwidth. The
method is stable in both the limiting cases of small and large permeability. Moreover,
the discontinuous pressure space enables efficient approximation of steep
gradients such as those occurring due to rapidly changing material coefficients or
boundary conditions, both of which are commonly seen in physical and biological
applications
A unified approach for a posteriori high-order curved mesh generation using solid mechanics
The paper presents a unified approach for the a posteriori generation of arbitrary high-order curvilinear meshes via a solid mechanics analogy. The approach encompasses a variety of methodologies, ranging from the popular incremental linear elastic approach to very sophisticated non-linear elasticity. In addition, an intermediate consistent incrementally linearised approach is also presented and applied for the first time in this context. Utilising a consistent derivation from energy principles, a theoretical comparison of the various approaches is presented which enables a detailed discussion regarding the material characterisation (calibration) employed for the different solid mechanics formulations. Five independent quality measures are proposed and their relations with existing quality indicators, used in the context of a posteriori mesh generation, are discussed. Finally, a comprehensive range of numerical examples, both in two and three dimensions, including challenging geometries of interest to the solids, fluids and electromagnetics communities, are shown in order to illustrate and thoroughly compare the performance of the different methodologies. This comparison considers the influence of material parameters and number of load increments on the quality of the generated high-order mesh, overall computational cost and, crucially, the approximation properties of the resulting mesh when considering an isoparametric finite element formulation
Mixed-Precision Preconditioners in Parallel Domain Decomposition Solvers
Motivated by accuracy reasons, many large-scale scientific applications and industrial numerical simulation codes are fully implemented in 64-bit floating-point arithmetic. On the other hand, many recent processor architectures exhibit 32-bit computational power that is significantly higher than for 64-bit. One recent and significan
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