Fast linear solver for radiative transport equation with multiple right hand sides in diffuse optical tomography.
It is well known that radiative transfer equation (RTE) provides more accurate tomographic results than its diffusion approximation (DA). However, RTE-based tomographic reconstruction codes have limited applicability in practice due to their high computational cost. In this article, we propose a new efficient method for solving the RTE forward problem with multiple light sources in anall-at-oncemanner instead of solving it for each source separately. To this end, we introduce here a novel linear solver called block biconjugate gradient stabilized method (block BiCGStab) that makes full use of the shared information between different right hand sides to accelerate solution convergence. Two parallelized block BiCGStab methods are proposed for additional acceleration under limited threads situation. We evaluate the performance of this algorithm with numerical simulation studies involving the Delta-Eddington approximation to the scattering phase function. The results show that the single threading block RTE solver proposed here reduces computation time by a factor of 1.5~3 as compared to the traditional sequential solution method and the parallel block solver by a factor of 1.5 as compared to the traditional parallel sequential method. This block linear solver is, moreover, independent of discretization schemes and preconditioners used; thus further acceleration and higher accuracy can be expected when combined with other existing discretization schemes or preconditioners.
Columbia University, Department of Biomedical Engineering, 351 Engineering Terrace, 1210 Amsterdam Avenue, New York, New York 10027.
Jingfei
J
Jia
Columbia University Medical Center, Department of Radiology, 630 West 168th Street, New York, New York 10032.
Hyun K
HK
Kim
Columbia University, Department of Biomedical Engineering, 351 Engineering Terrace, 1210 Amsterdam Avenue, New York, New York 10027 ; Columbia University Medical Center, Department of Radiology, 630 West 168th Street, New York, New York 10032 ; Columbia University, Department of Electrical Engineering, 1300 S.W. Mudd, 500 West 120th Street, New York, New York 10027.
Andreas H
AH
Hielscher
Block BiCGStab algorithm; Diffuse optical tomography; Multi-threading acceleration; Multiple right hand sides; Radiative transfer equation