Some properties of n-dimensional triangulations

A number of mathematical results relevant to the problem of constructing a triangulation, i.e., a simplicial tessellation, of the convex hull of an arbitrary finite set of points in n-space are described. The principal results achieved are: (1) a set of n+2 points in n-space may be triangulated in at most 2 different ways; (2) the sphere test defined in this report selects a preferred one of these two triangulations; (3) a set of parameters is defined that permits the characterization and enumeration of all sets of n+2 points in n-space that are significantly different from the point of view of their possible triangulation; (4) the local sphere test induces a global sphere test property for a triangulation; and (5) a triangulation satisfying the global sphere property is dual to the n-dimensional Dirichlet tesselation, i.e., it is a Delaunay triangulation

The covariance matrix for the solution vector of an equality-constrained least-squares problem

Methods are given for computing the covariance matrix for the solution vector of an equality-constrained least squares problem. The methods are matched to the solution algorithms given in the book, 'Solving Least Squares Problems.

Integrals of a C-1-compatible triangular surface element

Definite integrals are evaluated for the cardinal functions of an interpolation method which provides C sup 1 continuity over a triangular grid

Study of the accuracy of the double-precision arithmetic operations on the IBM 7094 computer

Accuracy of double-precision arithmetic operations on IBM 7094 compute

Sparse matrix methods based on orthogonality and conjugacy

A matrix having a high percentage of zero elements is called spares. In the solution of systems of linear equations or linear least squares problems involving large sparse matrices, significant saving of computer cost can be achieved by taking advantage of the sparsity. The conjugate gradient algorithm and a set of related algorithms are described

C super 1: Compatible interpolation over a triangle

An elementary derivation and a complete description is given of an algorithm for interpolation over a plane triangle when function values and first partial derivatives are given at the vertices. The method gives C1 continuity with neighboring triangles. The interpolation method is mathematically equivalent to one that has been discussed previously in the literature; however, the algorithmic form given here is more efficient than has previously been described

An initial feasibility stage for Stoer's constrained least squares algorithm

A procedure is described for computing an initial feasible vector, x sub 0, for Stoer's algorithm for solving the linear least squares problem subject to linear equality and inequality constraints. The procedure described fits well with Stoer's algorithm since much of the computation performed to determine x sub 0 accomplishes initializing transformations of the problem data, which would otherwise be done in Stoer's algorithm after being given an x sub 0

Conference on the Programming Environment for Development of Numerical Software

Systematic approaches to numerical software development and testing are presented

Software for C1 interpolation

The problem of mathematically defining a smooth surface, passing through a finite set of given points is studied. Literature relating to the problem is briefly reviewed. An algorithm is described that first constructs a triangular grid in the (x,y) domain, and first partial derivatives at the modal points are estimated. Interpolation in the triangular cells using a method that gives C sup.1 continuity overall is examined. Performance of software implementing the algorithm is discussed. Theoretical results are presented that provide valuable guidance in the development of algorithms for constructing triangular grids

The Oyster River Culvert Analysis Project

Studies have already detected intensification of precipitation events consistent with climate change projections. Communities may have a window of opportunity to prepare, but information sufficiently quantified and localized to support adaptation programs is sparse: published literature is typically characterized by general resilience building or regional vulnerability studies. The Fourth Assessment Report of the IPCC observed that adaptation can no longer be postponed pending the effective elimination of uncertainty. Methods must be developed that manage residual uncertainty, providing community leaders with decision-support information sufficient for implementing infrastructure adaptation programs. This study developed a local-scale and actionable protocol for maintaining historical risk levels for communities facing significant impacts from climate change and population growth. For a coastal watershed, the study assessed the capacity of the present stormwater infrastructure capacity for conveying expected peak flow resulting from climate change and population growth. The project transferred coupled-climate model projections to the culvert system, in a form understandable to planners, resource managers and decision-makers; applied standard civil engineering methods to reverse-engineer culverts to determine existing and required capacities; modeled the potential for LID methods to manage peak flow in lieu of, or combination with, drainage system upsizing; and estimated replacement costs using local and national construction cost data. The mid-21st century, most likely 25-year, 24-hour precipitation is estimated to be 35% greater than the TP-40 precipitation for the SRES A1b trajectory, and 64% greater than the TP-40 value for the SRES A1fi trajectory. 5% of culverts are already undersized for the TP-40 event to which they should have been designed. Under the most likely A1b trajectory, an additional 12% of culverts likely will be undersized, while under the most likely A1fi scenario, an additional 19% likely will be undersized. These conditions place people and property at greater risk than that historically acceptable from the TP-4025-year design storm. This risk level may be maintained by a long-term upgrade program, utilizing existing strategies to manage uncertainty and costs. At the upper-95% confidence limit for the A1fi 25-year event, 65% of culverts are adequately sized, and building the remaining 35%, and planned, culverts to thrice the cross-sectional area specified from TP-40 should provide adequate capacity through this event. Realizable LID methods can mitigate significant impacts from climate change and population growth, however effectiveness is limited for the more pessimistic climate change projections. Results indicate that uncertainty in coupled-climate model projections is not an impediment to adaptation. This study makes a significant contribution toward the generation of reliable and specific estimates of impacts from climate change, in support of programs to adapt civil infrastructures. This study promotes a solution to today\u27s arguably most significant challenge in civil infrastructure adaptation: translating the extensive corpus of adaptation theory and regional-scale impacts analyses into localscale action