DSJM is a software toolkit written in portable C++ that enables direct determination of sparse Jacobian matrices whose sparsity pattern is a priori known. Using the seed matrix S 2 Rn×p, the Jacobian A 2 Rm×n can be determined by solving AS = B, where B 2 Rm×p has been obtained via finite difference approximation or forward automatic differentiation. Seed matrix S is defined by the nonzero unknowns in A. DSJM includes well-known as well as new column ordering heuristics. Numerical testing is highly promising both in terms of running time and the number of matrix-vector products needed to determine A. / x, 71 leaves : ill. ; 29 cm

One of the main objectives of software development in scientific computing is efficiency. Being focused on highly specialized application domain, important software quality metrics, e.g., usability, extensibility ,etc may not be amongst the list of primary objectives. In this research, we have studied the design structures and iterative releases of scientific research software using Design Structure Matrix(DSM). We implemented a DSM partitioning algorithm using sparse matrix data structure Compressed Row Storage(CRS), and its timing was better than those obtained from the most widely used C++ library boost. Secondly, we computed several architectural complexity metrics, compared releases and total release costs of a number of open source scientific research software. One of the important finding is the absence of circular dependencies in studied software which attributes to the strong emphasis on computational performance of the code. Iterative release analysis indicates that there might be a correspondence between “clustering co-efficient” and “release rework cost” of the software. / x, 87 leaves : ill. ; 29 cm

No description available.

Thesis (Ph. D.)--University of Hong Kong, 2000. / Includes bibliographical references (leaves 160-169).

We consider high order discontinuous-Galerkin finite element methods for partial differential equations, with a focus on the neutron transport equation. We begin by examining a method for preprocessing block-sparse matrices, of the type that arise from discontinuous-Galerkin methods, prior to factorisation by a multifrontal solver. Numerical experiments on large two and three dimensional matrices show that this pre-processing method achieves a significant reduction in fill-in, when compared to methods that fail to exploit block structures. A discontinuous-Galerkin finite element method for the neutron transport equation is derived that employs high order finite elements in both space and angle. Parallel Krylov subspace based solvers are considered for both source problems and $k_{eff}$-eigenvalue problems. An a-posteriori error estimator is derived and implemented as part of an h-adaptive mesh refinement algorithm for neutron transport $k_{eff}$-eigenvalue problems. This algorithm employs a projection-based error splitting in order to balance the computational requirements between the spatial and angular parts of the computational domain. An hp-adaptive algorithm is presented and results are collected that demonstrate greatly improved efficiency compared to the h-adaptive algorithm, both in terms of reduced computational expense and enhanced accuracy. Computed eigenvalues and effectivities are presented for a variety of challenging industrial benchmarks. Accurate error estimation (with effectivities of 1) is demonstrated for a collection of problems with inhomogeneous, irregularly shaped spatial domains as well as multiple energy groups. Numerical results are presented showing that the hp-refinement algorithm can achieve exponential convergence with respect to the number of degrees of freedom in the finite element space

The paper describes a storage scheme for sparse symmetric or nonsymmetric matrices which has been developed and used for many years at the Technical University of Chemnitz. An overview of existing library subroutines using such matrices is included.

The first part of this thesis presents a convenient and flexible calibration method to estimate the relative rotation and translation among multiple cameras. A simple planar pattern is used for accurate calibration and is not required to be simultaneously observed by all cameras. Thus the method is especially suitable for widely spaced camera array. In order to fairly evaluate the calibration results for different camera setups, a novel accuracy metric is introduced based on the deflection angles of projection rays, which is insensitive to a number of setup factors. / The objective of this thesis is to develop a multiview system that can synthesize photorealistic novel views of the scene captured by sparse cameras distributed in a wide area. The system cost is largely reduced due to the small number of required cameras, and the image capture is greatly facilitated because the cameras are allowed to be widely spaced and flexibly placed. The key techniques to achieve this goal are investigated in this thesis. / Cui, Chunhui. / "November 2010." / Adviser: Ngan King Ngi. / Source: Dissertation Abstracts International, Volume: 73-04, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 140-155). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

The numerical solution of Stein (aka discrete Lyapunov) equations is the primary step in Newton's method for the solution of discrete-time algebraic Riccati equations (DARE). Here we present a low-rank Smith method as well as a low-rank alternating-direction-implicit-iteration to compute low-rank approximations to solutions of Stein equations arising in this context. Numerical results are given to verify the efficiency and accuracy of the proposed algorithms.

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Dissertation ueber die effektive Vorkonditionierung linearer Gleichungssysteme resultierend aus der Diskretisierung eines elliptischen Randwertproblems 2. Ordnung mittels der Methode der Finiten Elementen. Als Vorkonditionierer werden multi-level artige Vorkonditionierer (BPX, Multi-grid, Wavelets) benutzt.