Approximation by Complete and Incomplete Sets of Harmonic Polynomials.

摘要

An empirical investigation is reported concerning approximate solution of the two-dimensional Dirichlet problem in a finite region R by linear combinations of harmonic polynomials selected from either complete or incomplete sets. The negative results of an earlier similar investigation of torsion problems by Poritsky and Danforth are traced to the collocation method they employed. An alternative method involving least squares fitting at boundary points in excess of the number required for collocation is found to yield more reliable results. An algorithm is given for the formal generation of complete sets of harmonic polynomials (of given maximum degree) from corresponding incomplete sets. (Author)