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Stopping Criteria. Is the residual check appropriate as the stopping condition? It is known that relative corrections of field variables and design variables are independent of a grid size. Thus, see if these grid independent properties are adequate as the stopping condition.
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Stopping Criteria • Is the residual check appropriate as the stopping condition? • It is known that relative corrections of field variables and design variables are independent of a grid size. • Thus, see if these grid independent properties are adequate as the stopping condition.
Save do(w, θ) at the current grid Repeat MG cycle λk times Update the design Save d1(w, θ) and compute r = ||d1-do|| No converged? Yes Case #1 • Correction of field variables (w, θ) between the design updates is the stopping condition. • A fixed number of MG cycle is run before the design. (λk is 3 in the example)
converged? converged? Case #2 Save do(w, θ) at the current grid • This is an alternative of the case 1. Likewise, a correction of field variables is the stopping condition. • Only different is that we do not run a fixed number of MG cycle but use the residual checking. MG cycle No Yes Update the design Save d1(w, θ) and compute r = ||d1-do|| No Yes
Save bo(b) at the current grid Repeat MG cycle λk times Update the design Save b1(b) and compute r = ||b1-bo|| No converged? Yes Case #3 • Correction of design variables (b) between the design updates is the stopping condition. • A fixed number of MG cycle is run before the design. (λk is 3 in the example)
converged? converged? Case #4 Save bo(b) at the current grid • This is an alternative of the case 3. Likewise, a correction of design variables is the stopping condition. • Only different is that we do not run a fixed number of MG cycle but use the residual checking. MG cycle No Yes Update the design Save b1(b) and compute r = ||b1-bo|| No Yes
Result (Epsilon = 1e-3) Matrix solver’s results (1e-6)
