Scalable Adaptive Multilevel Solvers for Multiphysics Problems

Xu, Jinchao

关键词: Adaptive finite element methods;    multilevel methods;    parallel methods;    multi-physics;    Magnetohydrodynamics;    complex fluid;   

DOI  :  10.2172/1164597
RP-ID  :  DOE-PSU-6903-F
PID  :  OSTI ID: 1164597

学科分类：数学（综合）

美国|英语

来源: SciTech Connect

【 摘 要 】

In this project, we investigated adaptive, parallel, and multilevel methods for numerical modeling of various real-world applications, including Magnetohydrodynamics (MHD), complex fluids, Electromagnetism, Navier-Stokes equations, and reservoir simulation. First, we have designed improved mathematical models and numerical discretizaitons for viscoelastic fluids and MHD. Second, we have derived new a posteriori error estimators and extended the applicability of adaptivity to various problems. Third, we have developed multilevel solvers for solving scalar partial differential equations (PDEs) as well as coupled systems of PDEs, especially on unstructured grids. Moreover, we have integrated the study between adaptive method and multilevel methods, and made significant efforts and advances in adaptive multilevel methods of the multi-physics problems.