Dual Reciprocity Method with Multigrid Technique by C. Gaspar Szechenyi Istvan College, Department of Mathematics P.O.Box 701, H--9007 Gyor, Hungary e-mail: csgaspar@d7.szif.hu Abstract The Dual Reciprocity Method is a well known and widely used tool to generalize the Boundary Integral Equation Method to more complex problems (even to nonlinear problems). Its essential advantage is that both the discretization of the domain and the evaluation of domain integrals can be avoided by converting these integrals to a sum of boundary integrals. Thus, the main advantages of the Boundary Integral Equation Methods are preserved. However, the Dual Reciprocity Method is based on a special interpolation of irregularly spaced data, which has serious drawbacks from a numerical point of view (it produces large, dense and ill-conditioned system of algebraic equations) and the usual fast methods such as multigrid tools seem to be inapplicable. We present a method based on a biharmonic interpolation, which allows the use of highly efficient multigrid techniques. Though this interpolation, strictly speaking, leads to a domain type solution procedure, this subproblem can be solved completely independently of the original boundary integral equations, without using and discretizing its domain. The resulting method can be regarded as a combination of the dual and the multiple reciprocity methods. However, the solution of dense and ill- conditioned systems of equations is thus avoided, and also the memory requirement is significantly reduced.