A novel method for boundary constrained tetrahedral mesh generation is proposed based on Advancing Front Technique (AFT) and conforming Delaunay triangulation. Given a triangulated surface mesh, AFT is firstly applied to mesh several layers of elements adjacent to the boundary. The rest of the domain is then meshed by the conforming Delaunay triangulation. The non-conformal interface between two parts of meshes are adjusted. Mesh refinement and mesh optimization are then preformed to obtain a more reasonable-sized mesh with better quality. Robustness and quality of the proposed method is shown. Convergence proof of each stage as well as the whole algorithm is provided. Various numerical examples are included as well as the quality of the meshes.

The numerical simulation of the driving beams in a heavy ion fusion power plant is a challenging task, and simulation of the power plant as a whole, or even of the driver, is not yet possible. Despite the rapid progress in computer power, past and anticipated, one must consider the use of the most advanced numerical techniques, if we are to reach our goal expeditiously. One of the difficulties of these simulations resides in the disparity of scales, in time and in space, which must be resolved. When these disparities are in distinctive zones of the simulation region, a method which has proven to be effective in other areas (e.g., fluid dynamics simulations) is the mesh refinement technique. We discuss the challenges posed by the implementation of this technique into plasma simulations (due to the presence of particles and electromagnetic waves). We present the prospects for and projected benefits of its application to heavy ion fusion, in particular to the simulation of the ion source and the final beam propagation in the chamber. A collaboration project is under way at Lawrence Berkeley National Laboratory between the Applied Numerical Algorithms Group (ANAG) and the Heavy Ion Fusion group to couple the adaptive mesh refinement library CHOMBO developed by the ANAG group to the particle-in-cell accelerator code WARP developed by the Heavy Ion Fusion–Virtual National Laboratory. We describe our progress and present our initial findings.

We study a finite volume method, used to approximate the solution of the linear two dimensional convection diffusion equation, with mixed Dirichlet and Neumann boundary conditions, on Cartesian meshes refined by an automatic technique (which leads to meshes with hanging nodes). We propose an analysis through a discrete variational approach, in a discrete H 1 finite volume space. We actually prove the convergence of the scheme in a discrete H 1 norm, with an error estimate of order O(h) (on meshes of size h).