6,610 research outputs found
Real-time Error Control for Surgical Simulation
Objective: To present the first real-time a posteriori error-driven adaptive
finite element approach for real-time simulation and to demonstrate the method
on a needle insertion problem. Methods: We use corotational elasticity and a
frictional needle/tissue interaction model. The problem is solved using finite
elements within SOFA. The refinement strategy relies upon a hexahedron-based
finite element method, combined with a posteriori error estimation driven local
-refinement, for simulating soft tissue deformation. Results: We control the
local and global error level in the mechanical fields (e.g. displacement or
stresses) during the simulation. We show the convergence of the algorithm on
academic examples, and demonstrate its practical usability on a percutaneous
procedure involving needle insertion in a liver. For the latter case, we
compare the force displacement curves obtained from the proposed adaptive
algorithm with that obtained from a uniform refinement approach. Conclusions:
Error control guarantees that a tolerable error level is not exceeded during
the simulations. Local mesh refinement accelerates simulations. Significance:
Our work provides a first step to discriminate between discretization error and
modeling error by providing a robust quantification of discretization error
during simulations.Comment: 12 pages, 16 figures, change of the title, submitted to IEEE TBM
A Nitsche-based cut finite element method for a fluid--structure interaction problem
We present a new composite mesh finite element method for fluid--structure
interaction problems. The method is based on surrounding the structure by a
boundary-fitted fluid mesh which is embedded into a fixed background fluid
mesh. The embedding allows for an arbitrary overlap of the fluid meshes. The
coupling between the embedded and background fluid meshes is enforced using a
stabilized Nitsche formulation which allows us to establish stability and
optimal order \emph{a priori} error estimates,
see~\cite{MassingLarsonLoggEtAl2013}. We consider here a steady state
fluid--structure interaction problem where a hyperelastic structure interacts
with a viscous fluid modeled by the Stokes equations. We evaluate an iterative
solution procedure based on splitting and present three-dimensional numerical
examples.Comment: Revised version, 18 pages, 7 figures. Accepted for publication in
CAMCo
An exact general remeshing scheme applied to physically conservative voxelization
We present an exact general remeshing scheme to compute analytic integrals of
polynomial functions over the intersections between convex polyhedral cells of
old and new meshes. In physics applications this allows one to ensure global
mass, momentum, and energy conservation while applying higher-order polynomial
interpolation. We elaborate on applications of our algorithm arising in the
analysis of cosmological N-body data, computer graphics, and continuum
mechanics problems.
We focus on the particular case of remeshing tetrahedral cells onto a
Cartesian grid such that the volume integral of the polynomial density function
given on the input mesh is guaranteed to equal the corresponding integral over
the output mesh. We refer to this as "physically conservative voxelization".
At the core of our method is an algorithm for intersecting two convex
polyhedra by successively clipping one against the faces of the other. This
algorithm is an implementation of the ideas presented abstractly by Sugihara
(1994), who suggests using the planar graph representations of convex polyhedra
to ensure topological consistency of the output. This makes our implementation
robust to geometric degeneracy in the input. We employ a simplicial
decomposition to calculate moment integrals up to quadratic order over the
resulting intersection domain.
We also address practical issues arising in a software implementation,
including numerical stability in geometric calculations, management of
cancellation errors, and extension to two dimensions. In a comparison to recent
work, we show substantial performance gains. We provide a C implementation
intended to be a fast, accurate, and robust tool for geometric calculations on
polyhedral mesh elements.Comment: Code implementation available at https://github.com/devonmpowell/r3
Grid generation for the solution of partial differential equations
A general survey of grid generators is presented with a concern for understanding why grids are necessary, how they are applied, and how they are generated. After an examination of the need for meshes, the overall applications setting is established with a categorization of the various connectivity patterns. This is split between structured grids and unstructured meshes. Altogether, the categorization establishes the foundation upon which grid generation techniques are developed. The two primary categories are algebraic techniques and partial differential equation techniques. These are each split into basic parts, and accordingly are individually examined in some detail. In the process, the interrelations between the various parts are accented. From the established background in the primary techniques, consideration is shifted to the topic of interactive grid generation and then to adaptive meshes. The setting for adaptivity is established with a suitable means to monitor severe solution behavior. Adaptive grids are considered first and are followed by adaptive triangular meshes. Then the consideration shifts to the temporal coupling between grid generators and PDE-solvers. To conclude, a reflection upon the discussion, herein, is given
Persistent Homology Guided Force-Directed Graph Layouts
Graphs are commonly used to encode relationships among entities, yet their
abstractness makes them difficult to analyze. Node-link diagrams are popular
for drawing graphs, and force-directed layouts provide a flexible method for
node arrangements that use local relationships in an attempt to reveal the
global shape of the graph. However, clutter and overlap of unrelated structures
can lead to confusing graph visualizations. This paper leverages the persistent
homology features of an undirected graph as derived information for interactive
manipulation of force-directed layouts. We first discuss how to efficiently
extract 0-dimensional persistent homology features from both weighted and
unweighted undirected graphs. We then introduce the interactive persistence
barcode used to manipulate the force-directed graph layout. In particular, the
user adds and removes contracting and repulsing forces generated by the
persistent homology features, eventually selecting the set of persistent
homology features that most improve the layout. Finally, we demonstrate the
utility of our approach across a variety of synthetic and real datasets
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