Numerical Geometry Grid Generation and Scientific Computing : Proceedings of the 9th International Conference NUMGRID 2018 Voronoi 150 Celebrating the 150th Anniversary of G.F. Voronoi Moscow Russia December 2018 The focus of these conference proceedings is on research development and applications in the fields of numerical geometry scientific computing and numerical simulation particularly in mesh generation and related problems. In addition this year’s special focus is on Voronoi diagrams and their applications celebrating the 150th birthday of G.F. Voronoi. In terms of content the book strikes a balance between engineering algorithms and mathematical foundations. It presents an overview of recent advances in numerical geometry grid generation and adaptation in terms of mathematical foundations algorithm and software development and applications. The specific topics covered include: quasi conformal and quasi isometric mappings hyperelastic deformations multidimensional generalisations of the equidistribution principle discrete differential geometry spatial and metric encodings Voronoi Delaunay theory for tilings and partitions duality in mathematical programming and numerical geometry mesh based optimisation and optimal control methods. Further aspects examined include iterative solvers for variational problems and algorithm and software development. The applications of the methods discussed are multidisciplinary and include problems from mathematics physics biology chemistry material science and engineering Voronoi Meshing: Theory Algorithms and Applications Mesh Optimization Mesh Based Methods of Optimization and Optimal Control Numerical Geometry and Simulation Mesh Generation Software