A method for incorporating multi-resolution capabilities within pre-existingglobal 3-D spherical mantle convection codes is presented. The method, whichwe term "geometric multigrid refinement", is based upon the application ofa multigrid solver on non-uniform, structured grids and allows for theincorporation of local high-resolution grids within global models. Validationtests demonstrate that the method is accurate and robust, with highlyefficient solutions to large-scale non-uniform problems obtained.Significantly, the scheme is conceptually simple and straightforward toimplement, negating the need to reformulate and restructure large sections ofcode. Consequently, although more advanced techniques are under developmentat the frontiers of mesh refinement and solver technology research, thetechnique presented is capable of extending the lifetime and applicability ofpre-existing global mantle convection codes.
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