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Why Multilevel solvers for μ-Finite Elements of Bone Structures

Osteoporosis is a disease characterized by low bone mass and deterioration of bone microarchitecture. It leads to increased bone fragility and risk of fracture, particularly of the hip, spine and wrist. Worldwide, lifetime risk for osteoporotic fractures in women is estimated close to 40%; in men risk is 13%; osteoporosis is second only to cardiovascular disease as a leading health care problem (World Health Organization). Osteoporotic fractures are a major cause of severe long-term pain and physical disability, and have an enormous impact on the individual, society and health care social systems.

Osteoporotic fractures are a major cause of severe long-term pain and physical disability, and have an enormous impact on the individual, society and health care social systems. Osteoporosis is second only to cardiovascular disease as a leading health care problem. Since global parameters like bone density do not admit to predict the fracture risk, patients have to be treated in a more individual way. Today's approach consists of combining 3D high-resolution CT scans of individual bones with a micro-finite element (μ-FE) analysis.

With the advent of fast and powerful computers, simulation techniques are becoming popular for investigating the mechanical properties of bone. Using microstructural finite element (μ-FE) models generated directly from computer reconstructions of trabecular bone it is now possible to perform a 'virtual experiment', i.e. to simulate a mechanical test in great detail and with high precision.

The resulting FE models are computationally demanding and require special solution schemes. The preconditioning conjugate gradient method is the obvious solution method. However, finding a proper preconditioners is not easy. Element-by-element approaches have been proposed about 10 years ago and are now common. Their quality however deteriorates as the problems become large.

Goals of the ParFE project

The goal of the ParFE project is to develop massively solvers for finite element problems arising from bone modeling. The computationally intensive phase is the solution of the linear system

A x = b

arising from the FE discretization of the linear elasticity equations. In fact, although the equations their discretization techniques are well-known, much has to be done to solve them efficiently for real-life problems, especially on parallel, distributed memory computers. Several issues arise. First, the application must be able to read large mesh files from disk, compute the desired solution and write it to disk again. Then, an optimal solution technique must be determined.

The approach followed by ParFE developers consists in applying powerful multilevel preconditioners based on smoothed aggregation procedures. We consider both matrix-free and ready-ready environments (that is, our preconditioners can both solve the assembled linear system or use the element-by-element matrix-vector product).

ParFE is written in C++, and it is based on several high-performance libraries for scientific computing, mostly BLAS, LAPACK, MPI, ParMETIS, Trilinos and HDF5.


ParFE is released under the GNU Public License reported below.

ParFE: A Scalable Micro Finite Element Solver for Bone Modeling
Copyright (C) 2006 ETH Zurich, Institute of Computational Science,
Uche Mennel, Marzio Sala, and all other ParFE developers; see
http://parfe.sourceforge.net/developers.php for the complete list.

This library is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.

This library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
General Public License for more details.

You should have received a copy of the GNU General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA

For an overview of the GNU General Public Licence (GPL), see here. In particular, GPL means that you can analyze, modify and use the program, but if you do so, then you must redistribute the modified sources. Besides, any software using ParFE must also be released under the GPL licence.

Note that some parts of ParFE depend on third party code. Each third party code comes with its own copyright and/or licensing requirements. It is responsibility of the user to understand these requirements.

The authors accept that the GNU General Public License is incompatible with certain commercial requirements or third-party license stipulations. Consequently, ParFE may be licensed under alternative terms on an individual case-by-case basis by contacting the authors.