Capacity matrix techniques
Alan J. Wallcraft · Spiral (Imperial College London) · 1981
if* A w t 2 • 3 (e) where A is the leading principal sub-matrix over A^ in 2,3(e) and where U is an extension operator from £)Jlnto Ah, U is particularly simple in this case but always has Just one C, w -tL, A-. boundary is called the 'capacity matrix' or 'capacitance matrix' (sometimes these terms are applied to the inverse of O* and methods based on 2»3(f) are known as Capacity Matrix Technioues (C»M»T»)» This example has been specially chosen for its simplicity but the derivation can eaually well be applied to any finite difference Helmholtz problem, A general derivation is given in the next section but examples of types of boundary condition discretisations are now presented for the simple region above.Note that the position of the internal boundary nodes* can be determined from the dimension of A) Neumann -5 Point, B -I •I B -I I (B-I)