TY - GEN
T1 - A Monte Carlo synthetic acceleration method for the non-linear, time-dependent diffusion equation
AU - Evans, T. M.
AU - Mosher, S. W.
PY - 2009
Y1 - 2009
N2 - We present a Monte Carlo synthetic-acceleration method for solving the time-dependent, nonlinear, equilibrium diffusion equation in three-dimensions. The new scheme uses the adjoint Monte Carlo method as a relaxation step that accelerates standard Jacobi iteration. Results show that this method is 40% faster than regular Jacobi iteration and is competitive with Jacobi-preconditioned Conjugate Gradient methods. Furthermore, the new method is not limited to symmetric, positive-definite systems, and therefore, it can be used for non-symmetric systems. Such systems arise in fully coupled, nonlinear-consistent (Newton) solvers.
AB - We present a Monte Carlo synthetic-acceleration method for solving the time-dependent, nonlinear, equilibrium diffusion equation in three-dimensions. The new scheme uses the adjoint Monte Carlo method as a relaxation step that accelerates standard Jacobi iteration. Results show that this method is 40% faster than regular Jacobi iteration and is competitive with Jacobi-preconditioned Conjugate Gradient methods. Furthermore, the new method is not limited to symmetric, positive-definite systems, and therefore, it can be used for non-symmetric systems. Such systems arise in fully coupled, nonlinear-consistent (Newton) solvers.
KW - Linear solvers
KW - Monte Carlo
KW - Radiation diffusion
KW - Synthetic acceleration
UR - http://www.scopus.com/inward/record.url?scp=76749100309&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:76749100309
SN - 9781615673490
T3 - American Nuclear Society - International Conference on Mathematics, Computational Methods and Reactor Physics 2009, M and C 2009
SP - 1361
EP - 1370
BT - American Nuclear Society - International Conference on Mathematics, Computational Methods and Reactor Physics 2009, M and C 2009
T2 - International Conference on Mathematics, Computational Methods and Reactor Physics 2009, M and C 2009
Y2 - 3 May 2009 through 7 May 2009
ER -