An alternative approach for calculation of the first and higher order derivatives in the DRM-MD

Abstract

The partial derivatives (PDs) in the classical dual reciprocity method (DRM) are represented through PDs of the DRM approximation function. This approach is very flexible and easy to implement but may introduce singularities depending on the approximation function used, especially for higher order PDs. A new scheme is proposed that reduces the order of the PD of the DRM approximation function by one in respect to the one that appears in the classical DRM representation of PDs. This scheme can be applied for a case when the proportion of corner nodes is high, that is, in the DRM-MD approach. The new approach is tested and the results show improvements in the accuracy of at least one order of magnitude for the case when the derivatives of the approximation function introduce singularities.