Geometric Multigrid Methods on Triangular Grids: Application to Semi-structured Meshes

This book deals with the efficient solution of the large sparse systems of equations arising from the discretization of partial differential equations (PDEs) which mathematically model problems encountered in many applications to physics and engineering. This issue is one of the most important aspects in the numerical solution of many problems, and therefore it deserves important attention. With this purpose, our primary interest here is to design efficient finite element geometric multigrid methods on semi-structured triangular grids. To this end, a local Fourier analysis (LFA) on triangular grids is presented in this book, resulting in a very useful tool to choose suitable components of multigrid methods. The practical utility of this approach is illustrated with some examples of scalar and vector problems.