Bone structure analysis on multiple GPGPUs

Abstract

Osteoporosis is a disease that affects a growing number of people by increasing the fragility of their bones. To improve the understanding of the bone quality, large scale computer simulations are applied. A fast, scalable and memory efficient solver for such problems is ParOSol. It uses the preconditioned conjugate gradient algorithm with a multigrid preconditioner. A modification of ParOSol is presented that profits from the exorbitant compute capabilities of recent generalpurpose graphics processing units (GPGPUs). Adaptations of data structures for the GPGPU are discussed. The fastest implementation on a GPGPU achieves a speedup of more than five compared with the CPU implementation and scales from 1 to at least 256 GPGPUs.

Computational homogenization of elasticity on a staggered grid

“…For instance, to compute effective linear elastic properties on a 4096 3 CT image, the number of nodal displacement degrees of freedom amounts to approximately 206·10 9 . To solve problems of this size with conventional FEM, large computing clusters are required . These difficulties are commonly overcome by working with conventional FEM on a variety of smaller subsamples of moderate size.…”

AutoMat: automatic differentiation for generalized standard materials on GPUs

“…This is of importance on GPUs without good double precision performance, and can also speed up computations in general; especially material law evaluations with tangent seem to benefit performance-wise from single precision. We use OpenMP 4 for CPU parallelization; on the graphics card, CUDA 5 is used. We used version 9.0 of the CUDA SDK.…”

“…In the setting of Sect. 4 (12) for the derivative. By the properties of the implicit Euler scheme, the numerical solve of the undifferentiated evolution equation is guaranteed to converge with order one to the exact solution as h → 0.…”

AutoMat -- Automatic Differentiation for Generalized Standard Materials on GPUs

“…Traditionally, a finite element (FEM) discretization is applied, and during the solution procedure, the material law is evaluated locally at quadrature points. To solve problems of this size with conventional FEM, large computing clusters are required to handle the global stiffness matrices [1,2].…”