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For the electrically large problems, the discrete unknowns of surface integral equation are very large, resulting in the matrix condition is relatively poor. The high order hierarchical basis functions are utilized to reduce the discrete unknowns, thereby reducing the memory consumption and computation time. Meanwhile, modified multilevel compressed block decomposition (MMLCBD) is applied to accelerate the matrix-vector multiplication operations, which utilizes novel technique to improve the solving efficiency by combining a less accurate truncating threshold in MLCBD with a rapid and cheap iterative refinement process. Combining the high order hierarchical basis functions with MMLCBD can make good use of their respective advantages to analyze the large-scale electromagnetic problems efficiently. The numerical results demonstrate that the proposed method is much more efficient than conventional MLCBD for analyzing the large-scale electromagnetic problems. [ABSTRACT FROM AUTHOR]

Most conventional motion planning algorithms that are based on the model of the environment cannot perform well when dealing with the navigation problem for real-world mobile robots where the environment is unknown and can change dynamically. In this paper, a layered goal-oriented motion planning strategy using fuzzy logic is developed for a mobile robot navigating in an unknown environment The information about the global goal and the long-range sensory data are used by the first layer of the planner to produce an intermediate goal, referred to as the way-point, that gives a favorable direction in terms of seeking the goal within the detected area. The second layer of the planner takes this way-point as a subgoal and, using short-range sensory data, guides the robot to reach the subgoal while avoiding collisions. The resulting path, connecting an initial point to a goal position, is similar to the path produced by the visibility graph motion planning method, but in this approach there is no assumption about the environment. Due to its simplicity and capability for real-time implementation, fuzzy logic has been used for the proposed motion planning strategy. The resulting navigation system is implemented on a real mobile robot, Koala, and tested in various environments. Experimental results are presented which demonstrate the effectiveness of the proposed fuzzy navigation system. [ABSTRACT FROM AUTHOR]