Towards a Scalable Fully-Implicit Fully-coupled Resistive MHD Formulation with Stabilized FE Methods
This paper presents an initial study that is intended to explore the development of a scalable fully-implicit stabilized unstructured finite element (FE) capability for low-Mach-number resistive MHD. The discussion considers the development of the stabilized FE formulation and the underlying fully-coupled preconditioned Newton-Krylov nonlinear iterative solver. To enable robust, scalable and efficient solution of the large-scale sparse linear systems generated by the Newton linearization, fully-coupled algebraic multilevel preconditioners are employed. Verification results demonstrate the expected order-of-acuracy for the stabilized FE discretization of a 2D vector potential form for the steady and transient solution of the resistive MHD system. In addition, this study puts forth a set of challenging prototype problems that include the solution of an MHD Faraday conduction pump, a hydromagnetic Rayleigh-Bernard linear stability calculation, and a magnetic island coalescence problem. Initial results that explore the scaling of the solution methods are presented on up to 4096 processors for problems with up to 64M unknowns on a CrayXT3/4. Additionally, a large-scale proof-of-capability calculation for 1 billion unknowns for the MHD Faraday pump problem on 24,000 cores is presented.
- Research Organization:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 985484
- Report Number(s):
- LLNL-JRNL-413828; JCTPAH; TRN: US201016%%2019
- Journal Information:
- Journal of Computational Physics, Vol. 229, Issue 20; ISSN 0021-9991
- Country of Publication:
- United States
- Language:
- English
Similar Records
Initial performance of fully-coupled AMG and approximate block factorization preconditioners for solution of implicit FE resistive MHD.
Scalable implicit incompressible resistive MHD with stabilized FE and fully-coupled Newton–Krylov-AMG