GPU‐based acceleration of computations in nonlinear finite element deformation analysis

Abstract

The physics of deformation for biological soft-tissue is best described by nonlinear continuum mechanics-based models, which then can be discretized by the FEM for a numerical solution. However, computational complexity of such models have limited their use in applications requiring real-time or fast response. In this work, we propose a graphic processing unit-based implementation of the FEM using implicit time integration for dynamic nonlinear deformation analysis. This is the most general formulation of the deformation analysis. It is valid for large deformations and strains and can account for material nonlinearities. The data-parallel nature and the intense arithmetic computations of nonlinear FEM equations make it particularly suitable for implementation on a parallel computing platform such as graphic processing unit. In this work, we present and compare two different designs based on the matrix-free and conventional preconditioned conjugate gradients algorithms for solving the FEM equations arising in deformation analysis. The speedup achieved with the proposed parallel implementations of the algorithms will be instrumental in the development of advanced surgical simulators and medical image registration methods involving soft-tissue deformation.

Techniques of medical image processing and analysis accelerated by high-performance computing: a systematic literature review

“…The area of medical image processing and analysis has contributed to significant medical advances [7,23,50,81,83,88,101] by integrating systems and techniques that support more efficient clinical diagnosis. These systems and techniques are based on images acquired by different imaging modalities such as, endoscopy [52], X-ray [88], microscopy [47,68], computed tomography (CT) [26,57], optical coherence tomography (OCT) [67], magnetic resonance (MR) [2,15], functional magnetic resonance (fMR) [3,97], magnetic resonance elastography (MRE) [20], positron emission tomography (PET) [17,42,43], single photon emission computed tomography (SPECT) [28], and 3D ultrasound computer tomography (USCT) [7].…”

“…Such extraction of relevant clinical information is a complex task requiring advanced computational systems able to process and obtain image-based features accurately and consistently within the shortest possible runtime. As a result, a new research area has emerged that combines computational techniques used for medical image processing and analysis [23,81,88] and high-performance computing solutions [7,50,83,101]. These two components can be briefly described as follows:…”

“…• High-performance computing-The main goal of this area is to optimize computational methods to achieve greater robustness, effectiveness, efficiency, and faster execution. To accomplish these objectives, parallel computing techniques are usually exploited to use the maximum available performance in the computational architecture adopted [7,50,83,101].…”

An explicit dynamics GPU structural solver for thin shell finite elements

“…An explicit nonlinear finite element solver (which uses linear hexahedra and tetrahedra) for surgical simulations is presented in [9], showing a speedup of more than 20 times compared with a CPU implementation. Always considering surgical applications, [10] proposes GPU-based implementation of the FEM using implicit time integration for dynamic nonlinear deformation analysis. In [11], an explicit dynamics formulation for the simulation of sheet forming problems, based on the use of shell elements of the Belytschko-Tsay type, is discussed.…”

“…Hybrid implementations of multiscale finite element approaches, whereby constitutive material computations at Gauss point level are carried out on the GPU, are discussed in [13] and [14] In most of the above-mentioned applications, results are limited to single-precision arithmetic (e.g. [2,9,14,10]). It is important to recall, as suggested in [8], that, concerning NVIDIA GPUs, in all the implementations before CUDA compute capability 1.3, only single-precision floating point operations are supported directly by the hardware.…”