Dynamic deformation using adaptable, linked asynchronous FEM regions

Koçak, Umut Ziya; Palmerius, Karljohan Lundin; Cooper, Matthew

doi:10.1145/1980462.1980500

Cited by 3 publications

(2 citation statements)

References 29 publications

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“…For example, Wu and Heng [2005] and combine the use of condensation and CG solvers, while Cotin et al [2000] combine the use of a linear superposition method with explicit integration applied selectively to the dynamic, cuttable portion of a mesh. Koçak et al [2009] provided further support for this approach by describing a framework for building a consistent finite-element simulation when different regions of the mesh are solved at different update rates.…”

Section: Hybrid Solution Methodsmentioning

confidence: 98%

Interactively Cutting and Constraining Vertices in Meshes Using Augmented Matrices

2016

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We present a finite-element solution method that is well suited for interactive simulations of cutting meshes in the regime of linear elastic models. Our approach features fast updates to the solution of the stiffness system of equations to account for real-time changes in mesh connectivity and boundary conditions. Updates are accomplished by augmenting the stiffness matrix to keep it consistent with changes to the underlying model, without refactoring the matrix at each step of cutting. The initial stiffness matrix and its Cholesky factors are used to implicitly form and solve a Schur complement system using an iterative solver. As changes accumulate over many simulation timesteps, the augmented solution method slows down due to the size of the augmented matrix. However, by periodically refactoring the stiffness matrix in a concurrent background process, fresh Cholesky factors that incorporate recent model changes can replace the initial factors. This controls the size of the augmented matrices and provides a way to maintain a fast solution rate as the number of changes to a model grows. We exploit sparsity in the stiffness matrix, the right-hand-side vectors and the solution vectors to compute the solutions fast, and show that the time complexity of the update steps is bounded linearly by the size of the Cholesky factor of the initial matrix. Our complexity analysis and experimental results demonstrate that this approach scales well with problem size. Results for cutting and deformation of 3D linear elastic models are reported for meshes representing the brain, eye, and model problems with element counts up to 167,000; these show the potential of this method for real-time interactivity. An application to limbal incisions for surgical correction of astigmatism, for which linear elastic models and small deformations are sufficient, is included.

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Section: Hybrid Solution Methodsmentioning

confidence: 98%

Interactively Cutting and Constraining Vertices in Meshes Using Augmented Matrices

2016

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“…In recent years, several elastic deformation models based on complex geometries and boundary conditions were proposed, achieving good deformation simulation effects. 9–11 Mosbech et al 12 proposed an efficient data-driven deformation model to reflect the physical and physiological characteristics of soft tissue, while the model’s accuracy was restricted by the image quality and the obtained features. Faure et al 13 proposed a new deformation method based on complex curved surface and material properties.…”

Section: Related Workmentioning

confidence: 99%

GPU-assisted energy asynchronous diffusion parallel computing model for soft tissue deformation simulation

Liao

Yuan

et al. 2014

SIMULATION

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Soft tissue deformation simulation is a key technology of virtual surgical simulation. In this work, we present a graphics processing unit (GPU)-assisted energy asynchronous diffusion parallel computing model which is stable and fast in processing complex models, especially concave surface models. We adopt hexahedral voxels to represent the physical model of soft tissue to improve the visual realistic quality and computing efficiency of deformation simulation. We also adopt the concept of free boundary to simulate soft tissue geometric characteristics more precisely during the deformation process and introduce asynchronous diffusion by using the mechanical energy of mass points to achieve realistic soft tissue deformation effects. In order to meet the requirement of real-time surgery simulation, we accelerate the soft tissue deformation by using OpenCL (Open Computing Language) and optimize the parallel computing process in several means. Experimental results have shown that the GPU-assisted energy asynchronous diffusion parallel computing model for soft tissue deformation simulation implements satisfactory effects on deformation in visual realistic and real-time quality.

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