Trimmed Serendipity Finite Element Differential Forms

We introduce the family of trimmed serendipity finite element differential form spaces, defined on cubical meshes in any number of dimensions, for any polynomial degree, and for any form order. The relation between the trimmed serendipity family and the (non-trimmed) serendipity family developed by Arnold and Awanou [Math. Comp. 83(288) 2014] is analogous to the relation between the trimmed and (non-trimmed) polynomial finite element differential form families on simplicial meshes from finite element exterior calculus. We provide degrees of freedom in the general setting and prove that they are unisolvent for the trimmed serendipity spaces. The sequence of trimmed serendipity spaces with a fixed polynomial order r provides an explicit example of a system described by Christiansen and Gillette [ESAIM:M2AN 50(3) 2016], namely, a minimal compatible finite element system on squares or cubes containing order r-1 polynomial differential forms.Comment: Improved results, detailed comparison to prior and contemporary work, and further explanation of computational benefits have been added since the original version. This version has been accepted for publication in Mathematics of Computatio

Viking Orbiter completion mission and Viking Lander monitor mission

A brief history of the Viking Missions is presented. The status of the present Viking Orbiter and Landers for the period from February 1, 1980 through March 31, 1980 is discussed, with emphasis on data transmission abilities

Stable Mesh Decimation

Current mesh reduction techniques, while numerous, all primarily reduce mesh size by successive element deletion (e.g. edge collapses) with the goal of geometric and topological feature preservation. The choice of geometric error used to guide the reduction process is chosen independent of the function the end user aims to calculate, analyze, or adaptively refine. In this paper, we argue that such a decoupling of structure from function modeling is often unwise as small changes in geometry may cause large changes in the associated function. A stable approach to mesh decimation, therefore, ought to be guided primarily by an analysis of functional sensitivity, a property dependent on both the particular application and the equations used for computation (e.g. integrals, derivatives, or integral/partial differential equations). We present a methodology to elucidate the geometric sensitivity of functionals via two major functional discretization techniques: Galerkin finite element and discrete exterior calculus. A number of examples are given to illustrate the methodology and provide numerical examples to further substantiate our choices.Comment: 6 pages, to appear in proceedings of the SIAM-ACM Joint Conference on Geometric and Physical Modeling, 200

Serendipity and Tensor Product Affine Pyramid Finite Elements

Using the language of finite element exterior calculus, we define two families of $H^1$-conforming finite element spaces over pyramids with a parallelogram base. The first family has matching polynomial traces with tensor product elements on the base while the second has matching polynomial traces with serendipity elements on the base. The second family is new to the literature and provides a robust approach for linking between Lagrange elements on tetrahedra and serendipity elements on affinely-mapped cubes while preserving continuity and approximation properties. We define shape functions and degrees of freedom for each family and prove unisolvence and polynomial reproduction results.Comment: Accepted to SMAI Journal of Computational Mathematic

A Survey and Evaluation of High Energy Liquid Chemical Propulsion Systems

This report presents the results of a study to develop a procedure for evaluating liquid propellants in order (a) to select the most appropriate propellant (from among those under development) for each of several applications on each of the various missions in the NASA program, or (b) to select new propellants (from among those being proposed) for initiation or continuation of research and development. The analysis begins with a consideration of requirements--either for the specific application or for the various classes of applications. The known characteristics of the propellant or propellants to be evaluated are then put into a convenient form for evaluation. The next step is to determine whether or not there are requirements that simply cannot be met by the propellant. If the propellant passes this test, an optimum vehicle configuration using the propellant (and meeting all requirements) is estimated. (The configuration should be optimized with respect to the total resource consumption for all aspects of the mission, including R&D, production, logistics, and operation.) The total resource consumption for this configuration is then compared with that for similar configurations using other propellants (and meeting all requirements equally well). If all factors have been properly taken into account, this comparison of resource consumption will complete the evaluation. Such an evaluation may be performed several times, in increasing detail and with correspondingly increasing accuracy, as an R&D program proceeds, and the accuracy of the data as well as the cost of the next step in the program increase. The procedure is superior to those in common use in that it minimizes both the amount of analytical work and the number of points at which subjective value judgments are made

Fabrication of lightweight parabolic concentrators from a glass master Final report

Forming of optical lightweight solar concentrator on glass master - spray technique for resin substrate layer