Research in computer science

Several short summaries of the work performed during this reporting period are presented. Topics discussed in this document include: (1) resilient seeded errors via simple techniques; (2) knowledge representation for engineering design; (3) analysis of faults in a multiversion software experiment; (4) implementation of parallel programming environment; (5) symbolic execution of concurrent programs; (6) two computer graphics systems for visualization of pressure distribution and convective density particles; (7) design of a source code management system; (8) vectorizing incomplete conjugate gradient on the Cyber 203/205; (9) extensions of domain testing theory and; (10) performance analyzer for the pisces system

Numerical algorithms for finite element computations on arrays of microprocessors

The development of a multicolored successive over relaxation (SOR) program for the finite element machine is discussed. The multicolored SOR method uses a generalization of the classical Red/Black grid point ordering for the SOR method. These multicolored orderings have the advantage of allowing the SOR method to be implemented as a Jacobi method, which is ideal for arrays of processors, but still enjoy the greater rate of convergence of the SOR method. The program solves a general second order self adjoint elliptic problem on a square region with Dirichlet boundary conditions, discretized by quadratic elements on triangular regions. For this general problem and discretization, six colors are necessary for the multicolored method to operate efficiently. The specific problem that was solved using the six color program was Poisson's equation; for Poisson's equation, three colors are necessary but six may be used. In general, the number of colors needed is a function of the differential equation, the region and boundary conditions, and the particular finite element used for the discretization

Numerical algorithms for finite element computations on concurrent processors

The work of several graduate students which relate to the NASA grant is briefly summarized. One student has worked on a detailed analysis of the so-called ijk forms of Gaussian elemination and Cholesky factorization on concurrent processors. Another student has worked on the vectorization of the incomplete Cholesky conjugate method on the CYBER 205. Two more students implemented various versions of Gaussian elimination and Cholesky factorization on the FLEX/32

Research in computer science

The research efforts of University of Virginia students under a NASA sponsored program are summarized and the status of the program is reported. The research includes: testing method evaluations for N version programming; a representation scheme for modeling three dimensional objects; fault tolerant protocols for real time local area networks; performance investigation of Cyber network; XFEM implementation; and vectorizing incomplete Cholesky conjugate gradients

Research in computer science

Synopses are given for NASA supported work in computer science at the University of Virginia. Some areas of research include: error seeding as a testing method; knowledge representation for engineering design; analysis of faults in a multi-version software experiment; implementation of a parallel programming environment; two computer graphics systems for visualization of pressure distribution and convective density particles; task decomposition for multiple robot arms; vectorized incomplete conjugate gradient; and iterative methods for solving linear equations on the Flex/32

Research in computer science

Various graduate research activities in the field of computer science are reported. Among the topics discussed are: (1) failure probabilities in multi-version software; (2) Gaussian Elimination on parallel computers; (3) three dimensional Poisson solvers on parallel/vector computers; (4) automated task decomposition for multiple robot arms; (5) multi-color incomplete cholesky conjugate gradient methods on the Cyber 205; and (6) parallel implementation of iterative methods for solving linear equations

Hodge polynomials of the moduli spaces of pairs

Let $X$ be a smooth projective curve of genus $g\geq 2$ over the complex numbers. A holomorphic pair on $X$ is a couple $(E,\phi)$, where $E$ is a holomorphic bundle over $X$ of rank $n$ and degree $d$, and $\phi\in H^0(E)$ is a holomorphic section. In this paper, we determine the Hodge polynomials of the moduli spaces of rank 2 pairs, using the theory of mixed Hodge structures. We also deal with the case in which $E$ has fixed determinant.Comment: 23 pages, typos added, minor change

On the stability of Hamiltonian relative equilibria with non-trivial isotropy

We consider Hamiltonian systems with symmetry, and relative equilibria with isotropy subgroup of positive dimension. The stability of such relative equilibria has been studied by Ortega and Ratiu and by Lerman and Singer. In both papers the authors give sufficient conditions for stability which require first determining a splitting of a subspace of the Lie algebra of the symmetry group, with different splittings giving different criteria. In this note we remove this splitting construction and so provide a more general and more easily computed criterion for stability. The result is also extended to apply to systems whose momentum map is not coadjoint equivariant