Harri Hakula

Scale resolution locking, and high-order finite element modelling of shells

Abstract We demonstrate, both by theory and experiment, the benefits of using standard finite elements of relatively high degree in shell problems. The difficulty of shell problems lies in their asymptotic diversity at zero thickness and in the multiple-scale character of the deformation field when the thickness is small. Due to these characteristics, standard finite elements of low degree often resolve the length scales of practical shell deformation very poorly unless extremely fine meshes are used. However, with standard finite elements of sufficiently high degree, say cubic or quartic at least, the quality of numerical scale resolution improves remarkably. We show by simple error analysis that this effect is not problem-specific but rather robust among the diversity of shell problems. As numerical test cases, we analyze two challenging problems in cylindrical shell geometry.

The factorization method applied to the complete electrode model of impedance tomography

The factorization method is a tool for recovering inclusions inside a body when the Neumann-to-Dirichlet operator, which maps applied currents to measured voltages, is known. In practice this information is never at hand due to the discreteness and physical properties of the measurement devices. The complete electrode model of impedance tomography includes these physical characteristics but leads to a finite-dimensional data set, called the resistivity matrix. The main result of this work is an approximation link relating the resistivity matrix to the Neumann-to-Dirichlet operator in the

Conditionally Gaussian Hypermodels for Cerebral Source Localization

L^2

On Moduli of Rings and Quadrilaterals: Algorithms and Experiments

-operator norm. This result allows us to extend the factorization method to the framework of real-life electrode measurements using a regularized series criterion which is easy to implement in practice. The truncation index of the sequence criterion, which represents the stopping index of the regularization scheme, can be computed solely from the measured, perturbed, and finite-dimensional data. The functionality of ...

Dynamic journeying under uncertainty

Bayesian modeling and analysis of the magnetoencephalography and electroencephalography modalities provide a flexible framework for introducing prior information complementary to the measured data. This prior information is often qualitative in nature, making the translation of the available information into a computational model a challenging task. We propose a generalized gamma family of hyperpriors which allows the impressed currents to be focal and we advocate a fast and efficient iterative algorithm, the iterative alternating sequential algorithm for computing maximum a posteriori (MAP) estimates. Furthermore, we show that for particular choices of the scalar parameters specifying the hyperprior, the algorithm effectively approximates popular regularization strategies such as the minimum current estimate and the minimum support estimate. The connection between priorconditioning and adaptive regularization methods is also pointed out. The posterior densities are explored by means of a Markov chain Monte Carlo strategy suitable for this family of hypermodels. The computed experiments suggest that the known preference of regularization methods for superficial sources over deep sources is a property of the MAP estimators only, and that estimation of the posterior mean in the hierarchical model is better adapted for localizing deep sources.

Dynamic Journeying in Scheduled Networks

Moduli of rings and quadrilaterals are frequently applied in geometric function theory; see, e.g., the handbook by Kuhnau [Handbook of Complex Analysis: Geometric Function Theory, Vols. 1 and 2, North-Holland, Amsterdam, 2005]. Yet their exact values are known only in a few special cases. Previously, the class of planar domains with polygonal boundary has been studied by many authors from the point of view of numerical computation. We present here a new

ASYMPTOTIC AND NUMERICAL ANALYSIS OF THE EIGENVALUE PROBLEM FOR A CLAMPED CYLINDRICAL SHELL

hp

Conjugate function method for numerical conformal mappings

-FEM algorithm for the computation of moduli of rings and quadrilaterals and compare its accuracy and performance with previously known methods such as the Schwarz-Christoffel Toolbox of Driscoll and Trefethen. We also demonstrate that the

Two noniterative algorithms for locating inclusions using one electrode measurement of electric impedance tomography

hp

A High-order Finite Element Method for Electical Impedance Tomography

-FEM algorithm applies to the case of nonpolygonal boundary and report results with concrete error bounds.