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Xuechuan Wang's blog

Feedback-Accelerated Picard Iteration for Orbit Propagation and Lambert’s Problem

This paper presents a new Feedback-Accelerated Picard Iteration method for solving long-term orbit propagation problems and perturbed Lambert’s problems. This method is developed by combining the collocation method and the variational iteration method over large-time-steps. The resulting iterative formulae are explicitly derived so that they can be directly adopted to solve problems in orbital mechanics. Several typical orbit regimes incorporating high-order gravity and air drag force are used to demonstrate the application of the proposed method in orbit propagation.

A novel class of highly efficient and accurate time-integrators in nonlinear computational mechanics

A new class of time-integrators is presented for strongly nonlinear dynamical systems. These algorithms are far superior to the currently common time integrators in computational efficiency and accuracy. These three algorithms are based on a local variational iteration method applied over a finite interval of time. By using Chebyshev polynomials as trial functions and Dirac–Delta functions as the test functions over the finite time interval, the three algorithms are developed into three different discrete time-integrators through the collocation method.

Post-doctoral positions in the Center for Advanced Research in the Engineering Sciences, and the Institute for Materials, Manufacturing, and Sustainment at Texas Tech, Lubbock, TX

Post-doctoral research fellow positions are available immediately in the Labs of Professor Satya N. Atluri at Texas Tech University. Those possessing PhDs in the area of Data Fusion, Kalman Filtering, and Particle Filter Theories are sought. Qualified candidates from around the globe are encouraged to contact Professor Atluri directly at: snatluri.ttu@gmail.com .

Post-doctoral positions in the Center for Advanced Research in the Engineering Sciences, and the Institute for Materials, Manufacturing, and Sustainment at Texas Tech, Lubbock, TX

I belong to the Lab of Professor Satya N Atluri  (http://www.depts.ttu.edu/coe/CARES/atluri.php ).  Professor Atluri asked me to advertise in Imechanica that he will have 5 or 6 Post-doctoral positions in his labs, the Center for Advanced Research in the Engineering Sciences, and the Institute for Materials, Manufacturing, and

A Unification of the Concepts of Variational Iteration, Adomian Decomposition and Picard Iteration method; and a Local Variational Iteration Method

This paper compares the variational iteration method (VIM), the Adomian decomposition method (ADM) and the Picard iteration method (PIM) for solving a system of first order nonlinear ordinary differential equations (ODEs). A unification of the concepts underlying these three methods is attempted by considering a very general iterative algorithm for VIM. It is found that all the three methods can be regarded as special cases of using a very general matrix of Lagrange multipliers in the iterative algorithm of VIM.

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