Аңдатпа
Abstract. In this paper a nonlinear inverse problem in hemodynamics associated with thrombus formation in blood flow is studied. The inverse problem is formulated as the identification of an unknown constant diffusion coefficient in a twodimensional diffusion equation from final-time observations. The diffusion coefficient is reconstructed by minimizing a normalized least-squares objective functional using a gradient descent algorithm. The direct model describes blood flow in a planar vessel and incorporates a fibrin formation mechanism on the vessel wall. The governing diffusion equation is solved numerically by an alternating direction implicit (ADI) scheme, which provides unconditional stability for the twodimensional problem. To reduce the computational complexity, the gradient of the objective functional with respect to the unknown coefficient is evaluated numerically via a central finite-difference approximation, thereby avoiding the construction of an adjoint problem. Numerical experiments with synthetically generated data demonstrate stable convergence of the iterative process and accurate recovery of the diffusion coefficient for a wide range of initial guesses and step-size parameters. The results confirm the robustness, simplicity, and computational efficiency of the proposed gradient-based reconstruction approach for hemodynamic inverse problems.Keywords: nonlinear inverse problem; diffusion coefficient identification; thrombosis; gradient descent.