Optimization of Numerical Algorithms for Solving Inverse Problems of Ultrasonic Tomography on a Supercomputerстатья
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Дата последнего поиска статьи во внешних источниках: 24 апреля 2018 г.
Аннотация:The paper is dedicated to optimizing numerical algorithms to solve
wave tomography problems by using supercomputers. The problem is formulated
as a non-linear coefficient inverse problem for the wave equation. Due to the huge
amount of computations required, solving such problems is impossible without
the use of high-performance supercomputers. Gradient iterative methods are
employed to solve the problem. The gradient of the residual functional is calculated
from the solutions of the direct and the “conjugate” wave-propagation
problems with transparent boundary conditions. Two formulations of the transparency
condition are compared. We show that fourth-order finite-difference
schemes allow us to reduce the size of the grid by a factor of 1.5–2 in each
coordinate compared to second-order schemes. This makes it possible to significantly
reduce the amount of computations and memory required, which is
especially important for 3D problems of wave tomography. The primary application
of the method is medical ultrasonic tomography.