Mesh generation using differential methods

Jeff Shragge

jeff@sep.stanford.edu

ABSTRACT

This paper examines a differential gridding method for generating computational meshes appropriate for solving partial differential equations. Differential methods pose mesh generation as an elliptical boundary value problem within a framework of differential geometry. Generalized Laplacian operators are used to propagate the known coordinate values on the boundary points into the interior in a smooth manner. The methodology allows for the specification of monitor functions that provide mesh regularization and prevent grid clustering. Examples are provided for two seismic imaging applications: wave-equation Green's function generation and wave-equation migration from topography. In both cases, the resulting regularized meshes have minimal convexity and are conformal to the the prescribed boundaries.