McCormick 9521625 The principal investigator and his colleagues organize the seventh Copper Mountain conference on multigrid methods. Numerical methods for solving a differential equation usually begin by imposing a grid on the region where the equation holds. From the differential equation, algebraic equations are then developed; their solution represents the qolution of the differential equation. The accuracy of the approximate solution commonly is measured by the fineness of the grid. Multigrid methods are numerical methods for solving partial differential equations that systematically exploit the relationship between approximate solutions on different grids to arrive at a solution whose accuracy is consistent with the finest grid but for considerably less work. The methods are often dramatically more efficient than others. Research in the past dozen years has extended the methods to a broad range of problems of considerable practical import in engineerine, manufacturing, materials, physics, and fluid dynamics.