673 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
On the equivalence between the cell-based smoothed finite element method and the virtual element method
We revisit the cell-based smoothed finite element method (SFEM) for
quadrilateral elements and extend it to arbitrary polygons and polyhedrons in
2D and 3D, respectively. We highlight the similarity between the SFEM and the
virtual element method (VEM). Based on the VEM, we propose a new stabilization
approach to the SFEM when applied to arbitrary polygons and polyhedrons. The
accuracy and the convergence properties of the SFEM are studied with a few
benchmark problems in 2D and 3D linear elasticity. Later, the SFEM is combined
with the scaled boundary finite element method to problems involving
singularity within the framework of the linear elastic fracture mechanics in
2D
Controlling the Error on Target Motion through Real-time Mesh Adaptation: Applications to Deep Brain Stimulation
We present an error-controlled mesh refinement procedure for needle insertion
simulation and apply it to the simulation of electrode implantation for deep
brain stimulation, including brain shift. Our approach enables to control the
error in the computation of the displacement and stress fields around the
needle tip and needle shaft by suitably refining the mesh, whilst maintaining a
coarser mesh in other parts of the domain. We demonstrate through academic and
practical examples that our approach increases the accuracy of the displacement
and stress fields around the needle without increasing the computational
expense. This enables real-time simulations. The proposed methodology has
direct implications to increase the accuracy and control the computational
expense of the simulation of percutaneous procedures such as biopsy,
brachytherapy, regional anesthesia, or cryotherapy and can be essential to the
development of robotic guidance.Comment: 21 pages, 14 figure
Meshing or not meshing - Iso/sub/super-geometric analysis (adaptive unfitted methods for real-time simulations) Immersed collocation methods
MAgNET: A Graph U-Net Architecture for Mesh-Based Simulations
Mesh-based approaches are fundamental to solving physics-based simulations,
however, they require significant computational efforts, especially for highly
non-linear problems. Deep learning techniques accelerate physics-based
simulations, however, they fail to perform efficiently as the size and
complexity of the problem increases. Hence in this work, we propose MAgNET:
Multi-channel Aggregation Network, a novel geometric deep learning framework
for performing supervised learning on mesh-based graph data. MAgNET is based on
the proposed MAg (Multichannel Aggregation) operation which generalises the
concept of multi-channel local operations in convolutional neural networks to
arbitrary non-grid inputs. MAg can efficiently perform non-linear regression
mapping for graph-structured data. MAg layers are interleaved with the proposed
novel graph pooling operations to constitute a graph U-Net architecture that is
robust, handles arbitrary complex meshes and scales efficiently with the size
of the problem. Although not limited to the type of discretisation, we showcase
the predictive capabilities of MAgNET for several non-linear finite element
simulations
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