HIGHER NUMERICAL EFFICIENCY AND ACCURACY THROUGH MESHLESS EVALUATION OF DOMAIN INTEGRALS

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The main advantage of the boundary element methods is that in most linear problems accurate numerical analysis can be performed through mesh division of the boundary only. However, even for the linear problems of inhomogeneous materials where the property changes as a function of coordinates or of the inhomogeneous initial conditions, domain integrals inevitably arise in the boundary integral equation to be solved. In these cases, we have to evaluate the domain integrals using the cell or element division of the domain. This would lead to reducing attraction of the boundary element method. In other cases an "approximate" fundamental solution is employed for the formulation, we have to discretize the domain and include the nodal quantities in the domain as the final system of equations. Therefore, it has been one of the main subjects of the BEM how to effectively evaluate such domain integrals.In boundary element research so far, there are several methods available in the literature : The boundary-domain element or Green element method, multi-reciprocity or dual reciprocity method, the analog equation method, and so on. Among them, the dual reciprocity method seems to be very attractive to evaluate approximately the domain integrals by using rather simple functions.This paper is concerned with numerical investigations of the dual reciprocity method for some typical problems frequently encountered in practice. First, we had been collecting a wide range of approximate functions which can be used for the dual reciprocity method. Then, we had applied some selected functions to the problem solving and checked the numerical properties of solution procedure based on the dual reciprocity principle. Through these investigations we can develop very good computer codes for accurate, efficient analysis of the problems. A series of the academic papers on the topics have been submitted to international journals, and most of them have been already published.