Multigrid
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Parallel multigrid smoothing: polynomial versus Gauss--Seidel
Journal of Computational Physics
Proceedings of the 2004 ACM/IEEE conference on Supercomputing
Multi-level µ-finite element analysis for human bone structures
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
Extreme scalability challenges in micro-finite element simulations of human bone
Concurrency and Computation: Practice & Experience - International Supercomputing Conference
A Parallel Geometric Multigrid Method for Finite Elements on Octree Meshes
SIAM Journal on Scientific Computing
A highly scalable matrix-free multigrid solver for μFE analysis based on a pointer-less octree
LSSC'11 Proceedings of the 8th international conference on Large-Scale Scientific Computing
Preconditioning for large scale micro finite element analyses of 3d poroelasticity
PARA'12 Proceedings of the 11th international conference on Applied Parallel and Scientific Computing
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Micro-structural finite element (@mFE) analysis based on high-resolution computed tomography represents the current gold standard to predict bone stiffness and strength. Recent progress in solver technology makes possible simulations on large supercomputers that involve billions of degrees of freedom. In this paper we present an improved solver that has a significantly smaller memory footprint compared to the currently used solvers. This new approach fully exploits the information that is contained in the underlying CT image itself. It admits to execute all steps in the underlying multigrid-preconditioned conjugate gradient algorithm in matrix-free form. The reduced memory footprint allows to solve bigger bone models on a given hardware. It is an important step forward to the clinical usage of @mFE simulations. The new solver is fully parallel. We show almost perfect scalability up to 8000 cores of a Cray XT-5 supercomputer.