An iterative method based on boundary integrals for elliptic Cauchy problems in semi-infinite domains

In this study, we investigate the problem of reconstruction of a stationary temperature field from given temperature and heat flux on a part of the boundary of a semi-infinite region containing an inclusion. This situation can be modelled as a Cauchy problem for the Laplace operator and it is an ill-posed problem in the sense of Hadamard. We propose and investigate a Landweber-Fridman type iterative method, which preserve the (stationary) heat operator, for the stable reconstruction of the temperature field on the boundary of the inclusion. In each iteration step, mixed boundary value problems for the Laplace operator are solved in the semi-infinite region. Well-posedness of these problems is investigated and convergence of the procedures is discussed. For the numerical implementation of these mixed problems an efficient boundary integral method is proposed which is based on the indirect variant of the boundary integral approach. Using this approach the mixed problems are reduced to integral equations over the (bounded) boundary of the inclusion. Numerical examples are included showing that stable and accurate reconstructions of the temperature field on the boundary of the inclusion can be obtained also in the case of noisy data. These results are compared with those obtained with the alternating iterative method

An alternating potential based approach for a Cauchy problem for the Laplace equation in a planar domain with a cut

We consider a Cauchy problem for the Laplace equation in a bounded region containing a cut, where the region is formed by removing a sufficiently smooth arc (the cut) from a bounded simply connected domain D. The aim is to reconstruct the solution on the cut from the values of the solution and its normal derivative on the boundary of the domain D. We propose an alternating iterative method which involves solving direct mixed problems for the Laplace operator in the same region. These mixed problems have either a Dirichlet or a Neumann boundary condition imposed on the cut and are solved by a potential approach. Each of these mixed problems is reduced to a system of integral equations of the first kind with logarithmic and hypersingular kernels and at most a square root singularity in the densities at the endpoints of the cut. The full discretization of the direct problems is realized by a trigonometric quadrature method which has super-algebraic convergence. The numerical examples presented illustrate the feasibility of the proposed method

Boundary-integral approach to the numerical solution of the Cauchy problem for the Laplace equation

We present a survey of a direct method of boundary integral equations for the numerical solution of the Cauchy problem for the Laplace equation in doubly connected domains. The domain of solution is located between two closed boundary surfaces (curves in the case of two-dimensional domains). This Cauchy problem is reduced to finding the values of a harmonic function and its normal derivative on one of the two closed parts of the boundary according to the information about these quantities on the other boundary surface. This is an ill-posed problem in which the presence of noise in the input data may completely destroy the procedure of finding the approximate solution. We describe and present the results for a procedure of regularization aimed at the stable determination of the required quantities based on the representation of the solution to the Cauchy problem in the form a single-layer potential. For given data, this representation yields a system of boundary integral equations with two unknown densities. We establish the existence and uniqueness of these densities and propose a method for the numerical discretization in two- and three-dimensional domains. We also consider the cases of simply connected domains of the solution and unbounded domains. Numerical examples are presented both for two- and three-dimensional domains. These numerical results demonstrate that the proposed method gives good accuracy with relatively small amount of computations

Recovering boundary data in planar heat conduction using boundary integral equation method

We consider a Cauchy problem for the heat equation, where the temperature field is to be reconstructed from the temperature and heat flux given on a part of the boundary of the solution domain. We employ a Landweber type method proposed in [2], where a sequence of mixed well-posed problems are solved at each iteration step to obtain a stable approximation to the original Cauchy problem. We develop an efficient boundary integral equation method for the numerical solution of these mixed problems, based on the method of Rothe. Numerical examples are presented both with exact and noisy data, showing the efficiency and stability of the proposed procedure and approximations

Application of mixed formulations of quasi-reversibility to solve ill-posed problems for heat and wave equations: the 1d case

International audienceIn this paper we address some ill-posed problems involving the heat or the wave equation in one dimension, in particular the backward heat equation and the heat/wave equation with lateral Cauchy data. The main objective is to introduce some variational mixed formulations of quasi-reversibility which enable us to solve these ill-posed problems by using some classical La-grange finite elements. The inverse obstacle problems with initial condition and lateral Cauchy data for heat/wave equation are also considered, by using an elementary level set method combined with the quasi-reversibility method. Some numerical experiments are presented to illustrate the feasibility for our strategy in all those situations. 1. Introduction. The method of quasi-reversibility has now a quite long history since the pioneering book of Latt es and Lions in 1967 [1]. The original idea of these authors was, starting from an ill-posed problem which satisfies the uniqueness property, to introduce a perturbation of such problem involving a small positive parameter ε. This perturbation has essentially two effects. Firstly the perturbation transforms the initial ill-posed problem into a well-posed one for any ε, secondly the solution to such problem converges to the solution (if it exists) to the initial ill-posed problem when ε tends to 0. Generally, the ill-posedness in the initial problem is due to unsuitable boundary conditions. As typical examples of linear ill-posed problems one may think of the backward heat equation, that is the initial condition is replaced by a final condition, or the heat or wave equations with lateral Cauchy data, that is the usual Dirichlet or Neumann boundary condition on the boundary of the domain is replaced by a pair of Dirichlet and Neumann boundary conditions on the same subpart of the boundary, no data being prescribed on the complementary part of the boundary

Pattern of healthcare resource utilization and direct costs associated with manic episodes in Spain

<p>Abstract</p> <p>Background</p> <p>Although some studies indicate that bipolar disorder causes high health care resources consumption, no study is available addressing a cost estimation of bipolar disorder in Spain. The aim of this observational study was to evaluate healthcare resource utilization and the associated direct cost in patients with manic episodes in the Spanish setting.</p> <p>Methods</p> <p>Retrospective descriptive study was carried out in a consecutive sample of patients with a DSM-IV diagnosis of bipolar type I disorder with or without psychotic symptoms, aged 18 years or older, and who were having an active manic episode at the time of inclusion. Information regarding the current manic episode was collected retrospectively from the medical record and patient interview.</p> <p>Results</p> <p>Seven hundred and eighty-four evaluable patients, recruited by 182 psychiatrists, were included in the study. The direct cost associated with healthcare resource utilization during the manic episode was high, with a mean cost of nearly €4,500 per patient, of which approximately 55% corresponded to the cost of hospitalization, 30% to the cost of psychopharmacological treatment and 10% to the cost of specialized care.</p> <p>Conclusions</p> <p>Our results show the high cost of management of the patient with a manic episode, which is mainly due to hospitalizations. In this regard, any intervention on the management of the manic patient that could reduce the need for hospitalization would have a significant impact on the costs of the disease.</p

Quantitative estimates of unique continuation for parabolic equations, determination of unknown time-varying boundaries and optimal stability estimates

In this paper we will review the main results concerning the issue of stability for the determination unknown boundary portion of a thermic conducting body from Cauchy data for parabolic equations. We give detailed and selfcontained proofs. We prove that such problems are severely ill-posed in the sense that under a priori regularity assumptions on the unknown boundaries, up to any finite order of differentiability, the continuous dependence of unknown boundary from the measured data is, at best, of logarithmic type

Randomized pilot study to disseminate caries-control services in dentist offices

BACKGROUND: To determine whether education and financial incentives increased dentists' delivery of fluoride varnish and sealants to at risk children covered by capitation dental insurance in Washington state (U.S.). METHODS: In 1999, 53 dental offices in Washington Dental Service's capitation dental plan were invited to participate in the study, and consenting offices were randomized to intervention (n = 9) and control (n = 10) groups. Offices recruited 689 capitation children aged 6–14 and at risk for caries, who were followed for 2 years. Intervention offices received provider education and fee-for-service reimbursement for delivering fluoride varnish and sealants. Insurance records were used to calculate office service rates for fluoride, sealants, and restorations. Parents completed mail surveys after follow-up to measure their children's dental utilization, dental satisfaction, dental fear and oral health status. Regression models estimated differences in service rates between intervention and control offices, and compared survey measures between groups. RESULTS: Nineteen offices (34%) consented to participate in the study. Fluoride and sealant rates were greater in the intervention offices than the control offices, but the differences were not statistically significant. Restoration rates were lower in the intervention offices than the control offices. Parents in the intervention group reported their children had less dental fear than control group parents. CONCLUSION: Due to low dentist participation the study lacked power to detect an intervention effect on dentists' delivery of caries-control services. The intervention may have reduced children's dental fear

Factors contributing to attrition behavior in diabetes self-management programs: A mixed method approach

<p>Abstract</p> <p>Background</p> <p>Diabetes self-management education is a critical component in diabetes care. Despite worldwide efforts to develop efficacious DSME programs, high attrition rates are often reported in clinical practice. The objective of this study was to examine factors that may contribute to attrition behavior in diabetes self-management programs.</p> <p>Methods</p> <p>We conducted telephone interviews with individuals who had Type 2 diabetes (n = 267) and attended a diabetes education centre. Multivariable logistic regression was performed to identify factors associated with attrition behavior. Forty-four percent of participants (n = 118) withdrew prematurely from the program and were asked an open-ended question regarding their discontinuation of services. We used content analysis to code and generate themes, which were then organized under the Behavioral Model of Health Service Utilization.</p> <p>Results</p> <p>Working full and part-time, being over 65 years of age, having a regular primary care physician or fewer diabetes symptoms were contributing factors to attrition behaviour in our multivariable logistic regression. The most common reasons given by participants for attrition from the program were conflict between their work schedules and the centre's hours of operation, patients' confidence in their own knowledge and ability when managing their diabetes, apathy towards diabetes education, distance to the centre, forgetfulness, regular physician consultation, low perceived seriousness of diabetes, and lack of familiarity with the centre and its services. There was considerable overlap between our quantitative and qualitative results.</p> <p>Conclusion</p> <p>Reducing attrition behaviour requires a range of strategies targeted towards delivering convenient and accessible services, familiarizing individuals with these services, increasing communication between centres and their patients, and creating better partnerships between centres and primary care physicians.</p