A novel unconditionally stable explicit integration method for finite element method

Zheng, Mianlun; Yuan, Zhiyong; Tong, Qianqian; Zhang, Guian; Zhu, Weixu

doi:10.1007/s00371-017-1410-9

Cited by 5 publications

(5 citation statements)

References 27 publications

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“…The critical time step decreases as the mesh becomes finer for the blood vessels, increasing the number of simulation steps that prolongs the total computation time; therefore, a careful selection of the included blood vessels and other fine details of the liver needs to be considered for achieving a balance of critical time steps for efficient simulation. For numerical stability, it was reported that neural networks [60,61], adaptive semi-explicit/explicit time marching [59] and unconditionally stable explicit scheme [62] could achieve stable numerical analysis for non-linear dynamic systems; these methods may be incorporated into the proposed method for stable dynamic bio-heat transfer analysis under soft tissue deformation.…”

Section: Discussionmentioning

confidence: 99%

Fast computation of soft tissue thermal response under deformation based on fast explicit dynamics finite element algorithm for surgical simulation

Zhang

Chauhan

2020

Computer Methods and Programs in Biomedicine

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Background and Objectives: During thermal heating surgical procedures such as electrosurgery, thermal ablative treatment and hyperthermia, soft tissue deformation due to surgical tool-tissue interaction and patient movement can affect the distribution of thermal energy induced. Soft tissue temperature must be obtained from the deformed tissue for precise delivery of thermal energy. However, the classical Pennes bio-heat transfer model can handle only the static non-moving state of tissue. In addition, in order to enable a surgeon to visualize the simulated results immediately, the solution procedure must be suitable for real-time thermal applications.Methods: This paper presents a formulation of bio-heat transfer under the effect of soft tissue deformation for fast or near real-time tissue temperature prediction, based on fast explicit dynamics finite element algorithm (FED-FEM) for transient heat transfer. The proposed thermal analysis under deformation is achieved by transformation of the unknown deformed tissue state to the known initial static state via a mapping function. The appropriateness and effectiveness of the proposed formulation are evaluated on a realistic virtual human liver model with blood vessels to demonstrate a clinically relevant scenario of thermal ablation of hepatic cancer.Results: For numerical accuracy, the proposed formulation can achieve a typical 10 −3 level of normalized relative error at nodes and between 10 −4 and 10 −5 level of total errors for the simulation, by comparing solutions against the commercial finite element analysis package. For computation time, the proposed formulation under tissue deformation with anisotropic temperature-dependent properties consumes 2.518 × 10 −4 for one element thermal loads computation, compared to 2.237 × 10 −4 for the formulation without deformation which is 0.89 times of the former. Comparisons with three other formulations for isotropic and temperature-independent properties are also presented.Conclusions: Compared to conventional methods focusing on numerical accuracy, convergence and stability, the proposed formulation focuses on computational performance for fast tissue thermal analysis. Compared to the classical Pennes model that handles only the static state of tissue, the proposed formulation can achieve fast thermal analysis on deformed states of tissue and can be applied in addition to tissue deformable models for nonlinear heating analysis at even large deformation of soft tissue, leading to great translational potential in dynamic tissue temperature analysis and thermal dosimetry computation for computer-integrated medical education and personalized treatment.

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Section: Discussionmentioning

confidence: 99%

Fast computation of soft tissue thermal response under deformation based on fast explicit dynamics finite element algorithm for surgical simulation

Zhang

Chauhan

2020

Computer Methods and Programs in Biomedicine

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“…In the FEM explicit calculation, the plane displacement vector u p = [ u x , u y , u z ], phase-field variable ϕ , and hydrogen concentration C can be updated by the central difference method [ 35 , 36 , 37 ]. The computational time axis is given in Figure 3 .…”

Section: Methodsmentioning

confidence: 99%

Numerical Simulation for Hydrogen-Assisted Cracking: An Explicit Phase-Field Formulation

Wang

Chen

2023

Materials

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Hydrogen-assisted cracking is one of the most dominant failure modes in metal hydrogen-facing materials. Therefore, the hydrogen-assisted cracking mechanism has been a hot topic for a long time. To date, there is very little published research on numerical methods to describe hydrogen-assisted cracking. This paper presents a new method for the description of hydrogen embrittlement crack growth: an explicit phase-field formulation, which is based on the phase-field description of cracks, Fick’s mass diffusion law, and the relationship between hydrogen content and fracture surface energy. A novel computational framework is then developed using the self-developed FEM software DYNA-WD. We numerically calculate several typical conditions in the 3-D coordinates to validate the effectiveness of the proposed computational framework. Specifically, we discuss (i) the failure of a square plate in a hydrogenous environment, (ii) the CT specimen failed with the inner hydrogen, (iii) the plate /failed with the corrosives, and (iv) the failure of the disk test. Finally, the relationship between Mises stress, the concentration of hydrogen, the thickness of the disc, and the loading rate is investigated.

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“…In surgery simulation, the explicit integration schemes are widely adopted. 44,45 The main advantage is that the equations of motion can be solved independently. Unfortunately, these schemes are conditionally stable, which restrict the size of the time step.…”

Section: Deformation Methodsmentioning

confidence: 99%

“…In the finite element method, real‐time computation requires a calculation time less than the integration schemes. In surgery simulation, the explicit integration schemes are widely adopted . The main advantage is that the equations of motion can be solved independently.…”

Section: Introductionmentioning

confidence: 99%

A multi‐GPU finite element computation and hybrid collision handling process framework for brain deformation simulation

Tian

Shen

2018

Computer Animation & Virtual

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This paper offers a fast multi‐graphics processing unit (GPU) parallel simulation framework to the problem of real‐time and nonlinear finite element computation of brain deformation. A load balancing strategy is proposed to ensure the efficient distribution of nonlinear finite element computation on multi‐GPU. A data storage structure is designed to minimize the amount of data transfer and make full use of the overlay technique of GPU to reduce the transferring latency between multi‐GPUs. We further present a fast central processing unit (CPU)–GPU parallel continuous collision detection and response method, which not only can deal with the collision between the brain and skull but also can handle the self‐collision of the brain. Our method can make full use of CPU and GPU to implement a parallel computation about deformation and collision detection. Our experimental results show that our method is able to handle a brain geometric model with high detail gyrus composed of more than 40,000 tetrahedron elements. This can facilitate the fidelity of the current virtual brain surgery simulator. We evaluate our approach qualitatively and quantitatively and compare it with related works.

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A novel unconditionally stable explicit integration method for finite element method

Cited by 5 publications

References 27 publications

Fast computation of soft tissue thermal response under deformation based on fast explicit dynamics finite element algorithm for surgical simulation

Fast computation of soft tissue thermal response under deformation based on fast explicit dynamics finite element algorithm for surgical simulation

Numerical Simulation for Hydrogen-Assisted Cracking: An Explicit Phase-Field Formulation

A multi‐GPU finite element computation and hybrid collision handling process framework for brain deformation simulation

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