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In the recent past, the power of computing hardware has been growing exponentially, giving rise to many new possibilities in the field of numerical mathematics. Yet the vast majority of numerical algorithms today is still largely based on the same pointwise or linear algebra (matrix) techniques developed 50-100 years ago. Differential algebra (DA) provides a method to easily extend these linearization techniques and allows the implementation of efficient arbitrary order methods. The resulting techniques perform much faster and yield more accurate results in many mathematical, physical as well as engineering applications.
ESA has supported the implementation of a DA-based software tool for the efficient, nonlinear propagation of uncertainties in space dynamics. The entire software is divided in two main parts: the Differential Algebra Computational Engine (DACE) and the Differential Algebra Space Toolbox (DAST). DACE provides the user with the tools to perform all the basic DA operations by replacing the operations between single numbers by suitably chosen operations on polynomials. The same sequence of operations coded for floating point numbers can thusly be evaluated using this new meaning of each operator almost without changes to the code.
DAST is built on DACE and provides all the routines to perform uncertainty propagation in different space dynamics scenarios. Furthermore, the software allows the user to propagate uncertainties through different techniques (from classical Monte Carlo to range estimation using polynomial bounders or classical linear covariance propagation) Thanks to the use of DA techniques, DAST has been shown to be orders of magnitude more efficient than traditional Monte Carlo methods.
The objectives of the workshop are:
- To bring together engineers and researchers from the industry, research institutes, universities, and space agencies working on uncertainty propagation in space dynamics
- To introduce differential algebra, DACE, and DAST to the community and to show the potentials with respect to classical approaches for uncertainty propagation
- To gather the feedback and to promote the definition of common plans for software developments