Potential integrals on triangles
Provides a robust computational tool for engineers and scientists solving potential problems in electromagnetics and fluid dynamics, though the approach is incremental.
The paper presents exact, general formulae for evaluating potential integrals on planar triangular elements using polar coordinate decomposition, handling principal values and finite parts. The method is accurate and convergent, as demonstrated on a unit cube example.
The problem of evaluating potential integrals on planar triangular elements has been addressed using a polar coordinate decomposition. The resulting formulae are general, exact, easily implemented, and have only one special case, that of a field point lying in the plane of the element. Results are presented for the evaluation of the potential and its gradients, where the integrals must be treated as principal values or finite parts, for elements with constant and linearly varying source terms. These results are tested by application to a single triangular element to the evaluation of the potential gradient outside the unit cube. In both cases, the method is shown to be accurate and convergent.