Structural sensitivity analysis: Methods, applications, and needs

Some innovative techniques applicable to sensitivity analysis of discretized structural systems are reviewed. These techniques include a finite-difference step-size selection algorithm, a method for derivatives of iterative solutions, a Green's function technique for derivatives of transient response, a simultaneous calculation of temperatures and their derivatives, derivatives with respect to shape, and derivatives of optimum designs with respect to problem parameters. Computerized implementations of sensitivity analysis and applications of sensitivity derivatives are also discussed. Finally, some of the critical needs in the structural sensitivity area are indicated along with Langley plans for dealing with some of these needs

Finite element solution techniques for large-scale problems in computational fluid dynamics

Element-by-element approximate factorization, implicit-explicit and adaptive implicit-explicit approximation procedures are presented for the finite-element formulations of large-scale fluid dynamics problems. The element-by-element approximation scheme totally eliminates the need for formation, storage and inversion of large global matrices. Implicit-explicit schemes, which are approximations to implicit schemes, substantially reduce the computational burden associated with large global matrices. In the adaptive implicit-explicit scheme, the implicit elements are selected dynamically based on element level stability and accuracy considerations. This scheme provides implicit refinement where it is needed. The methods are applied to various problems governed by the convection-diffusion and incompressible Navier-Stokes equations. In all cases studied, the results obtained are indistinguishable from those obtained by the implicit formulations

A Solution of Fractional Laplace's Equation by Modified Separation of Variables

This paper applies the Modified separation of variables method (MSV) suggested by Pishkoo and Darus towards obtaining a solution for fractional Laplace's equation. The closed form expression for potential function is formulated in terms of Meijer's G-functions (MGFs). Moreover, the relationship between fractional dimension and parameters of Meijer’s G-function for spherical Laplacian in R, for radial functions is derived

Wave propagation and earth satellite radio emission studies

Radio propagation studies of the ionosphere using satellite radio beacons are described. The ionosphere is known as a dispersive, inhomogeneous, irregular and sometimes even nonlinear medium. After traversing through the ionosphere the radio signal bears signatures of these characteristics. A study of these signatures will be helpful in two areas: (1) It will assist in learning the behavior of the medium, in this case the ionosphere. (2) It will provide information of the kind of signal characteristics and statistics to be expected for communication and navigational satellite systems that use the similar geometry

Blowup in diffusion equations: A survey

AbstractThis paper deals with quasilinear reaction-diffusion equations for which a solution local in time exists. If the solution ceases to exist for some finite time, we say that it blows up. In contrast to linear equations blowup can occur even if the data are smooth and well-defined for all times. Depending on the equation either the solution or some of its derivatives become singular. We shall concentrate on those cases where the solution becomes unbounded in finite time. This can occur in quasilinear equations if the heat source is strong enough. There exist many theoretical studies on the question on the occurrence of blowup. In this paper we shall recount some of the most interesting criteria and most important methods for analyzing blowup. The asymptotic behavior of solutions near their singularities is only completely understood in the special case where the source is a power. A better knowledge would be useful also for their numerical treatment. Thus, not surprisingly, the numerical analysis of this type of problems is still at a rather early stage. The goal of this paper is to collect some of the known results and algorithms and to direct the attention to some open problems

The bulk-surface finite element method for reaction-diffusion systems on stationary volumes

In this work we present the bulk-surface finite element method (BSFEM) for solving coupled systems of bulk-surface reaction-diffusion equations (BSRDEs) on stationary volumes. Such systems of coupled bulk-surface partial differential equations arise naturally in biological applications and fluid dynamics, for example, in modelling of cellular dynamics in cell motility and transport and diffusion of surfactants in two phase flows. In this proposed framework, we define the surface triangulation as a collection of the faces of the elements of the bulk triangulation whose vertices lie on the surface. This implies that the surface triangulation is the trace of the bulk triangulation. As a result, we construct two finite element spaces for the interior and surface respectively. To discretise in space we use piecewise bilinear elements and the implicit second order fractional-step $\theta$ scheme is employed to discretise in time. Furthermore, we use the Newton method to treat the nonlinearities. The BSFEM applied to a coupled system of BSRDEs reveals interesting patterning behaviour. For a set of appropriate model parameter values, the surface reaction-diffusion system is not able to generate patterns everywhere in the bulk except for a small region close to the surface while the bulk reaction-diffusion system is able to induce patterning almost everywhere. Numerical experiments are presented to reveal such patterning processes associated with reaction-diffusion theory