A WAVELET OPTIMIZED ADAPTIVE MULTIDOMAIN METHOD

The formulation and implementation of wavelet based methods for the so lution of multi-dimensional partial differential equations in complex geometries is discussed. Utilizing the close connection between Daubec hies wavelets and finite difference methods on arbitrary grids, we for mulate a wavelet based collocation method, well suited for dealing wit h general boundary conditions and nonlinearities. To circumvent proble ms associated with completely arbitary grids and complex geometries we propose to use a multi-domain formulation in which to solve the parti al differential equation, with the ability to adapt the grid as well a s the order of the scheme within each subdomain. Besides supplying the required geometric flexibility, the multidomain formulation also prov ides a very natural load-balanced data-decomposition, suitable for par allel environments. The performance of the overall scheme is illustrat ed by solving two dimensional hyperbolic problems. (C) 1998 Academic P ress.