Improving the accuracy of the boundary element method by the use of second-order interpolation functions

The boundary element method (BEM) is a widely used method to solve biomedic al electromagnetic volume conduction problems. The commonly used formulatio n of this method uses constant interpolation functions for the potential an d flat triangular surface elements. Linear interpolation for the potential on a flat triangular mesh turned out to yield a better accuracy. In this pa per, we introduce quadratic interpolation functions for the potential and q uadratically curved surface elements, resulting from second-order spatial i nterpolation. Theoretically, this results in an accuracy that is inversely proportional to the third power of element size, The method is tested on a four concentric sphere geometry, representative for electroencephalogram mo deling, and compared to previous solutions of this problem in literature. I n addition, a cylindrical test configuration is used, We conclude that the use of quadratic interpolation functions for the potential and of quadratic ally curved surface elements in BER;I results in a significant increase in accuracy and in some cases even a reduction of the computation time with th e same number of nodes involved in the calculations.