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A derivative-based Uncertainty Quantification (UQ) method called HYPAD-UQ that utilizes sensitivities from a computational model was developed to approximate the statistical moments and Sobol' indices of the model output. HYPercomplex Automatic Differentiation (HYPAD) was used as a means to obtain accurate high-order partial derivatives from computational models such as finite element analyses. These sensitivities are used to construct a surrogate model of the output using a Taylor series expansion and subsequently used to estimate statistical moments (mean, variance, skewness, and kurtosis) and Sobol' indices using algebraic expansions. The uncertainty in a transient linear heat transfer analysis was quantified with HYPAD-UQ using first-order through seventh-order partial derivatives with respect to seven random variables encompassing material properties, geometry, and boundary conditions. Random sampling of the analytical solution and the regression-based stochastic perturbation finite element method were also conducted to compare accuracy and computational cost. The results indicate that HYPAD-UQ has superior accuracy for the same computational effort compared to the regression-based stochastic perturbation finite element method. Sensitivities calculated with HYPAD can allow higher-order Taylor series expansions to be an effective and practical UQ method.

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Currently, 3D rendering is accessible within Web browsers through open standards such as WebGL, X3D, and X3DOM. At the same time, there is wealth of mature desktop software which comprises algorithms, data structures, user interfaces, databases, etc. It is a challenge to reuse such desktop software using the Web visualization resources. In response to this challenge, this article presents a novel framework, called ReWeb3D, which minimizes the redevelopment for migration of existing 3D applications to the Web. The redeployed application runs on a Web server. ReWeb3D captures low-level graphic calls including geometry, texture, and shader programs. The captured content is then served as a WebGL-enabled web page that conveys full interactivity to the client. By splitting the graphics pipeline between client and server, the workload can be balanced, and high-level implementation details and 3D content are hidden. The feasibility of ReWeb3D has been tested with applications which use OpenSceneGraph as rendering platform. The approach shows good results for applications with large data sets (e.g. geodata), but is less suited for applications intensive in animations (e.g. games).