Fast Evaluation Of Domain Integrals In Complex Geometrics
Free (open access)
A A Mammoli
Recent work has shown that the solution of nonlinear problems by cell-based domain integration is computationally more economical and more accurate than by meshless methods. However, discretization of complexthree-dimensional geometries is still problematic. In the case of multiply-connected domains, it is advantageous to evaluate the domain integral by subtraction of overlapping domains which are meshed more easily. The difficulty that arises when using this method is that in some domains the integrand is not suitable for numerical integration because of gradient discontinuities. A technique for constructing auxiliary functions with the required level of smoothness for the purpose of improving the accuracy of the numerical integration is presented. It is shown that the function reconstruction does not introduce discernible additional error. In addition, the technique can be used in two- and three-dimensional domains with equal ease, and is trivially parallelized.