Table 4.3:
Quantitative results for the artificial tumor test-case in which we compare the L2 solver and the CSsolver. The ground truth forward solver parameters are indicated by ‘ ★’ and their respective reconstructed values by ‘rec’. We also report the relative error in the inverted coefficient values (eκ, eρ), the relative error in the final tumor reconstruction (μT,L2), the relative error in the reconstructed initial condition (μ0,L2), the relative error in the parameterization of the initial condition (μp,𝓁1), the relative change in the gradient (∥g∥rel) and solver timings (Tinv) in seconds. All simulations were run using 64 MPI tasks on 3 nodes of the Skylake partition of the Stampede2 system at TACC.
| Test case | Solver | κ* | ρ* | κrec | eK | ρrec | ep | μT,L2 | μ0,L2 | μp,1 | ‖g‖rel | Tinv [s] |
| AT-C1 | L2 | 2.50E-2 | 8E0 | 2.32E-2 | 7.17E-2 | 4.08E0 | 4.90E-1 | 3.13E-1 | 2.92E0 | 9.13E0 | 4.02E-3 | 2.31E2 |
| CS | 2.50E-2 | 8E0 | 2.50E-2 | 9.52E-4 | 8.01E0 | 6.99E-4 | 2.71E-4 | 1.24E-4 | 2.50E-2 | 1.75E-7 | 8.42E2 | |
| AT-C2 | L2 | 5E-2 | 1.20E1 | 2.13E-2 | 5.73E-1 | 4.13E0 | 6.56E-1 | 1.58E-1 | 5.66E0 | 2.35E1 | 7.39E-3 | 2.38E2 |
| CS | 5E-2 | 1.20E1 | 3.89E-2 | 2.23E-1 | 1.02E1 | 1.47E-1 | 1.72E-1 | 1.26E0 | 2.25E0 | 9.36E-6 | 6.43E2 | |
| AT-C3 | L2 | 2.50E-2 | 1E1 | 1.36E-2 | 4.57E-1 | 4.62E0 | 5.38E-1 | 1.84E-1 | 3.55E0 | 1.09E1 | 3.16E-4 | 3.21E2 |
| CS | 2.50E-2 | 1E1 | 2.67E-2 | 6.84E-2 | 9.91E0 | 8.60E-3 | 1.40E-1 | 6.92E-1 | 5.35E-1 | 2.08E-6 | 9.47E2 | |
| AT-C4 | L2 | 2.50E-2 | 8E0 | 1.57E-2 | 3.73E-1 | 3.95E0 | 5.06E-1 | 2.34E-1 | 2.42E0 | 8.23E0 | 2.64E-3 | 2.31E2 |
| CS | 2.50E-2 | 8E0 | 2.57E-2 | 2.64E-2 | 7.31E0 | 8.66E-2 | 2.92E-1 | 1.13E0 | 2.01E0 | 5.31E-6 | 1.41E3 | |