Preordering saddle-point systems for sparse LDLT factorization without pivoting

This paper focuses on efficiently solving large sparse symmetric indefinite systems of linear equations in saddle‐point form using a fill‐reducing ordering technique with a direct solver. Row and column permutations partition the saddle‐point matrix into a block structure constituting a priori pivots of order 1 and 2. The partitioned matrix is compressed by treating each nonzero block as a single entry, and a fill‐reducing ordering is applied to the corresponding compressed graph. It is shown that, provided the saddle‐point matrix satisfies certain criteria, a block LDLT factorization can be computed using the resulting pivot sequence without modification. Numerical results for a range of problems from practical applications using a modern sparse direct solver are presented to illustrate the effectiveness of the approach

Sparse block factorization of saddle point matrices

The factorization method presented in this paper takes advantage of the special structures and properties of saddle point matrices. A variant of Gaussian elimination equivalent to the Cholesky's factorization is suggested and implemented for factorizing the saddle point matrices block-wise with small blocks of order 1 and 2. The Gaussian elimination applied to these small blocks on block level also induces a block 3 x 3 structured factorization of which the blocks have special properties. We compare the new block factorization with the Schilders' factorization in terms of the sparsity of their factors and computational efficiency. The factorization can be used as a direct method, and also anticipate for preconditioning techniques

Diabetes Case Burden at Central Regional Referral Hospital, Gelephu, Bhutan; A Retrospective Study

BACKGROUND: Diabetes is a metabolic disorder affecting millions of people globally. The incidence of type 2 diabetes is increasing rapidly in Bhutan. Anecdotal evidences show poor compliance and loss to follow up among the Bhutanese population living with diabetes. This study was conducted to understand the case load, age and gender distribution and compliance to follow up among diabetic patients registered at Central Regional Referral Hospital, Gelephu, Bhutan. MATERIALS & METHOD: All the patients diagnosed and registered with Diabetic Clinic between 1st January 2014 to 31st December 2018 were included in the study.RESULTS: There was a sharp increase in number of registered diabetic patients from 641 cases in 2014 to 1590 cases in 2018. A total of 949 new cases were diagnosed and registered during the study period of which 52% were women. The overall diabetes prevalence under Gelephu CRRH catchment area is found to be 2.91% with lowest at Chhudzom (1.01%) and highest in Samtenling Gewog (3.18%). Lost to follow up among new cases for past four years was found to be 3.96%, 5.0%, 6.47% and 5.85% from 2015 to 2018 respectively.CONCLUSION: The ageing population and sedentary lifestyle has contributed to the sharp escalation of type 2 diabetes cases in Gelephu. The hospital recorded total of 1590 cases in 2018 which is a two-fold increase in case load within a span of five years. The current analysis found that loss to follow up was 3.96%, 5.0%, 6.47% and 5.85% from 2015 to 2018 respectively among new cases of diabetes registered with the hospital

A comparative study of null-space factorizations for sparse symmetric saddle point systems

Null-space methods for solving saddle point systems of equations have long been used to transform an indefinite system into a symmetric positive definite one of smaller dimension. A number of independent works in the literature have identified that we can interpret a null-space method as a matrix factorization. We review these findings, highlight links between them, and bring them into a unified framework. We also investigate the suitability of using null-space factorizations to derive sparse direct methods, and present numerical results for both practical and academic problems

Performance load testing and structural adequacy evaluation of road bridge decks

Many ageing road bridges, particularly timber bridges, require urgent improvement due to the demand imposed by the recent version of the Australian bridge loading code, AS 5100. As traffic volume plays a key role in the decision of budget allocations for bridge refurbishment/ replacement, many bridges in low volume traffic network remain in poor condition with axle load and/ or speed restrictions, thus disadvantaging many rural communities. This thesis examines an economical and environmentally sensible option of incorporating disused flat rail wagons (FRW) in the construction of bridges in low volume, high axle load road network. The constructability, economy and structural adequacy of the FRW road bridge is reported in the thesis with particular focus of a demonstration bridge commissioned in regional Queensland. The demonstration bridge comprises of a reinforced concrete slab (RCS) pavement resting on two FRWs with custom designed connection brackets at regular intervals along the span of the bridge. The FRW-RC bridge deck assembly is supported on elastomeric rubber pads resting on the abutment. As this type of bridge replacement technology is new and its structural design is not covered in the design standards, the in-service structural performance of the FRW bridge subjected to the high axle loadings prescribed in AS 5100 is examined through performance load testing. Both the static and the moving load tests are carried out using a fully laden commonly available three-axle tandem truck. The bridge deck is extensively strain gauged and displacement at several key locations is measured using linear variable displacement transducers (LVDTs). A high speed camera is used in the performance test and the digital image data are analysed using proprietary software to capture the locations of the wheel positions on the bridge span accurately. The wheel location is thus synchronised with the displacement and strain time series to infer the structural response of the FRW bridge. Field test data are used to calibrate a grillage model, developed for further analysis of the FRW bridge to various sets of high axle loads stipulated in the bridge design standard. Bridge behaviour predicted by the grillage model has exemplified that the live load stresses of the FRW bridge is significantly lower than the yield strength of steel and the deflections are well below the serviceability limit state set out in AS 5100. Based on the results reported in this thesis, it is concluded that the disused FRWs are competent to resist high axle loading prescribed in AS 5100 and are a viable alternative structural solution of bridge deck in the context of the low volume road networks

Review of Judicial Reforms in Bhutan

This essay highlights the anomalies of judicial reforms in Bhutan. It presents a historical perspective of Bhutanese judicial reforms and addresses recent developments. It discusses court performance and experiences and approaches adopted in making the courts efficient. Much of the reform initiatives emanate from the throne. His Majesty the King has always advocated an efficient judicial system for the Kingdom. In obedience to the Royal Commands, the judicial system and judicial process in Bhutan has been streamlined and improved. The judiciary is continuously reformed, the courts modernized, the judicial quality improved through training, the procedures shortened and accountability is enhanced

Effects of opening in the cross girders of the flat bottom rail wagons to the load transferring mechanism when used as road bridge deck

A Flat Bed Rail Wagon (FBRW) has been proposed as an alternative solution for replacing bridges on low traffic volume roads. The subject matter for this paper is to investigate the impediment to load transfer from cross girders to main girder, through visually identifiable structural flaws. Namely, the effect of having large openings at close proximity to the connection of the main girder to the cross girder of a FBRW was examined. It was clear that openings locally reduce the section modulus of the secondary members; however it was unclear how these reductions would affect the load transfer to the main girder. The results are presented through modeling grillage action for which the loads applied onto the FBRW were distributed through cross girders to the main girder