International Scholarly Research Notices

Research Article

Powering Multiparameter Homotopy-Based Simulation with a Fast Path-Following Technique

Table 1

Relevant points for homotopy simulations.
Hypersphereβ€”Init. point
where [ πœ† 1 , πœ† 2 ] = [ 0 , 0 ] 		No. Iter Time (Sec) Operating point [ 𝑣 1 , 𝑣 2 , 𝑣 3 , 𝑣 4 ]
where [ πœ† 1 , πœ† 2 ] = [ 1 , 1 ]
π‘₯ 𝑖 1 = [ βˆ’ 5 , βˆ’ 5 , βˆ’ 5 , βˆ’ 5 ] 519 7.70 π‘₯ 𝑠 1 = [ 0 . 3 8 3 0 , βˆ’ 3 . 5 4 4 6 , 0 . 3 8 5 1 , βˆ’ 4 . 0 9 9 0 ]
π‘₯ 𝑖 2 = [ βˆ’ 1 , βˆ’ 2 , βˆ’ 1 , 0 ] 202 3.59 π‘₯ 𝑠 2 = [ 0 . 3 8 6 9 , βˆ’ 4 . 6 3 2 1 , βˆ’ 0 . 8 0 0 2 , 0 . 3 7 7 5 ]
π‘₯ 𝑖 3 = [ βˆ’ 5 , βˆ’ 0 . 5 , βˆ’ 5 , 0 ] 2164.06 π‘₯ 𝑠 3 = [ βˆ’ 0 . 5 1 3 6 , 0 . 3 7 7 5 , βˆ’ 0 . 9 6 8 2 , 0 . 3 7 7 5 ]
π‘₯ 𝑖 4 = [ βˆ’ 1 , 0 , 0 , 0 ] 168 3.13 π‘₯ 𝑠 4 = [ βˆ’ 1 . 0 5 1 0 , 0 . 3 7 7 5 , 0 . 3 8 4 5 , βˆ’ 3 . 9 5 4 2 ]
Circleβ€”Init. point
where [ πœ† 1 , πœ† 2 ] = [ 0 , 0 ] 		No. Iter Time (Sec) Operating point [ 𝑣 1 , 𝑣 2 , 𝑣 3 , 𝑣 4 ]
where [ πœ† 1 , πœ† 2 ] = [ 1 , 1 ]
π‘₯ 𝑖 1 = [ βˆ’ 5 , βˆ’ 5 , βˆ’ 5 , βˆ’ 5 ] 48 0.86 π‘₯ 𝑠 1 = [ 0 . 3 8 3 0 , βˆ’ 3 . 5 4 4 6 , 0 . 3 8 5 1 , βˆ’ 4 . 0 9 9 0 ]
π‘₯ 𝑖 2 = [ βˆ’ 1 , βˆ’ 2 , βˆ’ 1 , 0 ] 48 0.89 π‘₯ 𝑠 2 = [ 0 . 3 8 6 9 , βˆ’ 4 . 6 3 2 1 , βˆ’ 0 . 8 0 0 2 , 0 . 3 7 7 5 ]
π‘₯ 𝑖 3 = [ βˆ’ 5 , βˆ’ 0 . 5 , βˆ’ 5 , 0 ] 48 0.74 π‘₯ 𝑠 4 = [ βˆ’ 0 . 5 1 3 6 , 0 . 3 7 7 5 , βˆ’ 0 . 9 6 8 2 , 0 . 3 7 7 5 ]
π‘₯ 𝑖 4 = [ βˆ’ 1 , 0 , 0 , 0 ] 48 0.82 π‘₯ 𝑠 4 = [ βˆ’ 1 . 0 5 1 0 , 0 . 3 7 7 5 , 0 . 3 8 4 5 , βˆ’ 3 . 9 5 4 2 ]