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Xuechuan Wang's blog

A Simple Local Variational Iteration Method and Related Algorithm for Nonlinear Science and Engineering

A very simple and efficient local variational iteration method for solving problems of nonlinear science is proposed in this paper. The analytical iteration formula of this method is derived first using a general form of first order nonlinear differential equations, followed by straightforward discretization using Chebyshev polynomials and collocation method. The resulting numerical algorithm is very concise and easy to use, only involving highly sparse matrix operations of addition and multiplication, and no inversion of the Jacobian in nonlinear problems.

Optimal-Feedback Accelerated Picard Iteration Method and a Fish-Scale Growing Method for Wide-Ranging and Multi-Revolution Perturbed Lambert's Problems

Wide-ranging and multiple-revolution perturbed Lambert’s problems are building blocks for practical missions such as development of cislunar space, interplanetary navigation, orbital rendezvous, etc. However, it is of a great challenge to solve these problems both accurately and efficiently, considering the long transfer time and the complexity of high-fidelity modeling of space environment. For that, a methodology combining Optimal-Feedback Accelerated Picard Iteration methods and Fish-Scale Growing Method is demonstrated.

Bifurcation & Chaos in Nonlinear Structural Dynamics: Novel & Highly Efficient Optimal-Feedback Accelerated Picard Iteration Algorithms

A new class of algorithms for solving nonlinear structural dynamical problems are derived in the present paper, as being based on optimal-feedback-accelerated Picard iteration, wherein the solution vectors for the displacements and velocities at any time in a finitely large time interval are corrected by a weighted (with a matrix) integral of the error. We present 3 approximations to solve the Euler-Lagrange equations for the optimal weighting functions; thus we present 3 algorithms denoted as Optimal-Feedback-Accelerated Picard Iteration (OFAPI) algorithms-1, 2, 3.

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: .

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  ( ).  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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