A PARALLEL PRECONDITIONER FOR SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS TO SOLVE THE NONLINEAR RADIANT HEAT CONDUCTION EQUATION IN THE "KORONA" CODE
S. V. Chebotar
VANT. Ser.: Mat. Mod. Fiz. Proc 2023. Вып.4. С. 34-43.
The paper describes the method of solving systems of linear algebraic equations when simulating the heat conduction processes on distributed-memory computers. The description of the parallel preconditioner used to solve linear equation systems with iterative schemes on Krylov sub-spaces in the heat conduction block of the KORONA code is given. The preconditioner is based on the parallel multilevel incomplete LU-factorization of sparse matrices in combination with incomplete block decomposition of an inverse matrix. The idea of the method is in recursively building the hierarchy of Schur complement addition matrices with successively reducing the number of processes. There has been implemented a possibility of stopping the recursion at a given level and building for the next matrix the Schur complement of incomplete block approximation of inverse matrix. The results of computational experiments obtained in solving problems with the KORONA code in parallel mode are presented. For comparison, there have been implemented several commonly used preconditioners using the ILU(t)-factorization as the basis: the block Jacobi method, the restricted additive Schwarz method, as well as the Spike family method using the reduced matrix. Keywords: parallel computations, systems of linear algebraic equations, preconditioner, the KORONA code, heat conduction.
|
English
