2,527 research outputs found
An Efficient Block Circulant Preconditioner For Simulating Fracture Using Large Fuse Networks
{\it Critical slowing down} associated with the iterative solvers close to
the critical point often hinders large-scale numerical simulation of fracture
using discrete lattice networks. This paper presents a block circlant
preconditioner for iterative solvers for the simulation of progressive fracture
in disordered, quasi-brittle materials using large discrete lattice networks.
The average computational cost of the present alorithm per iteration is , where the stiffness matrix is partioned into
-by- blocks such that each block is an -by- matrix, and
represents the operational count associated with solving a block-diagonal
matrix with -by- dense matrix blocks. This algorithm using the block
circulant preconditioner is faster than the Fourier accelerated preconditioned
conjugate gradient (PCG) algorithm, and alleviates the {\it critical slowing
down} that is especially severe close to the critical point. Numerical results
using random resistor networks substantiate the efficiency of the present
algorithm.Comment: 16 pages including 2 figure
Frictional dynamics of viscoelastic solids driven on a rough surface
We study the effect of viscoelastic dynamics on the frictional properties of
a (mean field) spring-block system pulled on a rough surface by an external
drive. When the drive moves at constant velocity V, two dynamical regimes are
observed: at fast driving, above a critical threshold Vc, the system slides at
the drive velocity and displays a friction force with velocity weakening. Below
Vc the steady sliding becomes unstable and a stick-slip regime sets in. In the
slide-hold-slide driving protocol, a peak of the friction force appears after
the hold time and its amplitude increases with the hold duration. These
observations are consistent with the frictional force encoded
phenomenologically in the rate-and-state equations. Our model gives a
microscopical basis for such macroscopic description.Comment: 10 figures, 7 pages, +4 pages of appendi
Localized Manifold Harmonics for Spectral Shape Analysis
The use of Laplacian eigenfunctions is ubiquitous in a wide range of computer graphics and geometry processing applications. In particular, Laplacian eigenbases allow generalizing the classical Fourier analysis to manifolds. A key drawback of such bases is their inherently global nature, as the Laplacian eigenfunctions carry geometric and topological structure of the entire manifold. In this paper, we introduce a new framework for local spectral shape analysis. We show how to efficiently construct localized orthogonal bases by solving an optimization problem that in turn can be posed as the eigendecomposition of a new operator obtained by a modification of the standard Laplacian. We study the theoretical and computational aspects of the proposed framework and showcase our new construction on the classical problems of shape approximation and correspondence. We obtain significant improvement compared to classical Laplacian eigenbases as well as other alternatives for constructing localized bases
A note on fractional derivative modeling of broadband frequency-dependent absorption: Model III
By far, the fractional derivative model is mainly related to the modelling of
complicated solid viscoelastic material. In this study, we try to build the
fractional derivative PDE model for broadband ultrasound propagation through
human tissues
Spatially Adaptive Stochastic Methods for Fluid-Structure Interactions Subject to Thermal Fluctuations in Domains with Complex Geometries
We develop stochastic mixed finite element methods for spatially adaptive
simulations of fluid-structure interactions when subject to thermal
fluctuations. To account for thermal fluctuations, we introduce a discrete
fluctuation-dissipation balance condition to develop compatible stochastic
driving fields for our discretization. We perform analysis that shows our
condition is sufficient to ensure results consistent with statistical
mechanics. We show the Gibbs-Boltzmann distribution is invariant under the
stochastic dynamics of the semi-discretization. To generate efficiently the
required stochastic driving fields, we develop a Gibbs sampler based on
iterative methods and multigrid to generate fields with computational
complexity. Our stochastic methods provide an alternative to uniform
discretizations on periodic domains that rely on Fast Fourier Transforms. To
demonstrate in practice our stochastic computational methods, we investigate
within channel geometries having internal obstacles and no-slip walls how the
mobility/diffusivity of particles depends on location. Our methods extend the
applicability of fluctuating hydrodynamic approaches by allowing for spatially
adaptive resolution of the mechanics and for domains that have complex
geometries relevant in many applications
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