Abstract: The $hp$-adaptive Finite Element Method ($hp$-FEM) generates a sequence of adaptive grids with different polynomial orders of approximation and element sizes. The $hp$-FEM delivers exponential convergence of the numerical error with respect to the mesh size. In this paper, we propose a heuristic algorithm to construct element partition trees. The trees can be transformed directly into the orderings, which control the execution of the multi-frontal direct solvers during the $hp$ refined finite element method. In particular, the orderings determine the number of floating point operations performed by the solver. Thus, the quality of the orderings obtained from the element partition trees is important for good performance of the solver. Our heuristic algorithm has been implemented in three-dimensions and tested on a sequence of $hp$-refined meshes, generated during the $hp$ finite element method computations. We compare the quality of the orderings found by the heuristic algorithm to those generated by alternative state-of-the-art algorithms. We show 50 percent reduction in the number of flops and execution time.

Abstract: Ellagic acid (EA) is a polyphenolic compound with antiviral activity against Chikungunya, a rapidly spreading tropical disease transmitted to humans by mosquitoes. The most common symptoms of chikungunya virus infection are fe-ver and joint pain. Other manifestations of infection can include encephalitis and an arthritis-like joint swelling with pain that may persist for months or years after the initial infection. In 2014, there were 11 locally-transmitted cases of Chikungunya virus in the U.S., all reported in Florida. There is no approved vac-cine to prevent or medicine to treat Chikungunya virus infections. In this study, the Estimated Daily Intake (EDI) of EA from the food supply established using the National Health and Nutrition Examination Survey (NHANES) is used to set a maximum dose of an EA formulation for the clinical trial.

Abstract: Parallel computing using MPI has become ubiquitous on multi-node computing clusters. A common problem while developing parallel codes is determining whether or not a deadlock condition can exist. Ideally we do not want to have to run a large number of examples to find deadlock conditions through trial and error procedures. In this paper we describe a methodology using both static analysis and symbolic execution of a MPI program to make a determination when it is possible. We note that using static analysis by itself is insufficient for realistic cases. Symbolic execution has the possibility of creating a nearly infinite number of logic branches to investigate. We provide a mechanism to limit the number of branches to something computable. We also provide examples and pointers to software necessary to test MPI programs.