SUMMARYThe scaled boundary finite element method is a novel semi-analytical technique, whose versatility, accuracy and efficiency are not only equal to, but potentially better than the finite element method and the boundary element method for certain problems. This paper investigates the possibility of using higher-order polynomial functions for the shape functions. Two techniques for generating the higher-order shape functions are investigated. In the first, the spectral element approach is used with Lagrange interpolation functions. In the second, hierarchical polynomial shape functions are employed to add new degrees of freedom into the domain without changing the existing ones, as in the pversion of the finite element method. To check the accuracy of the proposed procedures, a plane strain problem for which an exact solution is available is employed. A more complex example involving three scaled boundary subdomains is also addressed. The rates of convergence of these examples under p-refinement are compared with the corresponding rates of convergence achieved when uniform h-refinement is used, allowing direct comparison of the computational cost of the two approaches. The results show that it is advantageous to use higher-order elements, and that higher rates of convergence can be obtained using p-refinement instead of h-refinement.

ObjectivesThe purposes of this study were to assess the adherence to medication of hypertensive patients visiting community health stations in a rural area in Vietnam, to examine the relationship between levels of adherence and cardiovascular risk among hypertensive patients and to further understand factors influencing adherence.MethodsThis study is part of a prospective one-year study conducted on hypertension management in a population aged 35 to 64 years. Data on age, sex, blood pressure and blood test results were collected at baseline. Cardiovascular risk was based on the Cardiovascular Risk Prediction Model for populations in Asia. To calculate medication adherence, the number of days the drug was taken was divided by the number of days since the first day of the prescription. A threshold of 80% was applied to differentiate between adherence and non-adherence. In-depth interviews were conducted among 18 subjects, including subjects classified as adherent and as non-adherent.ResultsAmong 315 patients analyzed, 49.8% of the patients were adherent. Qualitative investigation revealed discrepancies in classification of adherence and non-adherence based on quantitative analysis and interviews. No significant difference in medication compliance between two cardiovascular disease risk groups (<10% vs. >10% risk) was found, also not after controlling for age, sex, and ethnicity (adjusted odds ratio at 1.068; 95% CI: 0.614 to 1.857). The odds of medication adherence in females was 1.531 times higher than in males but the difference was not statistically significant (95% CI: 0.957 to 2.448). Each one-year increase in age resulted in patients being 1.036 times more likely to be compliant (95% CI: 1.002 to 1.072). Awareness of complications related to hypertension was given as the main reason for adherence to therapy.ConclusionsMedication adherence rate was relatively low among hypertensive subjects. The data suggest that rather than risk profile, the factor of age should be considered for guiding the choice on who to target for improving medication adherence.

This study enhances the classical energy norm based adaptive procedure by introducing new refinement criteria, based on the projection-based interpolation technique and the steepest descent method, to drive mesh refinement for the scaled boundary finite element method. The technique is applied to p-adaptivity in this paper, but extension to h-and hp-adaptivity is straightforward. The reference solution, which is the solution of the fine mesh formed by uniformly refining the current mesh, is used to represent the unknown exact solution. In the new adaptive approach, a projection-based interpolation technique is developed for the 2D scaled boundary finite element method. New refinement criteria are proposed. The optimum mesh is assumed to be obtained by maximizing the decrease rate of the projectionbased interpolation error appearing in the current solution. This refinement strategy can be interpreted as applying the minimisation steepest descent method. Numerical studies show the new approach out-performs the conventional approach.

This paper introduces a new technique for solving concentrated load problems in the scaled boundary finite element method (FEM). By employing fundamental solutions for the displacements and the stresses, the solution is computed as summation of a fundamental solution part and a regular part. The singularity at the point of load application is modelled exactly by the fundamental solution, and only the regular part, which enforces the boundary conditions of the domain onto the fundamental solution, needs to be approximated in the solution space of the scaled boundary FEM. Examples are provided illustrating that the new approach is much simpler to implement and more accurate than the method currently used for solving concentrated load problems with the scaled boundary method. In each illustration, solution convergence is examined. The relative error is described in terms of the scalar energy norm of the stress field. Mesh refinement is performed using p-refinement with high order element based on the Lobatto shape functions. The proposed technique is described for two-dimensional problems in this paper, but extension to any linear problem, for which fundamental solutions exist, is straightforward

human errors which occur either as a result of negligence or as a result of several types of uncertainties. In this context, this study suggests a theoretical framework to address human errors and to mitigate the chances of slope failure.