  The multigrid algorithm is a multilevel approach to accelerate the numerical
solution of discretized differential equations in physical problems involving
long-range interactions. Multiresolution analysis of wavelet theory provides an
efficient representation of functions which exhibit localized bursts of short
length-scale behavior. Applications such as computing the electrostatic field
in and around a molecule should benefit from both approaches. In this work, we
demonstrate how a novel interpolating wavelet transform, which in itself is the
synthesis of finite element analysis and wavelet theory, may be used as the
mathematical bridge to connect the two approaches. The result is a specialized
multigrid algorithm which may be applied to problems expressed in wavelet
bases. With this approach, interpolation and restriction operators and grids
for the multigrid algorithm are predetermined by an interpolating
multiresolution analysis. We will present the new method and contrast its
efficiency with standard wavelet and multigrid approaches.
