A FAST ADAPTIVE WAVELET COLLOCATION ALGORITHM FOR MULTIDIMENSIONAL PDES

A fast multilevel wavelet collocation method for the solution of parti al differential equations in multiple dimensions is developed. The com putational cost of the algorithm is independent of the dimensionality of the problem and is O(N) where N is the total number of collocation points. The method can handle general boundary conditions. The multile vel structure of the algorithm provides a simple way to adapt computat ional refinements to local demands of the solution. High resolution co mputations are performed only in regions where singularities or sharp transitions occur. Numerical results demonstrate the ability of the me thod to resolve localized structures such as shocks, which change thei r location and steepness in space and time, The present results indica te that the method has clear advantages in comparison with well establ ished numerical algorithms. (C) 1997 Academic Press.