Custom Finite-Element Simulations Using GPGPU Technology: Towards Faster Patient-Specific Predictions

We present an implementation of a nonlinear explicit, displacement-based finite element code and its parallelization using GPGPU technology, applied using modern anisotropic, nearly incompressible constitutive models relevant to soft biological tissues. As clinical practice and even surgical theaters start to embrace simulation technology, the need arises for faster preoperative or intraoperative patient-specific analyses. Using modern computational hardware and techniques we detail an implementation capable of decreasing solution times by a factor of 5-20 or more. The proposed algorithm adopts a total Lagrangian worldview, and uses an explicit, constant-step central-difference integration scheme, cf. [1]. To solve representative boundary value problems and exercise our algorithm, we implement trilinear hexahedra, using either full, selective reduced, or under- integration, the later with perturbation hourglass control [2]. Therein, we implement state-of-the-art anisotropic fiber-reinforced hyperelastic constitutive models, calibrated with experimentally determined parameters, to describe the behavior of human arteries. To ensure efficient parallelization we tailor our algorithm for the newer generation GPGPU technology. For example, force storage routines for the models implemented make use of atomic operations. Furthermore, templated GPU kernels allow for easier switching between single and double precision computations, enabling use of much lower time-steps as sometimes required by the near-incompressibility of the materials or by limits in floating-point representation. We also implement texture memory usage as a template parameter for convenient switching, since the newer generations of GPUs generally prefer utilizing caching subsystems for throughput [3]. Additionally, all global-memory variables with non-random locality are re-organized and padded for faster coalesced accesses. Exemplary simulations show promising results when compared directly to well-established finite element codes. With equivalent results, we reduce solution times by a factor of 5-20 or more depending on the element type and mesh size, indicating significant potential for more efficient and economical analyses. To improve the robustness of our algorithm we are currently implementing mixed u-p-theta element formulations, enabling further optimization in terms enforcing (near) incompressibility without significant reductions in time-step size or stability. We demonstrate that our combination of modern GPGPU hardware and computational methods may soon enable finite element analyses relevant to modern clinical workflows. [1] Joldes et al., Comput Methods Appl Mech Engrg, 199:3305-3314, 2010. [2] Tarjuelo-Gutierrez et al., Med Biol Eng Comput, 52:159-168, 2014. [3] Nvidia Corp., CUDA C Best Practices Guide, 6.5:1-85, 2014status: publishe