### Table 4: Direct SLAE solvers

2007

"... In PAGE 6: ... The other classification is according to the way of elimination of unknown including by-element, by-row, by-column eliminations, etc. ( Table4 ). In other word, it reflects a way how zones of computation can be reduced.... ..."

### Table 3. Comparison of Direct and Distributed Solver

### TABLE II Elapsed time of AMG solver compared to a direct solver in the linear case

in Algebraic Multigrid Method for Solving 3D Nonlinear Electrostatic and Magnetostatic Field Problems

2000

Cited by 1

### TABLE III Elapsed time of AMG solver compared to a direct solver in the nonlinear case

in Algebraic Multigrid Method for Solving 3D Nonlinear Electrostatic and Magnetostatic Field Problems

2000

Cited by 1

### TABLE V Elapsed time of AMG solver compared to a direct solver in the linear case

in Algebraic Multigrid Method for Solving 3D Nonlinear Electrostatic and Magnetostatic Field Problems

2000

Cited by 1

### TABLE VI Elapsed time of AMG solver compared to a direct solver in the nonlinear case

2000

Cited by 1

### Table 7.7: Runtime measurement of direct solvers and the Gauss-Seidel iterative solver for Model II.

### Table 1 Performance comparison of direct and ADI solvers in VIPRE-02

"... In PAGE 2: ... For large, multi-dimen- sional problems a direct or tightly converged iterative solution to the continuity equation can represent a substantial computational burden. The computational profile for a typical PWR problem using the default convergence criteria for the inner and outer iterations is summarized in Table1 . This problem consists of 104 flow channels with 12 axial nodes per channel.... In PAGE 3: ...Proof As indicated in the Table, when a direct solver is used for the solution of the Mass continuity equation, the inner iteration (MASS in Table1 ) requires about 92% of the total CPU time. For this reason an iterative method is provided as an option in VIPRE-02 and as indicated in Table 1, the inner iteration execution time is reduced to about 26% of the total with the alternating direction implicit (ADI) iterative Fig.... In PAGE 3: ...Proof As indicated in the Table, when a direct solver is used for the solution of the Mass continuity equation, the inner iteration (MASS in Table 1) requires about 92% of the total CPU time. For this reason an iterative method is provided as an option in VIPRE-02 and as indicated in Table1 , the inner iteration execution time is reduced to about 26% of the total with the alternating direction implicit (ADI) iterative Fig.... In PAGE 4: ... However, a secondary objective was to examine the overall impact of an improved solution of the linearized continuity equation on convergence of the non- linear two-fluid equations. The results in Table1 indicate that the tighter convergence of the inner iteration achieved by the direct solution method reduced the number of outer iterations by 28%. This suggests that an improved iterative solution of the continuity equation such as a preconditioned Krylov method could have a significant eC128ect on the solution of the nonlinear problem.... ..."

### Table 3: Characteristics of A for the reducible test matrices and solution of Ax = b with direct solver.

"... In PAGE 13: ... None of these matrices have a symmetric nonzero pattern. The characteristics of A corresponding to the 5 test matrices appear in Table3... ..."