The toolbox PHG and its applications

Abstract

PHG (parallel hierarchical grid) is an open source toolbox, developed by the State Key Laboratory of Scientific and Engineering Computing at the Chinese Academy of Sciences, for writing parallel adaptive finite element programs. Among the many adaptive finite element toolboxes and software packages, PHG is characterized by the following features: 1) The ability to provide the most recent vertex bisection-based parallel local mesh refinement of unstructured conforming tetrahedral meshes. 2) It supports $h$-$p$ adaptive finite element computations. 3) It incorporates massively parallel with transparent dynamical load balancing. 4) It provides flexible preconditioning and solutions of large sparse linear systems of equations. In this paper, the main modules and some core algorithms of PHG are described, and some parallel applications based on PHG, including the computation of iron-loss for large power transformers, simulation of ionic transport in ion channels, parasitic extraction of interconnects in integrated circuits, ice sheet simulation, and spectral element simulation of elastic waves with PML, are introduced.