Topic:
Above: Comparison of several iterative solvers for multiscale simulations of a silicon diode. The implicit solvers are faster than standard explicit (EX) or implicit-explicit (IMEX) schemes. The reduced-order preconditioner gives another 50% speedup.
The Science
Researchers at ORNL have developed new solvers for implicit time discretization of a simplified Boltzmann-Poisson system.
The algorithm relies on:
- A memory-efficient Krylov solver
- A characteristic sweeping algorithm for nonlinear phase space advection
- Reduced-order fluid models for preconditioning in asymptotic regimes.
The Impact
- Kinetic equations are important for simulating charged-particle transport in non-equilibrium regimes, which are relevant to nanoscale electronic devices, as well as fusion plasmas in tokamaks.
- For extreme multiscale problems, the new approach yields order-of magnitude improvements in efficiency when compared to more conventional time discretization techniques.
PI(s)/Facility Lead(s): Cory Hauck
Publication: M, P. Laiu, Z. Chen, and C. D. Hauck, “A fast implicit solver for semiconductor models in one space dimension”, submitted to Journal of Computational Physics, arXiv preprint arXiv:1906.04174
CK Garrett, CD Hauck, “A Fast Solver for Implicit Integration of the Vlasov-Poisson System in the Eulerian Framework”, SIAM Journal on Scientific Computing 40 (2), B483-B506
Funding: DOE ASCR
