SUMMARYThe dual reciprocity boundary element method traditionally uses the linear radial basis function r for interpolation. Recently, however, the use of the r function has been questioned both in relation to accuracy and in relation to the number and position of internal nodes required to obtain satisfactory solutions. Much research has been done in an attempt to ®x criteria for choosing which approximation function should be used. One of the alternatives recently suggested is the augmented thin plate spline function, which consists of a thin plate spline function, r 2 logr, augmented with the ®rst three terms of a Pascal triangle expansion. In this paper families of similar functions are obtained by augmenting radial basis functions with appropriate global expansions: these functions will be called hybrid approximate functions. It will be shown that using an appropriate hybrid function accurate results can be obtained for many body forces or pseudo body forces in elasticity without the need for internal nodes.
The placement of source points constitutes a key issue for the method of the fundamental solutions. In particular, for problems with singularities of any kind the determination of the optimal placement of source points becomes relevant, as no linear combination of arbitrarily located source points can guarantee a reasonable approximation to the solution. This paper investigates the use of a ''Simulated Annealing'' algorithm in the optimal placement of source points in singular problems. The algorithm is essentially an iterative random search with adaptive moves along the coordinate directions. It permits uphill moves under the control of a probabilistic criterion, thus tending to avoid the first local minima encountered. The proposed methodology is employed with a variety of test problems. Results are compared to those of an analytical optimisation routine and their relatively merits and disadvantages discussed. Simulated annealing is shown to be an attractive option for the optimisation of singular problems, with a high rate of success, and able to solve problems for which analytical optimisation routines fail.
SUMMARYThe method of fundamental solutions (MFS) is proposed for the analysis of microstrip patch antennas of arbitrary shape. The MFS consists mainly in approximating the solution of a problem by a linear combination of known fundamental solutions associated with source points located outside the domain. The implementation of the MFS is simple and computationally efficient. Simulation results are obtained for rectangular, circular and triangular microstrip patch antennas. The resonance frequency and input impedance results are in good agreement with those published in the literature. Two prototypes have been fabricated and tested. Good agreement has been obtained between the MFS simulations and the experimental results.
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