Peter Arbenz

On the spectral decomposition of Hermitian matrices modified by low rank perturbations

We consider the problem of computing the eigenvalues and vectors of a matrix

Implant stability is affected by local bone microstructural quality

\tilde H = H + D

The Remote Computation System

which is obtained from an indefinite Hermitian low rank modification D of a Hermitian matrix H with k...

A Jacobi--Davidson Method for Solving Complex Symmetric Eigenvalue Problems

It is known that low bone quality, caused for instance by osteoporosis, not only increases the risk of fractures, but also decreases the performance of fracture implants; yet the specific mechanisms behind this phenomenon are still largely unknown. We hypothesized that especially peri-implant bone microstructure affects implant stability in trabecular bone, to a greater degree than more distant bone. To test this hypothesis we performed a computational study on implant stability in trabecular bone. Twelve humeral heads were measured using micro-computed tomography. Screws were inserted digitally into these heads at 25 positions. In addition, at each screw location, a virtual biopsy was taken. Bone structural quality was quantified by morphometric parameters. The stiffness of the 300 screw-bone constructs was quantified as a measure of implant stability. Global bone density correlated moderately with screw-bone stiffness (r2=0.52), whereas local bone density was a very good predictor (r2=0.91). The best correlation with screw-bone stiffness was found for local bone apparent Youngs modulus (r2=0.97), revealing that not only bone mass but also its arrangement in the trabecular microarchitecture are important for implant stability. In conclusion, we confirmed our hypothesis that implant stability is affected by the microstructural bone quality of the trabecular bone in the direct vicinity of the implant. Local bone density was the best single morphometric predictor of implant stability. The best predictability was provided by the mechanical competence of the peri-implant bone. A clinical implication of this work is that apparently good bone stock, such as assessed by DXA, does not guarantee good local bone quality, and hence does not guarantee good implant stability. New tools that could quantify the structural or mechanical quality of the peri-implant bone may help improve the surgical intervention in reaching better clinical outcomes for screw fixation.

Multi-level µ-finite element analysis for human bone structures

Today many high performance computers are reachable over some network However the access and use of these computers is often complicated This prevents many users to work on such machines The goal of our Remote Computation System RCS is to alleviate the usage of modern algorithms on high performance computers RCS has an easytouse mechanism for using computational resources remotely The computational resources available are used as eciently as possible in order to minimize the response time We report on experiments involving computations from highend workstations up to supercomputers

The remote computation system

We discuss variants of the Jacobi--Davidson method for solving the generalized complex symmetric eigenvalue problem. The Jacobi--Davidson algorithm can be considered as an accelerated inexact Rayleigh quotient iteration. We show that it is appropriate to replace the Euclidean inner product in

Restricted rank modification of the symmetric eigenvalue problem: Theoretical considerations

{\mathbb C}^n

A comparison of solvers for large eigenvalue problems occuring in the design of resonant cavities

with an indefinite inner product. The Rayleigh quotient based on this indefinite inner product leads to an asymptotically cubically convergent Rayleigh quotient iteration. Advantages of the method are illustrated by numerical examples. We deal with problems from electromagnetics that require the computation of interior eigenvalues. The main drawback that we experience in these particular examples is the lack of efficient preconditioners.

A scalable memory efficient multigrid solver for micro-finite element analyses based on CT images

Using microarchitectural bone imaging, it is now possible to assess both the apparent density and the trabecular microstructure of intact bones in a single measurement. In combination with microstructural finite element (µFE) analysis this could provide a powerful tool to improve strength assessment and individual fracture risk prediction. However, the resulting µFE models are very large and require dedicated solution techniques. Therefore, in this paper we investigate the efficient solution of the resulting large systems of linear equations by the preconditioned conjugate gradient algorithm. We detail the implementation strategies that lead to a fully parallel finite element solver. Our numerical results show that a human bone model of about 5 million elements can be solved in about a minute. These short solution times will allow to assess the mechanical quality of bone in vivo on a routine basis. Furthermore, our highly scalable solution methods make it possible to analyze the very large models of whole bones measured in vitro, which can have up to 1 billion degrees of freedom.

On a parallel multilevel preconditioned Maxwell eigensolver

Abstract Today many high performance computers are reachable over some network. However, the access and use of these computers is often complicated. This prevents many users from working on such machines. The goal of the remote computation system (RCS) is to provide easy access to modern parallel algorithms on supercomputers for the inexperienced user. RCS has an easy-to-use mechanism for using computational resources remotely. The computational resources available are used as efficiently as possible in order to minimize the response time.