Contribution on the Source Field Calculation through the Biot-Savart Equation Using Curvilinear Elements and an Adaptive Process

The analytical solution of the Biot-Savart equation can be complex in some cases, and its numerical integration is commonly more appropriate. In this paper, it is integrated using the GaussLegendre method through 1, 2 and 3-D domains, using first and second-order (curvilinear) isoparametric mapping. In order to verify the gain of accuracy with second-order elements, the results obtained are compared with analytical cases and with the Finite Element Method. Then this paper presents an adaptive method which profits from the accuracy along those elements with higher energy values, by reducing the number of Gauss points along the elements with lower energy. This approach reduces the total number of Gauss points evaluated during the integration process and provides a possibility to choose an interesting trade-off between simulation time and accuracy.