Table 2.

Summary of the parameters for the generation of the synthetic test cases and the inversion. We report values for the following parameters: N_i , i = 1, 2, 3 denotes the grid size used for the discretization of the problem; ρ_w and ρ_g are the characteristic reaction factors for white and gray matter, ρ _f is the overall reaction scaling factor; k_w and k_g are the characteristic diffusion parameters for white and gray matter, k _f the overall scaling parameter for the isotropic part of the inhomogeneous diffusion coefficient for net migration of cancerous cells into surrounding tissue; n _p is the number of Gaussian basis functions used for the parametrization of the tumor initial condition, σ is the standard deviation of the associated Gaussian basis functions, and maxit_i = (maxit_i,N , maxit_i,K ) denotes the maximum number of Newton iterations and Krylov iterations (for the KKT system) for the tumor inversion (i = T ) and registration (i = R), respectively,.

	SIN	ATAV-REAC	ATAV-DIF	ATAV-LD	RTRV
Ni	{64, 128, 256}	128	128	128	256
ρw	1	1	1	1	1
ρg	0	0	0	0	0.2
ρ f	15	15	{5, 10, 15}	{5, 10, 15}	{0, 5, 10, 15}
kw	1	1	1	1	1
kg	0	0	0	0	0.1
k f	0	0	{0, 1E−2}	{1E−2, 1E−1}	{0,1E−2}
n p	{8, 64, 512}	125	125	8	{125, 343}
σ	π/10	π/10	π/10	π/15	Auto
maxitT	(100, 100)	(50, 100)	(30, 60)	(30, 60)	(30, 30)
maxitR	(100, 100)	(50, 80)	(50, 80)	(50, 80)	(10, 20)