Szechenyi Istvan College,

Dept. of Mathematics,

P.O.Box 701,

H-9007 Gyor, Hungary.

The multigrid method, as is well known, significantly reduces the computational cost of some traditional methods of partial differential equations, since the number of the necessary algebraic operations is proportional only to the first power of the number of unknowns introduced. In order to speed up the method further, this number should be minimized. This can be carried out e.g. by local refinements (either in finite difference or in finite element context). A more efficient technique is the use of the quadtree/octree grids for the discretization procedure. This approach seems to be much more general technique as it can be used not only to produce a nonuniform (but Cartesian) computational grid, but it appears also in quite different fields, e.g., in the multipole method. In our talk, we briefly introduce the QT-grid generation algorithm and some multigrid techniques in the QT context. Next, we show some applications to potential problems, shallow water equations as well as multipole, interpolation and boundary element techniques.