NEPAL-an N/sup 1.5/ algorithm for solving the volume integral equation

The authors present an algorithm called the nested equivalence principle algorithm (NEPAL) to solve volume integral equations with computational complexity of N/sup 1.5/ in two dimensions and N/sup 2/ in three dimensions. The principal idea of this approach is to nest one algorithm within another so that a smaller problem is solved before a larger one. The size of the problem increases by a factor of 2/sup n/ at each stage where n is the dimension of the problem. In this manner, an N unknown problem is solved in log/sub n/ N steps. The authors have implemented NEPAL to solve volume integral equations and compared the results with the direct solution of the volume integral equations by the method of moments. The results are in good agreement for both E/sub z/ and H/sub z/ polarized waves. The authors have also studied the growth of computer time with the number of unknowns in the problem and found that NEPAL is very competitive with RATMA.<>