Optimal Control of a Second Order Parabolic Heat Equation

In this paper, we are concerned with the optimal control boundary control of a second order parabolic heat equation. Using the results in [Evtushenko, 1997] and spatial central finite difference with diagonally implicit Runge-Kutta method (DIRK) is applied to solve the parabolic heat equation. The conjugate gradient method (CGM) is applied to solve the distributed control problem. Numerical results are reported.

Inverse space-dependent force problems for the wave equation

The determination of the displacement and the space-dependent force acting on a vibrating structure from measured final or time-average displacement observation is thoroughly investigated. Several aspects related to the existence and uniqueness of a solution of the linear but ill-posed inverse force problems are highlighted. After that, in order to capture the solution a variational formulation is proposed and the gradient of the least-squares functional that is minimized is rigorously and explicitly derived. Numerical results obtained using the Landweber method and the conjugate gradient method are presented and discussed illustrating the convergence of the iterative procedures for exact input data. Furthermore, for noisy data the semi-convergence phenomenon appears, as expected, and stability is restored by stopping the iterations according to the discrepancy principle criterion once the residual becomes close to the amount of noise. The present investigation will be significant to researchers concerned with wave propagation and control of vibrating structures.

Quality balancing for parallel adaptive FEM

We present a dynamic distributed load balancing algorithm for parallel, adaptive finite element simulations using preconditioned conjugate gradient solvers based on domain-decomposition. The load balancer is designed to maintain good partition aspect ratios. It can calculate a balancing flow using different versions of diffusion and a variant of breadth first search. Elements to be migrated are chosen according to a cost function aiming at the optimization of subdomain shapes. We show how to use information from the second step to guide the first. Experimental results using Bramble's preconditioner and comparisons to existing state-ot-the-art load balancers show the benefits of the construction.

Load balancing for parallel adaptive FEM

We present a dynamic distributed load balancing algorithm for parallel, adaptive finite element simulations using preconditioned conjugate gradient solvers based on domain-decomposition. The load balancer is designed to maintain good partition aspect ratios. It calculates a balancing flow using different versions of diffusion and a variant of breadth first search. Elements to be migrated are chosen according to a cost function aiming at the optimization of subdomain shapes. We show how to use information from the second step to guide the first. Experimental results using Bramble's preconditioner and comparisons to existing state-of-the-art balancers show the benefits of the construction.

Reconstruction of inclusions in photothermal imaging

Photothermal imaging allows to inspect the structure of composite materials by means of nondestructive tests. The surface of a medium is heated at a number of locations. The resulting temperature field is recorded on the same surface. Thermal waves are strongly damped. Robust schemes are needed to reconstruct the structure of the medium from the decaying time dependent temperature field. The inverse problem is formulated as a weighted optimization problem with a time dependent constraint. The inclusions buried in the medium and their material constants are the design variables. We propose an approximation scheme in two steps. First, Laplace transforms are used to generate an approximate optimization problem with a small number of stationary constraints. Then, we implement a descent strategy alternating topological derivative techniques to reconstruct the geometry of inclusions with gradient methods to identify their material parameters. Numerical simulations assess the effectivity of the technique.

Optimal control of a Stefan problem with gradient-based methods in FEniCS

Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik, Masterarbeit, 2016

Analysis of genetic diversity of Trypanosoma cruzi: an application of riboprinting and gradient gel electrophoresis methods

Analysis of restriction fragment length polymorphism (RFLP) profiles derived from digestion of polymerase chain reaction (PCR) products of the ribosomal 18S from Trypanosoma cruzi yields a typical `riboprint' profile that can vary intraspecifically. A selection of 21 stocks of T. cruzi and three outgroup taxa: T. rangeli, T. conorhini and Leishmania braziliensis were analysed by riboprinting to assess divergence within and between taxa. T. rangeli, T. conorhini and L. braziliensis could be easily differentiated from each other and from T. cruzi. Phenetic analysis of PCR-RFLP profiles indicated that, with one or two exceptions, stocks of T. cruzi could be broadly partitioned into two groups that formally corresponded to T. cruzi I and T. cruzi II respectively. To test if ribosomal 18S sequences were homogeneous within each taxon, gradient gel electrophoresis methods were employed utilising either chemical or temperature gradients. Upon interpretation of the melting profiles of riboprints and a section of the 18S independently amplified by PCR, there would appear to be at least two divergent 18S types present within T. cruzi. Heterogeneity within copies of the ribosomal 18S within a single genome has therefore been demonstrated and interestingly, this dimorphic arrangement was also present in the outgroup taxa. Presumably the ancestral duplicative event that led to the divergent 18S types preceded that of speciation within this group. These divergent 18S paralogues may have, or had, different functional pressures or rates of molecular evolution. Whether or not these divergent types are equally transcriptionally active throughout the life cycle, remain to be assessed.

Gradient recovery in adaptive finite-element methods for parabolic problems

We derive energy-norm a posteriori error bounds, using gradient recovery (ZZ) estimators to control the spatial error, for fully discrete schemes for the linear heat equation. This appears to be the �rst completely rigorous derivation of ZZ estimators for fully discrete schemes for evolution problems, without any restrictive assumption on the timestep size. An essential tool for the analysis is the elliptic reconstruction technique.Our theoretical results are backed with extensive numerical experimentation aimed at (a) testing the practical sharpness and asymptotic behaviour of the error estimator against the error, and (b) deriving an adaptive method based on our estimators. An extra novelty provided is an implementation of a coarsening error "preindicator", with a complete implementation guide in ALBERTA in the appendix.

Hybrid topological derivative and gradient-based methods for electrical impedance tomography

We present a technique to reconstruct the electromagnetic properties of a medium or a set of objects buried inside it from boundary measurements when applying electric currents through a set of electrodes. The electromagnetic parameters may be recovered by means of a gradient method without a priori information on the background. The shape, location and size of objects, when present, are determined by a topological derivative-based iterative procedure. The combination of both strategies allows improved reconstructions of the objects and their properties, assuming a known background.

Evaluation of frozen ground conditions along a coastal topographic gradient at Byers Peninsula (Livingston Island, Antarctica) by geophysical and geoecological methods

Geophysical surveying and geoelectricalmethods are effective to study permafrost distribution and conditions in polar environments. Geoelectrical methods are particularly suited to study the spatial distribution of permafrost because of its high electrical resistivity in comparison with that of soil or rock above 0 °C. In the South Shetland Islands permafrost is considered to be discontinuous up to elevations of 20–40ma.s.l., changing to continuous at higher altitudes. There are no specific data about the distribution of permafrost in Byers Peninsula, in Livingston Island, which is the largest ice-free area in the South Shetland Islands. With the purpose of better understanding the occurrence of permanent frozen conditions in this area, a geophysical survey using an electrical resistivity tomography (ERT)methodologywas conducted during the January 2015 field season, combined with geomorphological and ecological studies. Three overlapping electrical resistivity tomographies of 78meach were done along the same profile which ran from the coast to the highest raised beaches. The three electrical resistivity tomographies are combined in an electrical resistivitymodel which represents the distribution of the electrical resistivity of the ground to depths of about 13malong 158m. Several patches of high electrical resistivity were found, and interpreted as patches of sporadic permafrost. The lower limits of sporadic to discontinuous permafrost in the area are confirmed by the presence of permafrost-related landforms nearby. There is a close correspondence between moss patches and permafrost patches along the geoelectrical transect.

Sequential injections as an alternative to gradient exploitation for implementing differential kinetic analysis in a flow injection system

A novel flow-based strategy for implementing simultaneous determinations of different chemical species reacting with the same reagent(s) at different rates is proposed and applied to the spectrophotometric catalytic determination of iron and vanadium in Fe-V alloys. The method relies on the influence of Fe(II) and V(IV) on the rate of the iodide oxidation by Cr(VI) under acidic conditions, the Jones reducing agent is then needed Three different plugs of the sample are sequentially inserted into an acidic KI reagent carrier stream, and a confluent Cr(VI) solution is added downstream Overlap between the inserted plugs leads to a complex sample zone with several regions of maximal and minimal absorbance values. Measurements performed on these regions reveal the different degrees of reaction development and tend to be more precise Data are treated by multivariate calibration involving the PLS algorithm The proposed system is very simple and rugged Two latent variables carried out ca 95% of the analytical information and the results are in agreement with ICP-OES. (C) 2010 Elsevier B V. All rights reserved.

Finite element modelling of temperature gradient driven rock alteration and mineralization in porous rock masses

We present finite element simulations of temperature gradient driven rock alteration and mineralization in fluid saturated porous rock masses. In particular, we explore the significance of production/annihilation terms in the mass balance equations and the dependence of the spatial patterns of rock alteration upon the ratio of the roll over time of large scale convection cells to the relaxation time of the chemical reactions. Special concepts such as the gradient reaction criterion or rock alteration index (RAI) are discussed in light of the present, more general theory. In order to validate the finite element simulation, we derive an analytical solution for the rock alteration index of a benchmark problem on a two-dimensional rectangular domain. Since the geometry and boundary conditions of the benchmark problem can be easily and exactly modelled, the analytical solution is also useful for validating other numerical methods, such as the finite difference method and the boundary element method, when they are used to dear with this kind of problem. Finally, the potential of the theory is illustrated by means of finite element studies related to coupled flow problems in materially homogeneous and inhomogeneous porous rock masses. (C) 1998 Elsevier Science S.A. All rights reserved.

An "openable," high-strength gradient set for orthopedic MRI

A novel three-axis gradient set and RF resonator for orthopedic MRT has been designed and constructed. The set is openable and may be wrapped around injured joints. The design methodology used was the minimization of magnetic field spherical harmonics by simulated annealing. Splitting of the longitudinal coil presents the major design challenge to a fully openable gradient set and in order to efficiently design such coils, we have developed a new fast algorithm for determining the magnetic field spherical harmonics generated by an are of multiturn wire. The algorithm allows a realistic impression of the effect of split longitudinal designs. A prototype set was constructed based on the new designs and tested in a 2-T clinical research system. The set generated 12 mT/m/A with a linear region of 12 cm and a switching time of 100 mu s, conforming closely with theoretical predictions. Preliminary images from the set are presented. (C) 1999 Academic Press.

Finite-difference time-domain-based studies of MRI pulsed field gradient-induced eddy currents inside the human body

In modern magnetic resonance imaging (MRI), patients are exposed to strong, rapidly switching magnetic gradient fields that, in extreme cases, may be able to elicit nerve stimulation. This paper presents theoretical investigations into the spatial distribution of induced current inside human tissues caused by pulsed z-gradient fields. A variety of gradient waveforms have been studied. The simulations are based on a new, high-definition, finite-difference time-domain method and a realistic inhomogeneous 10-mm resolution human body model with appropriate tissue parameters. it was found that the eddy current densities are affected not only by the pulse sequences but by many parameters such as the position of the body inside the gradient set, the local biological material properties and the geometry of the body. The discussion contains a comparison of these results with previous results found in the literature. This study and the new methods presented herein will help to further investigate the biological effects caused by the switched gradient fields in a MRI scan. (C) 2002 Wiley Periodicals, Inc.

The design of planar gradient coils. Part I: A winding path correction method

In this work a new approach for designing planar gradient coils is outlined for the use in an existing MRI apparatus. A technique that allows for gradient field corrections inside the diameter-sensitive volume is deliberated. These corrections are brought about by making changes to the wire paths that constitute the coil windings, and hence, is called the path correction method. The existing well-known target held method is used to gauge the performance of a typical gradient coil. The gradient coil design methodology is demonstrated for planar openable gradient coils that can be inserted into an existing MRI apparatus. The path corrected gradient coil is compared to the coil obtained using the target field method. It is shown that using a wire path correction with optimized variables, winding patterns that can deliver high magnetic gradient field strengths and large imaging regions can be obtained.