Stability Analysis and Performance Evaluation of Additive Mixed-Precision Runge-Kutta Methods

Additive Runge-Kutta methods designed for preserving highly accurate solutions in mixed-precision computation were previously proposed and analyzed.These specially designed methods use reduced precision for the implicit computations and full precision for the explicit computations.In this work,we analyze the stability properties of these methods and their sensitivity to the low-precision rounding errors,and demonstrate their performance in terms of accuracy and efficiency.We develop codes in FORTRAN and Julia to solve nonlinear systems of ODEs and PDEs using the mixed-precision additive Runge-Kutta(MP-ARK)methods.The convergence,accuracy,and runtime of these methods are explored.We show that for a given level of accuracy,suitably chosen MP-ARK methods may provide significant reductions in runtime.

MIXED COMPATIBLE ELEMENT AND MIXED HYBRID INCOMPATIBLE ELEMENT VARIATIONAL METHODS IN DYNAMICS OF VISCOUS BAROTROPIC FLUIDS

This paper presents and proves the mixed compatible finite element variationalprinciples in dynamics of viscous barotropic fluids. When the principles are proved, itis found that the compatibility conditions of stress can be naturally satisfied. The gene-rallzed variational principles with mixed hybrid incompatible finite elements are alsopresented and proved, and they can reduce the computation of incompatible elements indynamics of viscous barotropic flows.

Hybrid Strategy of Partitioned and Monolithic Methods for Solving Strongly Coupled Analysis of Inverse and Direct Piezoelectric and Circuit Coupling

The inverse and direct piezoelectric and circuit coupling are widely observed in advanced electro-mechanical systems such as piezoelectric energy harvesters.Existing strongly coupled analysis methods based on direct numerical modeling for this phenomenon can be classified into partitioned or monolithic formulations.Each formulation has its advantages and disadvantages,and the choice depends on the characteristics of each coupled problem.This study proposes a new option:a coupled analysis strategy that combines the best features of the existing formulations,namely,the hybrid partitioned-monolithic method.The analysis of inverse piezoelectricity and the monolithic analysis of direct piezoelectric and circuit interaction are strongly coupled using a partitioned iterative hierarchical algorithm.In a typical benchmark problem of a piezoelectric energy harvester,this research compares the results from the proposed method to those from the conventional strongly coupled partitioned iterative method,discussing the accuracy,stability,and computational cost.The proposed hybrid concept is effective for coupled multi-physics problems,including various coupling conditions.

Hybrid Effects on MHD Mixed Convective Boundary Layer Flow through a Sloped Plate in Existence of Nanofluid-Saturated Porous Medium

This study examines the effects of heat, mass, and boundary layer assumptions-based nanoparticle characteristics on the hybrid effects of using MHD in conjunction with mixed convective flow through a sloped vertical pore plate in the existence of medium of porous. Physical characteristics such as thermo-diffusion, injection-suction, and viscous dissipation are taken into consideration, in addition to an equally distributed magnetic force utilized as well in the completely opposite path of the flow. By means of several non-dimensional transformations, the momentum, energy, concentration, and nanoparticle volume fraction equations under investigation are converted in terms of nonlinear boundary layer equations and computationally resolved by utilizing the sixth-order Runge-Kutta strategy in combination together with the iteration of Nachtsheim-Swigert shooting procedure. By contrasting the findings produced for a few particular examples with those found in the published literature, the correctness of the numerical result is verified, and a rather good agreement is found. Utilizing various ranges of pertinent factors, computing findings are determined not only regarding velocity, temperature, and concentration as well as nanoparticle fraction of volume but also concerning with local skin-friction coefficient, local Nusselt and general Sherwood numbers associated with nanoparticle Sherwood number. The findings of the study demonstrate that increasing the fluid suction parameter decreases the velocity and temperature of the flow field in conjunction with concentration and has a variable impact on the nanoparticle fraction of volume, despite an increasing behavior in the local skin friction coefficient and local Nusselt as well as general Sherwood numbers and an increasing behavior in the local nanoparticle Sherwood number. Furthermore, enhancing a Schmidt number leads to a reduction in the local nanoparticle Sherwood number and a rise in the nanoparticle proportion of volume. Along with concentration, it also reduces temperature and velocity. However, it also raises the local Sherwood and Nusselt numbers and reduces the local skin friction coefficient.

Critical care nurses and their clinical reasoning for customizing monitor alarms:a mixed-method study

Objective:To explore the clinical rationale of critical care nurses for personalizing monitor alarms.One of the most crucial jobs assigned to critical care nurses is monitoring patients'physiological indicators and carrying out the necessary associated interventions.Successful use of equipment in the nursing practice environment will be improved by a thorough understanding of the nurse's approach to alarm configuration.Methods:A mixed-method design integrating quantitative and qualitative components was used.The sample of this study recruited a convenience sample of 60 nurses who have worked in critical care areas.This study took place at Lebanese American University Medical Center Rizk Hospital,utilizing a semi-structured interview with participants.Results:The study demonstrated the high incidence of nuisance alarms and the desensitization of critical care nurses to vital ones.According to the nurses,frequent false alarms and a shortage of staff are the 2 main causes of alarm desensitization.Age was significantly associated with the perception of Smart alarms,according to the data(P=0.03).Four interconnected themes and subcategories that reflect the clinical reasoning process for alarm customization were developed as a result of the study's qualitative component:(1)unit alarm environment;(2)nursing style;(3)motivation to customize;and(4)clinical and technological customization.Conclusions:According to this study,nurses believe that alarms are valuable.However,a qualitative analysis of the experiences revealed that customization has been severely limited since the healthcare team depends on nurses to complete these tasks independently.Additionally,a staffing shortage and lack of technical training at the start of placement have also hindered customization.

Multiscale Hybrid-Mixed Finite Element Method for Flow Simulation in Fractured Porous Media

The multiscale hybrid-mixed(MHM)method is applied to the numerical approximation of two-dimensional matrix fluid flow in porous media with fractures.The two-dimensional fluid flow in the reservoir and the one-dimensional flow in the discrete fractures are approximated using mixed finite elements.The coupling of the two-dimensional matrix flow with the one-dimensional fracture flow is enforced using the pressure of the one-dimensional flow as a Lagrange multiplier to express the conservation of fluid transfer between the fracture flow and the divergence of the one-dimensional fracture flux.A zero-dimensional pressure(point element)is used to express conservation of mass where fractures intersect.The issuing simulation is then reduced using the MHM method leading to accurate results with a very reduced number of global equations.A general system was developed where fracture geometries and conductivities are specified in an input file and meshes are generated using the public domain mesh generator GMsh.Several test cases illustrate the effectiveness of the proposed approach by comparing the multiscale results with direct simulations.

Factors Related to Engaging in Physical Activity: A Mixed Methods Study of Female University Students

Objective: As a needs assessment for intervention, quantitative and qualitative methods were used to examine attitude, subjective norms, perceived behavioral control, intention, knowledge, and weight control status related to physical activity in female university students within the Theory of Planned Behavior (TPB). Methods: A two-phase mixed method design was used. In Phase I, 362 students participated in an online survey, and in Phase II, 33 students participated in five focus group discussions. Ages of participants ranged from 18 to 45 years old, with 18 - 25 year olds making up over 74% of the sample. Results: Attitude, subjective norms, and perceived behavioral control, along with weight control status of trying to lose weight, were found to be significant predictors of intention to follow physical activity recommendations, which in turn were the strongest predictor of physical activity. Knowledge was not found to be significant. Group discussions revealed barriers to meeting physical activity recommendations, which included lack of companionship and social support, lack of motivation, time and cost restrictions, and lack of privacy in the gym. Social norms exerted both positive and negative influences. Conclusion: The mixed method approach provided a deeper insight into the influential factors pertaining to physical activity among female students, and results could be used in further research to develop effective interventions.

MIXED FINITE ELEMENT METHODS FOR THE SHALLOW WATER EQUATIONS INCLUDING CURRENT AND SILT SEDIMENTATION (Ⅱ)——THE DISCRETE-TIME CASE ALONG CHARACTERISTICS

The mixed finite element(MFE) methods for a shallow water equation system consisting of water dynamics equations,silt transport equation,and the equation of bottom topography change were derived.A fully discrete MFE scheme for the discrete_time along characteristics is presented and error estimates are established.The existence and convergence of MFE solution of the discrete current velocity,elevation of the bottom topography,thickness of fluid column,and mass rate of sediment is demonstrated.

Comparative structural and electrochemical properties of mixed P2/O′3-layered sodium nickel manganese oxide prepared by sol-gel and electrospinning methods:Effect of Na-excess content

The effect of Na-excess content in the precursor on the structural and electrochemical performances of sodium nickel manganese oxide(NNMO)prepared by sol-gel and electrospinning methods is investigated in this paper.X-ray diffraction results of the prepared NNMO without adding Na-excess content indicate sodium loss,while the mixed phase of P2/O′3-type layered NNMO presented after adding Na-excess content.Compared with the sol-gel method,the secondary phase of NiO is more suppressed by using the electrospinning method,which is further confirmed by field emission scanning electron microscope images.N_(2) adsorption-desorption isotherms show no remarkably difference in specific surface areas between different preparation methods and Na-excess contents.The analysis of X-ray absorption near edge structure indicates that the oxidation states of Ni and Mn are+2 and+4,respectively.For the electrochemical properties,superior electrochemical performance is observed in the NNMO electrode with a low Na-excess content of 5wt%.The highest specific capacitance is 36.07 F·g^(-1)at0.1 A·g^(-1)in the NNMO electrode prepared by using the sol-gel method.By contrast,the NNMO electrode prepared using the electrospinning method with decreased Na-excess content shows excellent cycling stability of 100%after charge-discharge measurements for 300 cycles.Therefore,controlling the Na excess in the precursor together with the preparation method is important for improving the electrochemical performance of Na-based electrode materials in supercapacitors.

Testing a mobile app for child abuse treatment: A mixed methods study

Objective:This study provides a preliminary evaluation of the usability and acceptability of a mobile application(sexual assault care algorithm,SACA).Methods:An explanatory sequential mixed methods research was used.A quantitative survey was followed up by a qualitative study.A convenience sample of participants(n=4)was recruited.The research was conducted on a one-on-one basis.In the quantitative phase,a random assignment technique was used to divide four participants into two groups of two participants each.Post-Study System Usability Questionnaire(PSSUQ)and Acceptability e-Scale were used to collect quantitative data.In the qualitative phase,interview,observation,and documentation were used to collect qualitative data.Data were analyzed both quantitative and qualitatively.The qualitative data were linked with the initial quantitative data to determine how the follow-up qualitative data helped explain the initial quantitative results.Results:The quantitative results suggested that SACA has high usability(5.05±1.83)and acceptability(3.81±1.22).The qualitative results further indicate that the participants thought SACA was easy to use and useful,and most of them would recommend it to others.Areas of improvement include adding features that would calculate and validate the elapsed time since the sexual assault,adding explanations to some buttons,and providing training.Conclusions:Our findings highlight the value of using a mixed methods research design to conduct a usability and acceptability test.Nurses are more likely to adopt a new technology for their evidencebased practice when the technology is easy to use and useful and requires less time to find the right piece of guideline evidence.Individualized training needs to be designed based on users'characteristics.

Error Estimates of H^1-Galerkin Mixed Methods for the Viscoelasticity Wave Equation

H1-Galerkin mixed methods are proposed for viscoelasticity wave equation.Depending on the physical quantities of interest,two methods are discussed.The optimal error estimates and the proof of the existence and uniqueness of semidiscrete solutions are derived for problems in one space dimension.And the methods don＇t require the LBB condition.

TWO LEVEL SCHWARZ METHODS OF MIXED FINITE ELEMENT APPROXIMATION OF BIHARMONIC PROBLEM

In this paper,the two level additive Schwarz algorithm of mixed finite element.dts-cretization of Inharmonic problem is presented,the rate of convergenece is obtained.Moreover,the two level multiplicative Schwarz algorithm is considered.

IMPLICIT-EXPLICIT MULTISTEP FINITE ELEMENT-MIXED FINITE ELEMENT METHODS FOR THE TRANSIENT BEHAVIOR OF A SEMICONDUCTOR DEVICE

The transient behavior of a semiconductor device consists of a Poisson equation for the electric potential and of two nonlinear parabolic equations for the electron density and hole density. The electric potential equation is discretized by a mixed finite element method. The electron and hole density equations are treated by implicit-explicit multistep finite element methods. The schemes are very efficient. The optimal order error estimates both in time and space are derived.

MIXED HYBRID PENALTY FINITE ELEMENT METHOD AND ITS APPLICATION

The penalty and hybrid methods are being much used in dealing with the general incompatible element, With the penalty method convergence can always be assured, but comparatively speaking its accuracy is lower, and the condition number and sparsity are not so good. With the hybrid method, convergence can be assured only when the rank condition is satisfied. So the construction of the element is extremely limited. This paper presents the mixed hybrid penalty element method, which combines the two methods together. And it is proved theoretically that this new method is convergent, and it has the same accuracy, condition number and sparsity as the compatible element. That is to say, they are optimal to each other.Finally, a new triangle element for plate bending with nine freedom degrees is constructed with this method (three degreesof freedom are given on each corner -- one displacement and tworotations), the calculating formula of the element stiffness matrix is almost the same as that of the old triangle element for plate bending with nine degrees of freedom But it is converged to true solution with arbitrary irregrlar triangle subdivision. If the true solution u?H3 with this method the linear and quadratic rates of convergence are obtianed for three bending moments and for the displacement and two rotations respectively.

NONLINEAR GALERKIN MIXED ELEMENT METHODS FOR STATIONARY INCOMPRESSIBLE MAGNETOHYDRODYNAMICS

A nonlinear Galerkin mixed element （NGME） method for the stationary incompressible magnetohydrodynamics equations is presented. And the existence and error estimates of the NGME solution are derived.

MIXED FINITE ELEMENT METHODS FOR THE SHALLOW WATER EQUATIONS INCLUDING CURRENT AND SILT SEDIMENTA-TION (Ⅰ)-THE CONTINUOUS-TIME CASE

An initial-boundary value problem for shallow equation system consisting of water dynamics equations,silt transport equation, the equation of bottom topography change,and of some boundary and initial conditions is studied, the existence of its generalized solution and semidiscrete mixed finite element(MFE) solution was discussed, and the error estimates of the semidiscrete MFE solution was derived.The error estimates are optimal.

Discrete formulation of mixed finite element methods for vapor deposition chemical reaction equations

The vapor deposition chemical reaction processes, which are of extremely extensive applications, can be classified as a mathematical model by the following governing nonlinear partial differential equations containing velocity vector, temperature field, pressure field, and gas mass field. The mixed finite element （MFE） method is employed to study the system of equations for the vapor deposition chemical reaction processes. The semidiscrete and fully discrete MFE formulations are derived. And the existence and convergence （error estimate） of the semidiscrete and fully discrete MFE solutions are demonstrated. By employing MFE method to treat the system of equations for the vapor deposition chemical reaction processes, the numerical solutions of the velocity vector, the temperature field, the pressure field, and the gas mass field can be found out simultaneously. Thus, these researches are not only of important theoretical means, but also of extremely extensive applied vistas.

Emerging HIV Epidemic in the North-Eastern State of Assam, India: An Exploratory Study Using Mixed-Methods Approach

Background: The national HIV scenario in India has improved impressively during past two decades. Contrastingly, the State-level HIV sentinel surveil-lance and routine programme data from various testing facilities indicated an increasing HIV prevalence among antenatal clinic attendees and female sex workers (FSWs) in three districts of Assam. Objectives: 1) To explore the reasons behind increasing adult HIV prevalence and 2) To understand the role of FSW and Migrants/long distance truckers as drivers of the HIV epi-demic in these districts. Methodology: Three sources of data were utilized in this concurrent mixed methods study—1) existing programme data for past three years;2) questionnaire-based data for a case-control study, where dur-ing past six months at designated testing facilities HIV(+) married women were “cases” and age-matched HIV(?) women from the same district were “controls”. Spouses of these women were also interviewed separately;and 3) a qualitative study, where focus group discussions were conducted among FSWs, outgoing male migrant labourers and long-distance truckers. Results: The study revealed high levels of unsafe sexual practices among the FSWs. Sometimes in poverty-struck areas, women, not identifying themselves as sex workers, sold sex on a part-time basis to earn extra money for financial sup-port and often remained invisible to the programme. The clients of the sex workers, male migrants and truckers also revealed various risk behaviours for contracting and transmitting HIV infection. Conclusion: Population and context specific programme strategies are required to halt the rising trend of HIV infection in the general population in Assam.

Determinants of Risky Sexual Behaviour among Inmates in Katsina Correctional Service: A Mixed Methods Study

Background: Incarceration does not vitiate sexual desire. Therefore, sexual activities occur behind bars, regardless of the stringent rules in correctional institutions. However, little has been documented about risky sexual behaviors, determinants, and experiences among inmates of correctional institutions in Katsina State, Nigeria. The study determined the sexual practices, prevalence, and determinants of risky sexual behaviors among prison inmates in Katsina. Methodology: A descriptive cross-sectional design with concurrent mixed methods of data collection was used to interview 216 inmates using a semi-structured questionnaire supplemented with 22 in-depth interviews. Result: Most (94%) respondents were male, almost half (44.4%) had secondary education, more than half (55.1%) were engaged in business or trading before incarceration, and the majority (75.9%) were awaiting trial. Nearly all inmates (98.6%) reported having sexual desire. Drug use (80.1%) and unprotected sex (79.2%) were quite common but sexual violence was low (7.4%). The number of sexual partners of respondents remained a significant predictor of sexual activity. Inmates who had one (1) or no sexual partner were 64% less likely to engage in risky sexual activity within the confines of the prison (AOR = 0.36, 95% CI = 0.20 - 0.63, p = 0.01). Qualitative interviews revealed the denial of occurrence of sexual activity in prison despite sexual desire felt by inmates;loneliness, poverty, and curiosity as motives for sexual relations;denial of occurrence of sexual violence in prison;and drug use and use of unsterilized sharps as risky sexual behaviors. Conclusion: Despite the disciplinary action meted out on inmates, prisoners still engaged in a range of risky sexual behaviors. Conjugal visitations for married inmates could be considered to reduce sexually deviant and risky alternatives of relieving sexual desire among prisoners.

Study and promotion of safety culture using mixed methods research

Objective:With a positive safety culture,institutions offer the best quality and safe care to their patients.The objective of this study was to analyze patient safety culture from the perspective of the multidisciplinary team,to identify factors that influence patient safety culture,and to create/promote-jointly with the study participants-strategies for improving processes of change.Methods:The study design represented a mixed methods research approach,with a sequential explanatory design.A multidisciplinary team of workers at a general hospital was eligible for the study.To collect quantitative data,we administered the Safety Attitudes Questionnaire(SAQ).The qualitative phase was accomplished via focus groups(FGs),with participants from the first phase of the study using the principles of deliberative dialogue(DD)as a knowledge-translation strategy.The STROBE guideline was used to develop the study.Results:The overall SAQ score was positive(75.1±10.4).Negative scores were found in the fields of Safety Climate,Working Conditions,and Stress Recognition.Focus group discussions identified the aspects that create a negative impact on safety culture,such as ineffective communication,punitive approach in the event of errors,the lack of commitment and adherence to the protocols,and the non-recognition of the stress and the mistakes.Actions for the promotion of safety culture were developed and implemented during the study.Conclusions:The use of the principles of DD as a strategy for knowledge translation(KT)made it possible to identify and plan for joint actions to generate improvements in safety culture.