Solving the Helmholtz Equation for the Neumann Boundary Condition for the Pseudosphere by the Galerkin Method

In this paper, the Helmholtz equation for the exterior Neumann boundary condition for the pseudosphere in three dimensions using the global Galerkin method is studied. The Galerkin method will be used to solve Jones’ modified integral equation approach (modified as a series of radiating waves will be added to the fundamental solution) for the Neumann problem for the Helmholtz equation, which uses a series of double sums to approximate the integral. A Fortran 77 program is used and some required subroutines from the Naval Warfare Center are called to help increase ouraccuracy since these boundary integrals are difficult to solve. The solutions obtained arecompared to the true solution for the Neumann problem to understand how well the method converges. The lower errors obtained show that the method for complete reflection of the sound waves off of the pseudosphere is accurate and successful. Also presented in this paper are both computational and theoretical details of the method ofdifferent values of k for the pseudosphere

The Numerical Solution of the Exterior Boundary Value Problems for the Helmholtz\u27s Equation for the Pseudosphere

In this paper, the global Galerkin method is used to numerically solve the exterior Neumann and Dirichlet problems for the Helmholtz equation for the Pseudosphere in three dimensions based on Jones\u27 modified integral equation approach. Warnapala and Morgan have used this method for the Oval of Cassini and obtained good results. Theoretical and computational details of the method for small values of k for the pseudosphere are presented

Additional file 1: of Predictors of delayed care seeking for tuberculosis in southern India: an observational study

The questionnaire that was used for data collection in this study. (PDF 139 kb

Comorbidities in pulmonary tuberculosis cases in Puducherry and Tamil Nadu, India: Opportunities for intervention

<div><p>Background</p><p>We aimed to define characteristics of TB patients in Puducherry and two districts of Tamil Nadu, India and calculate the population attributable fractions (PAF) of TB from malnutrition and alcohol.</p><p>Methods</p><p>New smear-positive TB cases were enrolled into the Regional Prospective Observational Research for Tuberculosis (RePORT India) cohort. Census and National Family Health Survey data were used for comparisons.</p><p>Results</p><p>Data were analyzed for 409 participants enrolled between May 2014-June 2016; 307 (75.1%) were male, 60.2% were malnourished (body mass index [BMI] <18.5 kg/m²), and 29.1% severely malnourished (BMI <16). “Hazardous” alcohol use (based on AUDIT-C score) was reported by 155/305 (50.8%) of males. Tuberculosis cases were more likely than the Puducherry population to be malnourished (62.6% v 10.2% males and 71.7% v 11.3% of females; both p<0.001), and male cases were more likely to use alcohol than male non-cases (84.4% v 41%; p < .001). The PAF of malnutrition was 57.4% in males and 61.5% in females; the PAF for alcohol use was 73.8% in males and 1.7% in females.</p><p>Conclusions</p><p>Alcohol use in men and malnutrition are helping drive the TB epidemic in Southern India. Reducing the TB burden in this population will require efforts to mitigate these risk factors.</p></div

Characteristics of TB patients in RePORT cohort, Puducherry and Tamil Nadu, (2014–16).

<p>Characteristics of TB patients in RePORT cohort, Puducherry and Tamil Nadu, (2014–16).</p

Comparison of TB case characteristics and the 2015 national family health survey for Puducherry for persons ages 15–49 years^a.

<p>Comparison of TB case characteristics and the 2015 national family health survey for Puducherry for persons ages 15–49 years<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0183195#t003fn001" target="_blank">^a</a>.</p

Comparison of TB case characteristics, household characteristics and Puducherry population based on 2011 census data.

<p>Comparison of TB case characteristics, household characteristics and Puducherry population based on 2011 census data.</p