Solution of Boundary-Value Problems in Frequency Domain by a Dual Grid Second-Order FD Technique

A second-order finite difference technique suitable to unstructured triangular grids is proposed for the solution of boundary-value problems in the frequency domain. The second-order behavior is achieved by proper weighting of two first-order equations, derived from a couple of Delaunay-Dirichlet grids, without any resorting to quadratic shape functions as usually done in finite/edge element methods. Numerical results have confirmed the improvement in error reduction and convergence rate in comparison to conventional first-order solution. This improvement concerns in particular the integral quantities that can be evaluated by the second-order field solution.