GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
An upwind differencing scheme for the equations of ideal magnetohydrodynamics
Journal of Computational Physics
A grid generation and flow solution method for the Euler equations on unstructured grids
Journal of Computational Physics
An implicit scheme for nonideal magnetohydrodynamics
Journal of Computational Physics
Efficient management of parallelism in object-oriented numerical software libraries
Modern software tools for scientific computing
A solution-adaptive upwind scheme for ideal magnetohydrodynamics
Journal of Computational Physics
Hyperbolic divergence cleaning for the MHD equations
Journal of Computational Physics
Adifor 2.0: Automatic Differentiation of Fortran 77 Programs
IEEE Computational Science & Engineering
Parallel Multilevel Graph Partitioning
IPPS '96 Proceedings of the 10th International Parallel Processing Symposium
Parallel Dense Gauss-Seidel Algorithm on Many-Core Processors
HPCC '09 Proceedings of the 2009 11th IEEE International Conference on High Performance Computing and Communications
Very high order PNPM schemes on unstructured meshes for the resistive relativistic MHD equations
Journal of Computational Physics
E-CUSP scheme for the equations of ideal magnetohydrodynamics with high order WENO Scheme
Journal of Computational Physics
Hi-index | 31.45 |
The resistive magneto-hydrodynamics (MHD) governing equations represent eight conservation equations for the evolution of density, momentum, energy and induced magnetic fields in an electrically conducting fluid, typically a plasma. A matrix free implicit method is developed to solve the conservation equations within the framework of an unstructured grid finite volume formulation. The analytic form of the convective flux Jacobian is derived on a general unstructured mesh and used in a Lower-Upper Symmetric Gauss Seidel (LU-SGS) technique developed as part of the implicit scheme. A grid coloring technique is also developed to create data parallelism in the algorithm. The computational efficiency of the matrix free method is compared with two common approaches: a global matrix solve technique that uses the GMRES (Generalized minimum residual) algorithm and an explicit method. The matrix-free method is observed to be overall computationally faster than the global matrix solve method and demonstrates excellent parallel scaling on multiple cores. The computational effort and memory requirements for the matrix free approach is comparable to the explicit approach which in turn is much lower than the global solve implicit approach. Both the matrix free and global solve implicit techniques exhibit superior steady state convergence compared to the explicit method.