methods that only discretize the boundary.
A new numerical method for the rapid solution of Laplace's equa-The FDM (finite difference method) and FEM (finite eletion in exterior domains and in interior domains with complicated ment method) belong to the first category. The second boundaries is presented. The method is based on a formula first stated by J. J. Thomson and later refined by the authors. The mathe-category includes the MOM (method of moments), but it matical foundations presented allow for the solution of field probis typically characterized by the rapidly evolving BEM lems by means of geometric construction principles. Specifically, (boundary element method).
the method utilizes the concept of representing equipotential sur-While comparing the advantages and disadvantages of faces by polynomials for the rapid tracing of these surfaces; and these two categories of algorithms is beyond the scope of is, therefore, fundamentally different from previously known techniques which are based on discretizing the domain or the boundary this paper (the reader should refer to [22, 23] for that of the problem. For the class of problems characterized by irregular purpose). An important distinction to be noted between domains, the fastest available techniques have traditionally required the two categories is the inability of algorithms which disan O(M ΠΈ N) computations, where M is the number of points incretize the entire domain to treat efficiently exterior side the domain at which the solution is computed and N is the boundary value problems, such as the problems encounnumber of points used on the boundary. The new method requires an O(M) computations only and is, therefore, more advantageous tered in aerodynamic calculations, for example, as well in large scale calculations. This paper presents only the twoas interior problems which have complicated or irregular dimensional version of the geometric solution of Laplace's equaboundaries. For such types of problems, the boundary eletion.